John Spohler, the New York stockbroker who successfully challenged the management of Computer Network Corp., has assumed the chairmanship of the company, according to the company's proxy statements received by stockholders last week.

Spohler assumed the chairmanship on July 18, less than a week after he and a group of fellow dissident shareholders, ousted all of the company's directors except for the company's chairman and president Lee Johnson.

The ouster ended a bitter court fight between Spohler and Johnson in which Spohler accused Johnson and other officers of misusing the company for their personal enhancement and not for the benefit of most stockholders.

Chief among Spohler's complaints were two compensation plans, one which automatically would have granted Johnson and three other officers five years of salary and benefits if the company were taken over or if the board of directors changed control. The other plan would have accelerated the vesting of stock options granted to officers if there were a challenge to management.

According to the proxy material, neither of these two compensation schemes was implemented in spite of the management change. Instead, Johnson reached a new employment agreement with the new directors that will pay him $145,000 a year, the same amount he received last year.

Spohler's chairmanship comes even though he said he had no intention of acquiring Comnet and running it himself--as Johnson had charged.

Last week, Spohler said that even though he is chairman, he is not running the company. "I am not operating management," he said. However, he noted, given his "substantial investment" 4 percent of the stock , he is "looking at the company very closely."

None of the directors--who own nearly one-fifth of the company's stock--"were very happy with the company's operating report" that was disclosed in the annual report with the proxy, Spohler said. The report said the company's profits totaled $377,000 for the fiscal year ending March 31, 1983--down from $517,000 earned during the previous year.

Operating losses continued for Comnet, totaling $211,000 for 1983, down from $217,000 during 1982. The decrease was in part attributable to a 13 percent increase in operating revenues to $14.5 million. However, the revenues were still below the company's record $21.2 million received in 1980. Earnings were achieved chiefly through interest income. But because interest rates were lower in 1983, this income was down from 1982 from $1.3 million to $829,000.