The Russian warlord whose 24-hour mutiny provoked the worst crisis to roil the country in three decades has been packed off to an uncertain exile — along with the foul-mouthed critiques of the Russian military that won him legions of followers, especially within the ranks.

Yet the problems identified by Yevgeny V. Prigozhin, the leader of the Wagner mercenary group, did not disappear with him, military analysts say, and are likely to continue to fester, enraging troops and further lowering already sickly morale.

These include an overall lack of command and control, rigid hierarchy, corruption, tangled logistics, equipment shortages and the absence of an honest, public assessment of the war in Ukraine. The emergence of several other private military companies like Wagner promises to further complicate matters.

“If Prigozhin is gone, the problems will not go with him,” said Dmitri Kuznets, a military analyst for Meduza, an independent Russian news website. “They are here to stay, this is a bigger problem than Prigozhin himself.”

During the uprising, the Telegram messaging app erupted with comments from those who supported Mr. Prigozhin’s diatribes against the military leadership — particularly those aimed at Defense Minister Sergei K. Shoigu and Gen. Valery V. Gerasimov, chief of the general staff — while also condemning his mutiny.

“Do you think that guys who ask for scopes, for example, are very flattering about big generals? Of course not,” wrote a military blogger who uses the name “Z-War Geeks” and has more than 760,000 followers on Telegram. However, he said, most soldiers distinguish between their country and the state. “The Motherland is unconditional,” he wrote. “You can’t betray it, or lose it.”

The reaction overall revealed an opposition bloc among soldiers, the volunteers who supply them and the Telegram community cheering on the war. “We knew that before, but we did not understand the scale of it,” said Mr. Kuznets. The uprising, he added, highlighted the gap between the commanders and the soldiers fighting the war, who generally endorse the idea that the army is badly run and headed for defeat.

“We can see that they agree with Prigozhin in general, but they don’t agree with his methods,” he added.

In some ways, the problems with the war go beyond the people involved and lie within the structure and culture of the Russian military.

Reforms begun more than a decade ago were meant to create a smaller, leaner, more flexible army. It was not built to conquer a large European country, so from that perspective President Vladimir V. Putin assigned the military a task beyond its grasp, said Aleksandr Golts, a Russian military analyst.

“Russia had forces that can win a short, local conflict,” he said. “That’s it.”

But the reformers fell short of achieving greater flexibility, which requires giving decision-making power to commanders in the field. That ran up against deep-seated cultural norms, particularly a penchant for rigid, hierarchical command structure and a callousness about soldiers’ casualties that some say is a legacy of Soviet times.

This month, the Ministry of Defense moved to assert control over the proliferating number of private military groups, insisting that they all sign contracts by July 1. That helped spark Mr. Prigozhin to mutiny, but it also highlighted an issue that to date has been discussed mostly among military bloggers and some Russian news outlets.

The crackdown “was a step in the right direction,” from a military perspective, said Mr. Golts, whose report for the Stockholm Centre for Eastern European Studies on the potential for civil war in Russia had predicted a similar uprising just days before it happened.

The number of private armies remains small. Gennady Timchenko, a wealthy Putin crony, started one called Redoubt. It was initially intended to protect his Stroytransgaz energy facility in Syria, but it began recruiting people for Ukraine after the war began, according to Russian news reports.

Mr. Prigozhin himself brought attention to the fact that Gazprom, the state energy company, had started three private armed groups: Potok, Fakel and Plamya, or Stream, Torch and Flame. Their independence from the Defense Ministry remains murky.

“Those people who have money think that it’s an awesome topic now — to collect P.M.C.s,” Mr. Prigozhin said in an interview broadcast on Telegram in April, referring to private military companies.

Although private militias remain technically illegal in Russia, and the government is now trying to rein them in, the fact that Wagner was paid nearly $1 billion for roughly the first year of the war offers an incentive to create such groups. And as Wagner just showed, they carry enormous potential to create havoc.

After the rebellion, “all people with arms in their hands understood that they can use those arms in their own interests, not in the interests of the state,” Mr. Golts said. “It was a very dramatic pivot. Prigozhin crossed the Rubicon.”

In Washington, senior Pentagon officials said the Kremlin’s response to the mutiny underscored the weaknesses in the Russian military’s command-and-control structure — its inability to react quickly to unexpected developments, and poor coordination between the military and other security services.

U.S. military officials were stunned that an armored column of Wagner forces advanced within 125 miles of Moscow. The mercenaries met no resistance on the ground, but shot down half a dozen Russian military helicopters and an Il-22 airborne command post that engaged the column.

Pentagon officials said that this reflected once again the lack of coordination between Russian air and ground forces. But the muted reaction might also have been a sign that many officers and soldiers were sympathetic to the mutineers, military analysts said.

Still, Mr. Prigozhin overplayed his hand, possibly thinking that months of phone calls from officers grousing about the Defense Ministry meant that some would join the rebellion. “I think Prigozhin overestimated his support — disdain for Gerasimov does not equal support for Prigozhin,” said Dara Massicot, a senior policy researcher at the RAND Corporation.

General Gerasimov replaced Gen. Sergei Surovikin in January as commander of Russian forces fighting Ukraine. General Surovikin and Mr. Prigozhin are allies since working together on Russia’s military operations in Syria.

The New York Times reported on Tuesday that U.S. officials said that General Surovikin had advance knowledge of the uprising, and they were trying to determine if he helped with the planning and if any other senior officers were involved.

U.S. military officials said there were no indications that the mutiny had caused Moscow to pull military units off the front lines in Ukraine. But it could adversely impact Russia’s battlefield performance, analysts and Pentagon officials said.

In Ukraine, the Russian military has been holding its own in recent weeks against the long-anticipated Ukrainian counteroffensive.

Strategic defenses — the minefields, trench networks and tank traps that the Russians have spent months building — have thus far blunted the Ukrainian effort.

Offense is another matter. Russia has never addressed the command, communications and logistical failures that undermined what was supposed to be its initial lightning assault to seize Ukraine.

Top military posts have been a revolving door, with Mr. Putin sidelining General Gerasimov for a time in favor of General Surovikin and then reversing himself in January — even though General Surovikin had earned praise for his professional handling of the Russian retreat from Kherson.

A pervading sense that high-level commanders aren’t held accountable can pose a substantive challenge to any military’s ability to command and control forces on the battlefield. Analysts say the lack of accountability undermined the authority of Mr. Shoigu and General Gerasimov in the ranks.

“It made both of them look weak,” said Rob Lee, a senior fellow with the Foreign Policy Research Institute. “Clearly there are a lot of systemic issues in the Russian military that are attributable to the leadership,” he added. “The reason Prigozhin had any support at all is that his criticisms of the Russian Ministry of Defense — many of them are reasonable.”

In the days after the rebellion, Mr. Shoigu appeared multiple times in public — a sign that he would stay in his position — while reports of a widespread purge in the military began to emerge from Russia’s military bloggers.

The lagging morale among the rank-and-file will only be worsened by the infighting and Mr. Putin’s response to the mutiny, if the early reports are accurate. “It did not give added morale to the mostly demoralized army,” said Pavel Luzin, a Russian military analyst.

Reporting was contributed by Paul Sonne in Berlin, Eric Schmitt and Helene Cooper in Washington, and Alina Lobzina in London.

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