Subgroups — Q₈×C₂₆₃⋊C₈ #30682064

Order 16832.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₂₆₃⋊C₈)	C₂	1	3	yes	maximal
2	C₄×C₂₆₃⋊C₈	C₂	1	3	yes	maximal
3	C₄×Q₈×C₂₆₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₆₃⋊C₈	C₂²	1	3	yes	—
5	C₂×C₂₆₃⋊C₈	C₂²	1	1	yes	characteristic
6	C₂×Q₈×C₂₆₃	C₄	1	1	yes	characteristic
7	C₄⋊C₄×C₂₆₃	C₄	1	3	yes	—
8	C₄²×C₂₆₃	C₂²	1	3	yes	—
9	C₂₆₃⋊C₈	—	2	3	no	—
10	C₂₆₃⋊C₈	Q₈	1	2	yes	direct product factor
11	Q₈×C₂₆₃	C₈	1	4	yes	complemented
12	C₂×C₄×C₂₆₃	C₂×C₄	1	3	yes	—
13	C₂×C₄×C₂₆₃	C₂×C₄	1	3	yes	—
14	C₂×C₄×C₂₆₃	C₂³	1	1	yes	characteristic
15	C₂²×C₂₆₃	C₂²×C₄	1	1	yes	characteristic
16	C₄×C₂₆₃	—	2	3	no	—
17	C₄×C₂₆₃	C₂×C₈	1	6	yes	—
18	C₄×C₂₆₃	C₂×Q₈	1	1	yes	characteristic
19	C₄×C₂₆₃	#41	1	1	yes	characteristic
20	C₂×C₂₆₃	C₄×Q₈	1	1	yes	characteristic
21	C₂×C₂₆₃	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₂₆₃	#131	1	1	yes	characteristic
23	C₂₆₃	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
24	C₈×Q₈	—	263	1	no	maximal, Sylow
25	C₄×Q₈	D₂₆₃	1	1	yes	characteristic
26	C₄⋊C₈	—	263	3	no	—
27	C₄×C₈	—	263	3	no	—
28	C₂×Q₈	Dic₂₆₃	1	1	yes	characteristic
29	C₂×C₈	—	263	1	no	—
30	C₂×C₈	—	263	3	no	—
31	C₄⋊C₄	Dic₂₆₃	1	3	yes	—
32	C₄²	C₂×D₂₆₃	1	3	yes	—
33	Q₈	C₂₆₃⋊C₈	1	4	yes	direct product factor
34	C₂×C₄	C₂×Dic₂₆₃	1	3	yes	—
35	C₂×C₄	C₂×Dic₂₆₃	1	3	yes	—
36	C₂×C₄	C₂²×D₂₆₃	1	1	yes	characteristic
37	C₈	—	263	2	no	—
38	C₈	—	526	3	no	—
39	C₂²	C₂²×Dic₂₆₃	1	1	yes	characteristic
40	C₄	—	2	3	no	—
41	C₄	C₂×C₂₆₃⋊C₈	1	6	yes	—
42	C₄	Q₈×D₂₆₃	1	1	yes	characteristic
43	C₄	#16862377	1	1	yes	characteristic
44	C₂	Q₈×Dic₂₆₃	1	1	yes	characteristic
45	C₂	C₂²×C₂₆₃⋊C₈	1	1	yes	characteristic
46	C₂	#22554477	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₆₃
commutator	C₂×C₂₆₃	C₂²×C₈
Fitting	C₄×Q₈×C₂₆₃	C₂
socle, prime radical	C₂²×C₂₆₃	C₂²×C₄
cosocle	C₂×C₄×C₂₆₃	C₂³
hypercenter	C₄×Q₈	D₂₆₃
hypocenter	C₂₆₃	C₈×Q₈
LCS	G ▷ C₂×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
10. C₂₆₃⋊C₈	Q₈	direct (N × H)
11. Q₈×C₂₆₃	C₈	semidirect
23. C₂₆₃	C₈×Q₈	semidirect
33. Q₈	C₂₆₃⋊C₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄⋊(C₂₆₃⋊C₈)	2
C₄×C₂₆₃⋊C₈	2
C₄×Q₈×C₂₆₃	2
C₈×Q₈	263

Subgroups — Q8×C263⋊C8 #30682064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₂₆₃⋊C₈ #30682064