Group #11795211 — subgroups

Subgroups — #11795211

Order 1152.

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

normal subgroups only

This group has 336 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	C₂×C₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#63378	C₂	1	1	yes	maximal, characteristic
3	#10588608	C₂	1	2	yes	maximal
4	#10588229	C₂	1	2	yes	maximal
5	#10588229	C₂	1	1	yes	maximal, characteristic
6	#70463	—	3	1	no	maximal
7	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
12	C₂×Dic₉⋊C₄	—	2	2	no	—
13	C₉×C₄⋊C₈	—	2	2	no	—
14	C₉⋊#95	—	2	2	no	—
15	#63378	—	2	2	no	—
16	C₂×C₃×C₄⋊C₈	D₃	1	1	yes	characteristic
17	C₂×#818	—	3	1	no	—
18	#4928	—	3	2	no	—
19	#4551	—	3	1	no	—
20	#4551	—	3	2	no	—
21	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
22	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
23	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
24	C₂²×Dic₉	—	2	2	no	—
25	C₂²×Dic₉	—	2	2	no	—
26	C₂×C₈×C₉	—	2	2	no	—
27	C₂×C₈×C₉	—	2	1	no	—
28	C₂×C₈×C₉	—	2	2	no	—
29	C₂×C₈×C₉	D₄	1	2	yes	—
30	C₄²×C₉	—	2	1	no	—
31	C₄²×C₉	—	2	1	no	—
32	C₄⋊Dic₉	—	2	2	no	—
33	C₄⋊Dic₉	—	2	2	no	—
34	C₄⋊Dic₉	—	2	2	no	—
35	C₄⋊Dic₉	Q₈	1	4	yes	—
36	Dic₉⋊C₄	—	4	4	no	—
37	#2087	—	9	1	no	Sylow
38	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
39	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
40	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
41	C₂×C₄⋊Dic₃	—	3	2	no	—
42	C₂×C₄⋊Dic₃	—	3	2	no	—
43	C₂×Dic₃⋊C₄	—	6	2	no	—
44	C₃×C₄⋊C₈	—	2	2	no	—
45	C₃⋊#95	—	6	2	no	—
46	#818	—	6	2	no	—
47	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₉	—	2	1	no	—
49	C₂×C₄×C₉	—	2	1	no	—
50	C₂×C₄×C₉	—	2	1	no	—
51	C₂×C₄×C₉	—	2	2	no	—
52	C₂×C₄×C₉	Q₁₆	1	2	yes	—
53	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
55	C₂×C₄×C₉	#41	1	1	yes	characteristic
56	C₂×C₄×C₉	#41	1	2	yes	—
57	C₂×Dic₉	—	2	4	no	—
58	C₂×Dic₉	—	4	2	no	—
59	C₂×Dic₉	—	4	2	no	—
60	C₂×Dic₉	—	4	2	no	—
61	C₂×Dic₉	—	4	2	no	—
62	C₂×Dic₉	—	4	2	no	—
63	C₈×C₉	—	2	2	no	—
64	C₈×C₉	—	4	1	no	—
65	C₂×#107	—	9	1	no	—
66	C₂×C₄⋊C₈	D₉	1	1	yes	characteristic
67	#389	—	9	2	no	—
68	#340	—	9	1	no	—
69	#340	—	9	2	no	—
70	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
71	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
72	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
73	C₂²×Dic₃	—	6	2	no	—
74	C₂²×Dic₃	—	6	2	no	—
75	C₂×C₃×C₈	—	2	2	no	—
76	C₂×C₃×C₈	—	2	2	no	—
77	C₂×C₃×C₈	—	2	1	no	—
78	C₂×C₃×C₈	#67	1	2	yes	—
79	C₃×C₄²	—	2	1	no	—
80	C₃×C₄²	—	2	1	no	—
81	C₄⋊Dic₃	—	3	4	no	—
82	C₄⋊Dic₃	—	6	2	no	—
83	C₄⋊Dic₃	—	6	2	no	—
84	C₄⋊Dic₃	—	6	2	no	—
85	Dic₃⋊C₄	—	12	4	no	—
86	C₂²×C₉	#121	1	1	yes	characteristic
87	C₂²×C₉	C₂²⋊Q₈	1	2	yes	—
88	C₂²×C₉	C₂×Q₁₆	1	1	yes	characteristic
89	C₂²×C₉	#135	1	1	yes	characteristic
90	C₂²×C₉	AGL(1,ℤ/8)	1	2	yes	—
91	C₄×C₉	—	2	2	no	—
92	C₄×C₉	—	4	1	no	—
93	C₄×C₉	#123	1	1	yes	characteristic
94	C₄×C₉	#125	1	2	yes	—
95	C₄×C₉	C₄⋊Q₈	1	1	yes	characteristic
96	Dic₉	—	4	4	no	—
97	Dic₉	—	8	2	no	—
98	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
99	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
100	C₂×C₄⋊C₄	—	9	2	no	—
101	C₂×C₄⋊C₄	—	9	2	no	—
102	C₂×C₄⋊C₄	—	18	2	no	—
103	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
104	#107	—	18	2	no	—
105	C₄⋊C₈	—	2	2	no	—
106	#95	—	18	2	no	—
107	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
108	C₂×C₃×C₄	—	2	1	no	—
109	C₂×C₃×C₄	—	2	1	no	—
110	C₂×C₃×C₄	—	2	2	no	—
111	C₂×C₃×C₄	—	2	1	no	—
112	C₂×C₃×C₄	Dic₁₂	1	2	yes	—
113	C₂×C₃×C₄	#235	1	1	yes	characteristic
114	C₂×C₃×C₄	#237	1	2	yes	—
115	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
116	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
117	C₂×Dic₃	—	6	4	no	—
118	C₂×Dic₃	—	12	2	no	—
119	C₂×Dic₃	—	12	2	no	—
120	C₂×Dic₃	—	12	2	no	—
121	C₂×Dic₃	—	12	2	no	—
122	C₂×Dic₃	—	12	2	no	—
123	C₃×C₈	—	2	2	no	—
124	C₃×C₈	—	4	1	no	—
125	C₂×C₉	#398	1	1	yes	characteristic
126	C₂×C₉	#467	1	1	yes	characteristic
127	C₂×C₉	#469	1	1	yes	characteristic
128	C₂×C₉	#477	1	2	yes	—
129	C₂×C₉	#478	1	2	yes	—
130	C₂²×C₄	—	18	2	no	—
131	C₂²×C₄	—	18	2	no	—
132	C₂²×C₄	D₃₆	1	1	yes	characteristic
133	C₂²×C₄	D₃₆	1	1	yes	characteristic
134	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
135	C₂×C₈	—	2	2	no	—
136	C₂×C₈	—	2	2	no	—
137	C₂×C₈	—	2	1	no	—
138	C₂×C₈	#611	1	2	yes	—
139	C₄⋊C₄	—	9	4	no	—
140	C₄⋊C₄	—	18	2	no	—
141	C₄⋊C₄	—	18	2	no	—
142	C₄⋊C₄	—	18	2	no	—
143	C₄⋊C₄	—	36	4	no	—
144	C₄²	—	2	1	no	—
145	C₄²	—	2	1	no	—
146	C₂²×C₃	#897	1	2	yes	—
147	C₂²×C₃	#904	1	1	yes	characteristic
148	C₂²×C₃	C₂×Dic₁₂	1	1	yes	characteristic
149	C₂²×C₃	#908	1	2	yes	—
150	C₂²×C₃	#930	1	1	yes	characteristic
151	C₃×C₄	—	2	2	no	—
152	C₃×C₄	—	4	1	no	—
153	C₃×C₄	#889	1	2	yes	—
154	C₃×C₄	#935	1	1	yes	characteristic
155	C₃×C₄	#944	1	1	yes	characteristic
156	Dic₃	—	12	4	no	—
157	Dic₃	—	24	2	no	—
158	C₉	#2087	1	1	yes	characteristic, complemented, Sylow
159	C₂³	C₂×D₃₆	1	1	yes	characteristic
160	C₂×C₄	—	2	1	no	—
161	C₂×C₄	—	2	1	no	—
162	C₂×C₄	—	2	1	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	18	4	no	—
165	C₂×C₄	—	36	2	no	—
166	C₂×C₄	—	36	2	no	—
167	C₂×C₄	—	36	2	no	—
168	C₂×C₄	—	36	2	no	—
169	C₂×C₄	—	36	2	no	—
170	C₂×C₄	Dic₃₆	1	2	yes	—
171	C₂×C₄	#3697	1	1	yes	characteristic
172	C₂×C₄	#3699	1	2	yes	—
173	C₂×C₄	Q₈×D₉	1	2	yes	—
174	C₂×C₄	C₂×#611	1	1	yes	characteristic
175	C₈	—	2	2	no	—
176	C₈	—	4	1	no	—
177	C₂×C₃	#4847	1	2	yes	—
178	C₂×C₃	#4850	1	2	yes	—
179	C₂×C₃	#4981	1	1	yes	characteristic
180	C₂×C₃	#5116	1	1	yes	characteristic
181	C₂×C₃	#5135	1	1	yes	characteristic
182	C₂²	#63459	1	2	yes	—
183	C₂²	C₂×Dic₃₆	1	1	yes	characteristic
184	C₂²	#63467	1	1	yes	characteristic
185	C₂²	#63470	1	2	yes	—
186	C₂²	#63492	1	1	yes	characteristic
187	C₄	—	2	2	no	—
188	C₄	—	4	1	no	—
189	C₄	—	36	4	no	—
190	C₄	—	72	2	no	—
191	C₄	#63451	1	2	yes	—
192	C₄	#63497	1	1	yes	characteristic
193	C₄	#63506	1	1	yes	characteristic
194	C₃	#70463	1	1	yes	characteristic
195	C₂	#10588514	1	2	yes	—
196	C₂	#10588531	1	2	yes	—
197	C₂	#10588661	1	1	yes	characteristic
198	C₂	#10588788	1	1	yes	characteristic
199	C₂	#10588817	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₉×C₄⋊C₈

C₂

yes

maximal, characteristic

C₂×#63378

C₂

yes

maximal, characteristic

#10588608

C₂

yes

maximal

#10588229

C₂

yes

maximal

#10588229

C₂

yes

maximal, characteristic

#70463

—

maximal

C₂²×C₈×C₉

C₂²

yes

characteristic

C₂²×C₈×C₉

C₂²

yes

characteristic

C₂×C₄²×C₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₉

C₂²

yes

—

C₂×C₄⋊Dic₉

C₂²

yes

—

C₂×Dic₉⋊C₄

—

C₉×C₄⋊C₈

—

C₉⋊#95

—

#63378

—

C₂×C₃×C₄⋊C₈

D₃

yes

—

—

—

—

C₂²×C₄×C₉

D₄

yes

characteristic

C₂²×C₄×C₉

D₄

yes

characteristic

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂²×Dic₉

—

C₂²×Dic₉

—

C₂×C₈×C₉

—

C₂×C₈×C₉

—

C₂×C₈×C₉

—

C₂×C₈×C₉

D₄

yes

—

C₄²×C₉

—

C₄²×C₉

—

C₄⋊Dic₉

—

C₄⋊Dic₉

—

C₄⋊Dic₉

—

C₄⋊Dic₉

Q₈

yes

—

Dic₉⋊C₄

—

#2087

—

Sylow

C₂²×C₃×C₈

C₂×D₃

yes

characteristic

C₂²×C₃×C₈

C₂×D₃

yes

characteristic

C₂×C₃×C₄²

C₂×D₃

yes

characteristic

C₂×C₄⋊Dic₃

—

C₂×C₄⋊Dic₃

—

C₂×Dic₃⋊C₄

—

C₃×C₄⋊C₈

—

C₃⋊#95

—

#818

—

C₂³×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

Q₁₆

yes

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×Q₈

yes

—

C₂×C₄×C₉

#41

yes

characteristic

C₂×C₄×C₉

#41

yes

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

C₈×C₉

—

C₈×C₉

—

C₂×#107

—

C₂×C₄⋊C₈

D₉

yes

—

—

—

C₂²×C₃×C₄

D₁₂

yes

characteristic

C₂²×C₃×C₄

D₁₂

yes

characteristic

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂²×Dic₃

—

C₂²×Dic₃

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

#67

yes

—

C₃×C₄²

—

C₃×C₄²

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

Dic₃⋊C₄

—

C₂²×C₉

#121

yes

characteristic

C₂²×C₉

C₂²⋊Q₈

yes

—

C₂²×C₉

C₂×Q₁₆

yes

C₂²×C₉

yes

C₂²×C₉

yes

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

#123

yes

characteristic

C₄×C₉

#125

yes

—

C₄×C₉

C₄⋊Q₈

yes

characteristic

Dic₉

—

Dic₉

—

C₂²×C₈

C₂×D₉

yes

characteristic

C₂²×C₈

C₂×D₉

yes

characteristic

100

C₂×C₄⋊C₄

—

101

C₂×C₄⋊C₄

—

102

C₂×C₄⋊C₄

—

103

C₂×C₄²

C₂×D₉

yes

characteristic

104

#107

—

105

C₄⋊C₈

—

106

#95

—

107

C₂³×C₃

C₂×D₁₂

yes

characteristic

108

C₂×C₃×C₄

—

109

C₂×C₃×C₄

—

110

C₂×C₃×C₄

—

111

C₂×C₃×C₄

—

112

C₂×C₃×C₄

Dic₁₂

yes

—

113

C₂×C₃×C₄

#235

yes

characteristic

114

C₂×C₃×C₄

#237

yes

—

115

C₂×C₃×C₄

D₃×Q₈

yes

—

116

C₂×C₃×C₄

C₂×#67

yes

characteristic

117

C₂×Dic₃

—

118

C₂×Dic₃

—

119

C₂×Dic₃

—

120

C₂×Dic₃

—

121

C₂×Dic₃

—

122

C₂×Dic₃

—

123

C₃×C₈

—

124

C₃×C₈

—

125

C₂×C₉

#398

yes

characteristic

126

C₂×C₉

#467

yes

characteristic

127

C₂×C₉

#469

yes

characteristic

128

C₂×C₉

#477

yes

—

129

C₂×C₉

#478

yes

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

D₃₆

yes

characteristic

133

C₂²×C₄

D₃₆

yes

characteristic

134

C₂²×C₄

C₂²×D₉

yes

characteristic

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

#611

yes

—

139

C₄⋊C₄

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄²

—

145

C₄²

—

146

C₂²×C₃

#897

yes

—

147

C₂²×C₃

#904

yes

characteristic

148

C₂²×C₃

C₂×Dic₁₂

yes

characteristic

149

C₂²×C₃

#908

yes

—

150

C₂²×C₃

#930

yes

characteristic

151

C₃×C₄

—

152

C₃×C₄

—

153

C₃×C₄

#889

yes

—

154

C₃×C₄

#935

yes

characteristic

155

C₃×C₄

#944

yes

characteristic

156

Dic₃

—

157

Dic₃

—

158

C₉

#2087

yes

characteristic, complemented, Sylow

159

C₂³

C₂×D₃₆

yes

characteristic

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

Dic₃₆

yes

—

171

C₂×C₄

#3697

yes

characteristic

172

C₂×C₄

#3699

yes

—

173

C₂×C₄

Q₈×D₉

yes

—

174

C₂×C₄

C₂×#611

yes

characteristic

175

C₈

—

176

C₈

—

177

C₂×C₃

#4847

yes

—

178

C₂×C₃

#4850

yes

—

179

C₂×C₃

#4981

yes

characteristic

180

C₂×C₃

#5116

yes

characteristic

181

C₂×C₃

#5135

yes

characteristic

182

C₂²

#63459

yes

—

183

C₂²

C₂×Dic₃₆

yes

characteristic

184

C₂²

#63467

yes

characteristic

185

C₂²

#63470

yes

—

186

C₂²

#63492

yes

characteristic

187

C₄

—

188

C₄

—

189

C₄

—

190

C₄

—

191

C₄

#63451

yes

—

192

C₄

#63497

yes

characteristic

193

C₄

#63506

yes

characteristic

194

C₃

#70463

yes

characteristic

195

C₂

#10588514

yes

—

196

C₂

#10588531

yes

—

197

C₂

#10588661

yes

characteristic

198

C₂

#10588788

yes

characteristic

199

C₂

#10588817

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₃₆
commutator, cosocle	C₂²×C₄×C₉	C₂³
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₂×C₉×C₄⋊C₈	C₂
socle, prime radical	C₂³×C₃	C₂×D₁₂
hypercenter	C₂×C₄⋊C₈	D₉
hypocenter	C₉	#2087
LCS	G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

subgroup

G/H

center

C₂³

C₂×D₃₆

commutator, cosocle

C₂²×C₄×C₉

C₂³

Frattini

C₂²×C₃×C₄

C₂²×D₃

Fitting

C₂×C₉×C₄⋊C₈

C₂

socle, prime radical

C₂³×C₃

C₂×D₁₂

hypercenter

C₂×C₄⋊C₈

D₉

hypocenter

C₉

#2087

LCS

G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
158. C₉	#2087	semidirect

H ≅ G/N

type

158. C₉

#2087

semidirect

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

subgroup	index
C₂×C₉×C₄⋊C₈	2
C₂×#63378	2
#10588608	2
#10588229	2
#70463	3

subgroup

index

C₂×C₉×C₄⋊C₈

Subgroups — #11795211

Conjugacy classes of subgroups

Complements

Maximal subgroups