The prosperity of location-based social networking has paved the way for new applications of group-based activity planning and marketing. While such applications heavily rely on geo-social group queries (GSGQs), existing studies fail to produce a cohesive group in terms of user acquaintance. In this paper, we propose a new family of GSGQs with minimum acquaintance constraints. They are more appealing to users as they guarantee a worst-case acquaintance level in the result group. For efficient processing of GSGQs on large location-based social networks, we devise two social-aware spatial index structures, namely SaR-tree and SaR*-tree. The latter improves on the former by considering both spatial and social distances when clustering objects. Based on SaR-tree and SaR*-tree, novel algorithms are developed to process various GSGQs. Extensive experiments on real datasets Gowalla and Twitter show that our proposed methods substantially outperform the baseline algorithms under various system settings.