Subgroups — #37548886

Order 23168.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042208	C₂	1	1	yes	maximal, characteristic
2	#26042206	C₂	1	1	yes	maximal, characteristic
3	#26041112	C₂	1	1	yes	maximal, characteristic
4	#19153887	—	2	1	no	—
5	#19153885	—	2	1	no	—
6	C₁₆×D₁₈₁	C₂²	1	1	yes	characteristic
7	#19153722	C₄	1	1	yes	characteristic, complemented
8	C₃₂×C₁₈₁	C₄	1	1	yes	characteristic, complemented
9	#15668459	—	4	1	no	—
10	C₄⋊#10624382	—	4	1	no	—
11	C₈×D₁₈₁	D₄	1	1	yes	characteristic
12	#15668424	Q₈	1	1	yes	characteristic
13	C₁₆×C₁₈₁	C₂×C₄	1	1	yes	characteristic
14	C₂×#10624382	—	8	1	no	—
15	#13089685	—	8	1	no	—
16	C₄×D₁₈₁	D₈	1	1	yes	characteristic
17	#13089678	Q₁₆	1	1	yes	characteristic
18	C₈×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
19	C₂×D₁₈₁	SD₃₂	1	1	yes	characteristic
20	#10624382	—	16	1	no	—
21	C₄×C₁₈₁	#107	1	1	yes	characteristic
22	Dic₁₈₁	SD₃₂	1	1	yes	characteristic
23	C₂×C₁₈₁	#367	1	1	yes	characteristic
24	D₁₈₁	—	2	1	no	—
25	C₁₈₁	#1426	1	1	yes	characteristic, complemented, Sylow
26	#1426	—	181	1	no	maximal, Sylow
27	M₆₄	—	181	1	no	—
28	#368	—	181	1	no	—
29	#367	—	181	1	no	—
30	C₂×C₁₆	—	181	1	no	—
31	#108	—	362	1	no	—
32	#107	—	362	1	no	—
33	C₃₂	—	181	1	no	—
34	C₃₂	#10624382	1	1	yes	characteristic, complemented
35	M₁₆	—	724	1	no	—
36	C₂×C₈	—	181	1	no	—
37	C₄⋊C₄	—	724	1	no	—
38	C₁₆	—	181	1	no	—
39	C₁₆	C₂×#10624382	1	1	yes	characteristic
40	C₂×C₄	—	1448	1	no	—
41	C₂×C₄	—	181	1	no	—
42	C₈	—	1448	1	no	—
43	C₈	—	181	1	no	—
44	C₈	C₄⋊#10624382	1	1	yes	characteristic
45	C₂²	—	181	1	no	—
46	C₄	—	2896	1	no	—
47	C₄	—	181	1	no	—
48	C₄	#19153885	1	1	yes	characteristic
49	C₂	—	362	1	no	—
50	C₂	#26042206	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26042206
commutator	C₁₆×C₁₈₁	C₂×C₄
Frattini	C₁₆	C₂×#10624382
Fitting	C₃₂×C₁₈₁	C₄
socle	C₂×C₁₈₁	#367
prime radical	C₂×D₁₈₁	SD₃₂
cosocle	C₁₆×D₁₈₁	C₂²
hypercenter	C₃₂	#10624382
hypocenter	C₁₈₁	#1426
LCS	G ▷ C₁₆×C₁₈₁ ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
7. #19153722	C₄	semidirect
8. C₃₂×C₁₈₁	C₄	semidirect
25. C₁₈₁	#1426	semidirect
34. C₃₂	#10624382	semidirect

Maximal subgroups

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

subgroup	index
#26042208	2
#26042206	2
#26041112	2
#1426	181