Group #11790773 — subgroups

Subgroups — #11790773

Order 1152.

540 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 134 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	#10589579	C₂	1	1	yes	maximal, characteristic
2	C₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#63384	C₂	1	4	yes	maximal, complemented
4	C₄²×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#70512	—	3	1	no	maximal
6	C₂×#3697	C₂²	1	2	yes	—
7	C₂×C₉×M₁₆	C₂²	1	2	yes	—
8	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
9	#63492	—	2	2	no	—
10	C₂×C₄×Dic₉	—	2	2	no	—
11	C₂×C₄×Dic₉	C₂²	1	2	yes	—
12	#63437	C₄	1	2	yes	complemented
13	#63436	C₄	1	1	yes	characteristic, complemented
14	C₄×D₃₆	—	2	2	no	—
15	#63431	C₄	1	1	yes	characteristic, complemented
16	C₉×C₄⋊C₈	—	2	2	no	—
17	#63384	—	2	8	no	—
18	#5477	—	3	1	no	—
19	C₃×#423	D₃	1	1	yes	characteristic
20	C₂×#825	—	3	4	no	—
21	C₄²×Dic₃	—	3	1	no	—
22	C₂²×C₄×C₉	D₄	1	2	yes	—
23	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
24	C₂×#611	—	2	2	no	—
25	C₂²×Dic₉	—	2	2	no	—
26	#3697	—	2	4	no	—
27	#3697	—	2	4	no	—
28	C₂×D₃₆	—	2	2	no	—
29	C₂×D₃₆	C₂×C₄	1	2	yes	—
30	C₂×C₄×D₉	—	2	2	no	—
31	C₂×Dic₁₈	C₂×C₄	1	2	yes	—
32	C₉×M₁₆	—	2	4	no	—
33	C₂×C₈×C₉	—	2	2	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	(C₂×D₉)⋊C₄	—	2	4	no	—
38	C₄⋊Dic₉	—	2	2	no	—
39	C₄×Dic₉	—	2	8	no	—
40	C₄×Dic₉	—	2	2	no	—
41	C₄×Dic₉	D₄	1	4	yes	complemented
42	#1962	—	9	1	no	Sylow
43	C₂×#235	—	3	2	no	—
44	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
45	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
46	#930	—	6	2	no	—
47	C₂×C₄×Dic₃	—	3	2	no	—
48	C₂×C₄×Dic₃	—	6	2	no	—
49	#875	—	3	2	no	—
50	#874	—	3	1	no	—
51	C₄×D₁₂	—	6	2	no	—
52	#869	—	3	1	no	—
53	C₃×C₄⋊C₈	—	2	2	no	—
54	#825	—	6	8	no	—
55	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×D₉	—	2	2	no	—
57	C₂×C₄×C₉	—	2	4	no	—
58	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
59	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
60	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
62	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₉	#41	1	2	yes	—
64	#611	—	4	4	no	—
65	C₂×Dic₉	—	2	8	no	—
66	C₂×Dic₉	—	2	4	no	—
67	C₂×Dic₉	—	2	2	no	—
68	D₃₆	—	2	4	no	—
69	D₃₆	—	4	4	no	—
70	C₄×D₉	—	4	2	no	—
71	C₄×D₉	—	4	2	no	—
72	Dic₁₈	—	2	4	no	—
73	C₈×C₉	—	4	2	no	—
74	#532	—	9	1	no	—
75	#423	D₉	1	1	yes	characteristic, complemented
76	C₂×#104	—	9	4	no	—
77	C₄³	—	9	1	no	—
78	C₂²×C₃×C₄	D₁₂	1	2	yes	—
79	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
80	C₂×#67	—	6	2	no	—
81	C₂²×Dic₃	—	6	2	no	—
82	#235	—	6	4	no	—
83	#235	—	6	4	no	—
84	C₂×D₁₂	—	3	2	no	—
85	C₂×D₁₂	—	6	2	no	—
86	C₂×C₄×D₃	—	6	2	no	—
87	C₂×Dic₆	—	3	2	no	—
88	C₃×M₁₆	—	2	4	no	—
89	C₂×C₃×C₈	—	2	2	no	—
90	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
91	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
92	C₃×C₄²	#67	1	2	yes	—
93	(C₂×D₃)⋊C₄	—	6	4	no	—
94	C₄⋊Dic₃	—	6	2	no	—
95	C₄×Dic₃	—	3	4	no	—
96	C₄×Dic₃	—	6	8	no	—
97	C₄×Dic₃	—	6	2	no	—
98	C₂²×C₉	—	2	2	no	—
99	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₉	#121	1	2	yes	—
101	C₂×D₉	—	4	2	no	—
102	C₂×D₉	—	4	4	no	—
103	C₄×C₉	—	2	2	no	—
104	C₄×C₉	#104	1	4	yes	complemented
105	C₄×C₉	C₄×D₄	1	2	yes	—
106	C₄×C₉	#124	1	1	yes	characteristic
107	C₄×C₉	#127	1	1	yes	characteristic
108	Dic₉	—	2	8	no	—
109	Dic₉	—	4	2	no	—
110	C₂×#41	—	9	2	no	—
111	C₂×M₁₆	C₂×D₉	1	2	yes	—
112	C₄⋊Q₈	—	9	1	no	—
113	#127	—	9	1	no	—
114	#124	—	9	2	no	—
115	#121	—	18	2	no	—
116	C₄×D₄	—	18	2	no	—
117	C₂×C₄²	—	9	2	no	—
118	C₂×C₄²	—	18	2	no	—
119	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
120	C₄⋊C₈	—	2	2	no	—
121	#104	—	18	8	no	—
122	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
123	C₂²×D₃	—	6	2	no	—
124	C₂×C₃×C₄	—	2	4	no	—
125	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
126	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
127	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
128	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
129	C₂×C₃×C₄	#239	1	2	yes	—
130	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
131	#67	—	12	4	no	—
132	C₂×Dic₃	—	6	8	no	—
133	C₂×Dic₃	—	6	4	no	—
134	C₂×Dic₃	—	6	2	no	—
135	D₁₂	—	6	4	no	—
136	D₁₂	—	12	4	no	—
137	C₄×D₃	—	12	2	no	—
138	C₄×D₃	—	12	2	no	—
139	Dic₆	—	6	4	no	—
140	C₃×C₈	—	4	2	no	—
141	C₂×C₉	—	2	2	no	—
142	C₂×C₉	#390	1	1	yes	characteristic
143	C₂×C₉	C₂×#104	1	2	yes	—
144	D₉	—	8	2	no	—
145	#41	—	18	4	no	—
146	#41	—	18	4	no	—
147	C₂×Q₈	—	9	2	no	—
148	C₂×D₄	—	9	2	no	—
149	C₂×D₄	—	18	2	no	—
150	C₂×D₄	—	18	2	no	—
151	C₂²×C₄	—	18	2	no	—
152	C₂²×C₄	—	18	2	no	—
153	C₂²×C₄	D₃₆	1	2	yes	—
154	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
155	M₁₆	—	2	4	no	—
156	C₂×C₈	—	2	2	no	—
157	C₄⋊C₄	—	18	2	no	—
158	C₂²⋊C₄	—	18	4	no	—
159	C₄²	—	9	4	no	—
160	C₄²	—	18	8	no	—
161	C₄²	—	18	2	no	—
162	C₄²	C₄×D₉	1	1	yes	characteristic
163	C₄²	C₄×D₉	1	1	yes	characteristic
164	C₄²	#611	1	2	yes	—
165	C₂²×C₃	—	2	2	no	—
166	C₂²×C₃	#895	1	2	yes	—
167	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
168	C₂×D₃	—	12	4	no	—
169	C₂×D₃	—	12	2	no	—
170	C₃×C₄	—	2	2	no	—
171	C₃×C₄	#825	1	4	yes	—
172	C₃×C₄	#893	1	2	yes	—
173	C₃×C₄	#940	1	1	yes	characteristic
174	C₃×C₄	#947	1	1	yes	characteristic
175	Dic₃	—	6	8	no	—
176	Dic₃	—	12	2	no	—
177	C₉	#1962	1	1	yes	characteristic, complemented, Sylow
178	C₂³	—	18	2	no	—
179	C₂³	C₂×D₃₆	1	1	yes	characteristic
180	Q₈	—	18	4	no	—
181	D₄	—	18	4	no	—
182	D₄	—	36	4	no	—
183	D₄	—	36	4	no	—
184	C₂×C₄	—	2	4	no	—
185	C₂×C₄	—	18	8	no	—
186	C₂×C₄	—	18	4	no	—
187	C₂×C₄	—	18	2	no	—
188	C₂×C₄	—	36	2	no	—
189	C₂×C₄	—	36	2	no	—
190	C₂×C₄	(C₂×D₉)⋊C₄	1	2	yes	—
191	C₂×C₄	(C₂×D₉)⋊C₄	1	2	yes	—
192	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
193	C₂×C₄	D₄×D₉	1	2	yes	—
194	C₂×C₄	#3701	1	2	yes	—
195	C₂×C₄	C₂×#611	1	1	yes	characteristic
196	C₈	—	4	2	no	—
197	C₂×C₃	—	2	2	no	—
198	C₂×C₃	#4988	1	1	yes	characteristic
199	C₂×C₃	C₂×#825	1	2	yes	—
200	D₃	—	24	2	no	—
201	C₂²	—	2	2	no	—
202	C₂²	—	36	4	no	—
203	C₂²	—	36	2	no	—
204	C₂²	#63457	1	2	yes	—
205	C₂²	C₂×(C₂×D₉)⋊C₄	1	1	yes	characteristic
206	C₄	—	2	2	no	—
207	C₄	—	18	8	no	—
208	C₄	—	36	2	no	—
209	C₄	#63384	1	4	yes	complemented
210	C₄	#63455	1	2	yes	—
211	C₄	#63502	1	1	yes	characteristic
212	C₄	#63509	1	1	yes	characteristic
213	C₃	#70512	1	1	yes	characteristic
214	C₂	—	2	2	no	—
215	C₂	—	72	2	no	—
216	C₂	#10588668	1	1	yes	characteristic
217	C₂	C₂×#63384	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#10589579

C₂

yes

maximal, characteristic

C₉×#423

C₂

yes

maximal, characteristic, complemented

C₂×#63384

C₂

yes

maximal, complemented

C₄²×Dic₉

C₂

yes

maximal, characteristic, complemented

#70512

—

maximal

C₂×#3697

C₂²

yes

—

C₂×C₉×M₁₆

C₂²

yes

—

C₂×C₄²×C₉

C₂²

yes

characteristic

#63492

—

C₂×C₄×Dic₉

—

C₂×C₄×Dic₉

C₂²

yes

—

#63437

C₄

yes

complemented

#63436

C₄

yes

characteristic, complemented

C₄×D₃₆

—

#63431

C₄

yes

characteristic, complemented

C₉×C₄⋊C₈

—

#63384

—

#5477

—

C₃×#423

D₃

yes

characteristic

C₂×#825

—

C₄²×Dic₃

—

C₂²×C₄×C₉

D₄

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂×#611

—

C₂²×Dic₉

—

#3697

—

#3697

—

C₂×D₃₆

—

C₂×D₃₆

C₂×C₄

yes

—

C₂×C₄×D₉

—

C₂×Dic₁₈

C₂×C₄

yes

—

C₉×M₁₆

—

C₂×C₈×C₉

—

C₄²×C₉

C₂×C₄

yes

characteristic

C₄²×C₉

C₂×C₄

yes

characteristic

C₄²×C₉

D₄

yes

—

(C₂×D₉)⋊C₄

—

C₄⋊Dic₉

—

C₄×Dic₉

—

C₄×Dic₉

—

C₄×Dic₉

D₄

yes

—

—

C₂×C₃×M₁₆

C₂×D₃

yes

—

C₂×C₃×C₄²

C₂×D₃

yes

characteristic

#930

—

C₂×C₄×Dic₃

—

C₂×C₄×Dic₃

—

#875

—

#874

—

C₄×D₁₂

—

#869

—

C₃×C₄⋊C₈

—

#825

—

C₂³×C₉

C₂×D₄

yes

characteristic

C₂²×D₉

—

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

—

#611

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

D₃₆

—

D₃₆

—

C₄×D₉

—

C₄×D₉

—

Dic₁₈

—

C₈×C₉

—

#532

—

#423

D₉

yes

characteristic, complemented

C₂×#104

—

C₄³

—

C₂²×C₃×C₄

D₁₂

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂×#67

—

C₂²×Dic₃

—

#235

—

#235

—

C₂×D₁₂

—

C₂×D₁₂

—

C₂×C₄×D₃

—

C₂×Dic₆

—

C₃×M₁₆

—

C₂×C₃×C₈

—

C₃×C₄²

C₄×D₃

yes

characteristic

C₃×C₄²

C₄×D₃

yes

characteristic

C₃×C₄²

#67

yes

—

(C₂×D₃)⋊C₄

—

C₄⋊Dic₃

—

C₄×Dic₃

—

C₄×Dic₃

—

C₄×Dic₃

—

C₂²×C₉

—

C₂²×C₉

C₂×C₂²⋊C₄

yes

characteristic

100

C₂²×C₉

#121

yes

—

101

C₂×D₉

—

102

C₂×D₉

—

103

C₄×C₉

—

104

C₄×C₉

#104

yes

complemented

105

C₄×C₉

C₄×D₄

yes

—

106

C₄×C₉

#124

yes

characteristic

107

C₄×C₉

#127

yes

characteristic

108

Dic₉

—

109

Dic₉

—

110

C₂×#41

—

111

C₂×M₁₆

C₂×D₉

yes

—

112

C₄⋊Q₈

—

113

#127

—

114

#124

—

115

#121

—

116

C₄×D₄

—

117

C₂×C₄²

—

118

C₂×C₄²

—

119

C₂×C₄²

C₂×D₉

yes

characteristic

120

C₄⋊C₈

—

121

#104

—

122

C₂³×C₃

C₂×D₁₂

yes

characteristic

123

C₂²×D₃

—

124

C₂×C₃×C₄

—

125

C₂×C₃×C₄

(C₂×D₃)⋊C₄

yes

—

126

C₂×C₃×C₄

(C₂×D₃)⋊C₄

yes

—

127

C₂×C₃×C₄

C₂×C₄×D₃

yes

characteristic

128

C₂×C₃×C₄

D₃×D₄

yes

—

129

C₂×C₃×C₄

#239

yes

—

130

C₂×C₃×C₄

C₂×#67

yes

characteristic

131

#67

—

132

C₂×Dic₃

—

133

C₂×Dic₃

—

134

C₂×Dic₃

—

135

D₁₂

—

136

D₁₂

—

137

C₄×D₃

—

138

C₄×D₃

—

139

Dic₆

—

140

C₃×C₈

—

141

C₂×C₉

—

142

C₂×C₉

#390

yes

characteristic

143

C₂×C₉

C₂×#104

yes

—

144

D₉

—

145

#41

—

146

#41

—

147

C₂×Q₈

—

148

C₂×D₄

—

149

C₂×D₄

—

150

C₂×D₄

—

151

C₂²×C₄

—

152

C₂²×C₄

—

153

C₂²×C₄

D₃₆

yes

—

154

C₂²×C₄

C₂²×D₉

yes

characteristic

155

M₁₆

—

156

C₂×C₈

—

157

C₄⋊C₄

—

158

C₂²⋊C₄

—

159

C₄²

—

160

C₄²

—

161

C₄²

—

162

C₄²

C₄×D₉

yes

characteristic

163

C₄²

C₄×D₉

yes

characteristic

164

C₄²

#611

yes

—

165

C₂²×C₃

—

166

C₂²×C₃

#895

yes

—

167

C₂²×C₃

C₂×(C₂×D₃)⋊C₄

yes

characteristic

168

C₂×D₃

—

169

C₂×D₃

—

170

C₃×C₄

—

171

C₃×C₄

#825

yes

—

172

C₃×C₄

#893

yes

—

173

C₃×C₄

#940

yes

characteristic

174

C₃×C₄

#947

yes

characteristic

175

Dic₃

—

176

Dic₃

—

177

C₉

#1962

yes

characteristic, complemented, Sylow

178

C₂³

—

179

C₂³

C₂×D₃₆

yes

characteristic

180

Q₈

—

181

D₄

—

182

D₄

—

183

D₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

(C₂×D₉)⋊C₄

yes

—

191

C₂×C₄

(C₂×D₉)⋊C₄

yes

—

192

C₂×C₄

C₂×C₄×D₉

yes

characteristic

193

C₂×C₄

D₄×D₉

yes

—

194

C₂×C₄

#3701

yes

—

195

C₂×C₄

C₂×#611

yes

characteristic

196

C₈

—

197

C₂×C₃

—

198

C₂×C₃

#4988

yes

characteristic

199

C₂×C₃

C₂×#825

yes

—

200

D₃

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

204

C₂²

#63457

yes

—

205

C₂²

C₂×(C₂×D₉)⋊C₄

yes

characteristic

206

C₄

—

207

C₄

—

208

C₄

—

209

C₄

#63384

yes

complemented

210

C₄

#63455

yes

—

211

C₄

#63502

yes

characteristic

212

C₄

#63509

yes

characteristic

213

C₃

#70512

yes

characteristic

214

C₂

—

215

C₂

—

216

C₂

#10588668

yes

characteristic

217

C₂

C₂×#63384

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×#611
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#423	C₂
socle	C₂²×C₃	C₂×(C₂×D₃)⋊C₄
prime radical	#10589579	C₂
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	#423	D₉
hypocenter	C₉	#1962
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂×C₄

C₂×#611

commutator

C₂×C₄×C₉

C₂²×C₄

Frattini

C₂²×C₃×C₄

C₂²×D₃

Fitting

C₉×#423

C₂

socle

C₂²×C₃

C₂×(C₂×D₃)⋊C₄

prime radical

#10589579

C₂

cosocle

C₂²×C₄×C₉

C₂³

D₉

C₉

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
2. C₉×#423	C₂	semidirect
3. C₂×#63384	C₂	semidirect
4. C₄²×Dic₉	C₂	semidirect
12. #63437	C₄	semidirect
13. #63436	C₄	semidirect
15. #63431	C₄	semidirect
41. C₄×Dic₉	D₄	semidirect
75. #423	D₉	semidirect
104. C₄×C₉	#104	semidirect
177. C₉	#1962	semidirect
209. C₄	#63384	semidirect

H ≅ G/N

type

2. C₉×#423

C₂

semidirect

3. C₂×#63384

C₂

semidirect

4. C₄²×Dic₉

C₂

semidirect

12. #63437

C₄

semidirect

13. #63436

C₄

semidirect

15. #63431

C₄

semidirect

41. C₄×Dic₉

D₄

semidirect

75. #423

D₉

semidirect

104. C₄×C₉

#104

semidirect

177. C₉

#1962

semidirect

209. C₄

#63384

semidirect

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

subgroup	index
#10589579	2
C₉×#423	2
C₂×#63384	2
C₄²×Dic₉	2
#70512	3

subgroup

index

C₄²×Dic₉

Subgroups — #11790773

Conjugacy classes of subgroups

Complements

Maximal subgroups