## Abstract

We prove the existence and uniqueness up to conjugacy of a new maximal subgroup of the algebraic group of type

*E*_{8}in characteristic 3. This has type*F*_{4}, 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*=^{3}*D*_{4}(2), namely that if*H*embeds in*E*_{8}(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*F*_{4}subgroup.Original language | English |
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Pages (from-to) | 1435–1448 |

Journal | Proceedings of the American Mathematical Society |

Volume | 150 |

Issue number | 4 |

Early online date | 20 Jan 2022 |

Publication status | Published - Apr 2022 |

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