# Subgroup structure of semidihedral group:SD16

From Groupprops

This article gives specific information, namely, subgroup structure, about a particular group, namely: semidihedral group:SD16.

View subgroup structure of particular groups | View other specific information about semidihedral group:SD16

We are interested in the group , the semidihedral group:SD16, given by the presentation:

where denotes the identity element.

The group has 16 elements:

## Tables for quick information

### Table classifying subgroups up to automorphisms

FACTS TO CHECK AGAINST FOR SUBGROUP STRUCTURE: (group of prime power order)

Lagrange's theorem (order of subgroup times index of subgroup equals order of whole group, so all subgroups have prime power orders)|order of quotient group divides order of group (and equals index of corresponding normal subgroup, so all quotients have prime power orders)

prime power order implies not centerless | prime power order implies nilpotent | prime power order implies center is normality-large

size of conjugacy class of subgroups divides index of center

congruence condition on number of subgroups of given prime power order: The total number of subgroups of any fixed prime power order is congruent to 1 mod the prime.