In contrast to single-user recommender systems, group recommender systems are designed to generate and explain recommendations for groups. This group-oriented setting introduces additional complexities, as several factors - absent in individual contexts - must be addressed. These include understanding group dynamics (e.g., social dependencies within the group), defining effective decision-making processes, ensuring that recommendations are suitable for all group members, and providing group-level explanations as well as explanations for individual users. In this paper, we analyze in which way large language models (LLMs) can support these aspects and help to increase the overall decision support quality and applicability of group recommender systems.