Group #11786073 — subgroups

Subgroups — #11786073

Order 1152.

370 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 74 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	#10593736	C₂	1	1	yes	maximal, characteristic
2	#10593735	C₂	1	1	yes	maximal, characteristic
3	C₃⋊D₃×#97	C₂	1	1	yes	maximal, characteristic
4	#10590182	C₂	1	4	yes	maximal
5	C₂×C₄⋊#157	—	2	2	no	—
6	C₂×C₄⋊#157	C₂²	1	2	yes	—
7	C₂×C₄⋊#157	C₂²	1	2	yes	—
8	C₂×C₈×C₃⋊D₃	C₂²	1	2	yes	—
9	C₄²×C₃⋊D₃	C₂²	1	1	yes	characteristic
10	#63781	—	2	2	no	—
11	C₃²×#97	C₄	1	1	yes	characteristic, complemented
12	#63642	C₄	1	2	yes	complemented
13	#63630	C₄	1	1	yes	characteristic, complemented
14	D₃×#97	—	6	2	no	—
15	C₂²×#157	—	2	2	no	—
16	C₂²×#157	—	2	2	no	—
17	C₂×C₄×C₃⋊D₃	D₄	1	2	yes	—
18	C₂×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
19	C₄⋊#157	—	2	4	no	—
20	C₄⋊#157	—	2	4	no	—
21	C₄⋊#157	—	4	4	no	—
22	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
23	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
24	C₄×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
25	C₄×C₃⋊Dic₃	Q₈	1	2	yes	—
26	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	2	yes	—
27	C₈×C₃⋊D₃	—	2	2	no	—
28	C₈×C₃⋊D₃	—	2	2	no	—
29	#1836	—	9	1	no	maximal, Sylow
30	C₂×D₃×C₈	—	6	4	no	—
31	C₄²×D₃	—	6	2	no	—
32	C₃×#97	—	2	2	no	—
33	#815	—	6	4	no	—
34	#803	—	6	2	no	—
35	C₂²×C₃⋊D₃	C₂×D₄	1	1	yes	characteristic
36	C₂×#157	—	4	2	no	—
37	C₂×#157	—	4	2	no	—
38	C₂×#157	—	4	2	no	—
39	C₂×#157	—	4	4	no	—
40	C₂×#157	—	4	2	no	—
41	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
42	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₃⋊Dic₃	C₄⋊C₄	1	2	yes	—
44	C₂×C₃⋊Dic₃	C₂×Q₈	1	1	yes	characteristic
45	C₄×C₃⋊D₃	—	2	2	no	—
46	C₄×C₃⋊D₃	—	2	2	no	—
47	C₄×C₃⋊D₃	#41	1	2	yes	—
48	C₄×C₃⋊D₃	#41	1	2	yes	—
49	C₃²×C₈	—	2	2	no	—
50	C₃⋊(C₃⋊C₈)	—	2	2	no	—
51	C₂×#97	—	9	1	no	—
52	#384	—	9	1	no	—
53	#382	—	9	1	no	—
54	#340	—	9	4	no	—
55	C₂×C₄×D₃	—	6	2	no	—
56	C₂×C₄×D₃	—	6	4	no	—
57	C₂×C₃×C₈	—	2	4	no	—
58	C₃×C₄²	—	2	2	no	—
59	C₄×Dic₃	—	6	2	no	—
60	C₄×Dic₃	—	6	4	no	—
61	C₂×C₃⋊C₈	—	6	4	no	—
62	D₃×C₈	—	6	8	no	—
63	D₃×C₈	—	6	8	no	—
64	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₃⋊D₃	#124	1	1	yes	characteristic
66	C₂×C₃⋊D₃	#124	1	1	yes	characteristic
67	C₂×C₃⋊D₃	AGL(1,ℤ/8)	1	2	yes	—
68	C₂×C₃⋊D₃	#137	1	2	yes	—
69	#157	—	8	2	no	—
70	#157	—	8	2	no	—
71	C₃²×C₄	—	2	2	no	—
72	C₃²×C₄	#117	1	2	yes	—
73	C₃⋊Dic₃	—	2	2	no	—
74	C₃⋊Dic₃	#125	1	2	yes	—
75	C₂²×C₈	—	9	2	no	—
76	C₂×C₄⋊C₄	—	9	2	no	—
77	C₂×C₄⋊C₄	—	9	2	no	—
78	C₂×C₄⋊C₄	—	18	2	no	—
79	C₂×C₄²	—	9	1	no	—
80	#97	—	9	2	no	—
81	#97	—	9	1	no	—
82	#97	#157	1	1	yes	characteristic, complemented
83	#95	—	18	2	no	—
84	C₂²×D₃	—	6	2	no	—
85	C₂×C₃×C₄	—	2	2	no	—
86	C₂×C₃×C₄	—	2	4	no	—
87	C₂×Dic₃	—	6	2	no	—
88	C₂×Dic₃	—	6	4	no	—
89	C₄×D₃	—	6	4	no	—
90	C₄×D₃	—	6	4	no	—
91	C₄×D₃	—	12	4	no	—
92	C₄×D₃	—	12	4	no	—
93	C₃×C₈	—	2	8	no	—
94	C₃⋊C₈	—	6	8	no	—
95	C₂×C₃²	#382	1	1	yes	characteristic
96	C₂×C₃²	#428	1	2	yes	—
97	C₃⋊D₃	#489	1	2	yes	—
98	C₃⋊D₃	#490	1	1	yes	characteristic
99	C₃⋊D₃	#491	1	1	yes	characteristic
100	C₂²×C₄	—	9	1	no	—
101	C₂²×C₄	—	9	2	no	—
102	C₂²×C₄	—	18	2	no	—
103	C₂²×C₄	—	18	2	no	—
104	C₂×C₈	—	9	2	no	—
105	C₂×C₈	—	18	2	no	—
106	C₂×C₈	—	18	2	no	—
107	C₂×C₈	C₂×#157	1	2	yes	—
108	C₄⋊C₄	—	18	4	no	—
109	C₄⋊C₄	—	18	4	no	—
110	C₄⋊C₄	—	36	4	no	—
111	C₄²	—	9	1	no	—
112	C₄²	—	9	2	no	—
113	C₄²	C₂×#157	1	1	yes	characteristic
114	C₂²×C₃	—	2	2	no	—
115	C₂×D₃	—	6	2	no	—
116	C₂×D₃	—	6	2	no	—
117	C₂×D₃	—	6	4	no	—
118	C₂×D₃	—	6	4	no	—
119	C₃×C₄	—	2	4	no	—
120	C₃×C₄	—	4	4	no	—
121	Dic₃	—	6	4	no	—
122	Dic₃	—	12	4	no	—
123	C₃²	#1836	1	1	yes	characteristic, complemented, Sylow
124	C₂³	—	9	1	no	—
125	C₂×C₄	—	9	1	no	—
126	C₂×C₄	—	9	2	no	—
127	C₂×C₄	—	9	2	no	—
128	C₂×C₄	—	9	2	no	—
129	C₂×C₄	—	18	2	no	—
130	C₂×C₄	—	18	2	no	—
131	C₂×C₄	—	36	2	no	—
132	C₂×C₄	—	36	2	no	—
133	C₂×C₄	—	36	4	no	—
134	C₂×C₄	—	36	2	no	—
135	C₂×C₄	—	36	2	no	—
136	C₂×C₄	C₄⋊#157	1	2	yes	—
137	C₂×C₄	C₂²×#157	1	1	yes	characteristic
138	C₈	—	2	2	no	—
139	C₈	—	18	2	no	—
140	C₂×C₃	—	2	2	no	—
141	C₂×C₃	—	2	4	no	—
142	D₃	—	6	4	no	—
143	D₃	—	6	2	no	—
144	D₃	—	6	2	no	—
145	C₂²	—	9	1	no	—
146	C₂²	—	9	1	no	—
147	C₂²	—	9	2	no	—
148	C₂²	—	9	2	no	—
149	C₂²	C₂×C₄⋊#157	1	1	yes	characteristic
150	C₄	—	2	2	no	—
151	C₄	—	9	2	no	—
152	C₄	—	18	2	no	—
153	C₄	—	72	2	no	—
154	C₄	—	72	2	no	—
155	C₄	#64286	1	2	yes	—
156	C₃	—	2	2	no	—
157	C₂	—	9	1	no	—
158	C₂	—	9	2	no	—
159	C₂	—	9	1	no	—
160	C₂	#10593736	1	1	yes	characteristic
161	C₂	#10593774	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#10593736

C₂

yes

maximal, characteristic

#10593735

C₂

yes

maximal, characteristic

C₃⋊D₃×#97

C₂

yes

maximal, characteristic

#10590182

C₂

yes

maximal

C₂×C₄⋊#157

—

C₂×C₄⋊#157

C₂²

yes

—

C₂×C₄⋊#157

C₂²

yes

—

C₂×C₈×C₃⋊D₃

C₂²

yes

—

C₄²×C₃⋊D₃

C₂²

yes

characteristic

#63781

—

C₃²×#97

C₄

yes

characteristic, complemented

#63642

C₄

yes

complemented

#63630

C₄

yes

characteristic, complemented

D₃×#97

—

C₂²×#157

—

C₂²×#157

—

C₂×C₄×C₃⋊D₃

D₄

yes

—

C₂×C₄×C₃⋊D₃

C₂³

yes

—

—

—

C₂×C₃²×C₈

C₂×C₄

yes

—

C₃²×C₄²

C₂×C₄

yes

characteristic

C₄×C₃⋊Dic₃

C₂×C₄

yes

characteristic

C₄×C₃⋊Dic₃

Q₈

yes

—

C₂×C₃⋊(C₃⋊C₈)

C₂×C₄

yes

—

C₈×C₃⋊D₃

—

C₈×C₃⋊D₃

—

#1836

—

maximal, Sylow

C₂×D₃×C₈

—

C₄²×D₃

—

C₃×#97

—

#815

—

#803

—

C₂²×C₃⋊D₃

C₂×D₄

yes

—

—

—

—

—

C₂×C₃²×C₄

C₄⋊C₄

yes

—

C₂×C₃²×C₄

C₂²×C₄

yes

characteristic

C₂×C₃⋊Dic₃

C₄⋊C₄

yes

—

C₂×C₃⋊Dic₃

C₂×Q₈

yes

characteristic

C₄×C₃⋊D₃

—

C₄×C₃⋊D₃

—

C₄×C₃⋊D₃

#41

yes

—

C₄×C₃⋊D₃

#41

yes

—

C₃²×C₈

—

C₃⋊(C₃⋊C₈)

—

C₂×#97

—

#384

—

#382

—

#340

—

C₂×C₄×D₃

—

C₂×C₄×D₃

—

C₂×C₃×C₈

—

C₃×C₄²

—

C₄×Dic₃

—

C₄×Dic₃

—

C₂×C₃⋊C₈

—

D₃×C₈

—

D₃×C₈

—

C₂²×C₃²

C₂×C₄⋊C₄

yes

C₂×C₃⋊D₃

yes

C₂×C₃⋊D₃

yes

C₂×C₃⋊D₃

yes

—

C₂×C₃⋊D₃

#137

yes

—

#157

—

#157

—

C₃²×C₄

—

C₃²×C₄

#117

yes

—

C₃⋊Dic₃

—

C₃⋊Dic₃

#125

yes

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

—

—

yes

characteristic, complemented

#95

—

C₂²×D₃

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×Dic₃

—

C₂×Dic₃

—

C₄×D₃

—

C₄×D₃

—

C₄×D₃

—

C₄×D₃

—

C₃×C₈

—

C₃⋊C₈

—

C₂×C₃²

#382

yes

characteristic

C₂×C₃²

#428

yes

—

C₃⋊D₃

#489

yes

—

C₃⋊D₃

yes

C₃⋊D₃

yes

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

C₂×#157

yes

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄²

—

112

C₄²

—

113

C₄²

C₂×#157

yes

characteristic

114

C₂²×C₃

—

115

C₂×D₃

—

116

C₂×D₃

—

117

C₂×D₃

—

118

C₂×D₃

—

119

C₃×C₄

—

120

C₃×C₄

—

121

Dic₃

—

122

Dic₃

—

123

C₃²

#1836

yes

characteristic, complemented, Sylow

124

C₂³

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

C₄⋊#157

yes

—

137

C₂×C₄

C₂²×#157

yes

characteristic

138

C₈

—

139

C₈

—

140

C₂×C₃

—

141

C₂×C₃

—

142

D₃

—

143

D₃

—

144

D₃

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

—

149

C₂²

C₂×C₄⋊#157

yes

characteristic

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

#64286

yes

—

156

C₃

—

157

C₂

—

158

C₂

—

159

C₂

—

160

C₂

#10593736

yes

characteristic

161

C₂

#10593774

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#157
commutator	C₂×C₃²×C₄	C₂²×C₄
Frattini	C₂×C₄	C₂²×#157
Fitting	C₃²×#97	C₄
socle	C₂²×C₃²	C₂×C₄⋊C₄
prime radical	C₂²×C₃⋊D₃	C₂×D₄
cosocle	C₂×C₄×C₃⋊D₃	C₂³
hypercenter	#97	#157
hypocenter	C₃²	#1836
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#157

commutator

C₂×C₃²×C₄

C₂²×C₄

Frattini

C₂×C₄

C₂²×#157

Fitting

C₃²×#97

C₄

socle

C₂²×C₃²

C₂×C₄⋊C₄

prime radical

C₂²×C₃⋊D₃

C₂×D₄

cosocle

C₂×C₄×C₃⋊D₃

C₂³

C₃²

G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
11. C₃²×#97	C₄	semidirect
12. #63642	C₄	semidirect
13. #63630	C₄	semidirect
82. #97	#157	semidirect
123. C₃²	#1836	semidirect

H ≅ G/N

type

11. C₃²×#97

C₄

semidirect

12. #63642

C₄

semidirect

13. #63630

C₄

semidirect

82. #97

#157

semidirect

123. C₃²

#1836

semidirect

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

subgroup	index
#10593736	2
#10593735	2
C₃⋊D₃×#97	2
#10590182	2
#1836	9

subgroup

index

C₃⋊D₃×#97

Subgroups — #11786073

Conjugacy classes of subgroups

Complements

Maximal subgroups