Subgroups — #37548749

Order 23168.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042201	C₂	1	2	yes	maximal
2	#26041054	C₂	1	1	yes	maximal, characteristic
3	#19153890	—	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	#15668452	—	4	2	no	—
8	C₂×#13089678	D₄	1	1	yes	characteristic
9	C₄×Dic₁₈₁	Q₈	1	1	yes	characteristic
10	#15668424	C₈	1	2	yes	—
11	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₈₁	—	2	1	no	—
13	C₂×Dic₁₈₁	—	2	1	no	—
14	#13089678	SD₁₆	1	2	yes	—
15	C₂×C₄×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
16	C₈×C₁₈₁	C₂×C₈	1	1	yes	characteristic
17	C₈×C₁₈₁	M₁₆	1	1	yes	characteristic
18	C₂²×C₁₈₁	#108	1	1	yes	characteristic
19	C₄×C₁₈₁	C₄⋊C₈	1	1	yes	characteristic
20	C₄×C₁₈₁	#106	1	1	yes	characteristic
21	Dic₁₈₁	—	4	1	no	—
22	C₂×C₁₈₁	—	2	1	no	—
23	C₂×C₁₈₁	#334	1	1	yes	characteristic
24	C₁₈₁	#1369	1	1	yes	characteristic, complemented, Sylow
25	#1369	—	181	1	no	maximal, Sylow
26	#364	—	181	2	no	—
27	#346	—	181	1	no	—
28	M₃₂	—	362	2	no	—
29	C₂×C₁₆	—	181	1	no	—
30	C₂×C₁₆	#10624382	1	1	yes	characteristic
31	C₄×C₈	—	181	1	no	—
32	C₂×C₈	—	181	1	no	—
33	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
34	C₄²	—	181	1	no	—
35	C₁₆	—	2	1	no	—
36	C₁₆	—	181	2	no	—
37	C₁₆	—	724	2	no	—
38	C₂×C₄	—	362	1	no	—
39	C₂×C₄	C₄⋊#10624382	1	1	yes	characteristic
40	C₈	—	181	2	no	—
41	C₈	D₁₈₁⋊C₈	1	1	yes	characteristic
42	C₈	#15668458	1	1	yes	characteristic
43	C₂²	#19153887	1	1	yes	characteristic
44	C₄	—	724	1	no	—
45	C₄	#19153883	1	1	yes	characteristic
46	C₄	#19153884	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#26042141	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19153884
commutator	C₈×C₁₈₁	C₂×C₈
Frattini	C₂×C₈	C₂×#10624382
Fitting	C₂×C₁₆×C₁₈₁	C₄
socle	C₂×C₁₈₁	#334
prime radical	C₂²×C₁₈₁	#108
cosocle	C₈×Dic₁₈₁	C₂²
hypercenter	C₂×C₁₆	#10624382
hypocenter	C₁₈₁	#1369
LCS	G ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
24. C₁₈₁	#1369	semidirect

Maximal subgroups

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

subgroup	index
#26042201	2
#26041054	2
#1369	181