Subgroups — Q₈⋊#11924003 #22607910

Order 9344.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11924003	C₂	1	1	yes	maximal, characteristic
2	C₄×#11924003	C₂	1	1	yes	maximal, characteristic
3	C₈×Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924003	—	2	1	no	—
5	C₂×#11924003	—	2	1	no	—
6	C₄×Q₈×C₇₃	C₄	1	1	yes	characteristic
7	C₄⋊C₈×C₇₃	—	2	1	no	—
8	C₄⋊C₈×C₇₃	C₄	1	1	yes	characteristic
9	C₄×C₈×C₇₃	—	2	1	no	—
10	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
11	#11924003	—	2	2	no	—
12	#11924003	—	4	1	no	—
13	C₂×Q₈×C₇₃	C₈	1	1	yes	characteristic
14	C₂×C₈×C₇₃	—	2	1	no	—
15	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
16	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
17	C₄⋊C₄×C₇₃	—	2	1	no	—
18	C₄⋊C₄×C₇₃	C₈	1	1	yes	characteristic
19	C₄²×C₇₃	—	2	1	no	—
20	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
21	Q₈×C₇₃	—	2	1	no	—
22	Q₈×C₇₃	C₁₆	1	2	yes	complemented
23	C₂×C₄×C₇₃	—	2	1	no	—
24	C₂×C₄×C₇₃	—	2	1	no	—
25	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
28	C₈×C₇₃	—	2	1	no	—
29	C₈×C₇₃	—	4	1	no	—
30	C₈×C₇₃	SD₁₆	1	1	yes	characteristic
31	C₈×C₇₃	Q₁₆	1	1	yes	characteristic
32	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
33	C₄×C₇₃	—	2	2	no	—
34	C₄×C₇₃	—	2	1	no	—
35	C₄×C₇₃	—	4	1	no	—
36	C₄×C₇₃	#103	1	1	yes	characteristic
37	C₄×C₇₃	#104	1	1	yes	characteristic
38	C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
39	C₄×C₇₃	M₃₂	1	1	yes	characteristic
40	C₂×C₇₃	Q₈⋊C₈	1	1	yes	characteristic
41	C₂×C₇₃	C₂²⋊C₁₆	1	1	yes	characteristic
42	C₂×C₇₃	#350	1	1	yes	characteristic
43	Q₈⋊C₁₆	—	73	1	no	maximal, Sylow
44	C₇₃	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
45	C₈×Q₈	D₇₃	1	1	yes	characteristic
46	C₄⋊C₁₆	—	73	1	no	—
47	C₄×C₁₆	—	73	1	no	—
48	C₄×Q₈	Dic₇₃	1	1	yes	characteristic
49	C₂×C₁₆	—	146	1	no	—
50	C₂×C₁₆	—	146	1	no	—
51	C₄⋊C₈	—	2	1	no	—
52	C₄⋊C₈	Dic₇₃	1	1	yes	characteristic
53	C₄×C₈	—	2	1	no	—
54	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
55	C₂×Q₈	#10596831	1	1	yes	characteristic
56	C₂×C₈	—	2	1	no	—
57	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
59	C₄⋊C₄	—	2	1	no	—
60	C₄⋊C₄	#10596831	1	1	yes	characteristic
61	C₄²	—	2	1	no	—
62	C₄²	C₂×Dic₇₃	1	1	yes	characteristic
63	C₁₆	—	292	1	no	—
64	C₁₆	—	146	2	no	—
65	Q₈	—	2	1	no	—
66	Q₈	#11924003	1	2	yes	complemented
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
70	C₂×C₄	C₂×#10596831	1	1	yes	characteristic
71	C₂×C₄	#11924012	1	1	yes	characteristic
72	C₈	—	2	1	no	—
73	C₈	—	4	1	no	—
74	C₈	#11924015	1	1	yes	characteristic
75	C₈	#11924018	1	1	yes	characteristic
76	C₂²	C₂²⋊#10596831	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	—	2	1	no	—
79	C₄	—	4	1	no	—
80	C₄	#14556515	1	1	yes	characteristic
81	C₄	#14556518	1	1	yes	characteristic
82	C₄	C₂×#11924003	1	1	yes	characteristic
83	C₄	#14556531	1	1	yes	characteristic
84	C₂	Q₈⋊#10596831	1	1	yes	characteristic
85	C₂	C₂²⋊#11924003	1	1	yes	characteristic
86	C₂	#17988371	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₇₃
commutator	C₄×C₇₃	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₇₃
Fitting	C₈×Q₈×C₇₃	C₂
socle	C₂²×C₇₃	C₂²⋊C₈
hypercenter	C₈×Q₈	D₇₃
hypocenter	C₇₃	Q₈⋊C₁₆
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×Q₈

Complements

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

N	H ≅ G/N	type
22. Q₈×C₇₃	C₁₆	semidirect
44. C₇₃	Q₈⋊C₁₆	semidirect
66. Q₈	#11924003	semidirect

Subgroups — Q8⋊#11924003 #22607910

Conjugacy classes of subgroups

Complements

Subgroups — Q₈⋊#11924003 #22607910