Subgroups — #37548745

Order 23168.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042140	C₂	1	2	yes	maximal
2	#26041054	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#13089685	—	2	2	no	—
4	C₂×#15668424	C₄	1	1	yes	characteristic
5	C₈×Dic₁₈₁	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₁₈₁	C₄	1	1	yes	characteristic
7	C₂×#13089685	—	4	2	no	—
8	C₂×#13089678	Q₈	1	1	yes	characteristic
9	C₄×Dic₁₈₁	D₄	1	1	yes	characteristic
10	#15668424	—	2	1	no	—
11	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₈₁	C₈	1	2	yes	complemented
13	#13089685	—	8	2	no	—
14	C₂×Dic₁₈₁	SD₁₆	1	2	yes	—
15	#13089678	—	2	1	no	—
16	C₂×C₄×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₈₁	C₂×C₈	1	1	yes	characteristic
18	C₈×C₁₈₁	M₁₆	1	1	yes	characteristic
19	C₂²×C₁₈₁	#106	1	1	yes	characteristic
20	C₄×C₁₈₁	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₁₈₁	#108	1	1	yes	characteristic
22	Dic₁₈₁	—	2	2	no	—
23	C₂×C₁₈₁	#334	1	1	yes	characteristic
24	C₂×C₁₈₁	#365	1	2	yes	—
25	C₁₈₁	#1368	1	1	yes	characteristic, complemented, Sylow
26	#1368	—	181	1	no	maximal, Sylow
27	#346	—	181	1	no	—
28	#334	—	181	2	no	—
29	C₂×C₁₆	—	181	1	no	—
30	C₂×C₁₆	#10624382	1	1	yes	characteristic
31	C₄⋊C₈	—	362	2	no	—
32	C₄×C₈	—	181	1	no	—
33	C₂×C₈	—	181	1	no	—
34	C₂×C₈	—	724	2	no	—
35	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
36	C₄²	—	181	1	no	—
37	C₁₆	—	362	1	no	—
38	C₁₆	#13089685	1	2	yes	complemented
39	C₂×C₄	—	181	2	no	—
40	C₂×C₄	C₄⋊#10624382	1	1	yes	characteristic
41	C₈	—	362	1	no	—
42	C₈	—	1448	2	no	—
43	C₈	C₂×#13089685	1	1	yes	characteristic
44	C₈	#15668459	1	1	yes	characteristic
45	C₂²	#19153884	1	1	yes	characteristic
46	C₄	—	362	2	no	—
47	C₄	C₄⋊#13089685	1	1	yes	characteristic
48	C₄	#19153886	1	1	yes	characteristic
49	C₂	#26042140	1	1	yes	characteristic
50	C₂	#26042203	1	2	yes	—

	subgroup	G/H
center	C₂²	#19153884
commutator	C₈×C₁₈₁	C₂×C₈
Frattini	C₂×C₈	C₂×#10624382
Fitting	C₂×C₁₆×C₁₈₁	C₄
socle, prime radical	C₂²×C₁₈₁	#106
cosocle	C₈×Dic₁₈₁	C₂²
hypercenter	C₂×C₁₆	#10624382
hypocenter	C₁₈₁	#1368
LCS	G ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
12. C₁₆×C₁₈₁	C₈	semidirect
25. C₁₈₁	#1368	semidirect
38. C₁₆	#13089685	semidirect

Maximal subgroups

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

subgroup	index
#26042140	2
#26041054	2
#1368	181