Subgroups — #37531928

Order 23168.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26041113	C₂	1	1	yes	maximal, characteristic
2	#26041107	C₂	1	1	yes	maximal, characteristic
3	#368×C₁₈₁	C₂	1	1	yes	maximal, characteristic
4	#19153750	—	2	1	no	—
5	#19153722	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₁₈₁	C₂²	1	1	yes	characteristic
7	#108×C₁₈₁	—	2	1	no	—
8	C₄⋊Dic₁₈₁	—	4	1	no	—
9	M₁₆×C₁₈₁	—	4	1	no	—
10	C₂×C₈×C₁₈₁	D₄	1	1	yes	characteristic
11	C₁₆×C₁₈₁	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₈₁	Q₈	1	1	yes	characteristic
13	C₂×Dic₁₈₁	—	8	1	no	—
14	C₂×C₄×C₁₈₁	D₈	1	1	yes	characteristic
15	C₈×C₁₈₁	—	8	1	no	—
16	C₈×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₈₁	Q₁₆	1	1	yes	characteristic
18	C₂²×C₁₈₁	SD₃₂	1	1	yes	characteristic
19	C₄×C₁₈₁	#107	1	1	yes	characteristic
20	C₄×C₁₈₁	SD₃₂	1	1	yes	characteristic
21	Dic₁₈₁	—	16	1	no	—
22	C₂×C₁₈₁	—	2	1	no	—
23	C₂×C₁₈₁	#367	1	1	yes	characteristic
24	C₁₈₁	#1426	1	1	yes	characteristic, complemented, Sylow
25	#1426	—	181	1	no	maximal, Sylow
26	M₆₄	—	181	1	no	—
27	#368	D₁₈₁	1	1	yes	characteristic
28	#367	—	181	1	no	—
29	C₂×C₁₆	C₂×D₁₈₁	1	1	yes	characteristic
30	#108	—	2	1	no	—
31	#107	—	362	1	no	—
32	C₃₂	—	181	2	no	—
33	M₁₆	—	4	1	no	—
34	C₂×C₈	C₂²⋊D₁₈₁	1	1	yes	characteristic
35	C₄⋊C₄	—	724	1	no	—
36	C₁₆	C₄×D₁₈₁	1	1	yes	characteristic
37	C₁₆	Dic₃₆₂	1	1	yes	characteristic
38	C₂×C₄	—	1448	1	no	—
39	C₂×C₄	#15668434	1	1	yes	characteristic
40	C₈	—	8	1	no	—
41	C₈	#15668428	1	1	yes	characteristic
42	C₈	#15668439	1	1	yes	characteristic
43	C₂²	#19153759	1	1	yes	characteristic
44	C₄	—	2896	1	no	—
45	C₄	#19153749	1	1	yes	characteristic
46	C₄	#19153760	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#26041106	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26041106
commutator	C₁₆×C₁₈₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₈₁
Fitting	#368×C₁₈₁	C₂
socle	C₂×C₁₈₁	#367
prime radical	C₂²×C₁₈₁	SD₃₂
cosocle	C₂×C₁₆×C₁₈₁	C₂²
hypercenter	#368	D₁₈₁
hypocenter	C₁₈₁	#1426
LCS	G ▷ C₁₆×C₁₈₁ ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
5. #19153722	C₄	semidirect
24. C₁₈₁	#1426	semidirect

Maximal subgroups

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

subgroup	index
#26041113	2
#26041107	2
#368×C₁₈₁	2
#1426	181