Subgroups — #103

Order 32.

21 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	Q₈	—	2	1	no	—
5	Q₈	C₄	1	2	yes	complemented
6	C₂×C₄	—	2	1	no	—
7	C₂×C₄	—	2	1	no	—
8	C₂×C₄	C₂²	1	1	yes	characteristic
9	C₈	—	2	1	no	—
10	C₂²	D₄	1	1	yes	characteristic
11	C₄	—	2	2	no	—
12	C₄	—	4	1	no	—
13	C₄	C₂×C₄	1	1	yes	characteristic
14	C₄	D₄	1	1	yes	characteristic
15	C₂	C₂²⋊C₄	1	1	yes	characteristic
16	C₂	SD₁₆	1	1	yes	characteristic
17	C₂	Q₁₆	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
5. Q₈	C₄	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.