Social network analysis is an area of research that is gathering interest and importance since the turn of the century, especially with increased technology proliferation. Graph theory is predominantly being used in the analysis of social networks. The maximum k-plex problem, which belongs to the category of clique relaxation problems has been studied by researchers in this field. This problem is known to be NP-hard. This paper proposes an amalgamation of a greedy randomized adaptive search procedure and tabu search metaheuristic to solve the problem. The performance of the proposed hybrid metaheuristic is tested on well-known instances of graphs and the computational results are reported.