Subgroups — Q₈⋊#14268661 #28407837

Order 14464.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14268661	C₂	1	1	yes	maximal, characteristic
2	C₄×#14268661	C₂	1	1	yes	maximal, characteristic
3	Q₈×#11744762	C₂	1	1	yes	maximal, characteristic
4	C₂×#14268661	—	2	1	no	—
5	C₂×#14268661	—	2	1	no	—
6	C₄⋊#11744762	—	2	1	no	—
7	C₄⋊#11744762	C₄	1	1	yes	characteristic
8	C₄×#11744762	—	2	1	no	—
9	C₄×#11744762	C₂²	1	1	yes	characteristic
10	Q₈×#90673	C₄	1	1	yes	characteristic
11	#14268661	—	2	2	no	—
12	#14268661	—	4	1	no	—
13	C₂×#11744762	—	2	1	no	—
14	C₂×#11744762	D₄	1	1	yes	characteristic
15	C₂×#11744762	D₄	1	1	yes	characteristic
16	C₄⋊#90673	—	2	1	no	—
17	C₄⋊#90673	C₈	1	1	yes	characteristic
18	C₄×#90673	—	2	1	no	—
19	C₄×#90673	C₂×C₄	1	1	yes	characteristic
20	Q₈×D₁₁₃	C₈	1	1	yes	characteristic
21	C₂×#90673	—	2	1	no	—
22	C₂×#90673	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×#90673	M₁₆	1	1	yes	characteristic
24	#11744762	—	2	1	no	—
25	#11744762	—	4	1	no	—
26	#11744762	SD₁₆	1	1	yes	characteristic
27	#11744762	Q₁₆	1	1	yes	characteristic
28	Q₈×C₁₁₃	C₁₆	1	1	yes	characteristic, complemented
29	C₄×D₁₁₃	—	2	1	no	—
30	C₄×D₁₁₃	C₂×C₈	1	1	yes	characteristic
31	Dic₂₂₆	—	2	1	no	—
32	Dic₂₂₆	C₁₆	1	1	yes	characteristic, complemented
33	C₂×D₁₁₃	C₂²⋊C₈	1	1	yes	characteristic
34	#90673	—	2	1	no	—
35	#90673	—	4	1	no	—
36	#90673	#103	1	1	yes	characteristic
37	#90673	#104	1	1	yes	characteristic
38	C₄×C₁₁₃	—	2	1	no	—
39	C₄×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
40	Dic₁₁₃	—	2	1	no	—
41	Dic₁₁₃	M₃₂	1	1	yes	characteristic
42	C₂×C₁₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
43	D₁₁₃	Q₈⋊C₈	1	1	yes	characteristic
44	D₁₁₃	#350	1	1	yes	characteristic
45	Q₈⋊C₁₆	—	113	1	no	maximal, Sylow
46	C₁₁₃	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
47	C₈×Q₈	—	113	1	no	—
48	C₄⋊C₁₆	—	113	1	no	—
49	C₄×C₁₆	—	113	1	no	—
50	C₄×Q₈	—	113	1	no	—
51	C₂×C₁₆	—	226	1	no	—
52	C₂×C₁₆	—	226	1	no	—
53	C₄⋊C₈	—	113	1	no	—
54	C₄⋊C₈	—	226	1	no	—
55	C₄×C₈	—	113	1	no	—
56	C₄×C₈	—	226	1	no	—
57	C₂×Q₈	—	113	1	no	—
58	C₂×C₈	—	113	1	no	—
59	C₂×C₈	—	113	1	no	—
60	C₂×C₈	—	226	1	no	—
61	C₄⋊C₄	—	113	1	no	—
62	C₄⋊C₄	—	226	1	no	—
63	C₄²	—	113	1	no	—
64	C₄²	—	226	1	no	—
65	C₁₆	—	452	1	no	—
66	C₁₆	—	226	2	no	—
67	Q₈	—	113	1	no	—
68	Q₈	—	226	1	no	—
69	Q₈	#14268661	1	1	yes	characteristic, complemented
70	C₂×C₄	—	113	1	no	—
71	C₂×C₄	—	113	1	no	—
72	C₂×C₄	—	113	1	no	—
73	C₂×C₄	—	226	1	no	—
74	C₂×C₄	—	226	1	no	—
75	C₈	—	113	1	no	—
76	C₈	—	113	1	no	—
77	C₈	—	452	1	no	—
78	C₈	—	226	1	no	—
79	C₂²	—	113	1	no	—
80	C₄	—	2	1	no	—
81	C₄	—	113	1	no	—
82	C₄	—	113	1	no	—
83	C₄	—	113	1	no	—
84	C₄	—	452	1	no	—
85	C₄	—	226	1	no	—
86	C₄	—	226	1	no	—
87	C₄	C₂×#14268661	1	1	yes	characteristic
88	C₂	—	113	1	no	—
89	C₂	—	113	1	no	—
90	C₂	C₂²⋊#14268661	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊#14268661
commutator	C₄×C₁₁₃	C₂×C₁₆
Frattini	C₄	C₂×#14268661
Fitting	Q₈×C₁₁₃	C₁₆
socle	C₂×C₁₁₃	C₂²⋊C₁₆
prime radical	C₂×D₁₁₃	C₂²⋊C₈
cosocle	C₄×#11744762	C₂²
hypercenter	Q₈	#14268661
hypocenter	C₁₁₃	Q₈⋊C₁₆
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
28. Q₈×C₁₁₃	C₁₆	semidirect
32. Dic₂₂₆	C₁₆	semidirect
46. C₁₁₃	Q₈⋊C₁₆	semidirect
69. Q₈	#14268661	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#14268661	2
C₄×#14268661	2
Q₈×#11744762	2
Q₈⋊C₁₆	113

Subgroups — Q8⋊#14268661 #28407837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈⋊#14268661 #28407837