Maryland's traditionally fractious Republicans ended a two-day love-in today by naming Sen. Charles Mc. Mathias and Rep. Robert Bauman -- the leaders of the party's liberal and conservative factions -- as co-chairmen of the state's national convention delegation.

This odd-couple pairing of the senator who is seen as a stalwart of moderate Republicanism and the congressman who once headed the American Conservative Union was suggested by members of Ronald Regan's national campaign staff, who are anxious to pull the party together behind their candidate.

As the state party convention broke up this morning amid contented smiles and compliments for all concerned, Bauman remarked, "These people are going out of here with the best feeling of any convention in my memory."

There was cause for optimism among the long-suffering underdogs of Maryland politics. While still outnumbered 2-to-1 by Democrats, state Republicans have 10 percent more registered voters than they did a year ago and $34,000 in a treasury once filled with "payment due" slips.

With Regan and the ever popular Mathias heading the ticket in November, they feel they can recover some of the congressional representatioin they lost during the lean years of the 1970s. Most of all, they were trying to show this weekend that they can stick together.

he only murmurings of discord came from partisans of Prince George's County Executive Lawrence Hogan. This group was furious to discover that Hogan's aggressive campaign for the delegation chaqirmanship had been thwarted by party leaders who worked out the Bauman-Mathias arrangement in a locked hotel room late Saturday night.

Hogan had arrived at this beach resort Friday with an entourage of about three dozen people. He spent the next 36 hours soliciting support from any of the 30 national convention delegates he could find and telling all comers that he already had 19 votes, or 17, or 21 -- in any case, a majority.

Hogan's son, Larry Hogan, R., even organized a contingent of Young Republicans Saturday morning to bring a free breakfast of strawberries, ham biscuits, coffee and juice to all 240 conventioneers. The Hogan hospitality suite, complete with liquor and hors d'oeuvres, seemed to be open 24 hours a day.

Some party members said they thought it was a little unseemly for Hogan to work so avidly for a largely ceremonial post, even if he did want statewide and national exposure to bolster his chances in a gubernatorial or senatorial campaign in 1982.

Hogan and his allies, however, had worked for several months to win the job and whatever prestige and visibility it entailed. They had solicited and received Mathias' support. They felt party chairman Allan Levey would help them since he won his job largely thorugh Hogan's efforts.

This morning they felt betrayed.

On Saturday night, several days after a move to block Hogan had been started, Bauman convened a meeting of senior party officials -- including Mathias and Levey -- in a Sheraton hotel room and pushed for the co-chairmen arrangement as a compromise. Worried that a fight between the pro- and anti-Hogan forces could crack the happy front of unity, the others agreed.

So it was a grim-faced Hogan who rose to tell the delegates' meeting this morning, "I have worked very hard to foster unity in the party . . . the more satisfactory solution to this problem would be for Sen. Mathias and Congressman Bauman to serve as co-chairmen.

Sighs of relief and a standing ovation greeted this announcement, and Hogan was immediately nominated and elected to a seat on the national convention's traditionally powerful Rules committee.

The remainder of the committee assignments for the convention were split almost evenly between Regan's backers and the moderates who had supported George Bush's losing bid for the nomination. In the delegation meeting, as in the state convention meeting on Saturday, the word unity was at the center of every speech.

"The Republicans see the chance of grabbing the brass ring this time and they don't want to mess up," said State Sen. Edward P. Thomas.Indeed the fierce ideological bickering that marked the 1976 state convention was entirely missing this year.

Instead, the newly optimistic Republicans were talking about thier chances of recapturing three congressional seats in Maryland, since the Republican National Committee is considering funneling large chunks of aid to the congressional candidates in Baltimore County, Montgomery County and western Maryland.

At the big dinner in the Sheraton Hotel Ballroom Saturday evening, party members sand songs to each other and clapped and cheered for everyone they could -- for Levey, who was named Republican Man of the Year, for national elected officials like Bauman, Mathias, and Rep. Majorie Holt, and for the Republican Woman of the Year and Yong Republican of the Year. a

They clapped even louder as House Minority Leader John J. Rhodes (R-Ariz.) excoriated President Carter and the Democratic majority in Congress. "The entire Carter record," Rhodes declared, is littered with broken promises."

The Democrats on Capitol Hill, Rhodes added, are responsible for today's inflaiton rate, and have "fostered the rapid growth of dependency" among Americans by setting up too many social programs and too much regulation.

When Rhodes finished, party chairman Levey gave a quick pep talk about the need to elect Republicans to the state legislature, then closed the meeting by having all 223 participants sing "God Bless America" together.