WASHINGTON  The Federal Aviation Administration proposed a record penalty of $10.2 million against Southwest Airlines on Thursday, saying the carrier had continued to fly 46 Boeing 737s that it said it had grounded because they had not been properly inspected for fuselage cracks.

At least one F.A.A. employee was aware of the airline’s misrepresentation, and told the airline it could keep flying the planes but that it should inspect them as soon as possible, an agency spokeswoman said. A supervisor at the F.A.A. who was aware of the arrangement has been removed from that job, said the spokeswoman, Diane Spitalieri.

The inspector general of the Transportation Department is investigating the F.A.A.’s handling of the incident, which occurred over several days last March, at the request of the chairman of the House Transportation and Infrastructure Committee.

Four of the planes had four-inch-long cracks, requiring repairs, said Ms. Spitalieri, although no deaths or injuries resulted.