Subgroups — Q₈⋊#90768 #16817471

Order 3712.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#90768	C₂	1	1	yes	maximal, characteristic
2	C₄×#90768	C₂	1	1	yes	maximal, characteristic
3	C₈×Q₈×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₄×Q₈×C₂₉	C₄	1	1	yes	characteristic
5	C₂₉×C₄⋊C₈	—	2	1	no	—
6	C₂₉×C₄⋊C₈	C₄	1	1	yes	characteristic
7	C₄×C₈×C₂₉	—	2	1	no	—
8	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×#90768	—	2	1	no	—
10	C₂×#90768	—	2	1	no	—
11	C₂×Q₈×C₂₉	C₈	1	1	yes	characteristic
12	C₂×C₈×C₂₉	—	2	1	no	—
13	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
14	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
15	C₄⋊C₄×C₂₉	—	2	1	no	—
16	C₄⋊C₄×C₂₉	C₈	1	1	yes	characteristic
17	C₄²×C₂₉	—	2	1	no	—
18	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
19	#90768	—	2	2	no	—
20	#90768	—	4	1	no	—
21	Q₈×C₂₉	—	2	1	no	—
22	Q₈×C₂₉	C₁₆	1	2	yes	complemented
23	C₂×C₄×C₂₉	—	2	1	no	—
24	C₂×C₄×C₂₉	—	2	1	no	—
25	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₂₉	M₁₆	1	1	yes	characteristic
28	C₈×C₂₉	—	2	1	no	—
29	C₈×C₂₉	—	4	1	no	—
30	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
31	C₈×C₂₉	Q₁₆	1	1	yes	characteristic
32	Q₈⋊C₁₆	—	29	1	no	maximal, Sylow
33	C₂²×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
34	C₄×C₂₉	—	2	2	no	—
35	C₄×C₂₉	—	2	1	no	—
36	C₄×C₂₉	—	4	1	no	—
37	C₄×C₂₉	#103	1	1	yes	characteristic
38	C₄×C₂₉	#104	1	1	yes	characteristic
39	C₄×C₂₉	C₂×C₁₆	1	1	yes	characteristic
40	C₄×C₂₉	M₃₂	1	1	yes	characteristic
41	C₈×Q₈	D₂₉	1	1	yes	characteristic
42	C₄⋊C₁₆	—	29	1	no	—
43	C₄×C₁₆	—	29	1	no	—
44	C₂×C₂₉	Q₈⋊C₈	1	1	yes	characteristic
45	C₂×C₂₉	C₂²⋊C₁₆	1	1	yes	characteristic
46	C₂×C₂₉	#350	1	1	yes	characteristic
47	C₄×Q₈	Dic₂₉	1	1	yes	characteristic
48	C₂×C₁₆	—	58	1	no	—
49	C₂×C₁₆	—	58	1	no	—
50	C₄⋊C₈	—	2	1	no	—
51	C₄⋊C₈	Dic₂₉	1	1	yes	characteristic
52	C₄×C₈	—	2	1	no	—
53	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
54	C₂₉	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₈	#6597	1	1	yes	characteristic
56	C₂×C₈	—	2	1	no	—
57	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
59	C₄⋊C₄	—	2	1	no	—
60	C₄⋊C₄	#6597	1	1	yes	characteristic
61	C₄²	—	2	1	no	—
62	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
63	C₁₆	—	58	2	no	—
64	C₁₆	—	116	1	no	—
65	Q₈	—	2	1	no	—
66	Q₈	#90768	1	2	yes	complemented
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	C₂×#6597	1	1	yes	characteristic
70	C₂×C₄	#90777	1	1	yes	characteristic
71	C₂×C₄	C₂²⋊Dic₂₉	1	1	yes	characteristic
72	C₈	—	2	1	no	—
73	C₈	—	4	1	no	—
74	C₈	#90784	1	1	yes	characteristic
75	C₈	#90785	1	1	yes	characteristic
76	C₂²	C₂²⋊#6597	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	—	2	1	no	—
79	C₄	—	4	1	no	—
80	C₄	C₂×#90768	1	1	yes	characteristic
81	C₄	#11745160	1	1	yes	characteristic
82	C₄	#11745183	1	1	yes	characteristic
83	C₄	#11745185	1	1	yes	characteristic
84	C₂	Q₈⋊#6597	1	1	yes	characteristic
85	C₂	C₂²⋊#90768	1	1	yes	characteristic
86	C₂	#14270947	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₂₉
commutator	C₄×C₂₉	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₂₉
Fitting	C₈×Q₈×C₂₉	C₂
socle, prime radical	C₂²×C₂₉	C₂²⋊C₈
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	C₈×Q₈	D₂₉
hypocenter	C₂₉	Q₈⋊C₁₆
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
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×C₂₉	C₁₆	semidirect
54. C₂₉	Q₈⋊C₁₆	semidirect
66. Q₈	#90768	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#90768	2
C₄×#90768	2
C₈×Q₈×C₂₉	2
Q₈⋊C₁₆	29

Subgroups — Q8⋊#90768 #16817471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈⋊#90768 #16817471