In social network applications, individual opinion is often influenced by groups, and most decisions usually reflect the majority’s opinions. This imposes the group influence maximization (GIM) problem that selects $k$ initial nodes, where each node belongs to multiple groups for a given social network and each group has a weight, to maximize the weight of the eventually activated groups. The GIM problem is apparently NP-hard, given the NP-hardness of the influence maximization (IM) problem that does not consider groups. Focusing on activating groups rather than individuals, this paper proposes the complementary maximum coverage (CMC) algorithm, which greedily and iteratively removes the node with the approximate least group influence until at most $k$ nodes remain. Although the evaluation of the current group influence against each node is only approximate, it nevertheless ensures the success of activating an approximate maximum number of groups. Moreover, we also propose the improved reverse influence sampling (IRIS) algorithm through fine-tuning of the renowned reverse influence sampling algorithm for GIM. Finally, we carry out experiments to evaluate CMC and IRIS, demonstrating that they both outperform the baseline algorithms respective of their average number of activated groups under the independent cascade (IC) model.