Subgroups — #37536000

Order 23168.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26041681	C₂	1	2	yes	maximal
2	#26041107	C₂	1	2	yes	maximal
3	#26041105	C₂	1	2	yes	maximal
4	C₄×C₁₆×C₁₈₁	C₂	1	1	yes	maximal, characteristic
5	#19153808	—	2	2	no	—
6	#19153750	C₂²	1	4	yes	—
7	#19153748	—	2	2	no	—
8	C₂×C₁₆×C₁₈₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₁₈₁	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₁₈₁	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₈₁	—	2	4	no	—
12	#15668428	—	4	4	no	—
13	C₂×C₈×C₁₈₁	D₄	1	1	yes	characteristic
14	C₂×C₈×C₁₈₁	C₂³	1	1	yes	characteristic
15	C₄²×C₁₈₁	D₄	1	1	yes	characteristic
16	C₁₆×C₁₈₁	Q₈	1	2	yes	—
17	C₁₆×C₁₈₁	Q₈	1	2	yes	—
18	C₂×Dic₁₈₁	—	4	4	no	—
19	C₂×C₄×C₁₈₁	D₈	1	2	yes	—
20	C₂×C₄×C₁₈₁	C₂×D₄	1	1	yes	characteristic
21	C₈×C₁₈₁	Q₁₆	1	2	yes	—
22	C₈×C₁₈₁	C₂×Q₈	1	1	yes	characteristic
23	C₈×C₁₈₁	C₂×Q₈	1	1	yes	characteristic
24	C₂²×C₁₈₁	C₂×D₈	1	1	yes	characteristic
25	C₄×C₁₈₁	—	2	2	no	—
26	C₄×C₁₈₁	C₄⋊Q₈	1	1	yes	characteristic
27	C₄×C₁₈₁	C₂×Q₁₆	1	1	yes	characteristic
28	Dic₁₈₁	—	8	4	no	—
29	C₂×C₁₈₁	#500	1	1	yes	characteristic
30	C₂×C₁₈₁	#508	1	2	yes	—
31	C₁₈₁	#2253	1	1	yes	characteristic, complemented, Sylow
32	#2253	—	181	1	no	maximal, Sylow
33	#499	—	181	2	no	—
34	#367	—	181	2	no	—
35	#366	—	181	2	no	—
36	C₄×C₁₆	D₁₈₁	1	1	yes	characteristic
37	#125	—	362	2	no	—
38	C₂×C₁₆	C₂×D₁₈₁	1	1	yes	characteristic
39	C₂×C₁₆	C₂×D₁₈₁	1	1	yes	characteristic
40	#107	—	181	4	no	—
41	#106	—	362	2	no	—
42	C₄×C₈	C₂×D₁₈₁	1	1	yes	characteristic
43	C₂×C₈	D₇₂₄	1	1	yes	characteristic
44	C₂×C₈	C₂²×D₁₈₁	1	1	yes	characteristic
45	C₄⋊C₄	—	362	4	no	—
46	C₄⋊C₄	—	724	4	no	—
47	C₄²	D₇₂₄	1	1	yes	characteristic
48	C₁₆	Dic₃₆₂	1	2	yes	—
49	C₁₆	Dic₃₆₂	1	2	yes	—
50	C₂×C₄	—	724	4	no	—
51	C₂×C₄	D₁₄₄₈	1	2	yes	—
52	C₂×C₄	C₂×D₇₂₄	1	1	yes	characteristic
53	C₈	Dic₇₂₄	1	2	yes	—
54	C₈	C₂×Dic₃₆₂	1	1	yes	characteristic
55	C₈	C₂×Dic₃₆₂	1	1	yes	characteristic
56	C₂²	C₂×D₁₄₄₈	1	1	yes	characteristic
57	C₄	—	2	2	no	—
58	C₄	—	1448	4	no	—
59	C₄	#19153816	1	1	yes	characteristic
60	C₄	C₂×Dic₇₂₄	1	1	yes	characteristic
61	C₂	#26041684	1	1	yes	characteristic
62	C₂	#26041711	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₄₄₈
commutator, cosocle	C₂×C₈×C₁₈₁	C₂³
Frattini	C₂×C₈	C₂²×D₁₈₁
Fitting	C₄×C₁₆×C₁₈₁	C₂
socle, prime radical	C₂²×C₁₈₁	C₂×D₈
hypercenter	C₄×C₁₆	D₁₈₁
hypocenter	C₁₈₁	#2253
LCS	G ▷ C₂×C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
31. C₁₈₁	#2253	semidirect

Maximal subgroups

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

subgroup	index
#26041681	2
#26041107	2
#26041105	2
C₄×C₁₆×C₁₈₁	2
#2253	181