Group #14672008 — subgroups

Subgroups — #14672008

Order 2816.

486 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 159 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×#10622312	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622130	C₂	1	4	yes	maximal
3	C₂×#10622099	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1846	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₄₄	—	2	1	no	—
6	C₂²×Dic₄₄	C₂²	1	2	yes	—
7	C₂×#66922	—	2	1	no	—
8	C₂×C₁₁×#107	C₂²	1	2	yes	—
9	C₂×C₁₁×#106	—	2	1	no	—
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₁₁×#382	—	2	1	no	—
12	C₂²×C₁₁⋊C₁₆	C₂²	1	2	yes	—
13	#10622312	—	2	2	no	—
14	#10622312	C₄	1	4	yes	complemented
15	#10622130	—	2	8	no	—
16	#10622099	—	2	2	no	—
17	C₂²×Dic₂₂	—	2	2	no	—
18	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
20	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
21	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₁	—	4	2	no	—
23	C₂×Dic₄₄	—	2	4	no	—
24	C₂×Dic₄₄	—	2	4	no	—
25	C₂×Dic₄₄	—	2	4	no	—
26	C₂×Dic₄₄	—	2	2	no	—
27	C₂×Dic₄₄	—	4	2	no	—
28	C₂×Dic₄₄	—	4	2	no	—
29	C₂×Dic₄₄	C₂×C₄	1	4	yes	—
30	#66922	—	2	4	no	—
31	#66922	—	4	2	no	—
32	C₁₁×#107	—	2	4	no	—
33	C₁₁×#106	—	4	2	no	—
34	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
35	C₄×C₈×C₁₁	D₄	1	2	yes	—
36	C₁₁×#95	—	4	2	no	—
37	C₂×C₁₁⋊C₁₆	—	2	2	no	—
38	C₂×C₁₁⋊C₁₆	—	2	2	no	—
39	C₂×C₁₁⋊C₁₆	D₄	1	4	yes	—
40	#13207	—	11	1	no	maximal, Sylow
41	C₂²×C₄×C₁₁	—	4	2	no	—
42	C₂²×C₄×C₁₁	D₈	1	2	yes	—
43	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
44	C₂²×Dic₁₁	—	4	2	no	—
45	C₂×Dic₂₂	—	2	4	no	—
46	C₂×Dic₂₂	—	4	2	no	—
47	C₂×Dic₂₂	—	4	2	no	—
48	C₂×Dic₂₂	—	4	2	no	—
49	C₂×Dic₂₂	—	4	2	no	—
50	C₂×Dic₂₂	—	4	2	no	—
51	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
52	C₂×C₈×C₁₁	D₈	1	2	yes	—
53	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
54	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
56	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
57	C₂×C₈×C₁₁	#41	1	2	yes	—
58	C₁₁×C₄⋊C₄	—	4	2	no	—
59	C₁₁×C₄⋊C₄	—	4	2	no	—
60	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
61	C₄²×C₁₁	SD₁₆	1	2	yes	—
62	C₄⋊Dic₁₁	—	4	8	no	—
63	Dic₄₄	—	2	8	no	—
64	Dic₄₄	—	4	8	no	—
65	Dic₄₄	—	4	4	no	—
66	C₁₁⋊C₁₆	—	2	4	no	—
67	C₂×#494	—	11	1	no	—
68	C₂×#358	—	11	4	no	—
69	C₂×#346	—	11	1	no	—
70	#1846	D₁₁	1	1	yes	characteristic
71	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
72	C₂×C₄×C₁₁	—	2	4	no	—
73	C₂×C₄×C₁₁	—	8	2	no	—
74	C₂×C₄×C₁₁	—	8	4	no	—
75	C₂×C₄×C₁₁	#102	1	4	yes	—
76	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
78	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
79	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
80	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
82	C₂×Dic₁₁	—	4	4	no	—
83	C₂×Dic₁₁	—	8	2	no	—
84	C₂×Dic₁₁	—	8	2	no	—
85	Dic₂₂	—	4	4	no	—
86	Dic₂₂	—	4	4	no	—
87	Dic₂₂	—	8	2	no	—
88	Dic₂₂	—	8	2	no	—
89	C₈×C₁₁	#102	1	4	yes	—
90	C₈×C₁₁	C₄×D₄	1	2	yes	—
91	C₈×C₁₁	#121	1	2	yes	—
92	C₂²×Q₁₆	—	11	2	no	—
93	C₂²×Q₁₆	—	22	1	no	—
94	C₂×C₄⋊Q₈	—	22	1	no	—
95	C₂²×C₁₆	—	11	2	no	—
96	#494	—	11	4	no	—
97	#494	—	22	2	no	—
98	C₂×#107	C₂×D₁₁	1	2	yes	—
99	C₂×#106	—	2	1	no	—
100	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
101	#382	—	2	1	no	—
102	#358	—	22	8	no	—
103	#346	—	22	2	no	—
104	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
105	C₂²×C₁₁	#486	1	1	yes	characteristic
106	C₂²×C₁₁	#493	1	1	yes	characteristic
107	C₂²×C₁₁	#510	1	4	yes	—
108	C₄×C₁₁	—	2	4	no	—
109	C₄×C₁₁	—	16	2	no	—
110	C₄×C₁₁	#390	1	1	yes	characteristic
111	C₄×C₁₁	C₂×#102	1	1	yes	characteristic
112	C₄×C₁₁	#486	1	1	yes	characteristic
113	C₄×C₁₁	#492	1	1	yes	characteristic
114	Dic₁₁	—	8	4	no	—
115	C₂²×Q₈	—	22	2	no	—
116	C₂×Q₁₆	—	11	4	no	—
117	C₂×Q₁₆	—	22	4	no	—
118	C₂×Q₁₆	—	22	2	no	—
119	C₂×Q₁₆	—	22	4	no	—
120	C₂×Q₁₆	—	22	4	no	—
121	C₂×Q₁₆	—	44	2	no	—
122	C₂×Q₁₆	—	44	2	no	—
123	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
124	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
125	C₄⋊Q₈	—	22	4	no	—
126	C₄⋊Q₈	—	44	2	no	—
127	C₂×C₄⋊C₄	—	2	2	no	—
128	C₂×C₄⋊C₄	—	44	2	no	—
129	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
130	C₂×C₁₆	—	11	4	no	—
131	C₂×C₁₆	—	22	2	no	—
132	C₂×C₁₆	—	22	2	no	—
133	#107	—	2	4	no	—
134	#106	—	4	2	no	—
135	C₄×C₈	C₄×D₁₁	1	2	yes	—
136	C₄×C₈	D₄₄	1	2	yes	—
137	#95	—	4	2	no	—
138	C₂×C₁₁	#1957	1	1	yes	characteristic
139	C₂×C₁₁	#2141	1	2	yes	—
140	C₂×C₁₁	#2245	1	2	yes	—
141	C₂×C₁₁	#2251	1	2	yes	—
142	C₂×Q₈	—	22	4	no	—
143	C₂×Q₈	—	44	2	no	—
144	C₂×Q₈	—	44	2	no	—
145	C₂×Q₈	—	44	2	no	—
146	C₂×Q₈	—	44	2	no	—
147	C₂×Q₈	—	44	2	no	—
148	C₂²×C₄	—	4	2	no	—
149	C₂²×C₄	—	44	2	no	—
150	C₂²×C₄	#4323	1	2	yes	—
151	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
152	Q₁₆	—	22	8	no	—
153	Q₁₆	—	44	8	no	—
154	Q₁₆	—	44	4	no	—
155	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
156	C₂×C₈	#4323	1	2	yes	—
157	C₂×C₈	#4325	1	2	yes	—
158	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
159	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
160	C₂×C₈	D₄×D₁₁	1	2	yes	—
161	C₂×C₈	#4343	1	2	yes	—
162	C₄⋊C₄	—	4	2	no	—
163	C₄⋊C₄	—	4	2	no	—
164	C₄⋊C₄	—	44	8	no	—
165	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
166	C₄²	#4325	1	2	yes	—
167	C₁₆	—	22	4	no	—
168	C₁₁	#13207	1	1	yes	characteristic, complemented, Sylow
169	C₂³	C₂×#4323	1	1	yes	characteristic
170	Q₈	—	44	4	no	—
171	Q₈	—	44	4	no	—
172	Q₈	—	88	2	no	—
173	Q₈	—	88	2	no	—
174	C₂×C₄	—	2	4	no	—
175	C₂×C₄	—	8	4	no	—
176	C₂×C₄	—	8	2	no	—
177	C₂×C₄	—	44	4	no	—
178	C₂×C₄	—	88	2	no	—
179	C₂×C₄	—	88	2	no	—
180	C₂×C₄	#66873	1	4	yes	—
181	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
182	C₂×C₄	C₂×#4323	1	1	yes	characteristic
183	C₂×C₄	#66993	1	1	yes	characteristic
184	C₂×C₄	C₂×#4325	1	1	yes	characteristic
185	C₂×C₄	C₂×#4325	1	1	yes	characteristic
186	C₂×C₄	#67000	1	1	yes	characteristic
187	C₈	#66873	1	4	yes	—
188	C₈	#66946	1	2	yes	—
189	C₈	#66948	1	2	yes	—
190	C₂²	C₂×#66873	1	1	yes	characteristic
191	C₂²	#10622686	1	1	yes	characteristic
192	C₂²	#10622701	1	1	yes	characteristic
193	C₂²	#10622808	1	4	yes	—
194	C₄	—	2	4	no	—
195	C₄	—	16	2	no	—
196	C₄	—	88	4	no	—
197	C₄	C₂×#66873	1	1	yes	characteristic
198	C₄	#10622601	1	1	yes	characteristic
199	C₄	#10622698	1	1	yes	characteristic
200	C₄	#10622701	1	1	yes	characteristic
201	C₂	#13069421	1	1	yes	characteristic
202	C₂	#13070335	1	2	yes	—
203	C₂	#13070863	1	2	yes	—
204	C₂	#13070888	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622312

C₂

yes

maximal, characteristic

C₂×#10622130

C₂

yes

maximal

C₂×#10622099

C₂

yes

maximal, characteristic

C₁₁×#1846

C₂

yes

maximal, characteristic

C₂²×Dic₄₄

—

C₂²×Dic₄₄

C₂²

yes

—

C₂×#66922

—

C₂×C₁₁×#107

C₂²

yes

—

C₂×C₁₁×#106

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₁₁×#382

—

C₂²×C₁₁⋊C₁₆

C₂²

yes

—

#10622312

—

#10622312

C₄

yes

complemented

#10622130

—

#10622099

—

C₂²×Dic₂₂

—

C₂²×C₈×C₁₁

D₄

yes

characteristic

C₂²×C₈×C₁₁

C₂³

yes

characteristic

C₂×C₁₁×C₄⋊C₄

—

C₂×C₄²×C₁₁

D₄

yes

characteristic

C₂×C₄⋊Dic₁₁

—

C₂×Dic₄₄

—

C₂×Dic₄₄

—

C₂×Dic₄₄

—

C₂×Dic₄₄

—

C₂×Dic₄₄

—

C₂×Dic₄₄

—

C₂×Dic₄₄

C₂×C₄

yes

—

#66922

—

#66922

—

C₁₁×#107

—

C₁₁×#106

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

D₄

yes

—

C₁₁×#95

—

C₂×C₁₁⋊C₁₆

—

C₂×C₁₁⋊C₁₆

—

C₂×C₁₁⋊C₁₆

D₄

yes

—

#13207

—

maximal, Sylow

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

D₈

yes

—

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×Dic₁₁

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

—

C₂×C₈×C₁₁

D₈

yes

—

C₂×C₈×C₁₁

SD₁₆

yes

—

C₂×C₈×C₁₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₁

C₂×D₄

yes

characteristic

C₂×C₈×C₁₁

C₂×D₄

yes

—

C₂×C₈×C₁₁

#41

yes

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₄²×C₁₁

C₂²⋊C₄

yes

—

C₄²×C₁₁

SD₁₆

yes

—

C₄⋊Dic₁₁

—

Dic₄₄

—

Dic₄₄

—

Dic₄₄

—

C₁₁⋊C₁₆

—

—

—

—

D₁₁

yes

characteristic

C₂³×C₁₁

C₂×D₈

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#102

yes

—

C₂×C₄×C₁₁

C₂×C₂²⋊C₄

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

C₂×C₄×C₁₁

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₁

C₂×SD₁₆

yes

characteristic

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

Dic₂₂

—

Dic₂₂

—

Dic₂₂

—

Dic₂₂

—

C₈×C₁₁

#102

yes

—

C₈×C₁₁

C₄×D₄

yes

—

C₈×C₁₁

#121

yes

—

C₂²×Q₁₆

—

C₂²×Q₁₆

—

C₂×C₄⋊Q₈

—

C₂²×C₁₆

—

#494

—

#494

—

C₂×#107

C₂×D₁₁

yes

—

C₂×#106

—

100

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

101

#382

—

102

#358

—

103

#346

—

104

C₂²×C₁₁

C₂×#102

yes

characteristic

105

C₂²×C₁₁

#486

yes

characteristic

106

C₂²×C₁₁

#493

yes

characteristic

107

C₂²×C₁₁

#510

yes

—

108

C₄×C₁₁

—

109

C₄×C₁₁

—

110

C₄×C₁₁

#390

yes

characteristic

111

C₄×C₁₁

C₂×#102

yes

characteristic

112

C₄×C₁₁

#486

yes

characteristic

113

C₄×C₁₁

#492

yes

characteristic

114

Dic₁₁

—

115

C₂²×Q₈

—

116

C₂×Q₁₆

—

117

C₂×Q₁₆

—

118

C₂×Q₁₆

—

119

C₂×Q₁₆

—

120

C₂×Q₁₆

—

121

C₂×Q₁₆

—

122

C₂×Q₁₆

—

123

C₂²×C₈

C₂²⋊D₁₁

yes

characteristic

124

C₂²×C₈

C₂²×D₁₁

yes

characteristic

125

C₄⋊Q₈

—

126

C₄⋊Q₈

—

127

C₂×C₄⋊C₄

—

128

C₂×C₄⋊C₄

—

129

C₂×C₄²

C₂²⋊D₁₁

yes

characteristic

130

C₂×C₁₆

—

131

C₂×C₁₆

—

132

C₂×C₁₆

—

133

#107

—

134

#106

—

135

C₄×C₈

C₄×D₁₁

yes

—

136

C₄×C₈

D₄₄

yes

—

137

#95

—

138

C₂×C₁₁

#1957

yes

characteristic

139

C₂×C₁₁

#2141

yes

—

140

C₂×C₁₁

#2245

yes

—

141

C₂×C₁₁

#2251

yes

—

142

C₂×Q₈

—

143

C₂×Q₈

—

144

C₂×Q₈

—

145

C₂×Q₈

—

146

C₂×Q₈

—

147

C₂×Q₈

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

#4323

yes

—

151

C₂²×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

152

Q₁₆

—

153

Q₁₆

—

154

Q₁₆

—

155

C₂×C₈

(C₂×D₁₁)⋊C₄

yes

—

156

C₂×C₈

#4323

yes

—

157

C₂×C₈

#4325

yes

—

158

C₂×C₈

C₂×C₄×D₁₁

yes

characteristic

159

C₂×C₈

C₂×D₄₄

yes

characteristic

160

C₂×C₈

D₄×D₁₁

yes

—

161

C₂×C₈

#4343

yes

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄²

(C₂×D₁₁)⋊C₄

yes

—

166

C₄²

#4325

yes

—

167

C₁₆

—

168

C₁₁

#13207

yes

characteristic, complemented, Sylow

169

C₂³

C₂×#4323

yes

characteristic

170

Q₈

—

171

Q₈

—

172

Q₈

—

173

Q₈

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

#66873

yes

—

181

C₂×C₄

C₂×(C₂×D₁₁)⋊C₄

yes

characteristic

182

C₂×C₄

C₂×#4323

yes

characteristic

183

C₂×C₄

#66993

yes

characteristic

184

C₂×C₄

C₂×#4325

yes

characteristic

185

C₂×C₄

C₂×#4325

yes

characteristic

186

C₂×C₄

#67000

yes

characteristic

187

C₈

#66873

yes

—

188

C₈

#66946

yes

—

189

C₈

#66948

yes

—

190

C₂²

C₂×#66873

yes

characteristic

191

C₂²

#10622686

yes

characteristic

192

C₂²

#10622701

yes

characteristic

193

C₂²

#10622808

yes

—

194

C₄

—

195

C₄

—

196

C₄

—

197

C₄

C₂×#66873

yes

characteristic

198

C₄

#10622601

yes

characteristic

199

C₄

#10622698

yes

characteristic

200

C₄

#10622701

yes

characteristic

201

C₂

#13069421

yes

characteristic

202

C₂

#13070335

yes

—

203

C₂

#13070863

yes

—

204

C₂

#13070888

yes

—

	subgroup	G/H
center	C₂³	C₂×#4323
commutator	C₂×C₈×C₁₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#1846	C₂
socle, prime radical	C₂³×C₁₁	C₂×D₈
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#1846	D₁₁
hypocenter	C₁₁	#13207
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1846

subgroup

G/H

center

C₂³

C₂×#4323

commutator

C₂×C₈×C₁₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₁

Fitting

C₁₁×#1846

C₂

socle, prime radical

C₂³×C₁₁

C₂×D₈

cosocle

C₂²×C₈×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1846

N	H ≅ G/N	type
14. #10622312	C₄	semidirect
168. C₁₁	#13207	semidirect

H ≅ G/N

type

14. #10622312

C₄

semidirect

168. C₁₁

#13207

semidirect

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

subgroup	index
C₂×#10622312	2
C₂×#10622130	2
C₂×#10622099	2
C₁₁×#1846	2
#13207	11

subgroup

index

C₁₁×#1846

Subgroups — #14672008

Conjugacy classes of subgroups

Complements

Maximal subgroups