Group #11766766 — subgroups

Subgroups — C₉×#2045 #11766766

Order 1152.

444 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 126 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	C₂²×C₉×D₈	C₂	1	1	yes	maximal, characteristic
2	C₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#418	C₂	1	2	yes	maximal, complemented
4	C₂×C₉×#100	C₂	1	2	yes	maximal, complemented
5	C₉×#341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2045	C₃	1	1	yes	maximal, characteristic
7	C₂²×D₄×C₉	C₂²	1	2	yes	—
8	C₂×C₉×D₈	—	2	4	no	—
9	C₂×C₉×D₈	—	2	2	no	—
10	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₉×M₁₆	C₂²	1	2	yes	—
12	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
13	C₉×#117	C₂²	1	1	yes	characteristic
14	C₉×C₄⋊C₈	—	2	2	no	—
15	C₉×#102	—	2	4	no	—
16	C₉×#100	—	2	4	no	—
17	C₂²×C₃×D₈	C₂×C₃	1	1	yes	characteristic
18	C₃×#424	C₂×C₃	1	1	yes	characteristic
19	C₃×#418	C₂×C₃	1	2	yes	—
20	C₂×C₃×#100	C₂×C₃	1	2	yes	—
21	C₃×#341	C₂×C₃	1	1	yes	characteristic
22	C₂⁴×C₉	—	2	2	no	—
23	C₂×D₄×C₉	—	2	2	no	—
24	C₂×D₄×C₉	—	2	2	no	—
25	C₂×D₄×C₉	—	2	2	no	—
26	C₂×D₄×C₉	—	2	2	no	—
27	C₂×D₄×C₉	—	2	2	no	—
28	C₂×D₄×C₉	D₄	1	4	yes	—
29	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
30	C₉×D₈	—	2	8	no	—
31	C₉×M₁₆	—	2	2	no	—
32	C₉×M₁₆	—	2	2	no	—
33	C₉×M₁₆	—	2	2	no	—
34	C₂×C₈×C₉	—	2	2	no	—
35	C₂×C₈×C₉	—	2	2	no	—
36	C₂×C₈×C₉	—	2	1	no	—
37	C₂×C₈×C₉	D₄	1	2	yes	—
38	C₉×C₄⋊C₄	D₄	1	2	yes	—
39	C₉×C₂²⋊C₄	—	2	1	no	—
40	C₄²×C₉	—	2	1	no	—
41	#2045	C₉	1	1	yes	characteristic, direct product factor, Sylow
42	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
43	C₂×C₃×D₈	—	2	4	no	—
44	C₂×C₃×D₈	—	2	2	no	—
45	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
46	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
47	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
48	C₃×#117	C₂²×C₃	1	1	yes	characteristic
49	C₃×C₄⋊C₈	—	2	2	no	—
50	C₃×#102	—	2	4	no	—
51	C₃×#100	—	2	4	no	—
52	C₂³×C₉	—	2	4	no	—
53	C₂³×C₉	—	4	2	no	—
54	C₂³×C₉	—	4	2	no	—
55	C₂³×C₉	—	8	4	no	—
56	C₂³×C₉	#41	1	1	yes	characteristic
57	D₄×C₉	—	2	4	no	—
58	D₄×C₉	—	2	4	no	—
59	D₄×C₉	—	4	2	no	—
60	D₄×C₉	—	4	2	no	—
61	C₂×C₄×C₉	—	2	2	no	—
62	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
63	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
64	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
65	C₂×C₄×C₉	#41	1	2	yes	—
66	C₈×C₉	—	2	2	no	—
67	C₈×C₉	—	4	1	no	—
68	C₈×C₉	—	4	2	no	—
69	C₂²×D₈	C₂×C₉	1	1	yes	characteristic
70	#424	C₂×C₉	1	1	yes	characteristic, complemented
71	#418	C₂×C₉	1	2	yes	complemented
72	C₂×#100	C₂×C₉	1	2	yes	complemented
73	#341	C₂×C₉	1	1	yes	characteristic, complemented
74	C₂⁴×C₃	—	2	2	no	—
75	C₂×C₃×D₄	—	2	2	no	—
76	C₂×C₃×D₄	—	2	2	no	—
77	C₂×C₃×D₄	—	2	2	no	—
78	C₂×C₃×D₄	—	2	2	no	—
79	C₂×C₃×D₄	—	2	2	no	—
80	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
81	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
82	C₃×D₈	—	2	8	no	—
83	C₃×M₁₆	—	2	2	no	—
84	C₃×M₁₆	—	2	2	no	—
85	C₃×M₁₆	—	2	2	no	—
86	C₂×C₃×C₈	—	2	2	no	—
87	C₂×C₃×C₈	—	2	2	no	—
88	C₂×C₃×C₈	—	2	1	no	—
89	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
90	C₃×C₄⋊C₄	C₃×D₄	1	2	yes	—
91	C₃×C₂²⋊C₄	—	2	1	no	—
92	C₃×C₄²	—	2	1	no	—
93	C₂²×C₉	—	2	2	no	—
94	C₂²×C₉	—	4	4	no	—
95	C₂²×C₉	—	8	4	no	—
96	C₂²×C₉	—	8	4	no	—
97	C₂²×C₉	—	8	4	no	—
98	C₂²×C₉	#121	1	1	yes	characteristic
99	C₂²×C₉	#123	1	2	yes	—
100	C₄×C₉	—	4	2	no	—
101	C₄×C₉	#120	1	1	yes	characteristic
102	C₄×C₉	#121	1	2	yes	—
103	C₄×C₉	#124	1	1	yes	characteristic
104	C₂²×D₄	C₂²×C₉	1	2	yes	—
105	C₂×D₈	—	2	4	no	—
106	C₂×D₈	—	2	2	no	—
107	C₂×M₁₆	C₂²×C₉	1	2	yes	—
108	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
109	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
110	#117	C₂²×C₉	1	1	yes	characteristic
111	C₄⋊C₈	—	2	2	no	—
112	#102	—	2	4	no	—
113	#100	—	2	4	no	—
114	C₂³×C₃	—	2	4	no	—
115	C₂³×C₃	—	4	2	no	—
116	C₂³×C₃	—	4	2	no	—
117	C₂³×C₃	—	8	4	no	—
118	C₂³×C₃	C₃×#41	1	1	yes	characteristic
119	C₃×D₄	—	2	4	no	—
120	C₃×D₄	—	2	4	no	—
121	C₃×D₄	—	4	2	no	—
122	C₃×D₄	—	4	2	no	—
123	C₂×C₃×C₄	—	2	2	no	—
124	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
125	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
126	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
127	C₂×C₃×C₄	C₃×#41	1	2	yes	—
128	C₃×C₈	—	2	2	no	—
129	C₃×C₈	—	4	1	no	—
130	C₃×C₈	—	4	2	no	—
131	C₂×C₉	—	2	2	no	—
132	C₂×C₉	—	8	4	no	—
133	C₂×C₉	#394	1	1	yes	characteristic
134	C₂×C₉	#472	1	2	yes	—
135	C₂⁴	—	2	2	no	—
136	C₂×D₄	—	2	2	no	—
137	C₂×D₄	—	2	2	no	—
138	C₂×D₄	—	2	2	no	—
139	C₂×D₄	—	2	2	no	—
140	C₂×D₄	—	2	2	no	—
141	C₂×D₄	D₄×C₉	1	4	yes	—
142	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
143	D₈	—	2	8	no	—
144	M₁₆	—	2	2	no	—
145	M₁₆	—	2	2	no	—
146	M₁₆	—	2	2	no	—
147	C₂×C₈	—	2	2	no	—
148	C₂×C₈	—	2	2	no	—
149	C₂×C₈	—	2	1	no	—
150	C₂×C₈	D₄×C₉	1	2	yes	—
151	C₄⋊C₄	D₄×C₉	1	2	yes	—
152	C₂²⋊C₄	—	2	1	no	—
153	C₄²	—	2	1	no	—
154	C₂²×C₃	—	2	2	no	—
155	C₂²×C₃	—	4	4	no	—
156	C₂²×C₃	—	8	4	no	—
157	C₂²×C₃	—	8	4	no	—
158	C₂²×C₃	—	8	4	no	—
159	C₂²×C₃	C₃×#121	1	1	yes	characteristic
160	C₂²×C₃	C₃×#123	1	2	yes	—
161	C₃×C₄	—	4	2	no	—
162	C₃×C₄	C₃×#120	1	1	yes	characteristic
163	C₃×C₄	C₃×#121	1	2	yes	—
164	C₃×C₄	C₃×#124	1	1	yes	characteristic
165	C₉	#2045	1	1	yes	characteristic, direct product factor, Sylow
166	C₂³	—	2	4	no	—
167	C₂³	—	4	2	no	—
168	C₂³	—	4	2	no	—
169	C₂³	—	8	4	no	—
170	C₂³	C₉×#41	1	1	yes	characteristic
171	D₄	—	2	4	no	—
172	D₄	—	2	4	no	—
173	D₄	—	4	2	no	—
174	D₄	—	4	2	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
177	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
178	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
179	C₂×C₄	C₉×#41	1	2	yes	—
180	C₈	—	2	2	no	—
181	C₈	—	4	1	no	—
182	C₈	—	4	2	no	—
183	C₂×C₃	—	2	2	no	—
184	C₂×C₃	—	8	4	no	—
185	C₂×C₃	C₃×#394	1	1	yes	characteristic
186	C₂×C₃	C₃×#472	1	2	yes	—
187	C₂²	—	2	2	no	—
188	C₂²	—	4	4	no	—
189	C₂²	—	8	4	no	—
190	C₂²	—	8	4	no	—
191	C₂²	—	8	4	no	—
192	C₂²	C₉×#121	1	1	yes	characteristic
193	C₂²	C₉×#123	1	2	yes	—
194	C₄	—	4	2	no	—
195	C₄	C₉×#120	1	1	yes	characteristic
196	C₄	C₉×#121	1	2	yes	—
197	C₄	C₉×#124	1	1	yes	characteristic
198	C₃	C₃×#2045	1	1	yes	characteristic
199	C₂	—	2	2	no	—
200	C₂	—	8	4	no	—
201	C₂	C₉×#394	1	1	yes	characteristic
202	C₂	C₉×#472	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₉×D₈

C₂

yes

maximal, characteristic

C₉×#424

C₂

yes

maximal, characteristic, complemented

C₉×#418

C₂

yes

maximal, complemented

C₂×C₉×#100

C₂

yes

maximal, complemented

C₉×#341

C₂

yes

maximal, characteristic, complemented

C₃×#2045

C₃

yes

maximal, characteristic

C₂²×D₄×C₉

C₂²

yes

—

C₂×C₉×D₈

—

C₂×C₉×D₈

—

C₂×C₉×M₁₆

C₂²

yes

characteristic

C₂×C₉×M₁₆

C₂²

yes

—

C₂²×C₈×C₉

C₂²

yes

characteristic

C₉×#117

C₂²

yes

characteristic

C₉×C₄⋊C₈

—

C₉×#102

—

C₉×#100

—

C₂²×C₃×D₈

C₂×C₃

yes

characteristic

C₃×#424

C₂×C₃

yes

characteristic

C₃×#418

C₂×C₃

yes

—

C₂×C₃×#100

C₂×C₃

yes

—

C₃×#341

C₂×C₃

yes

characteristic

C₂⁴×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

D₄

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₉×D₈

—

C₉×M₁₆

—

C₉×M₁₆

—

C₉×M₁₆

—

C₂×C₈×C₉

—

C₂×C₈×C₉

—

C₂×C₈×C₉

—

C₂×C₈×C₉

D₄

yes

—

C₉×C₄⋊C₄

D₄

yes

—

C₉×C₂²⋊C₄

—

C₄²×C₉

—

#2045

C₉

yes

characteristic, direct product factor, Sylow

C₂²×C₃×D₄

C₂²×C₃

yes

—

C₂×C₃×D₈

—

C₂×C₃×D₈

—

C₂×C₃×M₁₆

C₂²×C₃

yes

characteristic

C₂×C₃×M₁₆

C₂²×C₃

yes

—

C₂²×C₃×C₈

C₂²×C₃

yes

characteristic

C₃×#117

C₂²×C₃

yes

characteristic

C₃×C₄⋊C₈

—

C₃×#102

—

C₃×#100

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

#41

yes

characteristic

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

#41

yes

—

C₈×C₉

—

C₈×C₉

—

C₈×C₉

—

C₂²×D₈

C₂×C₉

yes

characteristic

#424

C₂×C₉

yes

characteristic, complemented

#418

C₂×C₉

yes

complemented

C₂×#100

C₂×C₉

yes

complemented

#341

C₂×C₉

yes

characteristic, complemented

C₂⁴×C₃

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

C₃×D₄

yes

—

C₂²×C₃×C₄

C₂³×C₃

yes

characteristic

C₃×D₈

—

C₃×M₁₆

—

C₃×M₁₆

—

C₃×M₁₆

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₃×D₄

yes

—

C₃×C₄⋊C₄

C₃×D₄

yes

—

C₃×C₂²⋊C₄

—

C₃×C₄²

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

#121

yes

characteristic

C₂²×C₉

#123

yes

—

100

C₄×C₉

—

101

C₄×C₉

#120

yes

characteristic

102

C₄×C₉

#121

yes

—

103

C₄×C₉

#124

yes

characteristic

104

C₂²×D₄

C₂²×C₉

yes

—

105

C₂×D₈

—

106

C₂×D₈

—

107

C₂×M₁₆

C₂²×C₉

yes

—

108

C₂×M₁₆

C₂²×C₉

yes

characteristic

109

C₂²×C₈

C₂²×C₉

yes

characteristic

110

#117

C₂²×C₉

yes

characteristic

111

C₄⋊C₈

—

112

#102

—

113

#100

—

114

C₂³×C₃

—

115

C₂³×C₃

—

116

C₂³×C₃

—

117

C₂³×C₃

—

118

C₂³×C₃

C₃×#41

yes

characteristic

119

C₃×D₄

—

120

C₃×D₄

—

121

C₃×D₄

—

122

C₃×D₄

—

123

C₂×C₃×C₄

—

124

C₂×C₃×C₄

C₂×C₃×D₄

yes

—

125

C₂×C₃×C₄

C₂×C₃×D₄

yes

characteristic

126

C₂×C₃×C₄

C₂×C₃×D₄

yes

characteristic

127

C₂×C₃×C₄

C₃×#41

yes

—

128

C₃×C₈

—

129

C₃×C₈

—

130

C₃×C₈

—

131

C₂×C₉

—

132

C₂×C₉

—

133

C₂×C₉

#394

yes

characteristic

134

C₂×C₉

#472

yes

—

135

C₂⁴

—

136

C₂×D₄

—

137

C₂×D₄

—

138

C₂×D₄

—

139

C₂×D₄

—

140

C₂×D₄

—

141

C₂×D₄

D₄×C₉

yes

—

142

C₂²×C₄

C₂³×C₉

yes

characteristic

143

D₈

—

144

M₁₆

—

145

M₁₆

—

146

M₁₆

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

D₄×C₉

yes

—

151

C₄⋊C₄

D₄×C₉

yes

—

152

C₂²⋊C₄

—

153

C₄²

—

154

C₂²×C₃

—

155

C₂²×C₃

—

156

C₂²×C₃

—

157

C₂²×C₃

—

158

C₂²×C₃

—

159

C₂²×C₃

C₃×#121

yes

characteristic

160

C₂²×C₃

C₃×#123

yes

—

161

C₃×C₄

—

162

C₃×C₄

C₃×#120

yes

characteristic

163

C₃×C₄

C₃×#121

yes

—

164

C₃×C₄

C₃×#124

yes

characteristic

165

C₉

#2045

yes

characteristic, direct product factor, Sylow

166

C₂³

—

167

C₂³

—

168

C₂³

—

169

C₂³

—

170

C₂³

C₉×#41

yes

characteristic

171

D₄

—

172

D₄

—

173

D₄

—

174

D₄

—

175

C₂×C₄

—

176

C₂×C₄

C₂×D₄×C₉

yes

—

177

C₂×C₄

C₂×D₄×C₉

yes

characteristic

178

C₂×C₄

C₂×D₄×C₉

yes

characteristic

179

C₂×C₄

C₉×#41

yes

—

180

C₈

—

181

C₈

—

182

C₈

—

183

C₂×C₃

—

184

C₂×C₃

—

185

C₂×C₃

C₃×#394

yes

characteristic

186

C₂×C₃

C₃×#472

yes

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

—

191

C₂²

—

192

C₂²

C₉×#121

yes

characteristic

193

C₂²

C₉×#123

yes

—

194

C₄

—

195

C₄

C₉×#120

yes

characteristic

196

C₄

C₉×#121

yes

—

197

C₄

C₉×#124

yes

characteristic

198

C₃

C₃×#2045

yes

characteristic

199

C₂

—

200

C₂

—

201

C₂

C₉×#394

yes

characteristic

202

C₂

C₉×#472

yes

—

	subgroup	G/H
center	C₂²×C₉	#121
commutator	C₂²×C₄	C₂³×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂²×C₃	C₃×#121
prime radical	C₂²×C₃×D₈	C₂×C₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂²×C₄×C₉ ◁ G

subgroup

G/H

center

C₂²×C₉

#121

commutator

C₂²×C₄

C₂³×C₉

Frattini, cosocle

C₂²×C₃×C₄

C₂³×C₃

socle

C₂²×C₃

C₃×#121

prime radical

C₂²×C₃×D₈

C₂×C₃

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₉ ◁ C₂²×C₄×C₉ ◁ G

N	H ≅ G/N	type
2. C₉×#424	C₂	semidirect
3. C₉×#418	C₂	semidirect
4. C₂×C₉×#100	C₂	semidirect
5. C₉×#341	C₂	semidirect
41. #2045	C₉	direct (N × H)
70. #424	C₂×C₉	semidirect
71. #418	C₂×C₉	semidirect
72. C₂×#100	C₂×C₉	semidirect
73. #341	C₂×C₉	semidirect
165. C₉	#2045	direct (N × H)

H ≅ G/N

type

2. C₉×#424

C₂

semidirect

3. C₉×#418

C₂

semidirect

4. C₂×C₉×#100

C₂

semidirect

5. C₉×#341

C₂

semidirect

41. #2045

C₉

direct (N × H)

70. #424

C₂×C₉

semidirect

71. #418

C₂×C₉

semidirect

72. C₂×#100

C₂×C₉

semidirect

73. #341

C₂×C₉

semidirect

165. C₉

#2045

direct (N × H)

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

subgroup	index
C₂²×C₉×D₈	2
C₉×#424	2
C₉×#418	2
C₂×C₉×#100	2
C₉×#341	2
C₃×#2045	3

subgroup

index

C₂²×C₉×D₈

C₂×C₉×#100

Subgroups — C₉×#2045 #11766766

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#2045 #11766766

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2045 #11766766