When the Howard Hughes Medical Institute put its chief asset up for sale earlier this year, it had no trouble finding interested buyers. Hughes Aircraft Co. has long been considered one of the aerospace industry's most desirable companies.

Despite a wave of embarrassing publicity last year about serious quality control problems at the firm's Tucson missile production facility, Hughes long has been coveted by a variety of companies because of its wealth of scientific expertise, its roster of profitable, high-technology programs and a unique decentralized management style that has provided it a competitive edge in the defense industry.

In addition, it is a leading member of an industry that, in spite of recent negative publicity over cost overruns and other controversies, remains a solid source of growth, earnings and technology. "There aren't very many companies out there that are available in a market that should be growing at 15 percent over the next few years, that can yield, theoretically at least, a 5 or 6 percent" profit margin, said Paul Nisbet, an analyst at Prudential-Bache Securities in New York.

Hughes Aircraft has been privately owned since its formation by Howard Hughes in 1932 and his subsequent transfer of the company to the nonprofit Hughes Medical Institute in 1953. In spite of its name, the company does not make aircraft and never has. Instead, it is a producer of sophisticated radar systems, missile systems, guidance and propulsion devices, electronic warfare and surveillance systems, laser products and a host of other devices.

As such, it has been perfectly positioned to capitalize on the recent U.S. defense buildup, with its focus on sophisticated electronics, communications and control systems.

The company's two largest segments are the Ground Systems Group, which produces automated command-and-control air defense systems, and the Space and Communications Group, which manufactures satellites, communications equipment and ground terminals. Each was estimated to have generated $1 billion in sales last year.

A third operation, the Electro-Optical and Data Systems Group, which manufactures data processors, software systems and high-energy lasers, is expected to grow in size if President Reagan's Strategic Defense Initiative program receives strong congressional funding. Company officials confirm that Hughes is involved in research for the "Star Wars" program.

With more than 73,000 employes -- most of whom are based in Southern California -- Hughes is California's largest industrial employer. More than one-third of its employes are degree-holding scientists, a high percentage by defense industry standards. Small manufacturing facilities of Hughes also operate in Alabama, Mississippi, South Carolina and Georgia.

The company has been consistently profitable, although specific earnings figures aren't public. Reportedly, it earned about $80 million last year.

Hughes spends a large amount on internal research and development and, not having public stockholders to answer to, has been able to take on more high-risk, long-term research ventures. In all, the company spends an estimated $200 million to $250 million annually for internal research, a figure that other major defense contractors only recently have begun to approach.

None of the company's 1,200 programs accounts for more than 6 percent of total sales, which were $4.9 billion in 1984 (approximately the same as in 1983). Sales totaled $4.4 billion in 1982 and $3.3 billion in 1981. With its diversification of programs, industry experts say, Hughes is shielded from unexpected program cuts.

But the company has not been immune to some of the charges that have troubled other defense contractors in recent months. Last year Pentagon inspectors found nearly 100 deficiencies in the radar unit produced by Hughes for an F14 jet. As a result, Hughes voluntarily stopped shipping radar equipment for the Air Force's F14 and the Navy's F18 for several months.

More significantly, in August 1984, Hughes completely shut down its missile assembly operations in Tucson for several weeks after Navy and Air Force officials discovered serious deficiencies in the Air Force's Maverick, Navy's Phoenix and Army's TOW missiles -- all key contracts for the company. The Department of Defense temporarily suspended payments to the company for the three programs, then removed the sanctions after Hughes improved its quality control procedures.

Industry analysts viewed the quality control problems and subsequent delivery delays as responsible for the scaling back of earlier estimates that had projected 1984 company sales at $5.6 billion.