Subgroups — Q₈⋊#11744762 #20299686

Order 7232.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11744762	C₂	1	1	yes	maximal, characteristic
2	C₄×#11744762	C₂	1	1	yes	maximal, characteristic
3	Q₈×#90673	C₂	1	1	yes	maximal, characteristic
4	C₂×#11744762	—	2	1	no	—
5	C₂×#11744762	—	2	1	no	—
6	C₄⋊#90673	—	2	1	no	—
7	C₄⋊#90673	C₄	1	1	yes	characteristic
8	C₄×#90673	—	2	1	no	—
9	C₄×#90673	C₂²	1	1	yes	characteristic
10	Q₈×D₁₁₃	C₄	1	1	yes	characteristic
11	C₂×#90673	—	2	1	no	—
12	C₂×#90673	D₄	1	1	yes	characteristic
13	C₂×#90673	D₄	1	1	yes	characteristic
14	#11744762	—	2	2	no	—
15	#11744762	—	4	1	no	—
16	Q₈×C₁₁₃	C₈	1	1	yes	characteristic, complemented
17	C₄×D₁₁₃	—	2	1	no	—
18	C₄×D₁₁₃	C₂×C₄	1	1	yes	characteristic
19	Dic₂₂₆	—	2	1	no	—
20	Dic₂₂₆	C₈	1	1	yes	characteristic, complemented
21	C₂×D₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
22	#90673	—	2	1	no	—
23	#90673	—	4	1	no	—
24	#90673	SD₁₆	1	1	yes	characteristic
25	#90673	Q₁₆	1	1	yes	characteristic
26	C₄×C₁₁₃	—	2	1	no	—
27	C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
28	Dic₁₁₃	—	2	1	no	—
29	Dic₁₁₃	M₁₆	1	1	yes	characteristic
30	C₂×C₁₁₃	C₂²⋊C₈	1	1	yes	characteristic
31	D₁₁₃	#103	1	1	yes	characteristic
32	D₁₁₃	#104	1	1	yes	characteristic
33	C₁₁₃	Q₈⋊C₈	1	1	yes	characteristic, complemented, Sylow
34	Q₈⋊C₈	—	113	1	no	maximal, Sylow
35	C₄×Q₈	—	113	1	no	—
36	C₄⋊C₈	—	113	1	no	—
37	C₄×C₈	—	113	1	no	—
38	C₂×Q₈	—	113	1	no	—
39	C₂×C₈	—	226	1	no	—
40	C₂×C₈	—	226	1	no	—
41	C₄⋊C₄	—	113	1	no	—
42	C₄⋊C₄	—	226	1	no	—
43	C₄²	—	113	1	no	—
44	C₄²	—	226	1	no	—
45	Q₈	—	113	1	no	—
46	Q₈	—	226	1	no	—
47	Q₈	#11744762	1	1	yes	characteristic, complemented
48	C₂×C₄	—	113	1	no	—
49	C₂×C₄	—	113	1	no	—
50	C₂×C₄	—	113	1	no	—
51	C₂×C₄	—	226	1	no	—
52	C₂×C₄	—	226	1	no	—
53	C₈	—	452	1	no	—
54	C₈	—	226	2	no	—
55	C₂²	—	113	1	no	—
56	C₄	—	2	1	no	—
57	C₄	—	113	1	no	—
58	C₄	—	113	1	no	—
59	C₄	—	113	1	no	—
60	C₄	—	452	1	no	—
61	C₄	—	226	1	no	—
62	C₄	—	226	1	no	—
63	C₄	C₂×#11744762	1	1	yes	characteristic
64	C₂	—	113	1	no	—
65	C₂	—	113	1	no	—
66	C₂	C₂²⋊#11744762	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊#11744762
commutator	C₄×C₁₁₃	C₂×C₈
Frattini	C₄	C₂×#11744762
Fitting	Q₈×C₁₁₃	C₈
socle	C₂×C₁₁₃	C₂²⋊C₈
hypercenter	Q₈	#11744762
hypocenter	C₁₁₃	Q₈⋊C₈
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₈

Complements

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

N	H ≅ G/N	type
16. Q₈×C₁₁₃	C₈	semidirect
20. Dic₂₂₆	C₈	semidirect
33. C₁₁₃	Q₈⋊C₈	semidirect
47. Q₈	#11744762	semidirect

Subgroups — Q8⋊#11744762 #20299686

Conjugacy classes of subgroups

Complements

Subgroups — Q₈⋊#11744762 #20299686