Subgroups — C₂×#16862360 #22554475

Order 8416.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16862360	C₂	1	4	yes	maximal, direct product factor
2	C₂×C₂₆₃⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×C₂₆₃	C₂	1	1	yes	maximal, characteristic
4	C₂₆₃⋊C₈	C₂²	1	4	yes	complemented
5	C₂³×C₂₆₃	C₄	1	1	yes	characteristic
6	C₂×C₄×C₂₆₃	C₄	1	2	yes	—
7	C₂×C₄×C₂₆₃	C₄	1	1	yes	characteristic
8	C₂×C₄×C₂₆₃	C₂²	1	2	yes	—
9	C₂×C₄×C₂₆₃	C₂²	1	1	yes	characteristic
10	C₂²×C₂₆₃	—	2	2	no	—
11	C₂²×C₂₆₃	C₂×C₄	1	2	yes	—
12	C₂²×C₂₆₃	C₂×C₄	1	1	yes	characteristic
13	C₄×C₂₆₃	C₂×C₄	1	2	yes	—
14	C₄×C₂₆₃	C₂×C₄	1	1	yes	characteristic
15	C₄×C₂₆₃	C₂³	1	1	yes	characteristic
16	C₂×C₂₆₃	—	2	2	no	—
17	C₂×C₂₆₃	M₁₆	1	2	yes	complemented
18	C₂×C₂₆₃	C₂²×C₄	1	1	yes	characteristic
19	C₂₆₃	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
20	C₂×M₁₆	—	263	1	no	maximal, Sylow
21	C₂²×C₄	D₂₆₃	1	1	yes	characteristic
22	M₁₆	—	263	4	no	—
23	C₂×C₈	—	263	2	no	—
24	C₂³	Dic₂₆₃	1	1	yes	characteristic
25	C₂×C₄	Dic₂₆₃	1	1	yes	characteristic
26	C₂×C₄	Dic₂₆₃	1	2	yes	—
27	C₂×C₄	C₂×D₂₆₃	1	2	yes	—
28	C₂×C₄	C₂×D₂₆₃	1	1	yes	characteristic
29	C₈	—	263	4	no	—
30	C₂²	—	2	2	no	—
31	C₂²	C₂×Dic₂₆₃	1	2	yes	—
32	C₂²	C₂×Dic₂₆₃	1	1	yes	characteristic
33	C₄	C₂×Dic₂₆₃	1	2	yes	—
34	C₄	C₂×Dic₂₆₃	1	1	yes	characteristic
35	C₄	C₂²×D₂₆₃	1	1	yes	characteristic
36	C₂	—	2	2	no	—
37	C₂	#16862360	1	2	yes	direct product factor
38	C₂	C₂²×Dic₂₆₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₂₆₃
commutator	C₂×C₂₆₃	C₂²×C₄
Frattini	C₄	C₂²×D₂₆₃
Fitting	C₂²×C₄×C₂₆₃	C₂
socle	C₂²×C₂₆₃	C₂×C₄
hypercenter	C₂²×C₄	D₂₆₃
hypocenter	C₂₆₃	C₂×M₁₆
LCS	G ▷ C₂×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. #16862360	C₂	direct (N × H)
2. C₂×C₂₆₃⋊C₈	C₂	semidirect
4. C₂₆₃⋊C₈	C₂²	semidirect
17. C₂×C₂₆₃	M₁₆	semidirect
19. C₂₆₃	C₂×M₁₆	semidirect
37. C₂	#16862360	direct (N × H)

Subgroups — C2×#16862360 #22554475

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16862360 #22554475