Group #37550085 — subgroups

Subgroups — #37550085

Order 23168.

152 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#15668452	C₂	1	2	yes	maximal, complemented
2	#26042174	C₂	1	2	yes	maximal
3	#26042168	C₂	1	2	yes	maximal, complemented
4	C₄×C₈×D₁₈₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#15668452	C₂²	1	4	yes	—
6	C₂×C₈×D₁₈₁	C₄	1	1	yes	characteristic
7	C₂×C₈×D₁₈₁	C₂²	1	1	yes	characteristic
8	C₄²×D₁₈₁	C₄	1	1	yes	characteristic
9	C₄×#13089678	C₂²	1	1	yes	characteristic
10	C₈×Dic₁₈₁	C₄	1	1	yes	characteristic
11	C₈×Dic₁₈₁	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₁₈₁	C₄	1	1	yes	characteristic
13	#15668452	—	2	4	no	—
14	C₂×C₄×D₁₈₁	C₈	1	1	yes	characteristic
15	C₂×C₄×D₁₈₁	C₈	1	1	yes	characteristic
16	C₂×C₄×D₁₈₁	C₂×C₄	1	1	yes	characteristic
17	C₂×#13089678	C₂×C₄	1	1	yes	characteristic
18	C₂×#13089678	C₂³	1	1	yes	characteristic
19	C₈×D₁₈₁	—	2	2	no	—
20	C₈×D₁₈₁	—	2	2	no	—
21	C₄×Dic₁₈₁	C₈	1	1	yes	characteristic
22	C₄×Dic₁₈₁	C₈	1	1	yes	characteristic
23	C₄×Dic₁₈₁	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
26	C₄²×C₁₈₁	C₂×C₄	1	1	yes	characteristic
27	C₂²×D₁₈₁	C₂×C₈	1	1	yes	characteristic
28	C₂×Dic₁₈₁	C₂×C₈	1	1	yes	characteristic
29	C₂×Dic₁₈₁	C₂×C₈	1	1	yes	characteristic
30	C₂×Dic₁₈₁	C₂×C₈	1	1	yes	characteristic
31	C₄×D₁₈₁	—	2	2	no	—
32	C₄×D₁₈₁	—	2	2	no	—
33	C₄×D₁₈₁	—	2	1	no	—
34	C₄×D₁₈₁	—	2	1	no	—
35	#13089678	—	2	1	no	—
36	#13089678	#41	1	2	yes	—
37	C₂×C₄×C₁₈₁	C₂×C₈	1	1	yes	characteristic
38	C₂×C₄×C₁₈₁	C₂×C₈	1	1	yes	characteristic
39	C₂×C₄×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
40	C₈×C₁₈₁	—	2	1	no	—
41	C₈×C₁₈₁	M₁₆	1	2	yes	—
42	C₂²×C₁₈₁	C₂²×C₈	1	1	yes	characteristic
43	C₂×D₁₈₁	—	2	1	no	—
44	C₂×D₁₈₁	—	2	1	no	—
45	C₂×D₁₈₁	M₃₂	1	2	yes	—
46	C₄×C₁₈₁	—	2	1	no	—
47	C₄×C₁₈₁	M₃₂	1	2	yes	—
48	C₄×C₁₈₁	#117	1	1	yes	characteristic
49	C₄×C₁₈₁	C₂×M₁₆	1	1	yes	characteristic
50	Dic₁₈₁	—	2	1	no	—
51	Dic₁₈₁	—	2	1	no	—
52	Dic₁₈₁	—	2	1	no	—
53	C₂×C₁₈₁	#431	1	1	yes	characteristic
54	C₂×C₁₈₁	C₂×M₃₂	1	1	yes	characteristic
55	C₂×C₁₈₁	C₂×M₃₂	1	1	yes	characteristic
56	D₁₈₁	—	2	2	no	—
57	C₁₈₁	#2163	1	1	yes	characteristic, complemented, Sylow
58	#2163	—	181	1	no	maximal, Sylow
59	C₂×C₄×C₈	—	181	1	no	—
60	C₄⋊C₁₆	—	181	2	no	—
61	C₂²⋊C₁₆	—	181	2	no	—
62	#346	—	181	2	no	—
63	C₂²×C₈	—	181	1	no	—
64	C₂²×C₈	—	181	1	no	—
65	C₂×C₄²	—	181	1	no	—
66	C₂×C₁₆	—	181	4	no	—
67	C₄×C₈	—	181	1	no	—
68	C₄×C₈	—	181	1	no	—
69	C₄×C₈	—	181	1	no	—
70	C₄×C₈	#10624382	1	1	yes	characteristic
71	C₂²×C₄	—	181	1	no	—
72	C₂²×C₄	—	181	1	no	—
73	C₂²×C₄	—	181	1	no	—
74	C₂×C₈	—	362	2	no	—
75	C₂×C₈	—	362	2	no	—
76	C₂×C₈	—	181	1	no	—
77	C₂×C₈	—	181	1	no	—
78	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
79	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
80	C₄²	—	181	1	no	—
81	C₄²	—	181	1	no	—
82	C₄²	—	181	1	no	—
83	C₄²	C₂×#10624382	1	1	yes	characteristic
84	C₁₆	—	362	4	no	—
85	C₂³	—	181	1	no	—
86	C₂×C₄	—	362	2	no	—
87	C₂×C₄	—	362	2	no	—
88	C₂×C₄	—	362	1	no	—
89	C₂×C₄	—	362	1	no	—
90	C₂×C₄	—	181	1	no	—
91	C₂×C₄	—	181	1	no	—
92	C₂×C₄	—	181	1	no	—
93	C₂×C₄	D₁₈₁⋊C₈	1	1	yes	characteristic
94	C₂×C₄	D₁₈₁⋊C₈	1	1	yes	characteristic
95	C₂×C₄	C₂²×#10624382	1	1	yes	characteristic
96	C₈	—	2	1	no	—
97	C₈	—	362	1	no	—
98	C₈	—	181	2	no	—
99	C₈	#15668459	1	2	yes	—
100	C₂²	—	362	1	no	—
101	C₂²	—	362	1	no	—
102	C₂²	—	181	2	no	—
103	C₂²	C₂×D₁₈₁⋊C₈	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	362	1	no	—
106	C₄	—	362	1	no	—
107	C₄	—	362	1	no	—
108	C₄	#19153891	1	2	yes	—
109	C₄	#19153895	1	1	yes	characteristic
110	C₄	C₂×#15668459	1	1	yes	characteristic
111	C₂	—	362	2	no	—
112	C₂	#26042298	1	1	yes	characteristic
113	C₂	D₁₈₁⋊M₃₂	1	1	yes	characteristic
114	C₂	C₂×#19153891	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊#15668452

C₂

yes

maximal, complemented

#26042174

C₂

yes

maximal

#26042168

C₂

yes

maximal, complemented

C₄×C₈×D₁₈₁

C₂

yes

maximal, characteristic

C₂×#15668452

C₂²

yes

—

C₂×C₈×D₁₈₁

C₄

yes

characteristic

C₂×C₈×D₁₈₁

C₂²

yes

characteristic

C₄²×D₁₈₁

C₄

yes

characteristic

C₄×#13089678

C₂²

yes

characteristic

C₈×Dic₁₈₁

C₄

yes

characteristic

C₈×Dic₁₈₁

C₂²

yes

characteristic

C₄×C₈×C₁₈₁

C₄

yes

characteristic

#15668452

—

C₂×C₄×D₁₈₁

C₈

yes

characteristic

C₂×C₄×D₁₈₁

C₈

yes

characteristic

C₂×C₄×D₁₈₁

C₂×C₄

yes

characteristic

C₂×#13089678

C₂×C₄

yes

characteristic

C₂×#13089678

C₂³

yes

characteristic

C₈×D₁₈₁

—

C₈×D₁₈₁

—

C₄×Dic₁₈₁

C₈

yes

characteristic

C₄×Dic₁₈₁

C₈

yes

characteristic

C₄×Dic₁₈₁

C₂×C₄

yes

characteristic

C₂×C₈×C₁₈₁

C₂×C₄

yes

characteristic

C₂×C₈×C₁₈₁

C₂×C₄

yes

characteristic

C₄²×C₁₈₁

C₂×C₄

yes

characteristic

C₂²×D₁₈₁

C₂×C₈

yes

characteristic

C₂×Dic₁₈₁

C₂×C₈

yes

characteristic

C₂×Dic₁₈₁

C₂×C₈

yes

characteristic

C₂×Dic₁₈₁

C₂×C₈

yes

characteristic

C₄×D₁₈₁

—

C₄×D₁₈₁

—

C₄×D₁₈₁

—

C₄×D₁₈₁

—

#13089678

—

#13089678

#41

yes

—

C₂×C₄×C₁₈₁

C₂×C₈

yes

characteristic

C₂×C₄×C₁₈₁

C₂×C₈

yes

characteristic

C₂×C₄×C₁₈₁

C₂²×C₄

yes

characteristic

C₈×C₁₈₁

—

C₈×C₁₈₁

M₁₆

yes

—

C₂²×C₁₈₁

C₂²×C₈

yes

characteristic

C₂×D₁₈₁

—

C₂×D₁₈₁

—

C₂×D₁₈₁

M₃₂

yes

—

C₄×C₁₈₁

—

C₄×C₁₈₁

M₃₂

yes

—

C₄×C₁₈₁

#117

yes

characteristic

C₄×C₁₈₁

C₂×M₁₆

yes

characteristic

Dic₁₈₁

—

Dic₁₈₁

—

Dic₁₈₁

—

C₂×C₁₈₁

#431

yes

characteristic

C₂×C₁₈₁

C₂×M₃₂

yes

characteristic

C₂×C₁₈₁

C₂×M₃₂

yes

characteristic

D₁₈₁

—

C₁₈₁

#2163

yes

characteristic, complemented, Sylow

#2163

—

181

maximal, Sylow

C₂×C₄×C₈

—

181

—

C₄⋊C₁₆

—

181

—

C₂²⋊C₁₆

—

181

—

#346

—

181

—

C₂²×C₈

—

181

—

C₂²×C₈

—

181

—

C₂×C₄²

—

181

—

C₂×C₁₆

—

181

—

C₄×C₈

—

181

—

C₄×C₈

—

181

—

C₄×C₈

—

181

—

C₄×C₈

#10624382

yes

characteristic

C₂²×C₄

—

181

—

C₂²×C₄

—

181

—

C₂²×C₄

—

181

—

C₂×C₈

—

362

—

C₂×C₈

—

362

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

181

—

C₄²

—

181

—

C₄²

—

181

—

C₄²

C₂×#10624382

yes

characteristic

C₁₆

—

362

—

C₂³

—

181

—

C₂×C₄

—

362

—

C₂×C₄

—

362

—

C₂×C₄

—

362

—

C₂×C₄

—

362

—

C₂×C₄

—

181

—

C₂×C₄

—

181

—

C₂×C₄

—

181

—

C₂×C₄

D₁₈₁⋊C₈

yes

characteristic

C₂×C₄

D₁₈₁⋊C₈

yes

characteristic

C₂×C₄

C₂²×#10624382

yes

characteristic

C₈

—

C₈

—

362

—

C₈

—

181

—

C₈

#15668459

yes

—

100

C₂²

—

362

—

101

C₂²

—

362

—

102

C₂²

—

181

—

103

C₂²

C₂×D₁₈₁⋊C₈

yes

characteristic

104

C₄

—

105

C₄

—

362

—

106

C₄

—

362

—

107

C₄

—

362

—

108

C₄

#19153891

yes

—

109

C₄

#19153895

yes

characteristic

110

C₄

C₂×#15668459

yes

characteristic

111

C₂

—

362

—

112

C₂

#26042298

yes

characteristic

113

C₂

D₁₈₁⋊M₃₂

yes

characteristic

114

C₂

C₂×#19153891

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#10624382
commutator, socle	C₂²×C₁₈₁	C₂²×C₈
Fitting	C₄×C₈×C₁₈₁	C₄
prime radical	C₂²×D₁₈₁	C₂×C₈
cosocle	C₂×#13089678	C₂³
hypercenter	C₄×C₈	#10624382
hypocenter	C₁₈₁	#2163
LCS	G ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#10624382

commutator, socle

C₂²×C₁₈₁

C₂²×C₈

Fitting

C₄×C₈×C₁₈₁

C₄

prime radical

C₂²×D₁₈₁

C₂×C₈

C₂³

C₄×C₈

C₁₈₁

G ▷ C₂²×C₁₈₁ ▷ C₁₈₁

C₁ ◁ C₂×C₄ ◁ C₄×C₈

N	H ≅ G/N	type
1. C₄⋊#15668452	C₂	semidirect
3. #26042168	C₂	semidirect
57. C₁₈₁	#2163	semidirect

H ≅ G/N

type

1. C₄⋊#15668452

C₂

semidirect

3. #26042168

C₂

semidirect

57. C₁₈₁

#2163

semidirect

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

subgroup	index
C₄⋊#15668452	2
#26042174	2
#26042168	2
C₄×C₈×D₁₈₁	2
#2163	181

subgroup

index

C₄×C₈×D₁₈₁

181

Subgroups — #37550085

Conjugacy classes of subgroups

Complements

Maximal subgroups