Subgroups — #22553089

Order 8384.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16862186	C₂	1	1	yes	maximal, characteristic
2	#16862156	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃₁⋊C₈	C₄	1	1	yes	characteristic
5	C₄×Dic₁₃₁	C₄	1	1	yes	characteristic
6	C₁₃₁⋊C₁₆	C₄	1	2	yes	complemented
7	C₂×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
8	C₁₆×C₁₃₁	C₄	1	2	yes	complemented
9	C₂×Dic₁₃₁	—	2	1	no	—
10	C₁₃₁⋊C₈	—	2	1	no	—
11	C₂×C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
13	C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₁₃₁	M₁₆	1	1	yes	characteristic
15	C₄×C₁₃₁	C₄²	1	1	yes	characteristic
16	C₄×C₁₃₁	M₁₆	1	1	yes	characteristic
17	Dic₁₃₁	—	4	1	no	—
18	C₂×C₁₃₁	—	2	1	no	—
19	C₂×C₁₃₁	#97	1	1	yes	characteristic
20	C₁₃₁	#347	1	1	yes	characteristic, complemented, Sylow
21	#347	—	131	1	no	maximal, Sylow
22	M₃₂	—	131	1	no	—
23	M₃₂	D₁₃₁	1	1	yes	characteristic
24	#97	—	131	1	no	—
25	C₂×C₈	—	131	1	no	—
26	C₂×C₈	C₂×D₁₃₁	1	1	yes	characteristic
27	C₄²	—	131	1	no	—
28	C₁₆	—	131	2	no	—
29	C₁₆	Dic₁₃₁	1	2	yes	complemented
30	C₂×C₄	—	262	1	no	—
31	C₂×C₄	C₄×D₁₃₁	1	1	yes	characteristic
32	C₈	—	262	1	no	—
33	C₈	C₄×D₁₃₁	1	1	yes	characteristic
34	C₈	C₂×Dic₁₃₁	1	1	yes	characteristic
35	C₂²	#14523496	1	1	yes	characteristic
36	C₄	—	524	1	no	—
37	C₄	C₄×Dic₁₃₁	1	1	yes	characteristic
38	C₄	#14523496	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	#16862156	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×Dic₁₃₁
commutator	C₄×C₁₃₁	C₄²
Frattini	C₂×C₈	C₂×D₁₃₁
Fitting	M₃₂×C₁₃₁	C₂
socle	C₂×C₁₃₁	#97
hypercenter	M₃₂	D₁₃₁
hypocenter	C₁₃₁	#347
LCS	G ▷ C₄×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₄ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
6. C₁₃₁⋊C₁₆	C₄	semidirect
8. C₁₆×C₁₃₁	C₄	semidirect
20. C₁₃₁	#347	semidirect
29. C₁₆	Dic₁₃₁	semidirect