Subgroups — Q₈⋊C₁₆ #1337

Order 128.

47 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₄×Q₈	C₄	1	1	yes	characteristic
5	C₂×C₁₆	—	2	1	no	—
6	C₂×C₁₆	—	2	1	no	—
7	C₄⋊C₈	—	2	1	no	—
8	C₄⋊C₈	C₄	1	1	yes	characteristic
9	C₄×C₈	—	2	1	no	—
10	C₄×C₈	C₂²	1	1	yes	characteristic
11	C₂×Q₈	C₈	1	1	yes	characteristic
12	C₂×C₈	—	2	1	no	—
13	C₂×C₈	D₄	1	1	yes	characteristic
14	C₂×C₈	D₄	1	1	yes	characteristic
15	C₄⋊C₄	—	2	1	no	—
16	C₄⋊C₄	C₈	1	1	yes	characteristic
17	C₄²	—	2	1	no	—
18	C₄²	C₂×C₄	1	1	yes	characteristic
19	C₁₆	—	2	2	no	—
20	C₁₆	—	4	1	no	—
21	Q₈	—	2	1	no	—
22	Q₈	C₁₆	1	2	yes	complemented
23	C₂×C₄	—	2	1	no	—
24	C₂×C₄	—	2	1	no	—
25	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄	M₁₆	1	1	yes	characteristic
28	C₈	—	2	1	no	—
29	C₈	—	4	1	no	—
30	C₈	SD₁₆	1	1	yes	characteristic
31	C₈	Q₁₆	1	1	yes	characteristic
32	C₂²	C₂²⋊C₈	1	1	yes	characteristic
33	C₄	—	2	2	no	—
34	C₄	—	2	1	no	—
35	C₄	—	4	1	no	—
36	C₄	#103	1	1	yes	characteristic
37	C₄	#104	1	1	yes	characteristic
38	C₄	C₂×C₁₆	1	1	yes	characteristic
39	C₄	M₃₂	1	1	yes	characteristic
40	C₂	Q₈⋊C₈	1	1	yes	characteristic
41	C₂	C₂²⋊C₁₆	1	1	yes	characteristic
42	C₂	#350	1	1	yes	characteristic

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

N	H ≅ G/N	type
22. Q₈	C₁₆	semidirect

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