在数学的紧李群及约化代数群理论中，极大子环是其中一类特别的子群，在这些群的分类及表示理论中扮演要角。

李群中的子环（面）是一个连通紧阿贝尔李子群，这类子群必然同构于环面。极大环面是其中维度最大者。非紧子群未必有极大环面（例如）。

对于紧李群，极大子环对应到李代数中的极大阿贝尔子代数。任意子环皆包含于某个极大子环，任两个极大子环彼此共轭。极大子环的维度称为该群的秩。

In the mathematical theory of compact Lie groups a special role is played by torus subgroups, in particular by the maximal torus subgroups.

A torus in a compact Lie group G is a compact, connected, abelian Lie subgroup of G (and therefore isomorphic to the standard torus T). A maximal torus is one which is maximal among such subgroups. That is, T is a maximal torus if for any other torus T′ containing T we have T = T′. Every torus is contained in a maximal torus simply by dimensional considerations. A noncompact Lie group need not have any nontrivial tori (e.g. R).