Group #11790862 — subgroups

Subgroups — #11790862

Order 1152.

594 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 150 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×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×#63391	C₂	1	4	yes	maximal, complemented
3	#10588604	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#3667	C₂	1	1	yes	maximal, characteristic, complemented
5	#71766	—	3	1	no	maximal
6	C₂²×D₄×C₉	C₄	1	4	yes	—
7	C₂²×D₄×C₉	C₂²	1	2	yes	—
8	C₉×#127	—	2	1	no	—
9	C₉×#127	—	2	1	no	—
10	C₉×#127	—	2	2	no	—
11	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
12	C₂×#3667	C₂²	1	2	yes	—
13	C₂×#3667	C₂²	1	2	yes	—
14	#63391	—	2	8	no	—
15	C₄⋊(C₉⋊C₈)	—	2	2	no	—
16	#63362	—	2	1	no	—
17	C₄×C₉⋊C₈	—	2	1	no	—
18	C₂×C₃×#127	D₃	1	1	yes	characteristic
19	C₂×#833	—	3	4	no	—
20	#4924	—	3	1	no	—
21	C₄×#208	—	3	1	no	—
22	C₂⁴×C₉	C₂×C₄	1	4	yes	—
23	C₂×D₄×C₉	—	2	4	no	—
24	C₂×D₄×C₉	—	2	4	no	—
25	C₂×D₄×C₉	—	2	2	no	—
26	C₂×D₄×C₉	—	2	2	no	—
27	C₂×D₄×C₉	—	2	4	no	—
28	C₂×D₄×C₉	—	2	4	no	—
29	C₂×D₄×C₉	—	4	8	no	—
30	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
31	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
32	C₄²×C₉	D₄	1	1	yes	characteristic
33	C₄²×C₉	D₄	1	1	yes	characteristic
34	C₄²×C₉	D₄	1	2	yes	—
35	#3667	—	2	2	no	—
36	#3667	—	2	4	no	—
37	#3667	D₄	1	4	yes	complemented
38	C₂×C₉⋊C₈	—	2	2	no	—
39	C₂×C₉⋊C₈	—	2	2	no	—
40	#1965	—	9	1	no	Sylow
41	C₂²×C₃×D₄	Dic₃	1	4	yes	—
42	C₂²×C₃×D₄	C₂×D₃	1	2	yes	—
43	C₃×#127	—	2	1	no	—
44	C₃×#127	—	2	1	no	—
45	C₃×#127	—	2	2	no	—
46	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
47	C₂×#208	—	3	2	no	—
48	C₂×#208	—	3	2	no	—
49	#833	—	6	8	no	—
50	C₄⋊(C₃⋊C₈)	—	6	2	no	—
51	#803	—	6	1	no	—
52	C₄×C₃⋊C₈	—	6	1	no	—
53	C₂³×C₉	—	2	4	no	—
54	C₂³×C₉	—	2	8	no	—
55	C₂³×C₉	—	4	8	no	—
56	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
57	D₄×C₉	—	4	8	no	—
58	D₄×C₉	—	4	8	no	—
59	D₄×C₉	—	4	4	no	—
60	D₄×C₉	—	4	2	no	—
61	D₄×C₉	—	4	2	no	—
62	C₂×C₄×C₉	—	2	4	no	—
63	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
64	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
65	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
66	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
67	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
68	C₂×C₄×C₉	#41	1	2	yes	—
69	C₉⋊C₈	—	2	4	no	—
70	C₉⋊C₈	—	4	2	no	—
71	C₂×#127	D₉	1	1	yes	characteristic
72	#423	—	9	1	no	—
73	C₂×#100	—	9	4	no	—
74	C₄×M₁₆	—	9	1	no	—
75	C₂⁴×C₃	C₂×Dic₃	1	4	yes	—
76	C₂×C₃×D₄	—	2	4	no	—
77	C₂×C₃×D₄	—	2	4	no	—
78	C₂×C₃×D₄	—	2	4	no	—
79	C₂×C₃×D₄	—	2	4	no	—
80	C₂×C₃×D₄	—	2	2	no	—
81	C₂×C₃×D₄	—	2	2	no	—
82	C₂×C₃×D₄	—	4	8	no	—
83	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
84	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
85	C₃×C₄²	#67	1	1	yes	characteristic
86	C₃×C₄²	#67	1	1	yes	characteristic
87	C₃×C₄²	#67	1	2	yes	—
88	#208	—	3	4	no	—
89	#208	—	6	2	no	—
90	#208	—	6	4	no	—
91	C₂×C₃⋊C₈	—	6	2	no	—
92	C₂×C₃⋊C₈	—	6	2	no	—
93	C₂²×C₉	—	2	2	no	—
94	C₂²×C₉	—	4	4	no	—
95	C₂²×C₉	—	4	8	no	—
96	C₂²×C₉	—	8	8	no	—
97	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₉	C₄×D₄	1	2	yes	—
99	C₄×C₉	—	2	2	no	—
100	C₄×C₉	#100	1	4	yes	complemented
101	C₄×C₉	#121	1	2	yes	—
102	C₄×C₉	#124	1	1	yes	characteristic
103	C₄×C₉	#127	1	1	yes	characteristic
104	C₂²×D₄	Dic₉	1	4	yes	—
105	C₂²×D₄	C₂×D₉	1	2	yes	—
106	C₂×M₁₆	—	9	2	no	—
107	C₂×M₁₆	—	9	2	no	—
108	#127	—	2	1	no	—
109	#127	—	2	1	no	—
110	#127	—	2	2	no	—
111	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
112	C₄⋊C₈	—	18	2	no	—
113	#100	—	18	8	no	—
114	#97	—	18	1	no	—
115	C₄×C₈	—	18	1	no	—
116	C₂³×C₃	—	2	4	no	—
117	C₂³×C₃	—	2	8	no	—
118	C₂³×C₃	—	4	8	no	—
119	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
120	C₃×D₄	—	4	8	no	—
121	C₃×D₄	—	4	8	no	—
122	C₃×D₄	—	4	2	no	—
123	C₃×D₄	—	4	4	no	—
124	C₃×D₄	—	4	2	no	—
125	C₂×C₃×C₄	—	2	4	no	—
126	C₂×C₃×C₄	#217	1	2	yes	—
127	C₂×C₃×C₄	#217	1	2	yes	—
128	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
129	C₂×C₃×C₄	#237	1	2	yes	—
130	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
131	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
132	C₃⋊C₈	—	6	4	no	—
133	C₃⋊C₈	—	12	2	no	—
134	C₂×C₉	—	2	2	no	—
135	C₂×C₉	—	8	4	no	—
136	C₂×C₉	#390	1	1	yes	characteristic
137	C₂×C₉	C₂×#100	1	2	yes	—
138	C₂⁴	C₂×Dic₉	1	4	yes	—
139	C₂×D₄	—	2	4	no	—
140	C₂×D₄	—	2	4	no	—
141	C₂×D₄	—	2	4	no	—
142	C₂×D₄	—	2	4	no	—
143	C₂×D₄	—	2	2	no	—
144	C₂×D₄	—	2	2	no	—
145	C₂×D₄	—	4	8	no	—
146	C₂²×C₄	C₂×Dic₉	1	2	yes	—
147	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
148	M₁₆	—	9	4	no	—
149	M₁₆	—	18	2	no	—
150	M₁₆	—	18	4	no	—
151	C₂×C₈	—	18	2	no	—
152	C₂×C₈	—	18	2	no	—
153	C₄²	#611	1	1	yes	characteristic
154	C₄²	#611	1	1	yes	characteristic
155	C₄²	#611	1	2	yes	—
156	C₂²×C₃	—	2	2	no	—
157	C₂²×C₃	—	4	8	no	—
158	C₂²×C₃	—	4	4	no	—
159	C₂²×C₃	—	8	8	no	—
160	C₂²×C₃	D₄×Dic₃	1	2	yes	—
161	C₂²×C₃	C₂×#217	1	1	yes	characteristic
162	C₃×C₄	—	2	2	no	—
163	C₃×C₄	#833	1	4	yes	—
164	C₃×C₄	#936	1	1	yes	characteristic
165	C₃×C₄	#938	1	2	yes	—
166	C₃×C₄	#940	1	1	yes	characteristic
167	C₉	#1965	1	1	yes	characteristic, complemented, Sylow
168	C₂³	—	2	4	no	—
169	C₂³	—	2	8	no	—
170	C₂³	—	4	8	no	—
171	C₂³	C₂²×Dic₉	1	1	yes	characteristic
172	D₄	—	4	8	no	—
173	D₄	—	4	2	no	—
174	D₄	—	4	4	no	—
175	D₄	—	4	2	no	—
176	D₄	—	4	8	no	—
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	#3676	1	2	yes	—
179	C₂×C₄	#3676	1	2	yes	—
180	C₂×C₄	D₄×D₉	1	2	yes	—
181	C₂×C₄	#3699	1	2	yes	—
182	C₂×C₄	C₂×#611	1	1	yes	characteristic
183	C₂×C₄	C₂×#611	1	1	yes	characteristic
184	C₈	—	18	4	no	—
185	C₈	—	36	2	no	—
186	C₂×C₃	—	2	2	no	—
187	C₂×C₃	—	8	4	no	—
188	C₂×C₃	C₂×#833	1	2	yes	—
189	C₂×C₃	#5221	1	1	yes	characteristic
190	C₂²	—	2	2	no	—
191	C₂²	—	4	8	no	—
192	C₂²	—	4	4	no	—
193	C₂²	—	8	8	no	—
194	C₂²	D₄×Dic₉	1	2	yes	—
195	C₂²	C₂×#3676	1	1	yes	characteristic
196	C₄	—	2	2	no	—
197	C₄	#63391	1	4	yes	complemented
198	C₄	#63498	1	1	yes	characteristic
199	C₄	#63500	1	2	yes	—
200	C₄	#63502	1	1	yes	characteristic
201	C₃	#71766	1	1	yes	characteristic
202	C₂	—	2	2	no	—
203	C₂	—	8	4	no	—
204	C₂	C₂×#63391	1	2	yes	—
205	C₂	#10588901	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₉×#127

C₂

yes

maximal, characteristic

C₂×#63391

C₂

yes

maximal, complemented

#10588604

C₂

yes

maximal, characteristic, complemented

C₄×#3667

C₂

yes

maximal, characteristic, complemented

#71766

—

maximal

C₂²×D₄×C₉

C₄

yes

—

C₂²×D₄×C₉

C₂²

yes

—

C₉×#127

—

C₉×#127

—

C₉×#127

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₂×#3667

C₂²

yes

—

C₂×#3667

C₂²

yes

—

#63391

—

C₄⋊(C₉⋊C₈)

—

#63362

—

C₄×C₉⋊C₈

—

C₂×C₃×#127

D₃

yes

—

—

—

C₂⁴×C₉

C₂×C₄

yes

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂²×C₄×C₉

C₂×C₄

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₄²×C₉

D₄

yes

characteristic

C₄²×C₉

D₄

yes

characteristic

C₄²×C₉

D₄

yes

—

#3667

—

#3667

—

#3667

D₄

yes

complemented

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

—

#1965

—

Sylow

C₂²×C₃×D₄

Dic₃

yes

—

C₂²×C₃×D₄

C₂×D₃

yes

—

C₃×#127

—

C₃×#127

—

C₃×#127

—

C₂×C₃×C₄²

C₂×D₃

yes

—

—

—

C₄⋊(C₃⋊C₈)

—

#803

—

C₄×C₃⋊C₈

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

C₂²×C₄

yes

characteristic

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂²⋊C₄

yes

—

C₂×C₄×C₉

C₂²⋊C₄

yes

—

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

—

C₉⋊C₈

—

C₉⋊C₈

—

C₂×#127

D₉

yes

characteristic

#423

—

C₂×#100

—

C₄×M₁₆

—

C₂⁴×C₃

C₂×Dic₃

yes

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂²×C₃×C₄

C₂×Dic₃

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

C₃×C₄²

yes

C₃×C₄²

yes

C₃×C₄²

yes

—

#208

—

#208

—

#208

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₉

C₄×D₄

yes

—

C₄×C₉

—

100

C₄×C₉

#100

yes

complemented

101

C₄×C₉

#121

yes

—

102

C₄×C₉

#124

yes

characteristic

103

C₄×C₉

#127

yes

characteristic

104

C₂²×D₄

Dic₉

yes

—

105

C₂²×D₄

C₂×D₉

yes

—

106

C₂×M₁₆

—

107

C₂×M₁₆

—

108

#127

—

109

#127

—

110

#127

—

111

C₂×C₄²

C₂×D₉

yes

characteristic

112

C₄⋊C₈

—

113

#100

—

114

#97

—

115

C₄×C₈

—

116

C₂³×C₃

—

117

C₂³×C₃

—

118

C₂³×C₃

—

119

C₂³×C₃

C₂²×Dic₃

yes

characteristic

120

C₃×D₄

—

121

C₃×D₄

—

122

C₃×D₄

—

123

C₃×D₄

—

124

C₃×D₄

—

125

C₂×C₃×C₄

—

126

C₂×C₃×C₄

#217

yes

—

127

C₂×C₃×C₄

#217

yes

—

128

C₂×C₃×C₄

D₃×D₄

yes

—

129

C₂×C₃×C₄

#237

yes

—

130

C₂×C₃×C₄

C₂×#67

yes

characteristic

131

C₂×C₃×C₄

C₂×#67

yes

characteristic

132

C₃⋊C₈

—

133

C₃⋊C₈

—

134

C₂×C₉

—

135

C₂×C₉

—

136

C₂×C₉

#390

yes

characteristic

137

C₂×C₉

C₂×#100

yes

—

138

C₂⁴

C₂×Dic₉

yes

—

139

C₂×D₄

—

140

C₂×D₄

—

141

C₂×D₄

—

142

C₂×D₄

—

143

C₂×D₄

—

144

C₂×D₄

—

145

C₂×D₄

—

146

C₂²×C₄

C₂×Dic₉

yes

—

147

C₂²×C₄

C₂²×D₉

yes

characteristic

148

M₁₆

—

149

M₁₆

—

150

M₁₆

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₄²

#611

yes

characteristic

154

C₄²

#611

yes

characteristic

155

C₄²

#611

yes

—

156

C₂²×C₃

—

157

C₂²×C₃

—

158

C₂²×C₃

—

159

C₂²×C₃

—

160

C₂²×C₃

D₄×Dic₃

yes

—

161

C₂²×C₃

C₂×#217

yes

characteristic

162

C₃×C₄

—

163

C₃×C₄

#833

yes

—

164

C₃×C₄

#936

yes

characteristic

165

C₃×C₄

#938

yes

—

166

C₃×C₄

#940

yes

characteristic

167

C₉

#1965

yes

characteristic, complemented, Sylow

168

C₂³

—

169

C₂³

—

170

C₂³

—

171

C₂³

C₂²×Dic₉

yes

characteristic

172

D₄

—

173

D₄

—

174

D₄

—

175

D₄

—

176

D₄

—

177

C₂×C₄

—

178

C₂×C₄

#3676

yes

—

179

C₂×C₄

#3676

yes

—

180

C₂×C₄

D₄×D₉

yes

—

181

C₂×C₄

#3699

yes

—

182

C₂×C₄

C₂×#611

yes

characteristic

183

C₂×C₄

C₂×#611

yes

characteristic

184

C₈

—

185

C₈

—

186

C₂×C₃

—

187

C₂×C₃

—

188

C₂×C₃

C₂×#833

yes

—

189

C₂×C₃

#5221

yes

characteristic

190

C₂²

—

191

C₂²

—

192

C₂²

—

193

C₂²

—

194

C₂²

D₄×Dic₉

yes

—

195

C₂²

C₂×#3676

yes

characteristic

196

C₄

—

197

C₄

#63391

yes

complemented

198

C₄

#63498

yes

characteristic

199

C₄

#63500

yes

—

200

C₄

#63502

yes

characteristic

201

C₃

#71766

yes

characteristic

202

C₂

—

203

C₂

—

204

C₂

C₂×#63391

yes

—

205

C₂

#10588901

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#3676
commutator	C₂³×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₂×C₉×#127	C₂
socle	C₂²×C₃	C₂×#217
prime radical	C₂×C₃×#127	D₃
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	C₂×#127	D₉
hypocenter	C₉	#1965
LCS	G ▷ C₂³×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#127

subgroup

G/H

center

C₂²

C₂×#3676

commutator

C₂³×C₉

C₂²×C₄

Frattini

C₂²×C₃×C₄

C₂²×D₃

Fitting

C₂×C₉×#127

C₂

socle

C₂²×C₃

C₂×#217

prime radical

C₂×C₃×#127

D₃

cosocle

C₂²×C₄×C₉

C₂³

D₉

C₉

G ▷ C₂³×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#127

N	H ≅ G/N	type
2. C₂×#63391	C₂	semidirect
3. #10588604	C₂	semidirect
4. C₄×#3667	C₂	semidirect
37. #3667	D₄	semidirect
100. C₄×C₉	#100	semidirect
167. C₉	#1965	semidirect
197. C₄	#63391	semidirect

H ≅ G/N

type

2. C₂×#63391

C₂

semidirect

3. #10588604

C₂

semidirect

4. C₄×#3667

C₂

semidirect

37. #3667

D₄

semidirect

100. C₄×C₉

#100

semidirect

167. C₉

#1965

semidirect

197. C₄

#63391

semidirect

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

subgroup	index
C₂×C₉×#127	2
C₂×#63391	2
#10588604	2
C₄×#3667	2
#71766	3

subgroup

index

C₂×C₉×#127

Subgroups — #11790862

Conjugacy classes of subgroups

Complements

Maximal subgroups