Group #37549933 — subgroups

Subgroups — #37549933

Order 23168.

184 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 96 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	C₂×D₁₈₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#26042242	C₂	1	1	yes	maximal, characteristic
3	#26042166	C₂	1	2	yes	maximal, complemented
4	C₁₆×#10624382	C₂	1	2	yes	maximal, complemented
5	M₃₂×D₁₈₁	C₂	1	1	yes	maximal, characteristic
6	D₁₈₁⋊M₁₆	C₄	1	1	yes	characteristic
7	#19153895	C₄	1	1	yes	characteristic
8	D₁₈₁⋊C₁₆	C₄	1	2	yes	complemented
9	D₁₈₁⋊C₁₆	C₂²	1	1	yes	characteristic
10	D₁₈₁⋊C₁₆	C₂²	1	1	yes	characteristic
11	C₂×#15668452	C₄	1	2	yes	complemented
12	#19153870	C₄	1	2	yes	—
13	C₈×#10624382	C₂²	1	2	yes	—
14	C₂×C₈×D₁₈₁	C₂²	1	1	yes	characteristic
15	#19153756	C₄	1	1	yes	characteristic, complemented
16	#19153755	C₄	1	2	yes	complemented
17	C₁₆×D₁₈₁	C₂²	1	2	yes	—
18	M₃₂×C₁₈₁	C₄	1	1	yes	characteristic, complemented
19	#15668459	C₈	1	2	yes	—
20	#15668458	C₈	1	2	yes	—
21	D₁₈₁⋊C₈	C₂×C₄	1	2	yes	—
22	C₄⋊#10624382	C₈	1	2	yes	—
23	C₂²⋊#10624382	C₈	1	2	yes	—
24	C₄×#10624382	C₂×C₄	1	2	yes	—
25	#15668452	C₂×C₄	1	2	yes	—
26	#15668452	C₂×C₄	1	2	yes	—
27	C₂×C₄×D₁₈₁	C₂×C₄	1	1	yes	characteristic
28	C₂×#13089678	C₂×C₄	1	1	yes	characteristic
29	C₈×D₁₈₁	C₂×C₄	1	1	yes	characteristic
30	C₈×D₁₈₁	C₂×C₄	1	1	yes	characteristic
31	C₈×D₁₈₁	C₂×C₄	1	1	yes	characteristic
32	C₈×D₁₈₁	C₂³	1	1	yes	characteristic
33	#15668424	C₂×C₄	1	2	yes	—
34	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
35	C₁₆×C₁₈₁	C₂×C₄	1	2	yes	—
36	C₂×#10624382	C₂×C₈	1	4	yes	—
37	#13089685	C₂×C₈	1	4	yes	—
38	C₂²×D₁₈₁	C₂×C₈	1	1	yes	characteristic
39	C₂×Dic₁₈₁	C₂×C₈	1	1	yes	characteristic
40	C₄×D₁₈₁	C₄²	1	1	yes	characteristic
41	C₄×D₁₈₁	C₂×C₈	1	1	yes	characteristic
42	C₄×D₁₈₁	C₂×C₈	1	1	yes	characteristic
43	C₄×D₁₈₁	C₂²×C₄	1	1	yes	characteristic
44	#13089678	C₄²	1	1	yes	characteristic
45	#13089678	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₄×C₁₈₁	C₄²	1	1	yes	characteristic
47	C₈×C₁₈₁	C₄²	1	1	yes	characteristic
48	C₈×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₁₈₁	C₄×C₈	1	1	yes	characteristic
50	C₂×D₁₈₁	—	2	2	no	—
51	C₂×D₁₈₁	C₄×C₈	1	1	yes	characteristic
52	C₂×D₁₈₁	C₂²×C₈	1	1	yes	characteristic
53	#10624382	—	2	4	no	—
54	C₄×C₁₈₁	C₄×C₈	1	1	yes	characteristic
55	C₄×C₁₈₁	C₂×C₄²	1	1	yes	characteristic
56	Dic₁₈₁	C₄×C₈	1	1	yes	characteristic
57	Dic₁₈₁	C₂²×C₈	1	1	yes	characteristic
58	C₂×C₁₈₁	—	2	1	no	—
59	C₂×C₁₈₁	C₂×C₄×C₈	1	1	yes	characteristic
60	D₁₈₁	—	2	1	no	—
61	D₁₈₁	#504	1	2	yes	—
62	C₁₈₁	#2108	1	1	yes	characteristic, complemented, Sylow
63	#2108	—	181	1	no	maximal, Sylow
64	C₂×M₃₂	—	181	1	no	—
65	C₂²×C₁₆	—	181	1	no	—
66	#405	—	181	1	no	—
67	#346	—	181	2	no	—
68	C₄×C₁₆	—	181	2	no	—
69	C₂×M₁₆	—	181	1	no	—
70	C₂²×C₈	—	181	1	no	—
71	#117	—	181	1	no	—
72	M₃₂	—	181	1	no	—
73	M₃₂	—	181	2	no	—
74	M₃₂	#10624382	1	1	yes	characteristic, complemented
75	C₂×C₁₆	—	181	1	no	—
76	C₂×C₁₆	—	181	1	no	—
77	C₂×C₁₆	—	181	2	no	—
78	C₂×C₁₆	—	181	2	no	—
79	C₂×C₁₆	—	181	2	no	—
80	#97	—	181	2	no	—
81	C₄×C₈	—	181	2	no	—
82	C₂²×C₄	—	181	1	no	—
83	M₁₆	—	181	2	no	—
84	M₁₆	—	181	2	no	—
85	C₂×C₈	—	181	2	no	—
86	C₂×C₈	—	181	1	no	—
87	C₂×C₈	—	181	1	no	—
88	C₂×C₈	—	181	1	no	—
89	C₂×C₈	—	181	1	no	—
90	C₂×C₈	—	181	1	no	—
91	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
92	C₄⋊C₄	—	181	2	no	—
93	C₂²⋊C₄	—	181	2	no	—
94	C₄²	—	181	2	no	—
95	C₁₆	—	181	2	no	—
96	C₁₆	—	181	2	no	—
97	C₁₆	—	181	2	no	—
98	C₁₆	C₂×#10624382	1	2	yes	—
99	C₂³	—	181	1	no	—
100	C₂×C₄	—	181	4	no	—
101	C₂×C₄	—	181	1	no	—
102	C₂×C₄	—	181	1	no	—
103	C₂×C₄	—	181	1	no	—
104	C₂×C₄	—	181	1	no	—
105	C₂×C₄	—	181	1	no	—
106	C₂×C₄	C₄×#10624382	1	1	yes	characteristic
107	C₈	—	181	4	no	—
108	C₈	—	181	1	no	—
109	C₈	—	181	1	no	—
110	C₈	C₄×#10624382	1	1	yes	characteristic
111	C₈	C₂²×#10624382	1	1	yes	characteristic
112	C₂²	—	362	2	no	—
113	C₂²	—	181	1	no	—
114	C₂²	—	181	1	no	—
115	C₂²	C₈×#10624382	1	1	yes	characteristic
116	C₄	—	362	4	no	—
117	C₄	—	181	1	no	—
118	C₄	—	181	1	no	—
119	C₄	C₈×#10624382	1	1	yes	characteristic
120	C₄	C₂×C₄×#10624382	1	1	yes	characteristic
121	C₂	—	2	1	no	—
122	C₂	—	362	1	no	—
123	C₂	—	181	2	no	—
124	C₂	C₂×C₈×#10624382	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₁₈₁⋊C₁₆

C₂

yes

maximal, characteristic

#26042242

C₂

yes

maximal, characteristic

#26042166

C₂

yes

maximal, complemented

C₁₆×#10624382

C₂

yes

maximal, complemented

M₃₂×D₁₈₁

C₂

yes

maximal, characteristic

D₁₈₁⋊M₁₆

C₄

yes

characteristic

#19153895

C₄

yes

characteristic

D₁₈₁⋊C₁₆

C₄

yes

complemented

D₁₈₁⋊C₁₆

C₂²

yes

characteristic

D₁₈₁⋊C₁₆

C₂²

yes

characteristic

C₂×#15668452

C₄

yes

complemented

#19153870

C₄

yes

—

C₈×#10624382

C₂²

yes

—

C₂×C₈×D₁₈₁

C₂²

yes

characteristic

#19153756

C₄

yes

characteristic, complemented

#19153755

C₄

yes

complemented

C₁₆×D₁₈₁

C₂²

yes

—

M₃₂×C₁₈₁

C₄

yes

characteristic, complemented

#15668459

C₈

yes

—

#15668458

C₈

yes

—

D₁₈₁⋊C₈

C₂×C₄

yes

—

C₄⋊#10624382

C₈

yes

—

C₂²⋊#10624382

C₈

yes

—

C₄×#10624382

C₂×C₄

yes

—

#15668452

C₂×C₄

yes

—

#15668452

C₂×C₄

yes

—

C₂×C₄×D₁₈₁

C₂×C₄

yes

characteristic

C₂×#13089678

C₂×C₄

yes

characteristic

C₈×D₁₈₁

C₂×C₄

yes

characteristic

C₈×D₁₈₁

C₂×C₄

yes

characteristic

C₈×D₁₈₁

C₂×C₄

yes

characteristic

C₈×D₁₈₁

C₂³

yes

characteristic

#15668424

C₂×C₄

yes

—

C₂×C₈×C₁₈₁

C₂×C₄

yes

characteristic

C₁₆×C₁₈₁

C₂×C₄

yes

—

C₂×#10624382

C₂×C₈

yes

—

#13089685

C₂×C₈

yes

—

C₂²×D₁₈₁

C₂×C₈

yes

characteristic

C₂×Dic₁₈₁

C₂×C₈

yes

characteristic

C₄×D₁₈₁

C₄²

yes

characteristic

C₄×D₁₈₁

C₂×C₈

yes

characteristic

C₄×D₁₈₁

C₂×C₈

yes

characteristic

C₄×D₁₈₁

C₂²×C₄

yes

characteristic

#13089678

C₄²

yes

characteristic

#13089678

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₈₁

C₄²

yes

characteristic

C₈×C₁₈₁

C₄²

yes

characteristic

C₈×C₁₈₁

C₂²×C₄

yes

characteristic

C₂²×C₁₈₁

C₄×C₈

yes

characteristic

C₂×D₁₈₁

—

C₂×D₁₈₁

C₄×C₈

yes

characteristic

C₂×D₁₈₁

C₂²×C₈

yes

characteristic

#10624382

—

C₄×C₁₈₁

C₄×C₈

yes

characteristic

C₄×C₁₈₁

C₂×C₄²

yes

characteristic

Dic₁₈₁

C₄×C₈

yes

characteristic

Dic₁₈₁

C₂²×C₈

yes

characteristic

C₂×C₁₈₁

—

C₂×C₁₈₁

C₂×C₄×C₈

yes

characteristic

D₁₈₁

—

D₁₈₁

#504

yes

—

C₁₈₁

#2108

yes

characteristic, complemented, Sylow

#2108

—

181

maximal, Sylow

C₂×M₃₂

—

181

—

C₂²×C₁₆

—

181

—

#405

—

181

—

#346

—

181

—

C₄×C₁₆

—

181

—

C₂×M₁₆

—

181

—

C₂²×C₈

—

181

—

#117

—

181

—

M₃₂

—

181

—

M₃₂

—

181

—

M₃₂

#10624382

yes

characteristic, complemented

C₂×C₁₆

—

181

—

C₂×C₁₆

—

181

—

C₂×C₁₆

—

181

—

C₂×C₁₆

—

181

—

C₂×C₁₆

—

181

—

#97

—

181

—

C₄×C₈

—

181

—

C₂²×C₄

—

181

—

M₁₆

—

181

—

M₁₆

—

181

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂×C₈

C₂×#10624382

yes

characteristic

C₄⋊C₄

—

181

—

C₂²⋊C₄

—

181

—

C₄²

—

181

—

C₁₆

—

181

—

C₁₆

—

181

—

C₁₆

—

181

—

C₁₆

C₂×#10624382

yes

—

C₂³

—

181

—

100

C₂×C₄

—

181

—

101

C₂×C₄

—

181

—

102

C₂×C₄

—

181

—

103

C₂×C₄

—

181

—

104

C₂×C₄

—

181

—

105

C₂×C₄

—

181

—

106

C₂×C₄

C₄×#10624382

yes

characteristic

107

C₈

—

181

—

108

C₈

—

181

—

109

C₈

—

181

—

110

C₈

C₄×#10624382

yes

characteristic

111

C₈

C₂²×#10624382

yes

characteristic

112

C₂²

—

362

—

113

C₂²

—

181

—

114

C₂²

—

181

—

115

C₂²

C₈×#10624382

yes

characteristic

116

C₄

—

362

—

117

C₄

—

181

—

118

C₄

—

181

—

119

C₄

C₈×#10624382

yes

characteristic

120

C₄

C₂×C₄×#10624382

yes

characteristic

121

C₂

—

122

C₂

—

362

—

123

C₂

—

181

—

124

C₂

C₂×C₈×#10624382

yes

characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×#10624382
commutator, socle	C₂×C₁₈₁	C₂×C₄×C₈
Fitting	M₃₂×C₁₈₁	C₄
prime radical	C₂²×D₁₈₁	C₂×C₈
cosocle	C₈×D₁₈₁	C₂³
hypercenter	M₃₂	#10624382
hypocenter	C₁₈₁	#2108
LCS	G ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₈ ◁ M₃₂

subgroup

G/H

center, Frattini

C₈

C₂²×#10624382

commutator, socle

C₂×C₁₈₁

C₂×C₄×C₈

Fitting

M₃₂×C₁₈₁

C₄

prime radical

C₂²×D₁₈₁

C₂×C₈

cosocle

C₈×D₁₈₁

C₂³

M₃₂

C₁₈₁

G ▷ C₂×C₁₈₁ ▷ C₁₈₁

C₁ ◁ C₈ ◁ M₃₂

N	H ≅ G/N	type
3. #26042166	C₂	semidirect
4. C₁₆×#10624382	C₂	semidirect
8. D₁₈₁⋊C₁₆	C₄	semidirect
11. C₂×#15668452	C₄	semidirect
15. #19153756	C₄	semidirect
16. #19153755	C₄	semidirect
18. M₃₂×C₁₈₁	C₄	semidirect
62. C₁₈₁	#2108	semidirect
74. M₃₂	#10624382	semidirect

H ≅ G/N

type

3. #26042166

C₂

semidirect

4. C₁₆×#10624382

C₂

semidirect

8. D₁₈₁⋊C₁₆

C₄

semidirect

11. C₂×#15668452

C₄

semidirect

15. #19153756

C₄

semidirect

16. #19153755

C₄

semidirect

18. M₃₂×C₁₈₁

C₄

semidirect

62. C₁₈₁

#2108

semidirect

74. M₃₂

#10624382

semidirect

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

subgroup	index
C₂×D₁₈₁⋊C₁₆	2
#26042242	2
#26042166	2
C₁₆×#10624382	2
M₃₂×D₁₈₁	2
#2108	181

subgroup

index

C₂×D₁₈₁⋊C₁₆

#26042242

#26042166

C₁₆×#10624382

M₃₂×D₁₈₁

#2108

181

Subgroups — #37549933

Conjugacy classes of subgroups

Complements

Maximal subgroups