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maximal subgroup

Idea

A maximal subgroup of a given group $G$ is a subgroup which is not all of $G$ and not contained in any other subgroup of $G$.

Hence a maximal subgroup is a maximal element of the lattice of subgroups after removing the trivial subgroup $G \subset G$ itself. More concisely it is a coatom of $G$‘s subgroup lattice.

Related concepts

• maximal compact subgroup

• maximal torus

References

See also

• Wikipedia, Maximal subgroup