Education department officials recovered nearly $12 million in misspent federal money and won 79 criminal convictions for fraud, theft and embezzlement during a six-month period this year, according to the latest report of the department's inspector general.

The last such report, released in June by Inspector General James B. Thomas Jr., said a total of $34 million was recovered for the previous reporting period, from October 1984 through March of this year.

The cases included a New York woman indicted for using 14 identities to apply for $52,000 in guaranteed student loans; a federal prisoner on a work-release program who received $57,500 in student loans using forged college transcripts, and a Kansas resident who arranged marriages between local prostitutes and aliens so the aliens would become eligible for student aid. The last case came to light when a Kansas judge noticed a large number of prostitutes he knew from the courtroom marrying foreign men.

The cases were detailed in the inspector general's semiannual report to Congress, released this week, which covers a six-month period starting April 1. In addition to the $11.8 million already recovered, the report also raised questions about $23 million in department grants and loans that may have been improperly used by state governments, colleges, banks and local school districts.

A total of $45.7 million in questionable and disallowed funds was found during the earlier reporting period.

The latest report, like the one before it, disclosed several complex and often bizarre schemes to bilk the department of funds, usually through the student loan program. The most common scheme involved a person using several fake identities or enrolling in several schools simultaneously to apply for -- and, in some cases, receive -- thousands of dollars in college loan money.

Some of the stranger cases included an employe in the financial-aid office at an unnamed community college in California who authorized federal loans and Pell grants to students who did not exist. This official managed to pocket more than $35,000 before being detected. She pled guilty to embezzlement charges and is awaiting sentencing.

One Illinois case involved a federal prisoner who created a bogus firm and a fake job to get himself released on a work-release program. While out of prison, he got an official seal from an unnamed college, and used that seal to forge school transcripts that allowed him to apply as a transfer student to dozens of schools. He then applied for and received 23 guaranteed student loans totalling $57,500. He was indicted in May on fraud charges and returned to prison.

Most of the money recovered came from auditing institutions that received federal money and either disbursed it to ineligible students or used sloppy accounting techniques. In one instance, an Iowa college used salesmen paid on commission to peddle student loans, which is illegal.

A total of $10.1 million was recovered from auditing; $1.7 million was retrieved through criminal investigations.

Several states are now challenging earlier Education department audits before the department's in-house appeals board. Those challenged audits, which eventually must be decided by Secretary William J. Bennett, involve millions of dollars in some states. The cases have taken on political overtones, while severely straining relations between the department and the state governments.

California, for example, was told to refund $6.2 million to the Education department; Florida, $11.2 million, and Indiana, $1.6 million.