The nonabelian simple groups 𝐺, ∣𝐺∣<10⁶—maximal subgroups

Abstract

The maximal subgroups of all the simple groups (except <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L left-parenthesis 2 comma q right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>L</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mi>q</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">L(2,q)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>) of order up to one million are given to within conjugacy. Permutation characters on the cosets of the maximal subgroups are given, as are orbit lengths (whenever practical).