Group #11785507 — subgroups

Subgroups — #11785507

Order 1152.

378 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 120 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×#63510	C₂	1	1	yes	maximal, characteristic
2	C₉×#413	C₂	1	1	yes	maximal, characteristic
3	#10588915	C₂	1	1	yes	maximal, characteristic
4	C₂×#63381	C₂	1	2	yes	maximal, complemented
5	C₉⋊#338	C₂	1	2	yes	maximal, complemented
6	#70134	—	3	1	no	maximal
7	C₂×C₉×#41	C₂²	1	1	yes	characteristic
8	C₂×C₉×M₁₆	C₂²	1	2	yes	—
9	#63510	—	2	4	no	—
10	C₂×#3667	C₄	1	2	yes	—
11	C₂×#3667	C₂²	1	2	yes	—
12	C₂×#3667	C₂²	1	1	yes	characteristic
13	C₂²×C₉⋊C₈	C₄	1	2	yes	—
14	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₉×#101	—	2	1	no	—
16	C₉×#100	—	2	1	no	—
17	#63394	—	2	1	no	—
18	#63391	—	2	1	no	—
19	#63381	—	2	4	no	—
20	C₂×#948	—	3	1	no	—
21	C₃×#413	D₃	1	1	yes	characteristic
22	#5237	—	3	1	no	—
23	C₂×#822	—	3	2	no	—
24	C₃⋊#338	—	3	2	no	—
25	C₉×#41	—	2	2	no	—
26	C₉×#41	—	2	2	no	—
27	C₂×Q₈×C₉	D₄	1	1	yes	characteristic
28	C₂×D₄×C₉	D₄	1	1	yes	characteristic
29	C₂×D₄×C₉	Q₈	1	2	yes	—
30	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
31	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
32	C₉×M₁₆	—	2	2	no	—
33	C₉×M₁₆	—	2	2	no	—
34	C₂×C₈×C₉	—	2	2	no	—
35	#3667	—	2	2	no	—
36	#3667	—	2	4	no	—
37	#3667	—	2	2	no	—
38	#3667	—	2	2	no	—
39	C₂×C₉⋊C₈	—	2	4	no	—
40	C₂×C₉⋊C₈	—	2	2	no	—
41	C₂×C₉⋊C₈	C₂×C₄	1	2	yes	—
42	C₂×C₉⋊C₈	C₂×C₄	1	1	yes	characteristic
43	C₂×C₉⋊C₈	C₂×C₄	1	1	yes	characteristic
44	C₂×C₉⋊C₈	D₄	1	4	yes	—
45	#1813	—	9	1	no	Sylow
46	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
47	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
48	#948	—	6	4	no	—
49	C₂×#208	—	3	2	no	—
50	C₂×#208	—	3	1	no	—
51	C₂×#208	—	3	2	no	—
52	C₂²×C₃⋊C₈	—	3	1	no	—
53	C₂²×C₃⋊C₈	—	3	2	no	—
54	C₃×#101	—	2	1	no	—
55	C₃×#100	—	2	1	no	—
56	#836	—	6	1	no	—
57	#833	—	6	1	no	—
58	#822	—	6	4	no	—
59	C₂³×C₉	C₄⋊C₄	1	2	yes	—
60	C₂³×C₉	C₂×Q₈	1	1	yes	characteristic
61	Q₈×C₉	—	2	2	no	—
62	D₄×C₉	—	2	4	no	—
63	D₄×C₉	—	2	2	no	—
64	C₂×C₄×C₉	—	2	2	no	—
65	C₂×C₄×C₉	—	2	2	no	—
66	C₂×C₄×C₉	C₄⋊C₄	1	2	yes	—
67	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
69	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₉	#41	1	2	yes	—
71	C₈×C₉	—	4	2	no	—
72	C₉⋊C₈	—	2	2	no	—
73	C₉⋊C₈	—	4	2	no	—
74	C₉⋊C₈	C₂²⋊C₄	1	2	yes	—
75	C₉⋊C₈	C₂²⋊C₄	1	2	yes	—
76	C₂×#131	—	9	1	no	—
77	C₂×#108	—	9	2	no	—
78	#413	—	9	1	no	—
79	#413	D₉	1	1	yes	characteristic
80	#338	—	9	2	no	—
81	C₃×#41	—	2	2	no	—
82	C₃×#41	—	2	2	no	—
83	C₂×C₃×Q₈	#67	1	1	yes	characteristic
84	C₂×C₃×D₄	Dic₆	1	2	yes	—
85	C₂×C₃×D₄	#67	1	1	yes	characteristic
86	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
87	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
88	C₃×M₁₆	—	2	2	no	—
89	C₃×M₁₆	—	2	2	no	—
90	C₂×C₃×C₈	—	2	2	no	—
91	#208	—	6	4	no	—
92	#208	—	6	2	no	—
93	#208	—	6	2	no	—
94	#208	—	6	2	no	—
95	C₂×C₃⋊C₈	—	3	1	no	—
96	C₂×C₃⋊C₈	—	3	1	no	—
97	C₂×C₃⋊C₈	—	3	4	no	—
98	C₂×C₃⋊C₈	—	3	2	no	—
99	C₂×C₃⋊C₈	—	6	4	no	—
100	C₂×C₃⋊C₈	—	6	2	no	—
101	C₂²×C₉	—	2	2	no	—
102	C₂²×C₉	—	4	1	no	—
103	C₂²×C₉	—	4	2	no	—
104	C₂²×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
105	C₂²×C₉	C₂²⋊Q₈	1	2	yes	—
106	C₄×C₉	—	2	2	no	—
107	C₄×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
108	C₄×C₉	#117	1	1	yes	characteristic
109	C₄×C₉	#121	1	2	yes	—
110	C₂×#41	C₂×D₉	1	1	yes	characteristic
111	#131	—	18	4	no	—
112	C₂×M₁₆	—	9	2	no	—
113	C₂×M₁₆	—	9	1	no	—
114	C₂×M₁₆	—	9	2	no	—
115	C₂×M₁₆	C₂×D₉	1	2	yes	—
116	C₂²×C₈	—	9	1	no	—
117	C₂²×C₈	—	9	2	no	—
118	#108	—	18	4	no	—
119	#101	—	2	1	no	—
120	#101	—	18	1	no	—
121	#100	—	2	1	no	—
122	#100	—	18	1	no	—
123	C₂³×C₃	Dic₃⋊C₄	1	2	yes	—
124	C₂³×C₃	C₂×Dic₆	1	1	yes	characteristic
125	C₃×Q₈	—	2	2	no	—
126	C₃×D₄	—	2	4	no	—
127	C₃×D₄	—	2	2	no	—
128	C₂×C₃×C₄	—	2	2	no	—
129	C₂×C₃×C₄	—	2	2	no	—
130	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
131	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
132	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
133	C₂×C₃×C₄	#237	1	2	yes	—
134	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
135	C₃×C₈	—	4	2	no	—
136	C₃⋊C₈	—	3	2	no	—
137	C₃⋊C₈	—	3	2	no	—
138	C₃⋊C₈	—	6	2	no	—
139	C₃⋊C₈	—	12	2	no	—
140	C₂×C₉	—	2	1	no	—
141	C₂×C₉	—	2	2	no	—
142	C₂×C₉	—	4	2	no	—
143	C₂×C₉	#380	1	1	yes	characteristic
144	#41	—	2	2	no	—
145	#41	—	2	2	no	—
146	C₂×Q₈	#611	1	1	yes	characteristic
147	C₂×D₄	Dic₁₈	1	2	yes	—
148	C₂×D₄	#611	1	1	yes	characteristic
149	C₂²×C₄	C₄×D₉	1	2	yes	—
150	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
151	M₁₆	—	2	2	no	—
152	M₁₆	—	2	2	no	—
153	M₁₆	—	18	4	no	—
154	M₁₆	—	18	2	no	—
155	M₁₆	—	18	2	no	—
156	M₁₆	—	18	2	no	—
157	C₂×C₈	—	2	2	no	—
158	C₂×C₈	—	9	1	no	—
159	C₂×C₈	—	9	1	no	—
160	C₂×C₈	—	9	4	no	—
161	C₂×C₈	—	9	2	no	—
162	C₂×C₈	—	18	4	no	—
163	C₂×C₈	—	18	2	no	—
164	C₂²×C₃	—	2	2	no	—
165	C₂²×C₃	—	4	1	no	—
166	C₂²×C₃	—	4	2	no	—
167	C₂²×C₃	#878	1	2	yes	—
168	C₂²×C₃	C₂×Dic₃⋊C₄	1	1	yes	characteristic
169	C₃×C₄	—	2	2	no	—
170	C₃×C₄	#877	1	1	yes	characteristic
171	C₃×C₄	D₃×C₂²⋊C₄	1	1	yes	characteristic
172	C₃×C₄	#939	1	2	yes	—
173	C₉	#1813	1	1	yes	characteristic, complemented, Sylow
174	C₂³	Dic₉⋊C₄	1	2	yes	—
175	C₂³	C₂×Dic₁₈	1	1	yes	characteristic
176	Q₈	—	2	2	no	—
177	D₄	—	2	4	no	—
178	D₄	—	2	2	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	Dic₉⋊C₄	1	2	yes	—
182	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
183	C₂×C₄	D₄×D₉	1	2	yes	—
184	C₂×C₄	#3699	1	2	yes	—
185	C₂×C₄	C₂×#611	1	1	yes	characteristic
186	C₈	—	4	2	no	—
187	C₈	—	9	2	no	—
188	C₈	—	9	2	no	—
189	C₈	—	18	2	no	—
190	C₈	—	36	2	no	—
191	C₂×C₃	—	2	1	no	—
192	C₂×C₃	—	2	2	no	—
193	C₂×C₃	—	4	2	no	—
194	C₂×C₃	#4942	1	1	yes	characteristic
195	C₂²	—	2	2	no	—
196	C₂²	—	4	1	no	—
197	C₂²	—	4	2	no	—
198	C₂²	#63440	1	2	yes	—
199	C₂²	C₂×Dic₉⋊C₄	1	1	yes	characteristic
200	C₄	—	2	2	no	—
201	C₄	#63439	1	1	yes	characteristic
202	C₄	C₂²⋊C₄×D₉	1	1	yes	characteristic
203	C₄	#63501	1	2	yes	—
204	C₃	#70134	1	1	yes	characteristic
205	C₂	—	2	1	no	—
206	C₂	—	2	2	no	—
207	C₂	—	4	2	no	—
208	C₂	#10588622	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#63510

C₂

yes

maximal, characteristic

C₉×#413

C₂

yes

maximal, characteristic

#10588915

C₂

yes

maximal, characteristic

C₂×#63381

C₂

yes

maximal, complemented

C₉⋊#338

C₂

yes

maximal, complemented

#70134

—

maximal

C₂×C₉×#41

C₂²

yes

characteristic

C₂×C₉×M₁₆

C₂²

yes

—

#63510

—

C₂×#3667

C₄

yes

—

C₂×#3667

C₂²

yes

—

C₂×#3667

C₂²

yes

characteristic

C₂²×C₉⋊C₈

C₄

yes

—

C₂²×C₉⋊C₈

C₂²

yes

—

—

—

—

—

—

D₃

yes

—

—

—

C₉×#41

—

C₉×#41

—

C₂×Q₈×C₉

D₄

yes

characteristic

C₂×D₄×C₉

D₄

yes

characteristic

C₂×D₄×C₉

Q₈

yes

—

C₂²×C₄×C₉

C₂×C₄

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₉×M₁₆

—

C₉×M₁₆

—

C₂×C₈×C₉

—

—

—

—

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

C₂×C₄

yes

—

C₂×C₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₉⋊C₈

D₄

yes

—

#1813

—

Sylow

C₂×C₃×#41

C₂×D₃

yes

characteristic

C₂×C₃×M₁₆

C₂×D₃

yes

—

—

—

—

—

C₂²×C₃⋊C₈

—

C₂²×C₃⋊C₈

—

—

—

—

—

—

C₂³×C₉

C₄⋊C₄

yes

—

C₂³×C₉

C₂×Q₈

yes

characteristic

Q₈×C₉

—

D₄×C₉

—

D₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₄⋊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

—

C₈×C₉

—

C₉⋊C₈

—

C₉⋊C₈

—

C₉⋊C₈

C₂²⋊C₄

yes

—

C₉⋊C₈

C₂²⋊C₄

yes

—

—

—

—

D₉

yes

characteristic

#338

—

C₃×#41

—

C₃×#41

—

C₂×C₃×Q₈

#67

yes

characteristic

C₂×C₃×D₄

Dic₆

yes

—

C₂×C₃×D₄

#67

yes

characteristic

C₂²×C₃×C₄

C₄×D₃

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₃×M₁₆

—

C₃×M₁₆

—

C₂×C₃×C₈

—

—

—

—

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

100

C₂×C₃⋊C₈

—

101

C₂²×C₉

—

102

C₂²×C₉

—

103

C₂²×C₉

—

104

C₂²×C₉

C₂×C₄⋊C₄

yes

characteristic

105

C₂²×C₉

C₂²⋊Q₈

yes

—

106

C₄×C₉

—

107

C₄×C₉

C₂×C₂²⋊C₄

yes

characteristic

108

C₄×C₉

#117

yes

characteristic

109

C₄×C₉

#121

yes

—

110

C₂×#41

C₂×D₉

yes

characteristic

111

#131

—

112

C₂×M₁₆

—

113

C₂×M₁₆

—

114

C₂×M₁₆

—

115

C₂×M₁₆

C₂×D₉

yes

—

116

C₂²×C₈

—

117

C₂²×C₈

—

118

#108

—

119

#101

—

120

#101

—

121

#100

—

122

#100

—

123

C₂³×C₃

Dic₃⋊C₄

yes

—

124

C₂³×C₃

C₂×Dic₆

yes

characteristic

125

C₃×Q₈

—

126

C₃×D₄

—

127

C₃×D₄

—

128

C₂×C₃×C₄

—

129

C₂×C₃×C₄

—

130

C₂×C₃×C₄

Dic₃⋊C₄

yes

—

131

C₂×C₃×C₄

C₂×C₄×D₃

yes

characteristic

132

C₂×C₃×C₄

D₃×D₄

yes

—

133

C₂×C₃×C₄

#237

yes

—

134

C₂×C₃×C₄

C₂×#67

yes

characteristic

135

C₃×C₈

—

136

C₃⋊C₈

—

137

C₃⋊C₈

—

138

C₃⋊C₈

—

139

C₃⋊C₈

—

140

C₂×C₉

—

141

C₂×C₉

—

142

C₂×C₉

—

143

C₂×C₉

#380

yes

characteristic

144

#41

—

145

#41

—

146

C₂×Q₈

#611

yes

characteristic

147

C₂×D₄

Dic₁₈

yes

—

148

C₂×D₄

#611

yes

characteristic

149

C₂²×C₄

C₄×D₉

yes

—

150

C₂²×C₄

C₂²×D₉

yes

characteristic

151

M₁₆

—

152

M₁₆

—

153

M₁₆

—

154

M₁₆

—

155

M₁₆

—

156

M₁₆

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂²×C₃

—

165

C₂²×C₃

—

166

C₂²×C₃

—

167

C₂²×C₃

#878

yes

—

168

C₂²×C₃

C₂×Dic₃⋊C₄

yes

characteristic

169

C₃×C₄

—

170

C₃×C₄

#877

yes

characteristic

171

C₃×C₄

D₃×C₂²⋊C₄

yes

characteristic

172

C₃×C₄

#939

yes

—

173

C₉

#1813

yes

characteristic, complemented, Sylow

174

C₂³

Dic₉⋊C₄

yes

—

175

C₂³

C₂×Dic₁₈

yes

characteristic

176

Q₈

—

177

D₄

—

178

D₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

Dic₉⋊C₄

yes

—

182

C₂×C₄

C₂×C₄×D₉

yes

characteristic

183

C₂×C₄

D₄×D₉

yes

—

184

C₂×C₄

#3699

yes

—

185

C₂×C₄

C₂×#611

yes

characteristic

186

C₈

—

187

C₈

—

188

C₈

—

189

C₈

—

190

C₈

—

191

C₂×C₃

—

192

C₂×C₃

—

193

C₂×C₃

—

194

C₂×C₃

#4942

yes

characteristic

195

C₂²

—

196

C₂²

—

197

C₂²

—

198

C₂²

#63440

yes

—

199

C₂²

C₂×Dic₉⋊C₄

yes

characteristic

200

C₄

—

201

C₄

#63439

yes

characteristic

202

C₄

C₂²⋊C₄×D₉

yes

characteristic

203

C₄

#63501

yes

—

204

C₃

#70134

yes

characteristic

205

C₂

—

206

C₂

—

207

C₂

—

208

C₂

#10588622

yes

characteristic

	subgroup	G/H
center	C₄	#63439
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#413	C₂
socle	C₂×C₃	#4942
prime radical	C₂×C₃×#41	C₂×D₃
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	#413	D₉
hypocenter	C₉	#1813
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #413

subgroup

G/H

center

C₄

#63439

commutator

C₂×C₄×C₉

C₂²×C₄

Frattini

C₂²×C₃×C₄

C₂²×D₃

C₂

C₂×C₃

C₂×C₃×#41

C₂×D₃

cosocle

C₂²×C₄×C₉

C₂³

D₉

C₉

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #413

N	H ≅ G/N	type
4. C₂×#63381	C₂	semidirect
5. C₉⋊#338	C₂	semidirect
173. C₉	#1813	semidirect

H ≅ G/N

type

4. C₂×#63381

C₂

semidirect

5. C₉⋊#338

C₂

semidirect

173. C₉

#1813

semidirect

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

subgroup	index
C₂×#63510	2
C₉×#413	2
#10588915	2
C₂×#63381	2
C₉⋊#338	2
#70134	3

subgroup

index

Subgroups — #11785507

Conjugacy classes of subgroups

Complements

Maximal subgroups