The social science of large language models (LLMs) examines how these systems evoke mind attributions, interact with one another, and transform human activity and institutions. We conducted a systematic review of 270 studies, combining text embeddings, unsupervised clustering and topic modeling to build a computational taxonomy. Three domains emerge organically across the reviewed literature. LLM as Social Minds examines whether and when models display behaviors that elicit attributions of cognition, morality and bias, while addressing challenges such as test leakage and surface cues. LLM Societies examines multi-agent settings where interaction protocols, architectures and mechanism design shape coordination, norms, institutions and collective epistemic processes. LLM-Human Interactions examines how LLMs reshape tasks, learning, trust, work and governance, and how risks arise at the human-AI interface. This taxonomy provides a reproducible map of a fragmented field, clarifies evidentiary standards across levels of analysis, and highlights opportunities for cumulative progress in the social science of artificial intelligence.