Subgroups of order 4 in groups of order 16

This article describes the occurrence of groups of order 4 as subgroups inside groups of order 16.

There are two groups of order 4: cyclic group:Z4 and Klein four-group. There are 14 groups of order 16.

Note the following:


 * A subgroup of order 4 in a group of order 16 is also a subgroup of index 4, because $$16/4 = 4$$.
 * A subgroup of order 4 in a group of order 16 need not be a normal subgroup. However, it has subnormal depth at most 2 so even if it is not normal, it is a 2-subnormal subgroup. If it is not normal, its normal core is a subgroup of order 2 and index 8, and its normal closure is a subgroup of order 8 and index 2.
 * There are a few cases where there are multiple automorphism classes of isomorphic subgroups of order 4 in a given group of order 16.

Numerical information on counts of subgroups
The table below presents information on counts of subgroups of order 4 in groups of order 16. Note the following: