Subgroups — #37549646

Order 23168.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042284	C₂	1	2	yes	maximal
2	#26042155	C₂	1	4	yes	maximal
3	C₄×C₈×D₁₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#15668459	C₂²	1	4	yes	—
5	#19153883	—	2	4	no	—
6	C₂×C₈×D₁₈₁	C₂²	1	2	yes	—
7	C₄²×D₁₈₁	C₂²	1	1	yes	characteristic
8	C₄×#13089678	C₄	1	1	yes	characteristic
9	C₈×Dic₁₈₁	C₄	1	2	yes	—
10	C₄×C₈×C₁₈₁	C₄	1	1	yes	characteristic
11	#15668459	—	2	8	no	—
12	C₂×#13089685	—	2	4	no	—
13	C₂×C₄×D₁₈₁	Q₈	1	2	yes	—
14	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
15	C₂×#13089678	C₂×C₄	1	2	yes	—
16	C₈×D₁₈₁	—	2	4	no	—
17	C₄×Dic₁₈₁	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₁₈₁	D₄	1	2	yes	—
19	C₂×C₈×C₁₈₁	C₂×C₄	1	2	yes	—
20	C₄²×C₁₈₁	C₂×C₄	1	1	yes	characteristic
21	#13089685	—	4	4	no	—
22	C₂²×D₁₈₁	C₂×Q₈	1	1	yes	characteristic
23	C₂×Dic₁₈₁	C₄⋊C₄	1	2	yes	—
24	C₂×Dic₁₈₁	C₂×D₄	1	1	yes	characteristic
25	C₄×D₁₈₁	—	2	4	no	—
26	C₄×D₁₈₁	#41	1	4	yes	—
27	#13089678	—	2	2	no	—
28	C₂×C₄×C₁₈₁	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
30	C₈×C₁₈₁	—	2	2	no	—
31	C₂²×C₁₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
32	C₂×D₁₈₁	—	2	2	no	—
33	C₂×D₁₈₁	#125	1	2	yes	—
34	C₄×C₁₈₁	—	2	2	no	—
35	C₄×C₁₈₁	#117	1	2	yes	—
36	Dic₁₈₁	#108	1	4	yes	—
37	Dic₁₈₁	#124	1	2	yes	—
38	C₂×C₁₈₁	#382	1	1	yes	characteristic
39	C₂×C₁₈₁	C₂×#108	1	2	yes	—
40	D₁₈₁	—	2	2	no	—
41	C₁₈₁	#1837	1	1	yes	characteristic, complemented, Sylow
42	#1837	—	181	1	no	maximal, Sylow
43	#423	—	181	2	no	—
44	C₂×C₄×C₈	—	181	1	no	—
45	#341	—	181	4	no	—
46	C₂×M₁₆	—	181	4	no	—
47	C₂²×C₈	—	181	2	no	—
48	C₂×C₄²	—	181	1	no	—
49	C₄⋊C₈	—	362	4	no	—
50	C₄×C₈	—	181	2	no	—
51	C₄×C₈	—	181	1	no	—
52	C₄×C₈	#10624382	1	1	yes	characteristic
53	C₂²×C₄	—	181	2	no	—
54	C₂²×C₄	—	181	1	no	—
55	M₁₆	—	362	8	no	—
56	C₂×C₈	—	362	4	no	—
57	C₂×C₈	—	362	4	no	—
58	C₂×C₈	—	181	2	no	—
59	C₂×C₈	C₂×#10624382	1	2	yes	—
60	C₄²	—	181	2	no	—
61	C₄²	—	181	1	no	—
62	C₄²	C₂×#10624382	1	1	yes	characteristic
63	C₂³	—	181	1	no	—
64	C₂×C₄	—	362	4	no	—
65	C₂×C₄	—	181	1	no	—
66	C₂×C₄	—	181	2	no	—
67	C₂×C₄	—	181	4	no	—
68	C₂×C₄	C₄⋊#10624382	1	2	yes	—
69	C₂×C₄	C₂²×#10624382	1	1	yes	characteristic
70	C₈	—	2	2	no	—
71	C₈	—	362	2	no	—
72	C₈	—	724	4	no	—
73	C₂²	—	362	2	no	—
74	C₂²	—	181	2	no	—
75	C₂²	C₂×C₄⋊#10624382	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	181	2	no	—
78	C₄	—	181	4	no	—
79	C₄	#19153895	1	2	yes	—
80	C₂	—	362	2	no	—
81	C₂	#26042223	1	1	yes	characteristic
82	C₂	D₁₈₁⋊#108	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#10624382
commutator	C₂×C₄×C₁₈₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#10624382
Fitting	C₄×C₈×C₁₈₁	C₄
socle	C₂²×C₁₈₁	C₂×C₄⋊C₄
prime radical	C₂²×D₁₈₁	C₂×Q₈
cosocle	C₂×C₄×D₁₈₁	C₂³
hypercenter	C₄×C₈	#10624382
hypocenter	C₁₈₁	#1837
LCS	G ▷ C₂×C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
41. C₁₈₁	#1837	semidirect

Maximal subgroups

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

subgroup	index
#26042284	2
#26042155	2
C₄×C₈×D₁₈₁	2
#1837	181