GAP:MaximalSubgroups

This article is about a GAP function.

Definition

Function type

MaximalSubgroups is a GAP function that takes as input one argument representing a group and outputs a list of groups.

Behavior

The command takes as input a group and outputs the list of all its maximal subgroups. It works only for finite groups.

• If the argument is a finite group, the function returns a list of the maximal subgroups.
• If the argument is an infinite group or is not a group at all, the function returns a NoMethodFound error.

Related functions

• GAP:MaximalNormalSubgroups: This returns the maximal normal subgroups. Note that maximal normal subgroups are maximal among proper normal subgroups, and need not themselves be maximal subgroups.
• GAP:ConjugacyClassesMaximalSubgroups: This returns the conjugacy classes of maximal subgroups.
• GAP:MaximalSubgroupClassReps: This returns a list comprising one representative from each conjugacy class of maximal subgroups of the whole group.