We prove the existence and uniqueness up to conjugacy of a new maximal subgroup of the algebraic group of type E8 in characteristic 3. This has type F4, and was missing from previous lists of maximal subgroups produced by Seitz and Liebeck–Seitz. We also prove a result about the finite group H = 3D4(2), namely that if H embeds in E8 (in any characteristic p) and has two composition factors on the adjoint module then p = 3 and H lies in a conjugate of this new maximal F4 subgroup.
|Proceedings of the American Mathematical Society
|Early online date
|20 Jan 2022
|Published - Apr 2022