Subgroups — #22576166

Order 8672.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864654	C₂	1	1	yes	maximal, characteristic
2	#16864638	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864637	C₂	1	2	yes	maximal, complemented
4	C₈×D₂₇₁	C₂	1	2	yes	maximal, complemented
5	C₂×C₈×C₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₅₄₂	C₄	1	1	yes	characteristic
7	D₁₀₈₄	C₄	1	1	yes	characteristic
8	C₂²⋊D₂₇₁	C₄	1	2	yes	—
9	C₄×D₂₇₁	C₂²	1	2	yes	—
10	C₂₇₁⋊C₈	C₂²	1	2	yes	—
11	C₂×C₄×C₂₇₁	C₂²	1	1	yes	characteristic
12	C₈×C₂₇₁	C₂²	1	1	yes	characteristic
13	C₈×C₂₇₁	C₂²	1	1	yes	characteristic
14	C₂²×C₂₇₁	C₂×C₄	1	1	yes	characteristic
15	C₂×D₂₇₁	C₂×C₄	1	2	yes	—
16	C₄×C₂₇₁	C₂×C₄	1	1	yes	characteristic
17	C₄×C₂₇₁	C₂³	1	1	yes	characteristic
18	Dic₂₇₁	C₂×C₄	1	2	yes	—
19	C₂×C₂₇₁	—	2	1	no	—
20	C₂×C₂₇₁	C₂²×C₄	1	1	yes	characteristic
21	D₂₇₁	—	2	2	no	—
22	C₂₇₁	#131	1	1	yes	characteristic, complemented, Sylow
23	#131	—	271	1	no	maximal, Sylow
24	#41	—	271	1	no	—
25	M₁₆	—	271	1	no	—
26	M₁₆	—	271	2	no	—
27	C₂×C₈	—	271	2	no	—
28	C₂×C₈	D₂₇₁	1	1	yes	characteristic, complemented
29	Q₈	—	271	1	no	—
30	D₄	—	271	2	no	—
31	D₄	—	271	1	no	—
32	C₂×C₄	—	271	2	no	—
33	C₂×C₄	C₂×D₂₇₁	1	1	yes	characteristic
34	C₈	—	271	2	no	—
35	C₈	C₂×D₂₇₁	1	1	yes	characteristic
36	C₈	C₂×D₂₇₁	1	1	yes	characteristic
37	C₂²	—	271	2	no	—
38	C₂²	C₄×D₂₇₁	1	1	yes	characteristic
39	C₄	—	271	2	no	—
40	C₄	C₄×D₂₇₁	1	1	yes	characteristic
41	C₄	C₂²×D₂₇₁	1	1	yes	characteristic
42	C₂	—	2	1	no	—
43	C₂	—	542	2	no	—
44	C₂	C₂×C₄×D₂₇₁	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₂₇₁
commutator, socle	C₂×C₂₇₁	C₂²×C₄
Frattini	C₄	C₂²×D₂₇₁
Fitting	C₂×C₈×C₂₇₁	C₂
hypercenter	C₂×C₈	D₂₇₁
hypocenter	C₂₇₁	#131
LCS	G ▷ C₂×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #16864638	C₂	semidirect
3. #16864637	C₂	semidirect
4. C₈×D₂₇₁	C₂	semidirect
5. C₂×C₈×C₂₇₁	C₂	semidirect
22. C₂₇₁	#131	semidirect
28. C₂×C₈	D₂₇₁	semidirect