C3 Inc., the Reston computer systems firm whose stock was suspended from trading briefly last year in a flap over a disputed Army contract, said its shares began trading yesterday on the New York Stock Exchange. It fell 1/4 to 21 on 100 shares traded. The stock had been trading over the counter.

The company said it had applied for the NYSE listing because of an increase in the number of its shareholders. C3 said the listing was "suitable at this stage in the company's growth because it will provide greater visibility and thus increase the stock's liquidity."

C3--the name stands for computers, communications and control--was founded in 1968 and first offered stock to the public a little over two years ago. It provides computer system design and assembly, primarily for government agencies.

Last fall, the Army suspended C3 from bidding on defense contracts for two weeks because of alleged false statements made in connection with one of the company's Army contracts. The Army lifted the suspension after C3 challenged it, and an Army spokesman said yesterday the investigation is continuing.

C3 stock tumbled at the time of the Army suspension, and trading was halted for a time at the company's request while the matter was being settled.