Subgroups — Q₈⋊#13089685 #26042128

Order 11584.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#13089685	C₂	1	1	yes	maximal, characteristic
2	C₄×#13089685	C₂	1	1	yes	maximal, characteristic
3	Q₈×Dic₁₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#13089685	—	2	1	no	—
5	C₂×#13089685	—	2	1	no	—
6	C₄⋊Dic₁₈₁	—	2	1	no	—
7	C₄⋊Dic₁₈₁	C₄	1	1	yes	characteristic
8	C₄×Dic₁₈₁	—	2	1	no	—
9	C₄×Dic₁₈₁	C₂²	1	1	yes	characteristic
10	C₂×Q₈×C₁₈₁	C₄	1	1	yes	characteristic
11	#13089685	—	2	2	no	—
12	#13089685	—	4	1	no	—
13	C₂×Dic₁₈₁	—	2	1	no	—
14	C₂×Dic₁₈₁	D₄	1	1	yes	characteristic
15	C₂×Dic₁₈₁	D₄	1	1	yes	characteristic
16	Q₈×C₁₈₁	—	2	1	no	—
17	Q₈×C₁₈₁	C₈	1	2	yes	complemented
18	C₂×C₄×C₁₈₁	—	2	1	no	—
19	C₂×C₄×C₁₈₁	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₈₁	—	2	2	no	—
22	C₄×C₁₈₁	C₂×C₈	1	1	yes	characteristic
23	C₄×C₁₈₁	M₁₆	1	1	yes	characteristic
24	Dic₁₈₁	—	2	1	no	—
25	Dic₁₈₁	—	4	1	no	—
26	Dic₁₈₁	SD₁₆	1	1	yes	characteristic
27	Dic₁₈₁	Q₁₆	1	1	yes	characteristic
28	C₂×C₁₈₁	C₂²⋊C₈	1	1	yes	characteristic
29	C₂×C₁₈₁	#103	1	1	yes	characteristic
30	C₂×C₁₈₁	#104	1	1	yes	characteristic
31	C₁₈₁	Q₈⋊C₈	1	1	yes	characteristic, complemented, Sylow
32	Q₈⋊C₈	—	181	1	no	maximal, Sylow
33	C₄×Q₈	—	181	1	no	—
34	C₄⋊C₈	—	181	1	no	—
35	C₄×C₈	—	181	1	no	—
36	C₂×Q₈	#10624382	1	1	yes	characteristic
37	C₂×C₈	—	362	1	no	—
38	C₂×C₈	—	362	1	no	—
39	C₄⋊C₄	—	362	1	no	—
40	C₄⋊C₄	—	181	1	no	—
41	C₄²	—	362	1	no	—
42	C₄²	—	181	1	no	—
43	Q₈	—	2	1	no	—
44	Q₈	#13089685	1	2	yes	complemented
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	362	1	no	—
47	C₂×C₄	—	181	1	no	—
48	C₂×C₄	—	181	1	no	—
49	C₂×C₄	C₂×#10624382	1	1	yes	characteristic
50	C₈	—	362	2	no	—
51	C₈	—	724	1	no	—
52	C₂²	C₂²⋊#10624382	1	1	yes	characteristic
53	C₄	—	2	2	no	—
54	C₄	—	362	1	no	—
55	C₄	—	181	1	no	—
56	C₄	—	181	1	no	—
57	C₄	—	724	1	no	—
58	C₄	C₂×#13089685	1	1	yes	characteristic
59	C₄	#15668458	1	1	yes	characteristic
60	C₂	C₂²⋊#13089685	1	1	yes	characteristic
61	C₂	#19153879	1	1	yes	characteristic
62	C₂	#19153881	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#10624382
commutator	C₄×C₁₈₁	C₂×C₈
Frattini	C₂×C₄	C₂×#10624382
Fitting	C₂×Q₈×C₁₈₁	C₄
socle, prime radical	C₂²×C₁₈₁	C₂²⋊C₄
cosocle	C₄×Dic₁₈₁	C₂²
hypercenter	C₂×Q₈	#10624382
hypocenter	C₁₈₁	Q₈⋊C₈
LCS	G ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
17. Q₈×C₁₈₁	C₈	semidirect
31. C₁₈₁	Q₈⋊C₈	semidirect
44. Q₈	#13089685	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#13089685	2
C₄×#13089685	2
Q₈×Dic₁₈₁	2
Q₈⋊C₈	181

Subgroups — Q8⋊#13089685 #26042128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈⋊#13089685 #26042128