Group #37572267 — subgroups

Subgroups — #37572267

Order 24448.

272 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 125 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×#20259232	C₂	1	2	yes	maximal
2	C₄²×Dic₁₉₁	C₂	1	1	yes	maximal, characteristic
3	#27132418	C₂	1	1	yes	maximal, characteristic
4	#27132417	C₂	1	2	yes	maximal
5	#336×C₁₉₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₉₁⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×Dic₁₉₁	C₄	1	2	yes	—
8	C₂×C₄×Dic₁₉₁	C₄	1	2	yes	—
9	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
11	#20259232	C₄	1	8	yes	complemented
12	C₂²×C₈×C₁₉₁	C₂²	1	2	yes	—
13	C₂×C₄²×C₁₉₁	C₂²	1	1	yes	characteristic
14	C₂²×Dic₁₉₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₁₉₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₁₉₁	C₂×C₄	1	2	yes	—
17	C₂×C₁₉₁⋊C₈	—	2	2	no	—
18	C₂×C₁₉₁⋊C₈	—	2	2	no	—
19	C₂×C₁₉₁⋊C₈	C₂×C₄	1	4	yes	—
20	C₄×Dic₁₉₁	—	2	4	no	—
21	C₄×Dic₁₉₁	—	2	4	no	—
22	C₄×Dic₁₉₁	—	2	1	no	—
23	C₄×Dic₁₉₁	—	2	1	no	—
24	C₄×Dic₁₉₁	C₂×C₄	1	4	yes	—
25	C₂²×C₄×C₁₉₁	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
27	C₂×C₈×C₁₉₁	—	2	2	no	—
28	C₂×C₈×C₁₉₁	—	2	2	no	—
29	C₂×C₈×C₁₉₁	C₂×C₄	1	4	yes	—
30	C₄²×C₁₉₁	—	2	2	no	—
31	C₂×Dic₁₉₁	—	2	2	no	—
32	C₂×Dic₁₉₁	—	2	2	no	—
33	C₂×Dic₁₉₁	—	2	2	no	—
34	C₂×Dic₁₉₁	—	2	2	no	—
35	C₂×Dic₁₉₁	C₄²	1	2	yes	—
36	C₂×Dic₁₉₁	C₄²	1	2	yes	—
37	C₂×Dic₁₉₁	M₁₆	1	4	yes	—
38	C₁₉₁⋊C₈	—	2	4	no	—
39	C₂³×C₁₉₁	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₄×C₁₉₁	—	2	2	no	—
41	C₂×C₄×C₁₉₁	—	2	2	no	—
42	C₂×C₄×C₁₉₁	M₁₆	1	4	yes	—
43	C₂×C₄×C₁₉₁	C₂²×C₄	1	2	yes	—
44	C₂×C₄×C₁₉₁	#41	1	2	yes	—
45	C₂×C₄×C₁₉₁	#41	1	1	yes	characteristic
46	C₂×C₄×C₁₉₁	#41	1	1	yes	characteristic
47	C₈×C₁₉₁	—	2	4	no	—
48	C₂²×C₁₉₁	C₂×C₄²	1	1	yes	characteristic
49	C₂²×C₁₉₁	#117	1	1	yes	characteristic
50	C₂²×C₁₉₁	#117	1	1	yes	characteristic
51	C₂²×C₁₉₁	C₂×M₁₆	1	2	yes	—
52	C₂²×C₁₉₁	C₂×M₁₆	1	2	yes	—
53	C₄×C₁₉₁	—	2	4	no	—
54	C₄×C₁₉₁	#117	1	2	yes	—
55	C₄×C₁₉₁	#117	1	2	yes	—
56	Dic₁₉₁	—	2	2	no	—
57	Dic₁₉₁	—	2	2	no	—
58	Dic₁₉₁	—	2	4	no	—
59	C₂×C₁₉₁	#376	1	1	yes	characteristic
60	C₂×C₁₉₁	C₄×M₁₆	1	1	yes	characteristic
61	C₂×C₁₉₁	C₄×M₁₆	1	1	yes	characteristic
62	C₂×C₁₉₁	#432	1	2	yes	—
63	C₂×C₁₉₁	#432	1	2	yes	—
64	C₁₉₁	#1745	1	1	yes	characteristic, complemented, Sylow
65	#1745	—	191	1	no	maximal, Sylow
66	C₂×#97	—	191	2	no	—
67	C₄³	—	191	1	no	—
68	#336	—	191	2	no	—
69	#336	—	191	1	no	—
70	#336	D₁₉₁	1	1	yes	characteristic
71	C₂²×C₈	—	191	2	no	—
72	C₂²×C₈	C₂×D₁₉₁	1	2	yes	—
73	C₂×C₄²	—	191	2	no	—
74	C₂×C₄²	—	191	2	no	—
75	C₂×C₄²	—	191	1	no	—
76	C₂×C₄²	—	191	1	no	—
77	C₂×C₄²	C₂×D₁₉₁	1	1	yes	characteristic
78	#97	—	191	8	no	—
79	C₂²×C₄	—	191	2	no	—
80	C₂²×C₄	—	191	1	no	—
81	C₂²×C₄	—	191	1	no	—
82	C₂²×C₄	C₄×D₁₉₁	1	2	yes	—
83	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
84	C₂×C₈	—	2	2	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	382	2	no	—
87	C₂×C₈	—	382	2	no	—
88	C₂×C₈	—	191	4	no	—
89	C₂×C₈	C₄×D₁₉₁	1	4	yes	—
90	C₄²	—	2	2	no	—
91	C₄²	—	382	4	no	—
92	C₄²	—	382	4	no	—
93	C₄²	—	382	1	no	—
94	C₄²	—	382	1	no	—
95	C₄²	—	191	4	no	—
96	C₂³	C₂×C₄×D₁₉₁	1	1	yes	characteristic
97	C₂×C₄	—	2	2	no	—
98	C₂×C₄	—	2	2	no	—
99	C₂×C₄	—	382	2	no	—
100	C₂×C₄	—	382	2	no	—
101	C₂×C₄	—	382	2	no	—
102	C₂×C₄	—	382	2	no	—
103	C₂×C₄	—	191	2	no	—
104	C₂×C₄	—	191	2	no	—
105	C₂×C₄	—	191	4	no	—
106	C₂×C₄	#15690270	1	4	yes	—
107	C₂×C₄	C₂×C₄×D₁₉₁	1	2	yes	—
108	C₂×C₄	#15690286	1	1	yes	characteristic
109	C₂×C₄	#15690286	1	2	yes	—
110	C₂×C₄	#15690288	1	1	yes	characteristic
111	C₈	—	2	4	no	—
112	C₈	—	382	4	no	—
113	C₂²	C₄²×D₁₉₁	1	1	yes	characteristic
114	C₂²	#20259278	1	1	yes	characteristic
115	C₂²	#20259280	1	1	yes	characteristic
116	C₂²	M₁₆×D₁₉₁	1	2	yes	—
117	C₂²	C₂×#15690270	1	2	yes	—
118	C₄	—	2	4	no	—
119	C₄	—	382	4	no	—
120	C₄	—	382	2	no	—
121	C₄	—	382	2	no	—
122	C₄	#20259278	1	2	yes	—
123	C₄	#20259280	1	2	yes	—
124	C₂	#27132508	1	1	yes	characteristic
125	C₂	C₄×#15690270	1	1	yes	characteristic
126	C₂	#27132615	1	1	yes	characteristic
127	C₂	#27132717	1	2	yes	—
128	C₂	#27132719	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#20259232

C₂

yes

maximal

C₄²×Dic₁₉₁

C₂

yes

maximal, characteristic

#27132418

C₂

yes

maximal, characteristic

#27132417

C₂

yes

maximal

#336×C₁₉₁

C₂

yes

maximal, characteristic

C₂²×C₁₉₁⋊C₈

C₂²

yes

—

C₂×C₄×Dic₁₉₁

C₄

yes

—

C₂×C₄×Dic₁₉₁

C₄

yes

—

C₂×C₄×Dic₁₉₁

C₂²

yes

characteristic

C₂×C₄×Dic₁₉₁

C₂²

yes

characteristic

#20259232

C₄

yes

complemented

C₂²×C₈×C₁₉₁

C₂²

yes

—

C₂×C₄²×C₁₉₁

C₂²

yes

characteristic

C₂²×Dic₁₉₁

C₂×C₄

yes

characteristic

C₂²×Dic₁₉₁

C₂×C₄

yes

characteristic

C₂²×Dic₁₉₁

C₂×C₄

yes

—

C₂×C₁₉₁⋊C₈

—

C₂×C₁₉₁⋊C₈

—

C₂×C₁₉₁⋊C₈

C₂×C₄

yes

—

C₄×Dic₁₉₁

—

C₄×Dic₁₉₁

—

C₄×Dic₁₉₁

—

C₄×Dic₁₉₁

—

C₄×Dic₁₉₁

C₂×C₄

yes

—

C₂²×C₄×C₁₉₁

C₂×C₄

yes

—

C₂²×C₄×C₁₉₁

C₂³

yes

characteristic

C₂×C₈×C₁₉₁

—

C₂×C₈×C₁₉₁

—

C₂×C₈×C₁₉₁

C₂×C₄

yes

—

C₄²×C₁₉₁

—

C₂×Dic₁₉₁

—

C₂×Dic₁₉₁

—

C₂×Dic₁₉₁

—

C₂×Dic₁₉₁

—

C₂×Dic₁₉₁

C₄²

yes

—

C₂×Dic₁₉₁

C₄²

yes

—

C₂×Dic₁₉₁

M₁₆

yes

—

C₁₉₁⋊C₈

—

C₂³×C₁₉₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉₁

—

C₂×C₄×C₁₉₁

—

C₂×C₄×C₁₉₁

M₁₆

yes

—

C₂×C₄×C₁₉₁

C₂²×C₄

yes

—

C₂×C₄×C₁₉₁

#41

yes

—

C₂×C₄×C₁₉₁

yes

C₂×C₄×C₁₉₁

yes

C₈×C₁₉₁

—

C₂²×C₁₉₁

C₂×C₄²

yes

C₂²×C₁₉₁

yes

C₂²×C₁₉₁

yes

C₂²×C₁₉₁

C₂×M₁₆

yes

—

C₂²×C₁₉₁

C₂×M₁₆

yes

—

C₄×C₁₉₁

—

C₄×C₁₉₁

#117

yes

—

C₄×C₁₉₁

#117

yes

—

Dic₁₉₁

—

Dic₁₉₁

—

Dic₁₉₁

—

C₂×C₁₉₁

#376

yes

characteristic

C₂×C₁₉₁

C₄×M₁₆

yes

characteristic

C₂×C₁₉₁

C₄×M₁₆

yes

characteristic

C₂×C₁₉₁

#432

yes

—

C₂×C₁₉₁

#432

yes

—

C₁₉₁

#1745

yes

characteristic, complemented, Sylow

#1745

—

191

maximal, Sylow

C₂×#97

—

191

—

C₄³

—

191

—

#336

—

191

—

#336

—

191

—

#336

D₁₉₁

yes

characteristic

C₂²×C₈

—

191

—

C₂²×C₈

C₂×D₁₉₁

yes

—

C₂×C₄²

—

191

—

C₂×C₄²

—

191

—

C₂×C₄²

—

191

—

C₂×C₄²

—

191

—

C₂×C₄²

C₂×D₁₉₁

yes

characteristic

#97

—

191

—

C₂²×C₄

—

191

—

C₂²×C₄

—

191

—

C₂²×C₄

—

191

—

C₂²×C₄

C₄×D₁₉₁

yes

—

C₂²×C₄

C₂²×D₁₉₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

382

—

C₂×C₈

—

382

—

C₂×C₈

—

191

—

C₂×C₈

C₄×D₁₉₁

yes

—

C₄²

—

C₄²

—

382

—

C₄²

—

382

—

C₄²

—

382

—

C₄²

—

382

—

C₄²

—

191

—

C₂³

C₂×C₄×D₁₉₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

382

—

100

C₂×C₄

—

382

—

101

C₂×C₄

—

382

—

102

C₂×C₄

—

382

—

103

C₂×C₄

—

191

—

104

C₂×C₄

—

191

—

105

C₂×C₄

—

191

—

106

C₂×C₄

#15690270

yes

—

107

C₂×C₄

C₂×C₄×D₁₉₁

yes

—

108

C₂×C₄

#15690286

yes

characteristic

109

C₂×C₄

#15690286

yes

—

110

C₂×C₄

#15690288

yes

characteristic

111

C₈

—

112

C₈

—

382

—

113

C₂²

C₄²×D₁₉₁

yes

characteristic

114

C₂²

#20259278

yes

characteristic

115

C₂²

#20259280

yes

characteristic

116

C₂²

M₁₆×D₁₉₁

yes

—

117

C₂²

C₂×#15690270

yes

—

118

C₄

—

119

C₄

—

382

—

120

C₄

—

382

—

121

C₄

—

382

—

122

C₄

#20259278

yes

—

123

C₄

#20259280

yes

—

124

C₂

#27132508

yes

characteristic

125

C₂

C₄×#15690270

yes

characteristic

126

C₂

#27132615

yes

characteristic

127

C₂

#27132717

yes

—

128

C₂

#27132719

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₉₁
commutator	C₂²×C₁₉₁	C₂×C₄²
Fitting	#336×C₁₉₁	C₂
socle, prime radical	C₂³×C₁₉₁	C₂²×C₄
cosocle	C₂²×C₄×C₁₉₁	C₂³
hypercenter	#336	D₁₉₁
hypocenter	C₁₉₁	#1745
LCS	G ▷ C₂²×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₉₁

commutator

C₂²×C₁₉₁

C₂×C₄²

Fitting

#336×C₁₉₁

C₂

socle, prime radical

C₂³×C₁₉₁

C₂²×C₄

cosocle

C₂²×C₄×C₁₉₁

C₂³

D₁₉₁

C₁₉₁

G ▷ C₂²×C₁₉₁ ▷ C₁₉₁

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
11. #20259232	C₄	semidirect
64. C₁₉₁	#1745	semidirect

H ≅ G/N

type

11. #20259232

C₄

semidirect

64. C₁₉₁

#1745

semidirect

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

subgroup	index
C₂×#20259232	2
C₄²×Dic₁₉₁	2
#27132418	2
#27132417	2
#336×C₁₉₁	2
#1745	191

subgroup

index

C₄²×Dic₁₉₁

#336×C₁₉₁

191

Subgroups — #37572267

Conjugacy classes of subgroups

Complements

Maximal subgroups