Subgroups — #37533859

Order 23168.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26041303	C₂	1	2	yes	maximal
2	#26041044	C₂	1	4	yes	maximal
3	C₂×C₄×C₈×C₁₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#15668433	C₂²	1	4	yes	—
5	C₄⋊#13089678	—	2	4	no	—
6	C₂²×C₈×C₁₈₁	C₂²	1	2	yes	—
7	C₂×C₄²×C₁₈₁	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₁₈₁	C₄	1	2	yes	—
9	C₄×C₈×C₁₈₁	C₄	1	2	yes	—
10	#15668433	—	2	8	no	—
11	C₂×#13089678	—	2	4	no	—
12	C₂²×C₄×C₁₈₁	Q₈	1	2	yes	—
13	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
14	C₂×C₈×C₁₈₁	—	2	4	no	—
15	C₂×C₈×C₁₈₁	C₂×C₄	1	4	yes	—
16	C₄²×C₁₈₁	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₁₈₁	C₂×C₄	1	1	yes	characteristic
18	C₄²×C₁₈₁	D₄	1	2	yes	—
19	#13089678	—	4	4	no	—
20	C₂³×C₁₈₁	C₂×Q₈	1	1	yes	characteristic
21	C₂×C₄×C₁₈₁	—	2	4	no	—
22	C₂×C₄×C₁₈₁	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₁₈₁	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₈₁	C₂×D₄	1	1	yes	characteristic
26	C₂×C₄×C₁₈₁	#41	1	4	yes	—
27	C₈×C₁₈₁	—	2	4	no	—
28	C₂²×C₁₈₁	—	2	2	no	—
29	C₂²×C₁₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
30	C₂²×C₁₈₁	#125	1	2	yes	—
31	C₄×C₁₈₁	—	2	2	no	—
32	C₄×C₁₈₁	#108	1	4	yes	—
33	C₄×C₁₈₁	#117	1	2	yes	—
34	C₄×C₁₈₁	#124	1	2	yes	—
35	C₂×C₁₈₁	—	2	2	no	—
36	C₂×C₁₈₁	#382	1	1	yes	characteristic
37	C₂×C₁₈₁	C₂×#108	1	2	yes	—
38	C₁₈₁	#1837	1	1	yes	characteristic, complemented, Sylow
39	#1837	—	181	1	no	maximal, Sylow
40	#423	—	181	2	no	—
41	C₂×C₄×C₈	D₁₈₁	1	1	yes	characteristic
42	#341	—	181	4	no	—
43	C₂×M₁₆	—	181	4	no	—
44	C₂²×C₈	C₂×D₁₈₁	1	2	yes	—
45	C₂×C₄²	C₂×D₁₈₁	1	1	yes	characteristic
46	C₄⋊C₈	—	362	4	no	—
47	C₄×C₈	Dic₁₈₁	1	2	yes	—
48	C₄×C₈	Dic₁₈₁	1	2	yes	—
49	C₂²×C₄	Dic₃₆₂	1	2	yes	—
50	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
51	M₁₆	—	362	8	no	—
52	C₂×C₈	—	2	4	no	—
53	C₂×C₈	—	362	4	no	—
54	C₂×C₈	C₂×Dic₁₈₁	1	4	yes	—
55	C₄²	C₂×Dic₁₈₁	1	1	yes	characteristic
56	C₄²	C₂×Dic₁₈₁	1	1	yes	characteristic
57	C₄²	D₇₂₄	1	2	yes	—
58	C₂³	C₂×Dic₃₆₂	1	1	yes	characteristic
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	C₄⋊Dic₁₈₁	1	2	yes	—
61	C₂×C₄	C₄⋊Dic₁₈₁	1	2	yes	—
62	C₂×C₄	C₂²×Dic₁₈₁	1	1	yes	characteristic
63	C₂×C₄	C₂×D₇₂₄	1	1	yes	characteristic
64	C₂×C₄	#15668449	1	4	yes	—
65	C₈	—	2	4	no	—
66	C₈	—	724	4	no	—
67	C₂²	—	2	2	no	—
68	C₂²	C₂×C₄⋊Dic₁₈₁	1	1	yes	characteristic
69	C₂²	#19153808	1	2	yes	—
70	C₄	—	2	2	no	—
71	C₄	#19153752	1	4	yes	—
72	C₄	#19153775	1	2	yes	—
73	C₄	#19153804	1	2	yes	—
74	C₂	—	2	2	no	—
75	C₂	#26041145	1	1	yes	characteristic
76	C₂	C₂×#19153752	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₇₂₄
commutator	C₂×C₄×C₁₈₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₈₁
Fitting	C₂×C₄×C₈×C₁₈₁	C₂
socle	C₂²×C₁₈₁	C₂×C₄⋊C₄
prime radical	C₂³×C₁₈₁	C₂×Q₈
cosocle	C₂²×C₄×C₁₈₁	C₂³
hypercenter	C₂×C₄×C₈	D₁₈₁
hypocenter	C₁₈₁	#1837
LCS	G ▷ C₂×C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

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

Maximal subgroups

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

subgroup	index
#26041303	2
#26041044	2
C₂×C₄×C₈×C₁₈₁	2
#1837	181