Subgroups — #37548934

Order 23168.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042295	C₂	1	2	yes	maximal
2	#13089685⋊C₈	C₂	1	4	yes	maximal, complemented
3	C₂×C₈×Dic₁₈₁	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#13089685	C₄	1	4	yes	—
5	C₂²⋊#13089685	C₄	1	4	yes	—
6	C₄×#13089685	C₂²	1	4	yes	—
7	C₂²×#13089678	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₁₈₁	C₂²	1	1	yes	characteristic
9	C₈×Dic₁₈₁	C₄	1	2	yes	—
10	C₈×Dic₁₈₁	C₂²	1	2	yes	—
11	C₂²×C₈×C₁₈₁	C₄	1	1	yes	characteristic
12	C₂×#13089685	C₂×C₄	1	8	yes	—
13	C₂²×Dic₁₈₁	C₂×C₄	1	2	yes	—
14	C₂×#13089678	—	2	2	no	—
15	C₂×#13089678	C₂×C₄	1	2	yes	—
16	C₄×Dic₁₈₁	C₂×C₄	1	2	yes	—
17	C₄×Dic₁₈₁	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₁₈₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₁₈₁	—	2	2	no	—
21	C₂×C₈×C₁₈₁	C₂×C₄	1	2	yes	—
22	#13089685	—	2	8	no	—
23	C₂×Dic₁₈₁	—	2	4	no	—
24	C₂×Dic₁₈₁	C₄²	1	2	yes	—
25	C₂×Dic₁₈₁	C₂²×C₄	1	2	yes	—
26	#13089678	—	2	2	no	—
27	C₂³×C₁₈₁	C₄²	1	1	yes	characteristic
28	C₂×C₄×C₁₈₁	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₁₈₁	M₁₆	1	2	yes	—
30	C₂×C₄×C₁₈₁	M₁₆	1	2	yes	—
31	C₂×C₄×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₁₈₁	—	2	2	no	—
33	C₂²×C₁₈₁	—	2	2	no	—
34	C₂²×C₁₈₁	#97	1	2	yes	—
35	C₂²×C₁₈₁	C₂×C₄²	1	1	yes	characteristic
36	C₄×C₁₈₁	#97	1	2	yes	—
37	C₄×C₁₈₁	C₂×M₁₆	1	1	yes	characteristic
38	C₄×C₁₈₁	C₂×M₁₆	1	1	yes	characteristic
39	Dic₁₈₁	—	2	2	no	—
40	Dic₁₈₁	#131	1	4	yes	—
41	C₂×C₁₈₁	—	2	2	no	—
42	C₂×C₁₈₁	C₂×#97	1	1	yes	characteristic
43	C₂×C₁₈₁	#405	1	2	yes	—
44	C₁₈₁	#1452	1	1	yes	characteristic, complemented, Sylow
45	#1452	—	181	1	no	maximal, Sylow
46	#431	—	181	2	no	—
47	C₂×C₄×C₈	—	181	1	no	—
48	#322	—	181	4	no	—
49	C₂²×C₈	—	181	1	no	—
50	C₂²×C₈	#10624382	1	1	yes	characteristic
51	C₂×C₄²	—	181	1	no	—
52	C₄⋊C₈	—	181	4	no	—
53	C₂²⋊C₈	—	181	4	no	—
54	C₄×C₈	—	181	4	no	—
55	C₄×C₈	—	181	2	no	—
56	C₄×C₈	—	181	2	no	—
57	C₂²×C₄	—	181	2	no	—
58	C₂²×C₄	C₂×#10624382	1	1	yes	characteristic
59	C₂×C₈	—	2	2	no	—
60	C₂×C₈	—	362	2	no	—
61	C₂×C₈	—	181	8	no	—
62	C₂×C₈	—	181	2	no	—
63	C₂×C₈	C₂×#10624382	1	2	yes	—
64	C₄²	—	181	2	no	—
65	C₄²	—	181	1	no	—
66	C₄²	—	181	1	no	—
67	C₂³	C₄×#10624382	1	1	yes	characteristic
68	C₂×C₄	—	362	4	no	—
69	C₂×C₄	—	181	2	no	—
70	C₂×C₄	—	181	2	no	—
71	C₂×C₄	C₄×#10624382	1	1	yes	characteristic
72	C₂×C₄	#15668458	1	2	yes	—
73	C₂×C₄	#15668459	1	2	yes	—
74	C₂×C₄	C₂²×#10624382	1	1	yes	characteristic
75	C₈	—	2	2	no	—
76	C₈	—	362	8	no	—
77	C₈	—	362	2	no	—
78	C₂²	—	2	2	no	—
79	C₂²	#19153871	1	2	yes	—
80	C₂²	C₂×C₄×#10624382	1	1	yes	characteristic
81	C₄	—	362	2	no	—
82	C₄	—	181	4	no	—
83	C₄	#19153871	1	2	yes	—
84	C₄	C₂×#15668458	1	1	yes	characteristic
85	C₄	C₂×#15668459	1	1	yes	characteristic
86	C₂	—	2	2	no	—
87	C₂	C₂×#19153871	1	1	yes	characteristic
88	C₂	#26042242	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#10624382
commutator, socle	C₂²×C₁₈₁	C₂×C₄²
Fitting	C₂²×C₈×C₁₈₁	C₄
prime radical	C₂³×C₁₈₁	C₄²
cosocle	C₄×Dic₁₈₁	C₂³
hypercenter	C₂²×C₈	#10624382
hypocenter	C₁₈₁	#1452
LCS	G ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #13089685⋊C₈	C₂	semidirect
44. C₁₈₁	#1452	semidirect

Maximal subgroups

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

subgroup	index
#26042295	2
#13089685⋊C₈	2
C₂×C₈×Dic₁₈₁	2
#1452	181