General Dynamics Corp., the nation's largest defense contractor over the last decade, is facing one of the most wide-ranging federal investigations in Defense Department history.

Included are allegations that the company has covered up massive cost overruns on nuclear submarines, filed fraudulent claims and billed the government for country club memberships and lavish entertainment.

When its geographically dispersed divisions were assembled into a defense conglomerate in the 1950s, General Dynamics' founder John Jay Hopkins envisioned it as a mammoth General Motors of the defense industry.

Today, it is among the nation's top three weapons suppliers, providing Trident ballistic-missile submarines and Los Angeles-class attack submarines to the Navy, M1 tanks to the Army and F16 fighter jets to the Air Force, along with an arsenal of other weapons.

A decade ago, when Lockheed, Northrop and other defense contractors faced public charges of bribery abroad and cost overruns, General Dynamics stood out as a model of relative integrity and good relations in Washington.

But over the last two years, the company has been forced to pay back tens of millions of dollars in improper billings on defense contracts, its executives have been pummeled in Congress as dishonest, and three of its former executive vice presidents and board members have been indicted on criminal charges.

Meanwhile, a federal task force of FBI agents, auditors and prosecutors continues work on additional investigations of management actions dating to the early 1970s.

The investigative saga began in the late 1970s when Adm. Hyman G. Rickover charged that the company's cost-overrun claims on attack submarines were inflated and possibly fraudulent. A series of investigations resulted, outliving Rickover's Navy tenure, and they have yet to be resolved.

The indictment in Los Angeles yesterday of National Aeronautics and Space Administration head James M. Beggs, a former General Dynamics executive vice president and board member, was originated by the Justice Department's fraud section.

That office is directing investigators assigned to General Dynamics task forces in New London, Conn., and Pomona, Calif.

Beggs vigorously denied charges in the indictment that he presided over false-billing procedures five years ago when General Dynamics was competing to build the Army's Divad antiaircraft gun.

The charges against Beggs follow the indictment in October of George A. Sawyer, the company's executive vice president in charge of the Army's M1 tank and other "land systems" programs.

Sawyer, as assistant Navy secretary for shipbuilding, allegedly failed to disclose his acceptance in 1983 of travel fees and his job discussions with General Dynamics' officials while he supervised Navy contracting business with the company.

Beggs and Sawyer were Reagan administration appointees. Sawyer was the principal architect of Navy Secretary John F. Lehman Jr.'s plans to achieve a 600-ship Navy as part of an overall defense buildup.

In September 1983, a federal grand jury in New York indicted P. Takis Veliotis, a company executive vice president, for allegedly sharing kickbacks on ship construction.

Veliotis had supervised General Dynamics' marine division, which included shipyards at Quincy, Mass., and the large submarine construction facility at Groton, Conn., where Tridents and Los Angeles-class subs are produced.

Last year, Veliotis provided the impetus for renewed Justice Department investigation when he began providing prosecutors with tapes and documents to support his allegations that the company engaged in a pattern of fraud in the submarine program.

General Dynamics Chairman David S. Lewis, the subject of many of Veliotis' allegations, has acknowledged that the company engaged in some improper billing practices. Generally, however, he has defended its integrity and portrayed it as the victim of unsubstantiated charges, rumors and innuendo.

Still uncertain is whether Lester Crown, heir to the company's largest block of stock, will be able to exercise his authority by maintaining a seat on the board. He is the son of industrialist Henry Crown.

The Defense Department told Lester Crown Sept. 18 that he will lose his top-secret security clearance, which board members must have, because he was named as an unindicted co-conspirator in the 1974 bribery of Illinois state legislators. He is contesting the Pentagon action.