Group #11790751 — subgroups

Subgroups — #11790751

Order 1152.

618 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 154 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×#63436	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#97	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#63380	C₂	1	4	yes	maximal, complemented
4	#10588616	C₂	1	1	yes	maximal, characteristic, complemented
5	#69823	—	3	1	no	maximal
6	C₂²×D₃₆	—	2	2	no	—
7	C₂²×D₃₆	C₂²	1	2	yes	—
8	C₂²×C₈×C₉	C₂²	1	2	yes	—
9	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
11	#63436	—	2	2	no	—
12	#63436	C₄	1	4	yes	complemented
13	C₉×#97	—	2	2	no	—
14	C₉⋊#95	—	2	2	no	—
15	#63380	—	2	8	no	—
16	C₂×#874	—	3	1	no	—
17	C₂×C₃×#97	D₃	1	1	yes	characteristic
18	C₂×#821	—	3	4	no	—
19	#4936	—	3	1	no	—
20	C₂³×D₉	—	2	2	no	—
21	C₂²×C₄×C₉	D₄	1	2	yes	—
22	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₉	—	2	2	no	—
24	C₂×D₃₆	—	2	4	no	—
25	C₂×D₃₆	—	2	4	no	—
26	C₂×D₃₆	—	2	8	no	—
27	C₂×D₃₆	—	2	2	no	—
28	C₂×D₃₆	—	4	8	no	—
29	C₂×D₃₆	C₂×C₄	1	4	yes	—
30	C₂×C₈×C₉	—	2	2	no	—
31	C₂×C₈×C₉	—	2	2	no	—
32	C₂×C₈×C₉	D₄	1	4	yes	complemented
33	C₄²×C₉	C₂×C₄	1	2	yes	—
34	C₄²×C₉	D₄	1	2	yes	—
35	C₄⋊Dic₉	—	2	4	no	—
36	#1961	—	9	1	no	Sylow
37	C₂²×D₁₂	—	3	2	no	—
38	C₂²×D₁₂	—	6	2	no	—
39	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
40	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
41	C₂×C₄⋊Dic₃	—	3	2	no	—
42	#874	—	3	4	no	—
43	#874	—	6	2	no	—
44	C₃×#97	—	2	2	no	—
45	C₃⋊#95	—	6	2	no	—
46	#821	—	6	8	no	—
47	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
48	C₂²×D₉	—	2	4	no	—
49	C₂²×D₉	—	4	2	no	—
50	C₂²×D₉	—	4	2	no	—
51	C₂²×D₉	—	4	8	no	—
52	C₂×C₄×C₉	—	2	4	no	—
53	C₂×C₄×C₉	C₂²⋊C₄	1	4	yes	—
54	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
56	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₉	#41	1	2	yes	—
58	C₂×Dic₉	—	4	2	no	—
59	C₂×Dic₉	—	4	4	no	—
60	D₃₆	—	2	8	no	—
61	D₃₆	—	4	16	no	—
62	D₃₆	—	4	4	no	—
63	C₈×C₉	—	2	4	no	—
64	C₂×#127	—	9	1	no	—
65	C₂×#102	—	9	4	no	—
66	C₂×#97	D₉	1	1	yes	characteristic, complemented
67	#382	—	9	1	no	—
68	C₂³×D₃	—	6	2	no	—
69	C₂²×C₃×C₄	D₁₂	1	2	yes	—
70	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
71	C₂²×Dic₃	—	6	2	no	—
72	C₂×D₁₂	—	3	4	no	—
73	C₂×D₁₂	—	6	4	no	—
74	C₂×D₁₂	—	6	4	no	—
75	C₂×D₁₂	—	6	8	no	—
76	C₂×D₁₂	—	6	2	no	—
77	C₂×D₁₂	—	12	8	no	—
78	C₂×C₃×C₈	—	2	2	no	—
79	C₂×C₃×C₈	—	2	2	no	—
80	C₂×C₃×C₈	D₁₂	1	4	yes	—
81	C₃×C₄²	C₄×D₃	1	2	yes	—
82	C₃×C₄²	#67	1	2	yes	—
83	C₄⋊Dic₃	—	6	4	no	—
84	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₉	#124	1	1	yes	characteristic
86	C₂²×C₉	#127	1	1	yes	characteristic
87	C₂²×C₉	AGL(1,ℤ/8)	1	4	yes	—
88	C₂×D₉	—	4	4	no	—
89	C₂×D₉	—	4	8	no	—
90	C₂×D₉	—	8	4	no	—
91	C₂×D₉	—	8	4	no	—
92	C₄×C₉	—	2	4	no	—
93	C₄×C₉	C₄×D₄	1	2	yes	—
94	C₄×C₉	#121	1	2	yes	—
95	Dic₉	—	8	2	no	—
96	C₂²×D₄	—	9	2	no	—
97	C₂²×D₄	—	18	2	no	—
98	C₂²×C₈	C₂×D₉	1	2	yes	—
99	#127	—	9	4	no	—
100	#127	—	18	2	no	—
101	C₂×C₄⋊C₄	—	9	2	no	—
102	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
103	#102	—	18	8	no	—
104	#97	—	2	2	no	—
105	#95	—	18	2	no	—
106	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
107	C₂²×D₃	—	6	4	no	—
108	C₂²×D₃	—	12	2	no	—
109	C₂²×D₃	—	12	2	no	—
110	C₂²×D₃	—	12	8	no	—
111	C₂×C₃×C₄	—	2	4	no	—
112	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	4	yes	—
113	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
114	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
115	C₂×C₃×C₄	#235	1	2	yes	—
116	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
117	C₂×Dic₃	—	12	2	no	—
118	C₂×Dic₃	—	12	4	no	—
119	D₁₂	—	6	8	no	—
120	D₁₂	—	12	16	no	—
121	D₁₂	—	12	4	no	—
122	C₃×C₈	—	2	4	no	—
123	C₂×C₉	#390	1	1	yes	characteristic
124	C₂×C₉	#418	1	2	yes	—
125	C₂×C₉	#490	1	2	yes	—
126	C₂×C₉	#496	1	2	yes	—
127	D₉	—	8	4	no	—
128	C₂⁴	—	18	2	no	—
129	C₂×D₄	—	9	4	no	—
130	C₂×D₄	—	18	8	no	—
131	C₂×D₄	—	18	4	no	—
132	C₂×D₄	—	18	4	no	—
133	C₂×D₄	—	18	2	no	—
134	C₂×D₄	—	36	8	no	—
135	C₂²×C₄	—	18	2	no	—
136	C₂²×C₄	D₃₆	1	2	yes	—
137	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
138	C₂×C₈	—	2	2	no	—
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	D₃₆	1	4	yes	complemented
141	C₄⋊C₄	—	18	4	no	—
142	C₄²	C₄×D₉	1	2	yes	—
143	C₄²	#611	1	2	yes	—
144	C₂²×C₃	#874	1	1	yes	characteristic
145	C₂²×C₃	#875	1	1	yes	characteristic
146	C₂²×C₃	#908	1	4	yes	—
147	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
148	C₂×D₃	—	12	8	no	—
149	C₂×D₃	—	12	4	no	—
150	C₂×D₃	—	24	4	no	—
151	C₂×D₃	—	24	4	no	—
152	C₃×C₄	—	2	4	no	—
153	C₃×C₄	C₄×D₁₂	1	2	yes	—
154	C₃×C₄	#930	1	2	yes	—
155	Dic₃	—	24	2	no	—
156	C₉	#1961	1	1	yes	characteristic, complemented, Sylow
157	C₂³	—	18	4	no	—
158	C₂³	—	36	2	no	—
159	C₂³	—	36	2	no	—
160	C₂³	—	36	8	no	—
161	C₂³	C₂×D₃₆	1	1	yes	characteristic
162	D₄	—	18	8	no	—
163	D₄	—	36	16	no	—
164	D₄	—	36	4	no	—
165	C₂×C₄	—	2	4	no	—
166	C₂×C₄	—	36	2	no	—
167	C₂×C₄	—	36	4	no	—
168	C₂×C₄	(C₂×D₉)⋊C₄	1	4	yes	—
169	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
170	C₂×C₄	C₂×D₃₆	1	2	yes	—
171	C₂×C₄	#3697	1	2	yes	—
172	C₂×C₄	C₂×#611	1	1	yes	characteristic
173	C₈	—	2	4	no	—
174	C₂×C₃	#4712	1	2	yes	—
175	C₂×C₃	#4713	1	2	yes	—
176	C₂×C₃	#4939	1	1	yes	characteristic
177	C₂×C₃	#5131	1	2	yes	—
178	D₃	—	24	4	no	—
179	C₂²	—	36	8	no	—
180	C₂²	—	36	4	no	—
181	C₂²	—	72	4	no	—
182	C₂²	—	72	4	no	—
183	C₂²	#63436	1	1	yes	characteristic
184	C₂²	#63437	1	1	yes	characteristic
185	C₂²	#63470	1	4	yes	—
186	C₂²	C₂×(C₂×D₉)⋊C₄	1	1	yes	characteristic
187	C₄	—	2	4	no	—
188	C₄	—	72	2	no	—
189	C₄	C₄×D₃₆	1	2	yes	—
190	C₄	#63492	1	2	yes	—
191	C₃	#69823	1	1	yes	characteristic
192	C₂	—	72	4	no	—
193	C₂	#10588393	1	2	yes	—
194	C₂	#10588394	1	2	yes	—
195	C₂	#10588619	1	1	yes	characteristic
196	C₂	#10588813	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#63436

C₂

yes

maximal, characteristic

C₂×C₉×#97

C₂

yes

maximal, characteristic, complemented

C₂×#63380

C₂

yes

maximal, complemented

#10588616

C₂

yes

maximal, characteristic, complemented

#69823

—

maximal

C₂²×D₃₆

—

C₂²×D₃₆

C₂²

yes

—

C₂²×C₈×C₉

C₂²

yes

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₉

C₂²

yes

—

#63436

—

#63436

C₄

yes

complemented

C₉×#97

—

C₉⋊#95

—

#63380

—

C₂×#874

—

C₂×C₃×#97

D₃

yes

characteristic

C₂×#821

—

#4936

—

C₂³×D₉

—

C₂²×C₄×C₉

D₄

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂²×Dic₉

—

C₂×D₃₆

—

C₂×D₃₆

—

C₂×D₃₆

—

C₂×D₃₆

—

C₂×D₃₆

—

C₂×D₃₆

C₂×C₄

yes

—

C₂×C₈×C₉

—

C₂×C₈×C₉

—

C₂×C₈×C₉

D₄

yes

complemented

C₄²×C₉

C₂×C₄

yes

—

C₄²×C₉

D₄

yes

—

C₄⋊Dic₉

—

#1961

—

Sylow

C₂²×D₁₂

—

C₂²×D₁₂

—

C₂²×C₃×C₈

C₂×D₃

yes

—

C₂×C₃×C₄²

C₂×D₃

yes

characteristic

C₂×C₄⋊Dic₃

—

#874

—

#874

—

C₃×#97

—

C₃⋊#95

—

#821

—

C₂³×C₉

C₂×D₄

yes

characteristic

C₂²×D₉

—

C₂²×D₉

—

C₂²×D₉

—

C₂²×D₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂²⋊C₄

yes

—

C₂×C₄×C₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

#41

yes

—

C₂×Dic₉

—

C₂×Dic₉

—

D₃₆

—

D₃₆

—

D₃₆

—

C₈×C₉

—

C₂×#127

—

C₂×#102

—

C₂×#97

D₉

yes

characteristic, complemented

#382

—

C₂³×D₃

—

C₂²×C₃×C₄

D₁₂

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂²×Dic₃

—

C₂×D₁₂

—

C₂×D₁₂

—

C₂×D₁₂

—

C₂×D₁₂

—

C₂×D₁₂

—

C₂×D₁₂

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

D₁₂

yes

—

C₃×C₄²

C₄×D₃

yes

—

C₃×C₄²

#67

yes

—

C₄⋊Dic₃

—

C₂²×C₉

C₂×C₂²⋊C₄

yes

C₂²×C₉

yes

C₂²×C₉

yes

C₂²×C₉

yes

—

C₂×D₉

—

C₂×D₉

—

C₂×D₉

—

C₂×D₉

—

C₄×C₉

—

C₄×C₉

C₄×D₄

yes

—

C₄×C₉

#121

yes

—

Dic₉

—

C₂²×D₄

—

C₂²×D₄

—

C₂²×C₈

C₂×D₉

yes

—

#127

—

100

#127

—

101

C₂×C₄⋊C₄

—

102

C₂×C₄²

C₂×D₉

yes

characteristic

103

#102

—

104

#97

—

105

#95

—

106

C₂³×C₃

C₂×D₁₂

yes

characteristic

107

C₂²×D₃

—

108

C₂²×D₃

—

109

C₂²×D₃

—

110

C₂²×D₃

—

111

C₂×C₃×C₄

—

112

C₂×C₃×C₄

(C₂×D₃)⋊C₄

yes

—

113

C₂×C₃×C₄

C₂×C₄×D₃

yes

characteristic

114

C₂×C₃×C₄

C₂×D₁₂

yes

—

115

C₂×C₃×C₄

#235

yes

—

116

C₂×C₃×C₄

C₂×#67

yes

characteristic

117

C₂×Dic₃

—

118

C₂×Dic₃

—

119

D₁₂

—

120

D₁₂

—

121

D₁₂

—

122

C₃×C₈

—

123

C₂×C₉

#390

yes

characteristic

124

C₂×C₉

#418

yes

—

125

C₂×C₉

#490

yes

—

126

C₂×C₉

#496

yes

—

127

D₉

—

128

C₂⁴

—

129

C₂×D₄

—

130

C₂×D₄

—

131

C₂×D₄

—

132

C₂×D₄

—

133

C₂×D₄

—

134

C₂×D₄

—

135

C₂²×C₄

—

136

C₂²×C₄

D₃₆

yes

—

137

C₂²×C₄

C₂²×D₉

yes

characteristic

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

D₃₆

yes

complemented

141

C₄⋊C₄

—

142

C₄²

C₄×D₉

yes

—

143

C₄²

#611

yes

—

144

C₂²×C₃

#874

yes

characteristic

145

C₂²×C₃

#875

yes

characteristic

146

C₂²×C₃

#908

yes

—

147

C₂²×C₃

C₂×(C₂×D₃)⋊C₄

yes

characteristic

148

C₂×D₃

—

149

C₂×D₃

—

150

C₂×D₃

—

151

C₂×D₃

—

152

C₃×C₄

—

153

C₃×C₄

C₄×D₁₂

yes

—

154

C₃×C₄

#930

yes

—

155

Dic₃

—

156

C₉

#1961

yes

characteristic, complemented, Sylow

157

C₂³

—

158

C₂³

—

159

C₂³

—

160

C₂³

—

161

C₂³

C₂×D₃₆

yes

characteristic

162

D₄

—

163

D₄

—

164

D₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

(C₂×D₉)⋊C₄

yes

—

169

C₂×C₄

C₂×C₄×D₉

yes

characteristic

170

C₂×C₄

C₂×D₃₆

yes

—

171

C₂×C₄

#3697

yes

—

172

C₂×C₄

C₂×#611

yes

characteristic

173

C₈

—

174

C₂×C₃

#4712

yes

—

175

C₂×C₃

#4713

yes

—

176

C₂×C₃

#4939

yes

characteristic

177

C₂×C₃

#5131

yes

—

178

D₃

—

179

C₂²

—

180

C₂²

—

181

C₂²

—

182

C₂²

—

183

C₂²

#63436

yes

characteristic

184

C₂²

#63437

yes

characteristic

185

C₂²

#63470

yes

—

186

C₂²

C₂×(C₂×D₉)⋊C₄

yes

characteristic

187

C₄

—

188

C₄

—

189

C₄

C₄×D₃₆

yes

—

190

C₄

#63492

yes

—

191

C₃

#69823

yes

characteristic

192

C₂

—

193

C₂

#10588393

yes

—

194

C₂

#10588394

yes

—

195

C₂

#10588619

yes

characteristic

196

C₂

#10588813

yes

—

	subgroup	G/H
center	C₂³	C₂×D₃₆
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₂×C₉×#97	C₂
socle	C₂³×C₃	C₂×D₁₂
prime radical	C₂×#63436	C₂
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	C₂×#97	D₉
hypocenter	C₉	#1961
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

C₂×D₃₆

commutator

C₂×C₄×C₉

C₂²×C₄

Frattini

C₂²×C₃×C₄

C₂²×D₃

Fitting

C₂×C₉×#97

C₂

socle

C₂³×C₃

C₂×D₁₂

prime radical

C₂×#63436

C₂

cosocle

C₂²×C₄×C₉

C₂³

hypercenter

C₂×#97

D₉

hypocenter

C₉

#1961

LCS

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
2. C₂×C₉×#97	C₂	semidirect
3. C₂×#63380	C₂	semidirect
4. #10588616	C₂	semidirect
12. #63436	C₄	semidirect
32. C₂×C₈×C₉	D₄	semidirect
66. C₂×#97	D₉	semidirect
140. C₂×C₈	D₃₆	semidirect
156. C₉	#1961	semidirect

H ≅ G/N

type

2. C₂×C₉×#97

C₂

semidirect

3. C₂×#63380

C₂

semidirect

4. #10588616

C₂

semidirect

12. #63436

C₄

semidirect

32. C₂×C₈×C₉

D₄

semidirect

66. C₂×#97

D₉

semidirect

140. C₂×C₈

D₃₆

semidirect

156. C₉

#1961

semidirect

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

subgroup	index
C₂×#63436	2
C₂×C₉×#97	2
C₂×#63380	2
#10588616	2
#69823	3

subgroup

index

C₂×C₉×#97

Subgroups — #11790751

Conjugacy classes of subgroups

Complements

Maximal subgroups