Group #11782437 — subgroups

Subgroups — #11782437

Order 1152.

336 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 86 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×#486	C₂	1	1	yes	maximal, characteristic, complemented
2	#10588770	C₂	1	1	yes	maximal, characteristic, complemented
3	#10588758	C₂	1	1	yes	maximal, characteristic, complemented
4	#10588755	C₂	1	1	yes	maximal, characteristic
5	#10588753	C₂	1	1	yes	maximal, characteristic, complemented
6	#10588376	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#71180	—	3	1	no	maximal
9	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₉×#127	C₂²	1	1	yes	characteristic
11	C₂×#3675	—	2	2	no	—
12	C₂×#3673	—	2	2	no	—
13	C₂×#3672	—	2	2	no	—
14	#63436	C₂²	1	1	yes	characteristic
15	#63431	C₂²	1	1	yes	characteristic
16	C₉×#102	—	2	2	no	—
17	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
18	#63380	—	2	2	no	—
19	#63366	—	2	2	no	—
20	C₄×C₉⋊C₈	C₂²	1	1	yes	characteristic
21	C₄×C₉⋊C₈	C₂²	1	1	yes	characteristic
22	C₃×#486	D₃	1	1	yes	characteristic
23	#5085	—	3	1	no	—
24	#5078	—	3	1	no	—
25	#5076	—	3	1	no	—
26	#5073	—	3	1	no	—
27	#4694	—	3	1	no	—
28	C₈×C₃⋊C₈	—	3	1	no	—
29	C₂×Q₈×C₉	—	2	1	no	—
30	C₂×D₄×C₉	—	2	1	no	—
31	C₂×D₄×C₉	—	2	1	no	—
32	C₂×D₄×C₉	—	2	1	no	—
33	C₂×D₃₆	—	2	1	no	—
34	C₂×D₃₆	—	2	1	no	—
35	C₂×D₃₆	—	2	1	no	—
36	C₂×Dic₁₈	—	2	1	no	—
37	C₂×C₈×C₉	D₄	1	2	yes	—
38	C₉×C₄⋊C₄	—	2	1	no	—
39	C₉×C₄⋊C₄	—	2	1	no	—
40	C₄²×C₉	C₂³	1	1	yes	characteristic
41	#3675	—	4	4	no	—
42	#3673	—	4	4	no	—
43	#3672	—	4	4	no	—
44	C₄⋊Dic₉	—	2	1	no	—
45	C₄⋊Dic₉	—	2	1	no	—
46	C₂×C₉⋊C₈	D₄	1	2	yes	—
47	C₂×C₉⋊C₈	D₄	1	2	yes	—
48	#1706	—	9	1	no	Sylow
49	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
50	C₃×#127	C₂×D₃	1	1	yes	characteristic
51	C₂×#215	—	6	2	no	—
52	C₂×#214	—	6	2	no	—
53	C₂×#213	—	6	2	no	—
54	#874	—	3	1	no	—
55	#869	—	3	1	no	—
56	C₃×#102	—	2	2	no	—
57	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
58	#821	—	6	2	no	—
59	#807	—	6	2	no	—
60	C₄×C₃⋊C₈	—	3	1	no	—
61	C₄×C₃⋊C₈	—	3	1	no	—
62	C₂³×C₉	—	4	1	no	—
63	C₂²×D₉	—	4	1	no	—
64	Q₈×C₉	—	4	2	no	—
65	D₄×C₉	—	4	2	no	—
66	D₄×C₉	—	4	2	no	—
67	D₄×C₉	—	4	2	no	—
68	C₂×C₄×C₉	—	4	1	no	—
69	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
71	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
72	C₂×Dic₉	—	4	1	no	—
73	D₃₆	—	4	2	no	—
74	D₃₆	—	4	2	no	—
75	D₃₆	—	4	2	no	—
76	Dic₁₈	—	4	2	no	—
77	C₈×C₉	—	2	2	no	—
78	C₉⋊C₈	D₈	1	4	yes	complemented
79	C₉⋊C₈	SD₁₆	1	4	yes	complemented
80	#500	—	9	1	no	—
81	#493	—	9	1	no	—
82	#492	—	9	1	no	—
83	#492	—	9	1	no	—
84	#486	—	9	1	no	—
85	#486	D₉	1	1	yes	characteristic, complemented
86	C₈²	—	9	1	no	—
87	C₂×C₃×Q₈	—	2	1	no	—
88	C₂×C₃×D₄	—	2	1	no	—
89	C₂×C₃×D₄	—	2	1	no	—
90	C₂×C₃×D₄	—	2	1	no	—
91	C₂×D₁₂	—	6	1	no	—
92	C₂×D₁₂	—	6	1	no	—
93	C₂×D₁₂	—	6	1	no	—
94	C₂×Dic₆	—	6	1	no	—
95	C₂×C₃×C₈	#67	1	2	yes	—
96	C₃×C₄⋊C₄	—	2	1	no	—
97	C₃×C₄⋊C₄	—	2	1	no	—
98	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
99	#215	—	12	4	no	—
100	#214	—	12	4	no	—
101	#213	—	12	4	no	—
102	C₄⋊Dic₃	—	6	1	no	—
103	C₄⋊Dic₃	—	6	1	no	—
104	C₂×C₃⋊C₈	—	3	2	no	—
105	C₂×C₃⋊C₈	—	3	2	no	—
106	C₂²×C₉	—	8	1	no	—
107	C₂²×C₉	—	8	1	no	—
108	C₂²×C₉	—	8	1	no	—
109	C₂²×C₉	#127	1	1	yes	characteristic
110	C₂×D₉	—	8	1	no	—
111	C₂×D₉	—	8	1	no	—
112	C₂×D₉	—	8	1	no	—
113	C₄×C₉	—	8	1	no	—
114	C₄×C₉	C₂×D₈	1	2	yes	—
115	C₄×C₉	C₂×SD₁₆	1	2	yes	—
116	C₄×C₉	#135	1	2	yes	—
117	Dic₉	—	8	1	no	—
118	C₂×SD₁₆	—	18	2	no	—
119	C₂×SD₁₆	—	18	2	no	—
120	C₂×D₈	—	18	2	no	—
121	C₄⋊Q₈	—	9	1	no	—
122	C₄⋊Q₈	C₂×D₉	1	1	yes	characteristic
123	#127	—	9	1	no	—
124	#127	C₂×D₉	1	1	yes	characteristic
125	#107	—	18	2	no	—
126	#102	—	2	2	no	—
127	#102	—	18	2	no	—
128	C₄×C₈	—	9	1	no	—
129	C₄×C₈	—	9	1	no	—
130	C₄×C₈	C₂×D₉	1	1	yes	characteristic
131	C₂³×C₃	—	4	1	no	—
132	C₂²×D₃	—	12	1	no	—
133	C₃×Q₈	—	4	2	no	—
134	C₃×D₄	—	4	2	no	—
135	C₃×D₄	—	4	2	no	—
136	C₃×D₄	—	4	2	no	—
137	C₂×C₃×C₄	—	4	1	no	—
138	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
140	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
141	C₂×Dic₃	—	12	1	no	—
142	D₁₂	—	12	2	no	—
143	D₁₂	—	12	2	no	—
144	D₁₂	—	12	2	no	—
145	Dic₆	—	12	2	no	—
146	C₃×C₈	—	2	2	no	—
147	C₃⋊C₈	—	3	4	no	—
148	C₃⋊C₈	—	3	4	no	—
149	C₂×C₉	—	16	1	no	—
150	C₂×C₉	#492	1	1	yes	characteristic
151	C₂×C₉	#493	1	1	yes	characteristic
152	C₂×C₉	#495	1	1	yes	characteristic
153	D₉	—	16	1	no	—
154	C₂×Q₈	—	2	1	no	—
155	C₂×Q₈	—	18	1	no	—
156	C₂×D₄	—	2	1	no	—
157	C₂×D₄	—	2	1	no	—
158	C₂×D₄	—	2	1	no	—
159	C₂×D₄	—	18	1	no	—
160	C₂×D₄	—	18	1	no	—
161	C₂×D₄	—	18	1	no	—
162	SD₁₆	—	36	4	no	—
163	SD₁₆	—	36	4	no	—
164	D₈	—	36	4	no	—
165	C₂×C₈	—	9	2	no	—
166	C₂×C₈	—	9	2	no	—
167	C₂×C₈	#611	1	2	yes	—
168	C₄⋊C₄	—	2	1	no	—
169	C₄⋊C₄	—	2	1	no	—
170	C₄⋊C₄	—	18	1	no	—
171	C₄⋊C₄	—	18	1	no	—
172	C₄²	C₂²×D₉	1	1	yes	characteristic
173	C₂²×C₃	—	8	1	no	—
174	C₂²×C₃	—	8	1	no	—
175	C₂²×C₃	—	8	1	no	—
176	C₂²×C₃	#940	1	1	yes	characteristic
177	C₂×D₃	—	24	1	no	—
178	C₂×D₃	—	24	1	no	—
179	C₂×D₃	—	24	1	no	—
180	C₃×C₄	—	8	1	no	—
181	C₃×C₄	D₃×D₈	1	2	yes	—
182	C₃×C₄	D₃×SD₁₆	1	2	yes	—
183	C₃×C₄	#950	1	2	yes	—
184	Dic₃	—	24	1	no	—
185	C₉	#1706	1	1	yes	characteristic, complemented, Sylow
186	C₂³	—	4	1	no	—
187	C₂³	—	36	1	no	—
188	Q₈	—	4	2	no	—
189	Q₈	—	36	2	no	—
190	D₄	—	4	2	no	—
191	D₄	—	4	2	no	—
192	D₄	—	4	2	no	—
193	D₄	—	36	2	no	—
194	D₄	—	36	2	no	—
195	D₄	—	36	2	no	—
196	C₂×C₄	—	4	1	no	—
197	C₂×C₄	—	36	1	no	—
198	C₂×C₄	D₄×D₉	1	1	yes	characteristic
199	C₂×C₄	D₄×D₉	1	1	yes	characteristic
200	C₂×C₄	C₂×#611	1	1	yes	characteristic
201	C₈	—	2	2	no	—
202	C₈	—	9	4	no	—
203	C₈	—	9	4	no	—
204	C₂×C₃	—	16	1	no	—
205	C₂×C₃	#5059	1	1	yes	characteristic
206	C₂×C₃	#5151	1	1	yes	characteristic
207	C₂×C₃	#5175	1	1	yes	characteristic
208	D₃	—	48	1	no	—
209	C₂²	—	8	1	no	—
210	C₂²	—	8	1	no	—
211	C₂²	—	8	1	no	—
212	C₂²	—	72	1	no	—
213	C₂²	—	72	1	no	—
214	C₂²	—	72	1	no	—
215	C₂²	#63502	1	1	yes	characteristic
216	C₄	—	8	1	no	—
217	C₄	—	72	1	no	—
218	C₄	D₈×D₉	1	2	yes	—
219	C₄	SD₁₆×D₉	1	2	yes	—
220	C₄	#63513	1	2	yes	—
221	C₃	#71180	1	1	yes	characteristic
222	C₂	—	16	1	no	—
223	C₂	—	144	1	no	—
224	C₂	#10588740	1	1	yes	characteristic
225	C₂	#10588831	1	1	yes	characteristic
226	C₂	#10588855	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#486

C₂

yes

maximal, characteristic, complemented

#10588770

C₂

yes

maximal, characteristic, complemented

#10588758

C₂

yes

maximal, characteristic, complemented

#10588755

C₂

yes

maximal, characteristic

#10588753

C₂

yes

maximal, characteristic, complemented

#10588376

C₂

yes

maximal, characteristic, complemented

C₈×C₉⋊C₈

C₂

yes

maximal, characteristic, complemented

#71180

—

maximal

C₉×C₄⋊Q₈

C₂²

yes

characteristic

C₉×#127

C₂²

yes

—

—

—

C₂²

yes

characteristic

#63431

C₂²

yes

characteristic

C₉×#102

—

C₄×C₈×C₉

C₂²

yes

characteristic

#63380

—

#63366

—

C₄×C₉⋊C₈

C₂²

yes

characteristic

C₄×C₉⋊C₈

C₂²

yes

characteristic

C₃×#486

D₃

yes

—

—

—

—

—

C₈×C₃⋊C₈

—

C₂×Q₈×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₃₆

—

C₂×D₃₆

—

C₂×D₃₆

—

C₂×Dic₁₈

—

C₂×C₈×C₉

D₄

yes

—

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

—

C₄²×C₉

C₂³

yes

—

—

—

C₄⋊Dic₉

—

C₄⋊Dic₉

—

C₂×C₉⋊C₈

D₄

yes

—

C₂×C₉⋊C₈

D₄

yes

—

#1706

—

Sylow

C₃×C₄⋊Q₈

C₂×D₃

yes

characteristic

C₃×#127

C₂×D₃

yes

—

—

—

—

—

—

C₃×C₄×C₈

C₂×D₃

yes

characteristic

#821

—

#807

—

C₄×C₃⋊C₈

—

C₄×C₃⋊C₈

—

C₂³×C₉

—

C₂²×D₉

—

Q₈×C₉

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×Dic₉

—

D₃₆

—

D₃₆

—

D₃₆

—

Dic₁₈

—

C₈×C₉

—

C₉⋊C₈

D₈

yes

complemented

C₉⋊C₈

SD₁₆

yes

—

—

—

—

—

D₉

yes

characteristic, complemented

C₈²

—

C₂×C₃×Q₈

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×D₁₂

—

C₂×D₁₂

—

C₂×D₁₂

—

C₂×Dic₆

—

C₂×C₃×C₈

#67

yes

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄²

C₂²×D₃

yes

characteristic

#215

—

100

#214

—

101

#213

—

102

C₄⋊Dic₃

—

103

C₄⋊Dic₃

—

104

C₂×C₃⋊C₈

—

105

C₂×C₃⋊C₈

—

106

C₂²×C₉

—

107

C₂²×C₉

—

108

C₂²×C₉

—

109

C₂²×C₉

#127

yes

characteristic

110

C₂×D₉

—

111

C₂×D₉

—

112

C₂×D₉

—

113

C₄×C₉

—

114

C₄×C₉

C₂×D₈

yes

—

115

C₄×C₉

C₂×SD₁₆

yes

—

116

C₄×C₉

#135

yes

—

117

Dic₉

—

118

C₂×SD₁₆

—

119

C₂×SD₁₆

—

120

C₂×D₈

—

121

C₄⋊Q₈

—

122

C₄⋊Q₈

C₂×D₉

yes

characteristic

123

#127

—

124

#127

C₂×D₉

yes

characteristic

125

#107

—

126

#102

—

127

#102

—

128

C₄×C₈

—

129

C₄×C₈

—

130

C₄×C₈

C₂×D₉

yes

characteristic

131

C₂³×C₃

—

132

C₂²×D₃

—

133

C₃×Q₈

—

134

C₃×D₄

—

135

C₃×D₄

—

136

C₃×D₄

—

137

C₂×C₃×C₄

—

138

C₂×C₃×C₄

D₃×D₄

yes

characteristic

139

C₂×C₃×C₄

D₃×D₄

yes

characteristic

140

C₂×C₃×C₄

C₂×#67

yes

characteristic

141

C₂×Dic₃

—

142

D₁₂

—

143

D₁₂

—

144

D₁₂

—

145

Dic₆

—

146

C₃×C₈

—

147

C₃⋊C₈

—

148

C₃⋊C₈

—

149

C₂×C₉

—

150

C₂×C₉

#492

yes

characteristic

151

C₂×C₉

#493

yes

characteristic

152

C₂×C₉

#495

yes

characteristic

153

D₉

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×D₄

—

157

C₂×D₄

—

158

C₂×D₄

—

159

C₂×D₄

—

160

C₂×D₄

—

161

C₂×D₄

—

162

SD₁₆

—

163

SD₁₆

—

164

D₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

#611

yes

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄²

C₂²×D₉

yes

characteristic

173

C₂²×C₃

—

174

C₂²×C₃

—

175

C₂²×C₃

—

176

C₂²×C₃

#940

yes

characteristic

177

C₂×D₃

—

178

C₂×D₃

—

179

C₂×D₃

—

180

C₃×C₄

—

181

C₃×C₄

D₃×D₈

yes

—

182

C₃×C₄

D₃×SD₁₆

yes

—

183

C₃×C₄

#950

yes

—

184

Dic₃

—

185

C₉

#1706

yes

characteristic, complemented, Sylow

186

C₂³

—

187

C₂³

—

188

Q₈

—

189

Q₈

—

190

D₄

—

191

D₄

—

192

D₄

—

193

D₄

—

194

D₄

—

195

D₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

D₄×D₉

yes

characteristic

199

C₂×C₄

D₄×D₉

yes

characteristic

200

C₂×C₄

C₂×#611

yes

characteristic

201

C₈

—

202

C₈

—

203

C₈

—

204

C₂×C₃

—

205

C₂×C₃

#5059

yes

characteristic

206

C₂×C₃

#5151

yes

characteristic

207

C₂×C₃

#5175

yes

characteristic

208

D₃

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

#63502

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

D₈×D₉

yes

—

219

C₄

SD₁₆×D₉

yes

—

220

C₄

#63513

yes

—

221

C₃

#71180

yes

characteristic

222

C₂

—

223

C₂

—

144

—

224

C₂

#10588740

yes

characteristic

225

C₂

#10588831

yes

characteristic

226

C₂

#10588855

yes

characteristic

	subgroup	G/H
center	C₂²	#63502
commutator, cosocle	C₄²×C₉	C₂³
Frattini	C₃×C₄²	C₂²×D₃
Fitting	C₉×#486	C₂
socle	C₂²×C₃	#940
prime radical	#10588755	C₂
hypercenter	#486	D₉
hypocenter	C₉	#1706
LCS	G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #486

subgroup

G/H

center

C₂²

#63502

commutator, cosocle

C₄²×C₉

C₂³

Frattini

C₃×C₄²

C₂²×D₃

C₂

C₂²×C₃

C₂

D₉

C₉

G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #486

N	H ≅ G/N	type
1. C₉×#486	C₂	semidirect
2. #10588770	C₂	semidirect
3. #10588758	C₂	semidirect
5. #10588753	C₂	semidirect
6. #10588376	C₂	semidirect
7. C₈×C₉⋊C₈	C₂	semidirect
78. C₉⋊C₈	D₈	semidirect
79. C₉⋊C₈	SD₁₆	semidirect
85. #486	D₉	semidirect
185. C₉	#1706	semidirect

H ≅ G/N

type

1. C₉×#486

C₂

semidirect

2. #10588770

C₂

semidirect

3. #10588758

C₂

semidirect

5. #10588753

C₂

semidirect

6. #10588376

C₂

semidirect

7. C₈×C₉⋊C₈

C₂

semidirect

78. C₉⋊C₈

D₈

semidirect

79. C₉⋊C₈

SD₁₆

semidirect

85. #486

D₉

semidirect

185. C₉

#1706

semidirect

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

subgroup	index
C₉×#486	2
#10588770	2
#10588758	2
#10588755	2
#10588753	2
#10588376	2
C₈×C₉⋊C₈	2
#71180	3

subgroup

index

C₈×C₉⋊C₈

Subgroups — #11782437

Conjugacy classes of subgroups

Complements

Maximal subgroups