Group #11766795 — subgroups

Subgroups — C₉×#2074 #11766795

Order 1152.

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

normal subgroups only

This group has 333 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	C₂×C₉×#103	C₂	1	2	yes	maximal
2	C₉×#391	C₂	1	1	yes	maximal, characteristic
3	C₉×#382	C₂	1	1	yes	maximal, characteristic
4	C₉×#340	C₂	1	2	yes	maximal
5	C₉×#336	C₂	1	1	yes	maximal, characteristic
6	C₃×#2074	C₃	1	1	yes	maximal, characteristic
7	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₉	C₂²	1	2	yes	—
9	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
12	C₉×#103	—	2	4	no	—
13	C₉×#95	—	2	2	no	—
14	C₉×#95	—	2	2	no	—
15	C₂×C₃×#103	C₂×C₃	1	2	yes	—
16	C₃×#391	C₂×C₃	1	1	yes	characteristic
17	C₃×#382	C₂×C₃	1	1	yes	characteristic
18	C₃×#340	C₂×C₃	1	2	yes	—
19	C₃×#336	C₂×C₃	1	1	yes	characteristic
20	C₂×Q₈×C₉	—	2	1	no	—
21	C₂×Q₈×C₉	—	2	2	no	—
22	C₂×Q₈×C₉	—	2	2	no	—
23	C₂×Q₈×C₉	D₄	1	2	yes	—
24	C₂²×C₄×C₉	—	2	1	no	—
25	C₂²×C₄×C₉	—	2	2	no	—
26	C₂²×C₄×C₉	—	2	1	no	—
27	C₂²×C₄×C₉	D₄	1	2	yes	—
28	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
29	C₂×C₈×C₉	—	2	2	no	—
30	C₂×C₈×C₉	—	2	2	no	—
31	C₂×C₈×C₉	—	2	2	no	—
32	C₉×C₄⋊C₄	—	2	2	no	—
33	C₉×C₄⋊C₄	—	2	2	no	—
34	C₉×C₄⋊C₄	—	2	2	no	—
35	C₄²×C₉	—	2	2	no	—
36	#2074	C₉	1	1	yes	characteristic, direct product factor, Sylow
37	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
38	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
39	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
40	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
41	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
42	C₃×#103	—	2	4	no	—
43	C₃×#95	—	2	2	no	—
44	C₃×#95	—	2	2	no	—
45	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
46	Q₈×C₉	—	2	4	no	—
47	Q₈×C₉	—	4	2	no	—
48	C₂×C₄×C₉	—	2	2	no	—
49	C₂×C₄×C₉	—	2	2	no	—
50	C₂×C₄×C₉	—	2	2	no	—
51	C₂×C₄×C₉	—	2	2	no	—
52	C₂×C₄×C₉	—	4	1	no	—
53	C₂×C₄×C₉	—	4	1	no	—
54	C₂×C₄×C₉	—	4	2	no	—
55	C₂×C₄×C₉	—	4	1	no	—
56	C₂×C₄×C₉	—	4	2	no	—
57	C₂×C₄×C₉	—	4	2	no	—
58	C₂×C₄×C₉	—	4	2	no	—
59	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
60	C₂×C₄×C₉	#41	1	2	yes	—
61	C₂×C₄×C₉	#41	1	2	yes	—
62	C₂×C₄×C₉	#41	1	1	yes	characteristic
63	C₈×C₉	—	4	2	no	—
64	C₂×#103	C₂×C₉	1	2	yes	—
65	#391	C₂×C₉	1	1	yes	characteristic
66	#382	C₂×C₉	1	1	yes	characteristic
67	#340	C₂×C₉	1	2	yes	—
68	#336	C₂×C₉	1	1	yes	characteristic
69	C₂×C₃×Q₈	—	2	1	no	—
70	C₂×C₃×Q₈	—	2	2	no	—
71	C₂×C₃×Q₈	—	2	2	no	—
72	C₂×C₃×Q₈	C₃×D₄	1	2	yes	—
73	C₂²×C₃×C₄	—	2	1	no	—
74	C₂²×C₃×C₄	—	2	2	no	—
75	C₂²×C₃×C₄	—	2	1	no	—
76	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
77	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
78	C₂×C₃×C₈	—	2	2	no	—
79	C₂×C₃×C₈	—	2	2	no	—
80	C₂×C₃×C₈	—	2	2	no	—
81	C₃×C₄⋊C₄	—	2	2	no	—
82	C₃×C₄⋊C₄	—	2	2	no	—
83	C₃×C₄⋊C₄	—	2	2	no	—
84	C₃×C₄²	—	2	2	no	—
85	C₂²×C₉	#121	1	1	yes	characteristic
86	C₂²×C₉	#123	1	1	yes	characteristic
87	C₂²×C₉	#124	1	1	yes	characteristic
88	C₂²×C₉	#135	1	2	yes	—
89	C₂²×C₉	#137	1	2	yes	—
90	C₄×C₉	—	4	2	no	—
91	C₄×C₉	—	4	2	no	—
92	C₄×C₉	—	8	2	no	—
93	C₄×C₉	—	8	1	no	—
94	C₄×C₉	#123	1	2	yes	—
95	C₄×C₉	#126	1	2	yes	—
96	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
97	C₂²×C₈	C₂²×C₉	1	2	yes	—
98	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
99	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
100	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
101	#103	—	2	4	no	—
102	#95	—	2	2	no	—
103	#95	—	2	2	no	—
104	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
105	C₃×Q₈	—	2	4	no	—
106	C₃×Q₈	—	4	2	no	—
107	C₂×C₃×C₄	—	2	2	no	—
108	C₂×C₃×C₄	—	2	2	no	—
109	C₂×C₃×C₄	—	2	2	no	—
110	C₂×C₃×C₄	—	2	2	no	—
111	C₂×C₃×C₄	—	4	1	no	—
112	C₂×C₃×C₄	—	4	1	no	—
113	C₂×C₃×C₄	—	4	2	no	—
114	C₂×C₃×C₄	—	4	1	no	—
115	C₂×C₃×C₄	—	4	2	no	—
116	C₂×C₃×C₄	—	4	2	no	—
117	C₂×C₃×C₄	—	4	2	no	—
118	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
119	C₂×C₃×C₄	C₃×#41	1	2	yes	—
120	C₂×C₃×C₄	C₃×#41	1	2	yes	—
121	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
122	C₃×C₈	—	4	2	no	—
123	C₂×C₉	#397	1	1	yes	characteristic
124	C₂×C₉	#464	1	2	yes	—
125	C₂×C₉	#485	1	2	yes	—
126	C₂×C₉	#488	1	1	yes	characteristic
127	C₂×C₉	#491	1	1	yes	characteristic
128	C₂×Q₈	—	2	1	no	—
129	C₂×Q₈	—	2	2	no	—
130	C₂×Q₈	—	2	2	no	—
131	C₂×Q₈	D₄×C₉	1	2	yes	—
132	C₂²×C₄	—	2	1	no	—
133	C₂²×C₄	—	2	2	no	—
134	C₂²×C₄	—	2	1	no	—
135	C₂²×C₄	D₄×C₉	1	2	yes	—
136	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
137	C₂×C₈	—	2	2	no	—
138	C₂×C₈	—	2	2	no	—
139	C₂×C₈	—	2	2	no	—
140	C₄⋊C₄	—	2	2	no	—
141	C₄⋊C₄	—	2	2	no	—
142	C₄⋊C₄	—	2	2	no	—
143	C₄²	—	2	2	no	—
144	C₂²×C₃	C₃×#121	1	1	yes	characteristic
145	C₂²×C₃	C₃×#123	1	1	yes	characteristic
146	C₂²×C₃	C₃×#124	1	1	yes	characteristic
147	C₂²×C₃	C₃×#135	1	2	yes	—
148	C₂²×C₃	C₃×#137	1	2	yes	—
149	C₃×C₄	—	4	2	no	—
150	C₃×C₄	—	4	2	no	—
151	C₃×C₄	—	8	2	no	—
152	C₃×C₄	—	8	1	no	—
153	C₃×C₄	C₃×#123	1	2	yes	—
154	C₃×C₄	C₃×#126	1	2	yes	—
155	C₉	#2074	1	1	yes	characteristic, direct product factor, Sylow
156	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
157	Q₈	—	2	4	no	—
158	Q₈	—	4	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	4	1	no	—
164	C₂×C₄	—	4	1	no	—
165	C₂×C₄	—	4	2	no	—
166	C₂×C₄	—	4	1	no	—
167	C₂×C₄	—	4	2	no	—
168	C₂×C₄	—	4	2	no	—
169	C₂×C₄	—	4	2	no	—
170	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
171	C₂×C₄	C₉×#41	1	2	yes	—
172	C₂×C₄	C₉×#41	1	2	yes	—
173	C₂×C₄	C₉×#41	1	1	yes	characteristic
174	C₈	—	4	2	no	—
175	C₂×C₃	C₃×#397	1	1	yes	characteristic
176	C₂×C₃	C₃×#464	1	2	yes	—
177	C₂×C₃	C₃×#485	1	2	yes	—
178	C₂×C₃	C₃×#488	1	1	yes	characteristic
179	C₂×C₃	C₃×#491	1	1	yes	characteristic
180	C₂²	C₉×#121	1	1	yes	characteristic
181	C₂²	C₉×#123	1	1	yes	characteristic
182	C₂²	C₉×#124	1	1	yes	characteristic
183	C₂²	C₉×#135	1	2	yes	—
184	C₂²	C₉×#137	1	2	yes	—
185	C₄	—	4	2	no	—
186	C₄	—	4	2	no	—
187	C₄	—	8	2	no	—
188	C₄	—	8	1	no	—
189	C₄	C₉×#123	1	2	yes	—
190	C₄	C₉×#126	1	2	yes	—
191	C₃	C₃×#2074	1	1	yes	characteristic
192	C₂	C₉×#397	1	1	yes	characteristic
193	C₂	C₉×#464	1	2	yes	—
194	C₂	C₉×#485	1	2	yes	—
195	C₂	C₉×#488	1	1	yes	characteristic
196	C₂	C₉×#491	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₉×#103

C₂

yes

maximal

C₉×#391

C₂

yes

maximal, characteristic

C₉×#382

C₂

yes

maximal, characteristic

C₉×#340

C₂

yes

maximal

C₉×#336

C₂

yes

maximal, characteristic

C₃×#2074

C₃

yes

maximal, characteristic

C₂²×Q₈×C₉

C₂²

yes

characteristic

C₂²×C₈×C₉

C₂²

yes

—

C₂×C₉×C₄⋊C₄

C₂²

yes

—

C₂×C₉×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₄²×C₉

C₂²

yes

characteristic

C₉×#103

—

C₉×#95

—

C₉×#95

—

C₂×C₃×#103

C₂×C₃

yes

—

C₃×#391

C₂×C₃

yes

characteristic

C₃×#382

C₂×C₃

yes

characteristic

C₃×#340

C₂×C₃

yes

—

C₃×#336

C₂×C₃

yes

characteristic

C₂×Q₈×C₉

—

C₂×Q₈×C₉

—

C₂×Q₈×C₉

—

C₂×Q₈×C₉

D₄

yes

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

D₄

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂×C₈×C₉

—

C₂×C₈×C₉

—

C₂×C₈×C₉

—

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

—

C₄²×C₉

—

#2074

C₉

yes

characteristic, direct product factor, Sylow

C₂²×C₃×Q₈

C₂²×C₃

yes

characteristic

C₂²×C₃×C₈

C₂²×C₃

yes

—

C₂×C₃×C₄⋊C₄

C₂²×C₃

yes

—

C₂×C₃×C₄⋊C₄

C₂²×C₃

yes

characteristic

C₂×C₃×C₄²

C₂²×C₃

yes

characteristic

C₃×#103

—

C₃×#95

—

C₃×#95

—

C₂³×C₉

C₂×D₄

yes

characteristic

Q₈×C₉

—

Q₈×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

#41

yes

—

C₂×C₄×C₉

#41

yes

—

C₂×C₄×C₉

#41

yes

characteristic

C₈×C₉

—

C₂×#103

C₂×C₉

yes

—

#391

C₂×C₉

yes

characteristic

#382

C₂×C₉

yes

characteristic

#340

C₂×C₉

yes

—

#336

C₂×C₉

yes

characteristic

C₂×C₃×Q₈

—

C₂×C₃×Q₈

—

C₂×C₃×Q₈

—

C₂×C₃×Q₈

C₃×D₄

yes

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

C₃×D₄

yes

—

C₂²×C₃×C₄

C₂³×C₃

yes

characteristic

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄²

—

C₂²×C₉

yes

C₂²×C₉

yes

C₂²×C₉

yes

C₂²×C₉

yes

—

C₂²×C₉

#137

yes

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

#123

yes

—

C₄×C₉

#126

yes

—

C₂²×Q₈

C₂²×C₉

yes

characteristic

C₂²×C₈

C₂²×C₉

yes

—

C₂×C₄⋊C₄

C₂²×C₉

yes

characteristic

C₂×C₄⋊C₄

C₂²×C₉

yes

—

100

C₂×C₄²

C₂²×C₉

yes

characteristic

101

#103

—

102

#95

—

103

#95

—

104

C₂³×C₃

C₂×C₃×D₄

yes

characteristic

105

C₃×Q₈

—

106

C₃×Q₈

—

107

C₂×C₃×C₄

—

108

C₂×C₃×C₄

—

109

C₂×C₃×C₄

—

110

C₂×C₃×C₄

—

111

C₂×C₃×C₄

—

112

C₂×C₃×C₄

—

113

C₂×C₃×C₄

—

114

C₂×C₃×C₄

—

115

C₂×C₃×C₄

—

116

C₂×C₃×C₄

—

117

C₂×C₃×C₄

—

118

C₂×C₃×C₄

C₂×C₃×D₄

yes

characteristic

119

C₂×C₃×C₄

C₃×#41

yes

—

120

C₂×C₃×C₄

C₃×#41

yes

—

121

C₂×C₃×C₄

C₃×#41

yes

characteristic

122

C₃×C₈

—

123

C₂×C₉

#397

yes

characteristic

124

C₂×C₉

#464

yes

—

125

C₂×C₉

#485

yes

—

126

C₂×C₉

#488

yes

characteristic

127

C₂×C₉

#491

yes

characteristic

128

C₂×Q₈

—

129

C₂×Q₈

—

130

C₂×Q₈

—

131

C₂×Q₈

D₄×C₉

yes

—

132

C₂²×C₄

—

133

C₂²×C₄

—

134

C₂²×C₄

—

135

C₂²×C₄

D₄×C₉

yes

—

136

C₂²×C₄

C₂³×C₉

yes

characteristic

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄⋊C₄

—

143

C₄²

—

144

C₂²×C₃

C₃×#121

yes

characteristic

145

C₂²×C₃

C₃×#123

yes

characteristic

146

C₂²×C₃

C₃×#124

yes

characteristic

147

C₂²×C₃

C₃×#135

yes

—

148

C₂²×C₃

C₃×#137

yes

—

149

C₃×C₄

—

150

C₃×C₄

—

151

C₃×C₄

—

152

C₃×C₄

—

153

C₃×C₄

C₃×#123

yes

—

154

C₃×C₄

C₃×#126

yes

—

155

C₉

#2074

yes

characteristic, direct product factor, Sylow

156

C₂³

C₂×D₄×C₉

yes

characteristic

157

Q₈

—

158

Q₈

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

C₂×D₄×C₉

yes

characteristic

171

C₂×C₄

C₉×#41

yes

—

172

C₂×C₄

C₉×#41

yes

—

173

C₂×C₄

C₉×#41

yes

characteristic

174

C₈

—

175

C₂×C₃

C₃×#397

yes

characteristic

176

C₂×C₃

C₃×#464

yes

—

177

C₂×C₃

C₃×#485

yes

—

178

C₂×C₃

C₃×#488

yes

characteristic

179

C₂×C₃

C₃×#491

yes

characteristic

180

C₂²

C₉×#121

yes

characteristic

181

C₂²

C₉×#123

yes

characteristic

182

C₂²

C₉×#124

yes

characteristic

183

C₂²

C₉×#135

yes

—

184

C₂²

C₉×#137

yes

—

185

C₄

—

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

C₉×#123

yes

—

190

C₄

C₉×#126

yes

—

191

C₃

C₃×#2074

yes

characteristic

192

C₂

C₉×#397

yes

characteristic

193

C₂

C₉×#464

yes

—

194

C₂

C₉×#485

yes

—

195

C₂

C₉×#488

yes

characteristic

196

C₂

C₉×#491

yes

characteristic

	subgroup	G/H
center	C₂³×C₉	C₂×D₄
commutator	C₂²×C₄	C₂³×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle, prime radical	C₂³×C₃	C₂×C₃×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ C₂×C₄²×C₉ ◁ G

subgroup

G/H

center

C₂³×C₉

C₂×D₄

commutator

C₂²×C₄

C₂³×C₉

Frattini, cosocle

C₂²×C₃×C₄

C₂³×C₃

socle, prime radical

C₂³×C₃

C₂×C₃×D₄

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₉ ◁ C₂×C₄²×C₉ ◁ G

N	H ≅ G/N	type
36. #2074	C₉	direct (N × H)
155. C₉	#2074	direct (N × H)

H ≅ G/N

type

36. #2074

C₉

direct (N × H)

155. C₉

#2074

direct (N × H)

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

subgroup	index
C₂×C₉×#103	2
C₉×#391	2
C₉×#382	2
C₉×#340	2
C₉×#336	2
C₃×#2074	3

subgroup

index

C₂×C₉×#103

Subgroups — C₉×#2074 #11766795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#2074 #11766795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2074 #11766795