Subgroups — Q₈⋊C₈ #326

Order 64.

35 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈	C₄	1	1	yes	characteristic
5	C₂×C₈	—	2	1	no	—
6	C₂×C₈	—	2	1	no	—
7	C₄⋊C₄	—	2	1	no	—
8	C₄⋊C₄	C₄	1	1	yes	characteristic
9	C₄²	—	2	1	no	—
10	C₄²	C₂²	1	1	yes	characteristic
11	Q₈	—	2	1	no	—
12	Q₈	C₈	1	2	yes	complemented
13	C₂×C₄	—	2	1	no	—
14	C₂×C₄	—	2	1	no	—
15	C₂×C₄	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄	D₄	1	1	yes	characteristic
17	C₂×C₄	D₄	1	1	yes	characteristic
18	C₈	—	2	2	no	—
19	C₈	—	4	1	no	—
20	C₂²	C₂²⋊C₄	1	1	yes	characteristic
21	C₄	—	2	2	no	—
22	C₄	—	2	1	no	—
23	C₄	—	4	1	no	—
24	C₄	C₂×C₈	1	1	yes	characteristic
25	C₄	M₁₆	1	1	yes	characteristic
26	C₄	SD₁₆	1	1	yes	characteristic
27	C₄	Q₁₆	1	1	yes	characteristic
28	C₂	C₂²⋊C₈	1	1	yes	characteristic
29	C₂	#103	1	1	yes	characteristic
30	C₂	#104	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. Q₈	C₈	semidirect

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