Maximal subgroups of exceptional groups of Lie type, finite and algebraic

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The maximal closed subgroups of positive dimension in simple algebraic groups of exceptional type over algebraically closed fields are determined, subject to certain restrictions on the characteristic. This result is used to prove a reduction theorem for maximal subgroups of finite exceptional groups of Lie type: such a subgroup is either of known type, or it is almost simple. Finally, the “generic” almost simple maximal subgroups are determined for large characteristic.