Subgroups — #22554476

Order 8416.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16862376	C₂	1	1	yes	maximal, characteristic
2	#16862360	C₂	1	1	yes	maximal, characteristic, complemented
3	#16862359	C₂	1	2	yes	maximal, complemented
4	C₈×D₂₆₃	C₂	1	2	yes	maximal, complemented
5	C₂×C₈×C₂₆₃	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₅₂₆	C₄	1	1	yes	characteristic
7	D₁₀₅₂	C₄	1	1	yes	characteristic
8	C₂²⋊D₂₆₃	C₄	1	2	yes	—
9	C₄×D₂₆₃	C₂²	1	2	yes	—
10	C₂₆₃⋊C₈	C₂²	1	2	yes	—
11	C₂×C₄×C₂₆₃	C₂²	1	1	yes	characteristic
12	C₈×C₂₆₃	C₂²	1	1	yes	characteristic
13	C₈×C₂₆₃	C₂²	1	1	yes	characteristic
14	C₂²×C₂₆₃	C₂×C₄	1	1	yes	characteristic
15	C₂×D₂₆₃	C₂×C₄	1	2	yes	—
16	C₄×C₂₆₃	C₂×C₄	1	1	yes	characteristic
17	C₄×C₂₆₃	C₂³	1	1	yes	characteristic
18	Dic₂₆₃	C₂×C₄	1	2	yes	—
19	C₂×C₂₆₃	—	2	1	no	—
20	C₂×C₂₆₃	C₂²×C₄	1	1	yes	characteristic
21	D₂₆₃	—	2	2	no	—
22	C₂₆₃	#131	1	1	yes	characteristic, complemented, Sylow
23	#131	—	263	1	no	maximal, Sylow
24	#41	—	263	1	no	—
25	M₁₆	—	263	1	no	—
26	M₁₆	—	263	2	no	—
27	C₂×C₈	—	263	2	no	—
28	C₂×C₈	D₂₆₃	1	1	yes	characteristic, complemented
29	Q₈	—	263	1	no	—
30	D₄	—	263	2	no	—
31	D₄	—	263	1	no	—
32	C₂×C₄	—	263	2	no	—
33	C₂×C₄	C₂×D₂₆₃	1	1	yes	characteristic
34	C₈	—	263	2	no	—
35	C₈	C₂×D₂₆₃	1	1	yes	characteristic
36	C₈	C₂×D₂₆₃	1	1	yes	characteristic
37	C₂²	—	263	2	no	—
38	C₂²	C₄×D₂₆₃	1	1	yes	characteristic
39	C₄	—	263	2	no	—
40	C₄	C₄×D₂₆₃	1	1	yes	characteristic
41	C₄	C₂²×D₂₆₃	1	1	yes	characteristic
42	C₂	—	2	1	no	—
43	C₂	—	526	2	no	—
44	C₂	C₂×C₄×D₂₆₃	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₂₆₃
commutator, socle	C₂×C₂₆₃	C₂²×C₄
Frattini	C₄	C₂²×D₂₆₃
Fitting	C₂×C₈×C₂₆₃	C₂
hypercenter	C₂×C₈	D₂₆₃
hypocenter	C₂₆₃	#131
LCS	G ▷ C₂×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #16862360	C₂	semidirect
3. #16862359	C₂	semidirect
4. C₈×D₂₆₃	C₂	semidirect
5. C₂×C₈×C₂₆₃	C₂	semidirect
22. C₂₆₃	#131	semidirect
28. C₂×C₈	D₂₆₃	semidirect