Self-dealing, nepotism and conflicts of interest are widespread at dozens of the nonprofit groups that run New York City’s $4 billion network of homeless shelters, according to a sweeping report released on Thursday.

The comprehensive review, which was conducted by the city’s Department of Investigation, found that some shelter operators were enriching themselves as homelessness climbed to record levels.

They were paid more than $700,000 a year, hired their family members and simultaneously held jobs at other companies, like security firms, that did business with their nonprofit groups and received city money, the report found.

One nonprofit group awarded millions of dollars in city business to a security company tied to one of the group’s executives, allowing him to collect nearly $200,000. Another group employed at least five relatives of senior employees, including the child and niece of its executive director.

In total, the review identified hundreds of problems, including financial mismanagement and conflicts of interest, at 51 of the nonprofit groups that run New York City’s shelters. (When the review began, there were about 70 such groups contracted by the city — that number has since grown.)

“When it comes to protecting the vast taxpayer resources that city-funded nonprofits receive, prevention is key,” Jocelyn E. Strauber, the commissioner of the Department of Investigation, said in a statement.