Maximal subgroups of almost simple groups with socle $\PSL(2,q)$

TL;DR

This paper classifies all maximal subgroups of almost simple groups with socle PSL(2,q), covering groups between PSL(2,q) and its automorphism group for q ≥ 4, providing a comprehensive subgroup structure analysis.

Contribution

It provides a complete classification of maximal subgroups of almost simple groups with socle PSL(2,q), extending previous partial results to all relevant groups.

Findings

Complete list of maximal subgroups for groups with socle PSL(2,q)

Identification of subgroup types within these groups

Extension of known classifications to all q ≥ 4

Abstract

We determine all maximal subgroups of the almost simple groups with socle $T=\PSL(2,q)$, that is, of all groups $G$ such that $\PSL(2,q)\leqslant G\leqslant\PGammaL(2,q)$, with $q\geq 4$.