Group #11790806 — subgroups

Subgroups — #11790806

Order 1152.

480 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 138 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	C₉×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×#63396	C₂	1	4	yes	maximal, complemented
3	#10588612	C₂	1	1	yes	maximal, characteristic, complemented
4	#10588604	C₂	1	1	yes	maximal, characteristic, complemented
5	#71816	—	3	1	no	maximal
6	C₂×C₉×#41	C₂²	1	2	yes	—
7	C₉×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
8	C₉×#127	C₄	1	1	yes	characteristic, complemented
9	C₉×#124	C₄	1	2	yes	complemented
10	C₉×#121	—	2	2	no	—
11	C₄×D₄×C₉	—	2	2	no	—
12	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₉	C₂²	1	2	yes	—
14	C₂×#3667	C₂²	1	2	yes	—
15	#63396	—	2	8	no	—
16	C₉⋊#95	—	2	2	no	—
17	C₄⋊(C₉⋊C₈)	—	2	2	no	—
18	C₃×#532	D₃	1	1	yes	characteristic
19	C₂×#837	—	3	4	no	—
20	#4932	—	3	1	no	—
21	#4924	—	3	1	no	—
22	C₉×#41	—	2	4	no	—
23	C₉×#41	—	2	4	no	—
24	C₂×Q₈×C₉	C₂×C₄	1	2	yes	—
25	C₂×D₄×C₉	—	2	2	no	—
26	C₂×D₄×C₉	—	2	2	no	—
27	C₂×D₄×C₉	C₂×C₄	1	2	yes	—
28	C₂²×C₄×C₉	—	2	2	no	—
29	C₂²×C₄×C₉	D₄	1	2	yes	—
30	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
31	C₂²×Dic₉	—	2	2	no	—
32	C₉×C₄⋊C₄	—	2	2	no	—
33	C₉×C₂²⋊C₄	—	2	4	no	—
34	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
35	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
36	C₄²×C₉	D₄	1	2	yes	—
37	C₄×Dic₉	—	2	2	no	—
38	C₄×Dic₉	D₄	1	4	yes	complemented
39	#3667	—	2	4	no	—
40	C₂×C₉⋊C₈	—	2	2	no	—
41	#1963	—	9	1	no	Sylow
42	C₂×C₃×#41	C₂×D₃	1	2	yes	—
43	C₃×C₄⋊Q₈	Dic₃	1	1	yes	characteristic
44	C₃×#127	Dic₃	1	1	yes	characteristic
45	C₃×#124	Dic₃	1	2	yes	—
46	C₃×#121	—	2	2	no	—
47	C₃×C₄×D₄	—	2	2	no	—
48	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
49	C₂×C₄×Dic₃	—	3	2	no	—
50	C₂×#208	—	3	2	no	—
51	#837	—	6	8	no	—
52	C₃⋊#95	—	6	2	no	—
53	C₄⋊(C₃⋊C₈)	—	6	2	no	—
54	C₂³×C₉	—	2	2	no	—
55	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
56	Q₈×C₉	—	2	4	no	—
57	D₄×C₉	—	2	4	no	—
58	D₄×C₉	—	4	4	no	—
59	D₄×C₉	—	4	4	no	—
60	C₂×C₄×C₉	—	2	2	no	—
61	C₂×C₄×C₉	—	4	2	no	—
62	C₂×C₄×C₉	—	4	2	no	—
63	C₂×C₄×C₉	—	4	2	no	—
64	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
65	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
66	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
68	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
69	C₂×C₄×C₉	#41	1	2	yes	—
70	C₂×Dic₉	—	2	4	no	—
71	C₂×Dic₉	—	4	4	no	—
72	C₉⋊C₈	—	4	2	no	—
73	#532	D₉	1	1	yes	characteristic
74	#423	—	9	1	no	—
75	C₂×#104	—	9	4	no	—
76	#376	—	9	1	no	—
77	C₃×#41	—	2	4	no	—
78	C₃×#41	—	2	4	no	—
79	C₂×C₃×Q₈	C₂×Dic₃	1	2	yes	—
80	C₂×C₃×D₄	—	2	2	no	—
81	C₂×C₃×D₄	—	2	2	no	—
82	C₂×C₃×D₄	C₂×Dic₃	1	2	yes	—
83	C₂²×C₃×C₄	—	2	2	no	—
84	C₂²×C₃×C₄	#67	1	2	yes	—
85	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
86	C₂²×Dic₃	—	6	2	no	—
87	C₃×C₄⋊C₄	—	2	2	no	—
88	C₃×C₂²⋊C₄	—	2	4	no	—
89	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
90	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
91	C₃×C₄²	#67	1	2	yes	—
92	C₄×Dic₃	—	3	4	no	—
93	C₄×Dic₃	—	6	2	no	—
94	#208	—	6	4	no	—
95	C₂×C₃⋊C₈	—	6	2	no	—
96	C₂²×C₉	—	2	2	no	—
97	C₂²×C₉	—	4	2	no	—
98	C₂²×C₉	—	4	4	no	—
99	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₉	#121	1	2	yes	—
101	C₄×C₉	—	2	2	no	—
102	C₄×C₉	—	2	2	no	—
103	C₄×C₉	—	4	2	no	—
104	C₄×C₉	C₄×D₄	1	2	yes	—
105	C₄×C₉	#124	1	1	yes	characteristic
106	C₄×C₉	#127	1	1	yes	characteristic
107	Dic₉	—	4	4	no	—
108	C₂×#41	C₂×D₉	1	2	yes	—
109	C₂×M₁₆	—	9	2	no	—
110	C₄⋊Q₈	Dic₉	1	1	yes	characteristic, complemented
111	#127	Dic₉	1	1	yes	characteristic, complemented
112	#124	Dic₉	1	2	yes	complemented
113	#121	—	2	2	no	—
114	C₄×D₄	—	2	2	no	—
115	C₂×C₄²	—	9	2	no	—
116	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
117	C₄⋊C₈	—	18	2	no	—
118	#104	—	18	8	no	—
119	#95	—	18	2	no	—
120	C₂³×C₃	—	2	2	no	—
121	C₂³×C₃	C₂×#67	1	1	yes	characteristic
122	C₃×Q₈	—	2	4	no	—
123	C₃×D₄	—	2	4	no	—
124	C₃×D₄	—	4	4	no	—
125	C₃×D₄	—	4	4	no	—
126	C₂×C₃×C₄	—	2	2	no	—
127	C₂×C₃×C₄	—	4	2	no	—
128	C₂×C₃×C₄	—	4	2	no	—
129	C₂×C₃×C₄	—	4	2	no	—
130	C₂×C₃×C₄	#217	1	2	yes	—
131	C₂×C₃×C₄	#217	1	2	yes	—
132	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
133	C₂×C₃×C₄	#237	1	2	yes	—
134	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
135	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
136	C₂×Dic₃	—	6	4	no	—
137	C₂×Dic₃	—	12	4	no	—
138	C₃⋊C₈	—	12	2	no	—
139	C₂×C₉	—	2	2	no	—
140	C₂×C₉	—	8	2	no	—
141	C₂×C₉	#390	1	1	yes	characteristic
142	C₂×C₉	#421	1	2	yes	—
143	#41	—	2	4	no	—
144	#41	—	2	4	no	—
145	C₂×Q₈	C₂×Dic₉	1	2	yes	—
146	C₂×D₄	—	2	2	no	—
147	C₂×D₄	—	2	2	no	—
148	C₂×D₄	C₂×Dic₉	1	2	yes	—
149	C₂²×C₄	—	2	2	no	—
150	C₂²×C₄	—	18	2	no	—
151	C₂²×C₄	#611	1	2	yes	—
152	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
153	M₁₆	—	18	4	no	—
154	C₂×C₈	—	18	2	no	—
155	C₄⋊C₄	—	2	2	no	—
156	C₂²⋊C₄	—	2	4	no	—
157	C₄²	—	9	4	no	—
158	C₄²	—	18	2	no	—
159	C₄²	C₂×Dic₉	1	1	yes	characteristic
160	C₄²	C₂×Dic₉	1	1	yes	characteristic
161	C₄²	#611	1	2	yes	—
162	C₂²×C₃	—	2	2	no	—
163	C₂²×C₃	—	4	2	no	—
164	C₂²×C₃	—	4	4	no	—
165	C₂²×C₃	#938	1	2	yes	—
166	C₂²×C₃	C₂×#217	1	1	yes	characteristic
167	C₃×C₄	—	2	2	no	—
168	C₃×C₄	—	2	2	no	—
169	C₃×C₄	—	4	2	no	—
170	C₃×C₄	D₄×Dic₃	1	2	yes	—
171	C₃×C₄	#936	1	1	yes	characteristic
172	C₃×C₄	#940	1	1	yes	characteristic
173	Dic₃	—	12	4	no	—
174	C₉	#1963	1	1	yes	characteristic, complemented, Sylow
175	C₂³	—	2	2	no	—
176	C₂³	C₂×#611	1	1	yes	characteristic
177	Q₈	—	2	4	no	—
178	D₄	—	2	4	no	—
179	D₄	—	4	4	no	—
180	D₄	—	4	4	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	4	2	no	—
183	C₂×C₄	—	4	2	no	—
184	C₂×C₄	—	4	2	no	—
185	C₂×C₄	—	18	4	no	—
186	C₂×C₄	—	36	4	no	—
187	C₂×C₄	#3676	1	2	yes	—
188	C₂×C₄	#3676	1	2	yes	—
189	C₂×C₄	D₄×D₉	1	2	yes	—
190	C₂×C₄	#3699	1	2	yes	—
191	C₂×C₄	C₂²×Dic₉	1	1	yes	characteristic
192	C₂×C₄	C₂×#611	1	1	yes	characteristic
193	C₈	—	36	2	no	—
194	C₂×C₃	—	2	2	no	—
195	C₂×C₃	—	8	2	no	—
196	C₂×C₃	#5221	1	1	yes	characteristic
197	C₂×C₃	#5236	1	2	yes	—
198	C₂²	—	2	2	no	—
199	C₂²	—	4	2	no	—
200	C₂²	—	4	4	no	—
201	C₂²	#63500	1	2	yes	—
202	C₂²	C₂×#3676	1	1	yes	characteristic
203	C₄	—	2	2	no	—
204	C₄	—	2	2	no	—
205	C₄	—	4	2	no	—
206	C₄	—	36	4	no	—
207	C₄	D₄×Dic₉	1	2	yes	—
208	C₄	#63498	1	1	yes	characteristic
209	C₄	#63502	1	1	yes	characteristic
210	C₃	#71816	1	1	yes	characteristic
211	C₂	—	2	2	no	—
212	C₂	—	8	2	no	—
213	C₂	#10588901	1	1	yes	characteristic
214	C₂	#10588914	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#532

C₂

yes

maximal, characteristic

C₂×#63396

C₂

yes

maximal, complemented

#10588612

C₂

yes

maximal, characteristic, complemented

#10588604

C₂

yes

maximal, characteristic, complemented

#71816

—

maximal

C₂×C₉×#41

C₂²

yes

—

C₉×C₄⋊Q₈

C₄

yes

characteristic, complemented

C₉×#127

C₄

yes

characteristic, complemented

C₉×#124

C₄

yes

complemented

C₉×#121

—

C₄×D₄×C₉

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₂×C₄×Dic₉

C₂²

yes

—

C₂×#3667

C₂²

yes

—

#63396

—

C₉⋊#95

—

C₄⋊(C₉⋊C₈)

—

C₃×#532

D₃

yes

—

—

—

C₉×#41

—

C₉×#41

—

C₂×Q₈×C₉

C₂×C₄

yes

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

C₂×C₄

yes

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

D₄

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂²×Dic₉

—

C₉×C₄⋊C₄

—

C₉×C₂²⋊C₄

—

C₄²×C₉

C₂×C₄

yes

characteristic

C₄²×C₉

C₂×C₄

yes

characteristic

C₄²×C₉

D₄

yes

—

C₄×Dic₉

—

C₄×Dic₉

D₄

yes

complemented

#3667

—

C₂×C₉⋊C₈

—

#1963

—

Sylow

C₂×C₃×#41

C₂×D₃

yes

—

C₃×C₄⋊Q₈

Dic₃

yes

characteristic

C₃×#127

Dic₃

yes

characteristic

C₃×#124

Dic₃

yes

—

C₃×#121

—

C₃×C₄×D₄

—

C₂×C₃×C₄²

C₂×D₃

yes

characteristic

C₂×C₄×Dic₃

—

C₂×#208

—

#837

—

C₃⋊#95

—

C₄⋊(C₃⋊C₈)

—

C₂³×C₉

—

C₂³×C₉

C₂×D₄

yes

characteristic

Q₈×C₉

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂²⋊C₄

yes

—

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

—

C₉⋊C₈

—

#532

D₉

yes

—

—

—

C₃×#41

—

C₃×#41

—

C₂×C₃×Q₈

C₂×Dic₃

yes

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

C₂×Dic₃

yes

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

#67

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂²×Dic₃

—

C₃×C₄⋊C₄

—

C₃×C₂²⋊C₄

—

C₃×C₄²

C₂×Dic₃

yes

characteristic

C₃×C₄²

C₂×Dic₃

yes

characteristic

C₃×C₄²

#67

yes

—

C₄×Dic₃

—

C₄×Dic₃

—

#208

—

C₂×C₃⋊C₈

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

C₂×C₂²⋊C₄

yes

characteristic

100

C₂²×C₉

#121

yes

—

101

C₄×C₉

—

102

C₄×C₉

—

103

C₄×C₉

—

104

C₄×C₉

C₄×D₄

yes

—

105

C₄×C₉

#124

yes

characteristic

106

C₄×C₉

#127

yes

characteristic

107

Dic₉

—

108

C₂×#41

C₂×D₉

yes

—

109

C₂×M₁₆

—

110

C₄⋊Q₈

Dic₉

yes

characteristic, complemented

111

#127

Dic₉

yes

characteristic, complemented

112

#124

Dic₉

yes

complemented

113

#121

—

114

C₄×D₄

—

115

C₂×C₄²

—

116

C₂×C₄²

C₂×D₉

yes

characteristic

117

C₄⋊C₈

—

118

#104

—

119

#95

—

120

C₂³×C₃

—

121

C₂³×C₃

C₂×#67

yes

characteristic

122

C₃×Q₈

—

123

C₃×D₄

—

124

C₃×D₄

—

125

C₃×D₄

—

126

C₂×C₃×C₄

—

127

C₂×C₃×C₄

—

128

C₂×C₃×C₄

—

129

C₂×C₃×C₄

—

130

C₂×C₃×C₄

#217

yes

—

131

C₂×C₃×C₄

#217

yes

—

132

C₂×C₃×C₄

D₃×D₄

yes

—

133

C₂×C₃×C₄

#237

yes

—

134

C₂×C₃×C₄

C₂²×Dic₃

yes

characteristic

135

C₂×C₃×C₄

C₂×#67

yes

characteristic

136

C₂×Dic₃

—

137

C₂×Dic₃

—

138

C₃⋊C₈

—

139

C₂×C₉

—

140

C₂×C₉

—

141

C₂×C₉

#390

yes

characteristic

142

C₂×C₉

#421

yes

—

143

#41

—

144

#41

—

145

C₂×Q₈

C₂×Dic₉

yes

—

146

C₂×D₄

—

147

C₂×D₄

—

148

C₂×D₄

C₂×Dic₉

yes

—

149

C₂²×C₄

—

150

C₂²×C₄

—

151

C₂²×C₄

#611

yes

—

152

C₂²×C₄

C₂²×D₉

yes

characteristic

153

M₁₆

—

154

C₂×C₈

—

155

C₄⋊C₄

—

156

C₂²⋊C₄

—

157

C₄²

—

158

C₄²

—

159

C₄²

C₂×Dic₉

yes

characteristic

160

C₄²

C₂×Dic₉

yes

characteristic

161

C₄²

#611

yes

—

162

C₂²×C₃

—

163

C₂²×C₃

—

164

C₂²×C₃

—

165

C₂²×C₃

#938

yes

—

166

C₂²×C₃

C₂×#217

yes

characteristic

167

C₃×C₄

—

168

C₃×C₄

—

169

C₃×C₄

—

170

C₃×C₄

D₄×Dic₃

yes

—

171

C₃×C₄

#936

yes

characteristic

172

C₃×C₄

#940

yes

characteristic

173

Dic₃

—

174

C₉

#1963

yes

characteristic, complemented, Sylow

175

C₂³

—

176

C₂³

C₂×#611

yes

characteristic

177

Q₈

—

178

D₄

—

179

D₄

—

180

D₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

#3676

yes

—

188

C₂×C₄

#3676

yes

—

189

C₂×C₄

D₄×D₉

yes

—

190

C₂×C₄

#3699

yes

—

191

C₂×C₄

C₂²×Dic₉

yes

characteristic

192

C₂×C₄

C₂×#611

yes

characteristic

193

C₈

—

194

C₂×C₃

—

195

C₂×C₃

—

196

C₂×C₃

#5221

yes

characteristic

197

C₂×C₃

#5236

yes

—

198

C₂²

—

199

C₂²

—

200

C₂²

—

201

C₂²

#63500

yes

—

202

C₂²

C₂×#3676

yes

characteristic

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

—

207

C₄

D₄×Dic₉

yes

—

208

C₄

#63498

yes

characteristic

209

C₄

#63502

yes

characteristic

210

C₃

#71816

yes

characteristic

211

C₂

—

212

C₂

—

213

C₂

#10588901

yes

characteristic

214

C₂

#10588914

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×#611
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#532	C₂
socle	C₂²×C₃	C₂×#217
prime radical	C₃×#532	D₃
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	#532	D₉
hypocenter	C₉	#1963
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #532

subgroup

G/H

center

C₂×C₄

C₂×#611

commutator

C₂×C₄×C₉

C₂²×C₄

Frattini

C₂²×C₃×C₄

C₂²×D₃

C₂

C₂²×C₃

D₃

C₂²×C₄×C₉

C₂³

D₉

C₉

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #532

N	H ≅ G/N	type
2. C₂×#63396	C₂	semidirect
3. #10588612	C₂	semidirect
4. #10588604	C₂	semidirect
7. C₉×C₄⋊Q₈	C₄	semidirect
8. C₉×#127	C₄	semidirect
9. C₉×#124	C₄	semidirect
38. C₄×Dic₉	D₄	semidirect
110. C₄⋊Q₈	Dic₉	semidirect
111. #127	Dic₉	semidirect
112. #124	Dic₉	semidirect
174. C₉	#1963	semidirect

H ≅ G/N

type

2. C₂×#63396

C₂

semidirect

3. #10588612

C₂

semidirect

4. #10588604

C₂

semidirect

7. C₉×C₄⋊Q₈

C₄

semidirect

8. C₉×#127

C₄

semidirect

9. C₉×#124

C₄

semidirect

38. C₄×Dic₉

D₄

semidirect

110. C₄⋊Q₈

Dic₉

semidirect

111. #127

Dic₉

semidirect

112. #124

Dic₉

semidirect

174. C₉

#1963

semidirect

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

subgroup	index
C₉×#532	2
C₂×#63396	2
#10588612	2
#10588604	2
#71816	3

subgroup

index

Subgroups — #11790806

Conjugacy classes of subgroups

Complements

Maximal subgroups