Group #37533844 — subgroups

Subgroups — #37533844

Order 23168.

172 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 81 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×#19153752	C₂	1	1	yes	maximal, characteristic
2	#26041234	C₂	1	1	yes	maximal, characteristic
3	#26041049	C₂	1	2	yes	maximal
4	#26041035	C₂	1	2	yes	maximal
5	#427×C₁₈₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#15668433	C₂²	1	2	yes	—
7	C₂×#15668433	C₂²	1	1	yes	characteristic
8	#19153775	C₂²	1	1	yes	characteristic
9	#19153752	—	2	1	no	—
10	#19153752	—	2	1	no	—
11	#19153726	C₄	1	2	yes	complemented
12	C₈×Dic₁₈₁	C₄	1	2	yes	complemented
13	C₂²×C₈×C₁₈₁	C₂²	1	1	yes	characteristic
14	#117×C₁₈₁	C₂²	1	2	yes	—
15	#107×C₁₈₁	—	2	1	no	—
16	#106×C₁₈₁	—	2	1	no	—
17	#15668433	—	2	2	no	—
18	#15668433	—	2	1	no	—
19	#15668433	—	2	1	no	—
20	#15668433	—	2	2	no	—
21	C₂×#13089678	—	2	2	no	—
22	C₂×#13089678	C₂×C₄	1	2	yes	—
23	C₄⋊Dic₁₈₁	—	2	1	no	—
24	C₂²⋊Dic₁₈₁	—	2	1	no	—
25	C₄×Dic₁₈₁	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
27	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
29	C₂×C₈×C₁₈₁	D₄	1	1	yes	characteristic
30	C₂×C₈×C₁₈₁	D₄	1	1	yes	characteristic
31	C₂×C₈×C₁₈₁	Q₈	1	1	yes	characteristic
32	C₂×C₈×C₁₈₁	Q₈	1	1	yes	characteristic
33	C₄⋊C₄×C₁₈₁	—	2	2	no	—
34	C₂²⋊C₄×C₁₈₁	—	2	2	no	—
35	C₄²×C₁₈₁	—	2	2	no	—
36	C₂×Dic₁₈₁	—	2	2	no	—
37	#13089678	—	2	2	no	—
38	#13089678	—	4	2	no	—
39	C₂³×C₁₈₁	#41	1	1	yes	characteristic
40	C₂×C₄×C₁₈₁	—	4	2	no	—
41	C₂×C₄×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₄×C₁₈₁	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₁₈₁	C₂×Q₈	1	1	yes	characteristic
44	C₂×C₄×C₁₈₁	#41	1	1	yes	characteristic
45	C₂×C₄×C₁₈₁	#41	1	1	yes	characteristic
46	C₂×C₄×C₁₈₁	#41	1	1	yes	characteristic
47	C₈×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
48	C₈×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
49	C₈×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
50	C₈×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
51	C₂²×C₁₈₁	—	4	1	no	—
52	C₂²×C₁₈₁	#117	1	1	yes	characteristic
53	C₂²×C₁₈₁	#124	1	1	yes	characteristic
54	C₂²×C₁₈₁	#125	1	1	yes	characteristic
55	C₄×C₁₈₁	—	8	2	no	—
56	C₄×C₁₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₄×C₁₈₁	#117	1	1	yes	characteristic
58	C₄×C₁₈₁	#124	1	1	yes	characteristic
59	C₄×C₁₈₁	#125	1	1	yes	characteristic
60	Dic₁₈₁	—	4	2	no	—
61	C₂×C₁₈₁	—	2	1	no	—
62	C₂×C₁₈₁	—	2	1	no	—
63	C₂×C₁₈₁	—	2	1	no	—
64	C₂×C₁₈₁	#382	1	1	yes	characteristic
65	C₁₈₁	#1833	1	1	yes	characteristic, complemented, Sylow
66	#1833	—	181	1	no	maximal, Sylow
67	C₂×#108	—	181	1	no	—
68	#427	D₁₈₁	1	1	yes	characteristic
69	#405	—	181	1	no	—
70	#344	—	181	2	no	—
71	H(3,ℤ/4)	—	181	2	no	—
72	C₂×M₁₆	—	181	2	no	—
73	C₂×M₁₆	—	181	1	no	—
74	C₂²×C₈	C₂×D₁₈₁	1	1	yes	characteristic
75	#117	—	181	1	no	—
76	#117	C₂×D₁₈₁	1	2	yes	—
77	#108	—	362	1	no	—
78	#108	—	362	1	no	—
79	#107	—	2	1	no	—
80	#106	—	2	1	no	—
81	#97	—	181	2	no	—
82	C₄×C₈	—	181	2	no	—
83	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
84	M₁₆	—	362	1	no	—
85	M₁₆	—	362	1	no	—
86	M₁₆	—	362	2	no	—
87	M₁₆	—	362	2	no	—
88	C₂×C₈	—	362	2	no	—
89	C₂×C₈	—	181	2	no	—
90	C₂×C₈	C₄×D₁₈₁	1	1	yes	characteristic
91	C₂×C₈	C₄×D₁₈₁	1	1	yes	characteristic
92	C₂×C₈	C₂²⋊D₁₈₁	1	1	yes	characteristic
93	C₂×C₈	C₂²⋊D₁₈₁	1	1	yes	characteristic
94	C₂×C₈	Dic₃₆₂	1	1	yes	characteristic
95	C₂×C₈	Dic₃₆₂	1	1	yes	characteristic
96	C₄⋊C₄	—	2	2	no	—
97	C₄⋊C₄	—	362	1	no	—
98	C₂²⋊C₄	—	2	2	no	—
99	C₂²⋊C₄	—	362	1	no	—
100	C₄²	—	2	2	no	—
101	C₄²	—	181	2	no	—
102	C₂³	#15668448	1	1	yes	characteristic
103	C₂×C₄	—	4	2	no	—
104	C₂×C₄	—	362	2	no	—
105	C₂×C₄	C₂×C₄×D₁₈₁	1	1	yes	characteristic
106	C₂×C₄	C₂×C₂²⋊D₁₈₁	1	1	yes	characteristic
107	C₂×C₄	C₂×Dic₃₆₂	1	1	yes	characteristic
108	C₂×C₄	#15668448	1	1	yes	characteristic
109	C₂×C₄	#15668450	1	1	yes	characteristic
110	C₂×C₄	#15668450	1	1	yes	characteristic
111	C₈	—	362	2	no	—
112	C₈	—	724	2	no	—
113	C₈	#15668428	1	1	yes	characteristic
114	C₈	#15668428	1	1	yes	characteristic
115	C₈	#15668428	1	1	yes	characteristic
116	C₈	#15668428	1	1	yes	characteristic
117	C₂²	—	4	1	no	—
118	C₂²	#19153774	1	1	yes	characteristic
119	C₂²	#19153803	1	1	yes	characteristic
120	C₂²	#19153807	1	1	yes	characteristic
121	C₄	—	8	2	no	—
122	C₄	—	724	2	no	—
123	C₄	C₂×#15668428	1	1	yes	characteristic
124	C₄	#19153774	1	1	yes	characteristic
125	C₄	#19153805	1	1	yes	characteristic
126	C₄	#19153807	1	1	yes	characteristic
127	C₂	—	2	1	no	—
128	C₂	—	2	1	no	—
129	C₂	—	2	1	no	—
130	C₂	#26041144	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19153752

C₂

yes

maximal, characteristic

#26041234

C₂

yes

maximal, characteristic

#26041049

C₂

yes

maximal

#26041035

C₂

yes

maximal

#427×C₁₈₁

C₂

yes

maximal, characteristic

C₂×#15668433

C₂²

yes

—

C₂×#15668433

C₂²

yes

characteristic

#19153775

C₂²

yes

—

—

C₄

yes

complemented

C₈×Dic₁₈₁

C₄

yes

complemented

C₂²×C₈×C₁₈₁

C₂²

yes

characteristic

#117×C₁₈₁

C₂²

yes

—

#107×C₁₈₁

—

#106×C₁₈₁

—

—

—

—

—

—

C₂×C₄

yes

—

C₄⋊Dic₁₈₁

—

C₂²⋊Dic₁₈₁

—

C₄×Dic₁₈₁

C₂×C₄

yes

—

C₂²×C₄×C₁₈₁

C₂³

yes

characteristic

C₂×C₈×C₁₈₁

C₂×C₄

yes

characteristic

C₂×C₈×C₁₈₁

C₂×C₄

yes

characteristic

C₂×C₈×C₁₈₁

D₄

yes

characteristic

C₂×C₈×C₁₈₁

D₄

yes

characteristic

C₂×C₈×C₁₈₁

Q₈

yes

characteristic

C₂×C₈×C₁₈₁

Q₈

yes

characteristic

C₄⋊C₄×C₁₈₁

—

C₂²⋊C₄×C₁₈₁

—

C₄²×C₁₈₁

—

C₂×Dic₁₈₁

—

#13089678

—

#13089678

—

C₂³×C₁₈₁

#41

yes

characteristic

C₂×C₄×C₁₈₁

—

C₂×C₄×C₁₈₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₈₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₈₁

C₂×Q₈

yes

C₂×C₄×C₁₈₁

yes

C₂×C₄×C₁₈₁

yes

C₂×C₄×C₁₈₁

yes

C₈×C₁₈₁

C₄⋊C₄

yes

characteristic

C₈×C₁₈₁

C₄⋊C₄

yes

characteristic

C₈×C₁₈₁

C₄⋊C₄

yes

characteristic

C₈×C₁₈₁

C₄⋊C₄

yes

characteristic

C₂²×C₁₈₁

—

C₂²×C₁₈₁

yes

C₂²×C₁₈₁

yes

C₂²×C₁₈₁

yes

C₄×C₁₈₁

—

C₄×C₁₈₁

C₂×C₄⋊C₄

yes

C₄×C₁₈₁

yes

C₄×C₁₈₁

yes

C₄×C₁₈₁

yes

Dic₁₈₁

—

C₂×C₁₈₁

—

C₂×C₁₈₁

—

C₂×C₁₈₁

—

C₂×C₁₈₁

#382

yes

characteristic

C₁₈₁

#1833

yes

characteristic, complemented, Sylow

#1833

—

181

maximal, Sylow

C₂×#108

—

181

—

#427

D₁₈₁

yes

characteristic

#405

—

181

—

#344

—

181

—

H(3,ℤ/4)

—

181

—

C₂×M₁₆

—

181

—

C₂×M₁₆

—

181

—

C₂²×C₈

C₂×D₁₈₁

yes

characteristic

#117

—

181

—

#117

C₂×D₁₈₁

yes

—

#108

—

362

—

#108

—

362

—

#107

—

#106

—

#97

—

181

—

C₄×C₈

—

181

—

C₂²×C₄

C₂²×D₁₈₁

yes

characteristic

M₁₆

—

362

—

M₁₆

—

362

—

M₁₆

—

362

—

M₁₆

—

362

—

C₂×C₈

—

362

—

C₂×C₈

—

181

—

C₂×C₈

C₄×D₁₈₁

yes

characteristic

C₂×C₈

C₄×D₁₈₁

yes

characteristic

C₂×C₈

C₂²⋊D₁₈₁

yes

characteristic

C₂×C₈

C₂²⋊D₁₈₁

yes

characteristic

C₂×C₈

Dic₃₆₂

yes

characteristic

C₂×C₈

Dic₃₆₂

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

362

—

C₂²⋊C₄

—

C₂²⋊C₄

—

362

—

100

C₄²

—

101

C₄²

—

181

—

102

C₂³

#15668448

yes

characteristic

103

C₂×C₄

—

104

C₂×C₄

—

362

—

105

C₂×C₄

C₂×C₄×D₁₈₁

yes

characteristic

106

C₂×C₄

C₂×C₂²⋊D₁₈₁

yes

characteristic

107

C₂×C₄

C₂×Dic₃₆₂

yes

characteristic

108

C₂×C₄

#15668448

yes

characteristic

109

C₂×C₄

#15668450

yes

characteristic

110

C₂×C₄

#15668450

yes

characteristic

111

C₈

—

362

—

112

C₈

—

724

—

113

C₈

#15668428

yes

characteristic

114

C₈

#15668428

yes

characteristic

115

C₈

#15668428

yes

characteristic

116

C₈

#15668428

yes

characteristic

117

C₂²

—

118

C₂²

#19153774

yes

characteristic

119

C₂²

#19153803

yes

characteristic

120

C₂²

#19153807

yes

characteristic

121

C₄

—

122

C₄

—

724

—

123

C₄

C₂×#15668428

yes

characteristic

124

C₄

#19153774

yes

characteristic

125

C₄

#19153805

yes

characteristic

126

C₄

#19153807

yes

characteristic

127

C₂

—

128

C₂

—

129

C₂

—

130

C₂

#26041144

yes

characteristic

	subgroup	G/H
center	C₄	#19153774
commutator	C₂×C₄×C₁₈₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₈₁
Fitting	#427×C₁₈₁	C₂
socle	C₂×C₁₈₁	#382
prime radical	C₂³×C₁₈₁	#41
cosocle	C₂²×C₄×C₁₈₁	C₂³
hypercenter	#427	D₁₈₁
hypocenter	C₁₈₁	#1833
LCS	G ▷ C₂×C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #427

subgroup

G/H

center

C₄

#19153774

commutator

C₂×C₄×C₁₈₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₈₁

Fitting

#427×C₁₈₁

C₂

C₂×C₁₈₁

C₂³×C₁₈₁

C₂²×C₄×C₁₈₁

C₂³

D₁₈₁

C₁₈₁

G ▷ C₂×C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #427

N	H ≅ G/N	type
11. #19153726	C₄	semidirect
12. C₈×Dic₁₈₁	C₄	semidirect
65. C₁₈₁	#1833	semidirect

H ≅ G/N

type

11. #19153726

C₄

semidirect

12. C₈×Dic₁₈₁

C₄

semidirect

65. C₁₈₁

#1833

semidirect

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

subgroup	index
C₂×#19153752	2
#26041234	2
#26041049	2
#26041035	2
#427×C₁₈₁	2
#1833	181

subgroup

index

#427×C₁₈₁

181

Subgroups — #37533844

Conjugacy classes of subgroups

Complements

Maximal subgroups