Group #14653232 — subgroups

Subgroups — #14653232

Order 2816.

414 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 155 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×#10622295	C₂	1	1	yes	maximal, characteristic
2	#13068788	C₂	1	1	yes	maximal, characteristic
3	#13067300	C₂	1	2	yes	maximal
4	#13067296	C₂	1	2	yes	maximal
5	C₁₁×#1450	C₂	1	1	yes	maximal, characteristic
6	C₂×#66922	C₂²	1	2	yes	—
7	C₁₁×#431	C₂²	1	1	yes	characteristic
8	C₁₁×#431	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×#66883	—	2	2	no	—
11	C₂×#66882	—	2	2	no	—
12	#10622537	C₂²	1	2	yes	—
13	#10622295	—	2	1	no	—
14	#10622295	—	2	1	no	—
15	#10622295	C₄	1	4	yes	—
16	C₁₁×#322	—	2	1	no	—
17	C₈²×C₁₁	—	2	1	no	—
18	#10622120	—	2	4	no	—
19	#10622119	—	2	4	no	—
20	C₂²×Dic₂₂	—	2	2	no	—
21	C₂²×C₈×C₁₁	D₄	1	2	yes	—
22	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
23	C₂×C₄⋊Dic₁₁	—	2	2	no	—
24	C₂×C₄⋊Dic₁₁	—	2	2	no	—
25	C₂×#4318	—	2	2	no	—
26	#66922	—	2	2	no	—
27	#66922	—	2	2	no	—
28	#66922	—	2	2	no	—
29	#66922	C₂×C₄	1	4	yes	—
30	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
31	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
32	C₁₁×C₂²⋊C₈	—	2	1	no	—
33	C₁₁×C₂²⋊C₈	—	2	1	no	—
34	C₄×C₈×C₁₁	—	2	1	no	—
35	C₄×C₈×C₁₁	—	2	1	no	—
36	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
37	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
38	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
39	#66883	—	4	4	no	—
40	#66882	—	2	4	no	—
41	#66882	—	2	4	no	—
42	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
43	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
44	#9771	—	11	1	no	maximal, Sylow
45	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
47	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
48	C₂²×Dic₁₁	—	4	2	no	—
49	C₂×Dic₂₂	—	2	4	no	—
50	C₂×Dic₂₂	—	4	2	no	—
51	C₂×Dic₂₂	—	8	4	no	—
52	C₂×C₈×C₁₁	—	2	2	no	—
53	C₂×C₈×C₁₁	—	2	2	no	—
54	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
55	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
56	C₂×C₈×C₁₁	SD₁₆	1	4	yes	—
57	C₂×C₈×C₁₁	Q₁₆	1	4	yes	—
58	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
59	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
60	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
61	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
62	C₄⋊Dic₁₁	—	2	4	no	—
63	C₄⋊Dic₁₁	—	2	4	no	—
64	C₄⋊Dic₁₁	—	4	2	no	—
65	C₄⋊Dic₁₁	—	4	2	no	—
66	#4318	—	4	4	no	—
67	C₂×C₁₁⋊C₈	—	4	2	no	—
68	C₂×#500	—	11	1	no	—
69	#1848	—	11	1	no	—
70	#1549	—	11	2	no	—
71	#1548	—	11	2	no	—
72	#1450	D₁₁	1	1	yes	characteristic
73	C₂³×C₁₁	#124	1	1	yes	characteristic
74	C₂×C₄×C₁₁	—	2	2	no	—
75	C₂×C₄×C₁₁	—	2	2	no	—
76	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
78	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
79	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
80	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
81	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
82	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
83	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
84	C₂×Dic₁₁	—	4	4	no	—
85	C₂×Dic₁₁	—	8	4	no	—
86	Dic₂₂	—	8	4	no	—
87	Dic₂₂	—	8	4	no	—
88	C₈×C₁₁	—	4	2	no	—
89	C₈×C₁₁	—	4	2	no	—
90	C₈×C₁₁	#103	1	4	yes	—
91	C₈×C₁₁	#103	1	4	yes	—
92	C₁₁⋊C₈	—	8	2	no	—
93	C₂×C₄⋊Q₈	—	11	2	no	—
94	#500	—	11	4	no	—
95	#500	—	22	1	no	—
96	#500	—	22	1	no	—
97	#431	C₂×D₁₁	1	1	yes	characteristic
98	#431	C₂×D₁₁	1	1	yes	characteristic
99	C₂×#108	—	22	2	no	—
100	C₂×#107	—	22	2	no	—
101	#423	—	11	2	no	—
102	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
103	#333	—	22	4	no	—
104	#332	—	22	4	no	—
105	#322	—	2	1	no	—
106	C₈²	—	2	1	no	—
107	C₂²×C₁₁	—	2	1	no	—
108	C₂²×C₁₁	—	2	1	no	—
109	C₂²×C₁₁	#390	1	1	yes	characteristic
110	C₂²×C₁₁	#487	1	2	yes	—
111	C₄×C₁₁	—	2	1	no	—
112	C₄×C₁₁	—	2	1	no	—
113	C₄×C₁₁	C₂×#103	1	2	yes	—
114	C₄×C₁₁	#472	1	2	yes	—
115	C₄×C₁₁	#473	1	2	yes	—
116	C₄×C₁₁	#492	1	1	yes	characteristic
117	C₄×C₁₁	#494	1	1	yes	characteristic
118	Dic₁₁	—	8	4	no	—
119	C₂²×Q₈	—	22	2	no	—
120	C₂×M₁₆	—	22	2	no	—
121	C₂²×C₈	D₄₄	1	2	yes	—
122	C₄⋊Q₈	—	11	4	no	—
123	C₄⋊Q₈	—	22	2	no	—
124	C₄⋊Q₈	—	22	2	no	—
125	C₄⋊Q₈	—	22	2	no	—
126	C₂×C₄⋊C₄	—	22	2	no	—
127	C₂×C₄⋊C₄	—	22	2	no	—
128	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
129	#108	—	44	4	no	—
130	#107	—	22	4	no	—
131	#107	—	22	4	no	—
132	C₄⋊C₈	—	22	2	no	—
133	C₄⋊C₈	—	22	2	no	—
134	C₄⋊C₈	D₄₄	1	2	yes	—
135	C₄⋊C₈	D₄₄	1	2	yes	—
136	C₂²⋊C₈	—	2	1	no	—
137	C₂²⋊C₈	—	2	1	no	—
138	C₄×C₈	—	2	1	no	—
139	C₄×C₈	—	2	1	no	—
140	C₄×C₈	C₄×D₁₁	1	2	yes	—
141	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
142	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
143	C₂×C₁₁	—	2	2	no	—
144	C₂×C₁₁	#1956	1	1	yes	characteristic
145	C₂×C₁₁	#1978	1	1	yes	characteristic
146	C₂×C₁₁	#1979	1	1	yes	characteristic
147	C₂×Q₈	—	22	4	no	—
148	C₂×Q₈	—	44	2	no	—
149	C₂×Q₈	—	88	4	no	—
150	C₂²×C₄	—	44	2	no	—
151	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
152	C₂²×C₄	#4339	1	1	yes	characteristic
153	C₂²×C₄	#4339	1	1	yes	characteristic
154	M₁₆	—	44	4	no	—
155	C₂×C₈	—	2	2	no	—
156	C₂×C₈	—	2	2	no	—
157	C₂×C₈	—	44	2	no	—
158	C₂×C₈	#4314	1	4	yes	—
159	C₂×C₈	Dic₄₄	1	4	yes	—
160	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
161	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
162	C₄⋊C₄	—	22	4	no	—
163	C₄⋊C₄	—	22	4	no	—
164	C₄⋊C₄	—	44	2	no	—
165	C₄⋊C₄	—	44	2	no	—
166	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
167	C₄²	C₂×D₄₄	1	1	yes	characteristic
168	C₄²	C₂×D₄₄	1	1	yes	characteristic
169	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
170	C₁₁	#9771	1	1	yes	characteristic, complemented, Sylow
171	C₂³	#66928	1	1	yes	characteristic
172	Q₈	—	88	4	no	—
173	Q₈	—	88	4	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	44	4	no	—
177	C₂×C₄	—	88	4	no	—
178	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
179	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
180	C₂×C₄	#66927	1	1	yes	characteristic
181	C₂×C₄	C₂×#4314	1	2	yes	—
182	C₂×C₄	C₂×Dic₄₄	1	2	yes	—
183	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
184	C₂×C₄	#66983	1	1	yes	characteristic
185	C₂×C₄	#66983	1	1	yes	characteristic
186	C₈	—	4	2	no	—
187	C₈	—	4	2	no	—
188	C₈	—	88	2	no	—
189	C₈	#66880	1	4	yes	—
190	C₈	#66880	1	4	yes	—
191	C₂²	—	2	1	no	—
192	C₂²	—	2	1	no	—
193	C₂²	#10622294	1	2	yes	—
194	C₂²	#10622552	1	1	yes	characteristic
195	C₄	—	2	1	no	—
196	C₄	—	2	1	no	—
197	C₄	—	88	4	no	—
198	C₄	#10622306	1	1	yes	characteristic
199	C₄	#10622312	1	1	yes	characteristic
200	C₄	C₂×#66880	1	2	yes	—
201	C₄	#10622755	1	2	yes	—
202	C₄	#10622756	1	2	yes	—
203	C₂	—	2	2	no	—
204	C₂	#13069418	1	1	yes	characteristic
205	C₂	#13069526	1	1	yes	characteristic
206	C₂	#13069531	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622295

C₂

yes

maximal, characteristic

#13068788

C₂

yes

maximal, characteristic

#13067300

C₂

yes

maximal

#13067296

C₂

yes

maximal

C₁₁×#1450

C₂

yes

maximal, characteristic

C₂×#66922

C₂²

yes

—

C₁₁×#431

C₂²

yes

characteristic

C₁₁×#431

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₁

C₂²

yes

—

—

C₂²

yes

—

#10622295

—

#10622295

—

#10622295

C₄

yes

—

C₁₁×#322

—

C₈²×C₁₁

—

#10622120

—

#10622119

—

C₂²×Dic₂₂

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₁

—

C₂×C₄⋊Dic₁₁

—

—

—

—

—

C₂×C₄

yes

—

C₁₁×C₄⋊C₈

D₄

yes

—

C₁₁×C₄⋊C₈

D₄

yes

—

C₁₁×C₂²⋊C₈

—

C₁₁×C₂²⋊C₈

—

C₄×C₈×C₁₁

—

C₄×C₈×C₁₁

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

D₄

yes

characteristic

C₄×C₈×C₁₁

D₄

yes

—

—

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

#9771

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

C₂²×C₄×C₁₁

yes

C₂²×C₄×C₁₁

yes

C₂²×Dic₁₁

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

—

C₂×C₈×C₁₁

SD₁₆

yes

—

C₂×C₈×C₁₁

Q₁₆

yes

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

#4318

—

C₂×C₁₁⋊C₈

—

—

—

—

—

D₁₁

yes

characteristic

C₂³×C₁₁

#124

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₄×D₄

yes

characteristic

C₂×C₄×C₁₁

C₄×D₄

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

C₂×SD₁₆

yes

—

C₂×C₄×C₁₁

C₂×Q₁₆

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

Dic₂₂

—

Dic₂₂

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

#103

yes

—

C₈×C₁₁

#103

yes

—

C₁₁⋊C₈

—

C₂×C₄⋊Q₈

—

—

—

—

C₂×D₁₁

yes

characteristic

#431

C₂×D₁₁

yes

characteristic

C₂×#108

—

100

C₂×#107

—

101

#423

—

102

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

103

#333

—

104

#332

—

105

#322

—

106

C₈²

—

107

C₂²×C₁₁

—

108

C₂²×C₁₁

—

109

C₂²×C₁₁

#390

yes

characteristic

110

C₂²×C₁₁

#487

yes

—

111

C₄×C₁₁

—

112

C₄×C₁₁

—

113

C₄×C₁₁

C₂×#103

yes

—

114

C₄×C₁₁

#472

yes

—

115

C₄×C₁₁

#473

yes

—

116

C₄×C₁₁

#492

yes

characteristic

117

C₄×C₁₁

#494

yes

characteristic

118

Dic₁₁

—

119

C₂²×Q₈

—

120

C₂×M₁₆

—

121

C₂²×C₈

D₄₄

yes

—

122

C₄⋊Q₈

—

123

C₄⋊Q₈

—

124

C₄⋊Q₈

—

125

C₄⋊Q₈

—

126

C₂×C₄⋊C₄

—

127

C₂×C₄⋊C₄

—

128

C₂×C₄²

C₂²×D₁₁

yes

characteristic

129

#108

—

130

#107

—

131

#107

—

132

C₄⋊C₈

—

133

C₄⋊C₈

—

134

C₄⋊C₈

D₄₄

yes

—

135

C₄⋊C₈

D₄₄

yes

—

136

C₂²⋊C₈

—

137

C₂²⋊C₈

—

138

C₄×C₈

—

139

C₄×C₈

—

140

C₄×C₈

C₄×D₁₁

yes

—

141

C₄×C₈

C₂²⋊D₁₁

yes

characteristic

142

C₄×C₈

C₂²⋊D₁₁

yes

characteristic

143

C₂×C₁₁

—

144

C₂×C₁₁

#1956

yes

characteristic

145

C₂×C₁₁

#1978

yes

characteristic

146

C₂×C₁₁

#1979

yes

characteristic

147

C₂×Q₈

—

148

C₂×Q₈

—

149

C₂×Q₈

—

150

C₂²×C₄

—

151

C₂²×C₄

C₂×D₄₄

yes

characteristic

152

C₂²×C₄

#4339

yes

characteristic

153

C₂²×C₄

#4339

yes

characteristic

154

M₁₆

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

#4314

yes

—

159

C₂×C₈

Dic₄₄

yes

—

160

C₂×C₈

(C₂×D₁₁)⋊C₄

yes

—

161

C₂×C₈

(C₂×D₁₁)⋊C₄

yes

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄²

C₂×C₄×D₁₁

yes

characteristic

167

C₄²

C₂×D₄₄

yes

characteristic

168

C₄²

C₂×D₄₄

yes

characteristic

169

C₄²

C₂×C₂²⋊D₁₁

yes

characteristic

170

C₁₁

#9771

yes

characteristic, complemented, Sylow

171

C₂³

#66928

yes

characteristic

172

Q₈

—

173

Q₈

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

C₄×D₄₄

yes

characteristic

179

C₂×C₄

C₄×D₄₄

yes

characteristic

180

C₂×C₄

#66927

yes

characteristic

181

C₂×C₄

C₂×#4314

yes

—

182

C₂×C₄

C₂×Dic₄₄

yes

—

183

C₂×C₄

C₂×(C₂×D₁₁)⋊C₄

yes

characteristic

184

C₂×C₄

#66983

yes

characteristic

185

C₂×C₄

#66983

yes

characteristic

186

C₈

—

187

C₈

—

188

C₈

—

189

C₈

#66880

yes

—

190

C₈

#66880

yes

—

191

C₂²

—

192

C₂²

—

193

C₂²

#10622294

yes

—

194

C₂²

#10622552

yes

characteristic

195

C₄

—

196

C₄

—

197

C₄

—

198

C₄

#10622306

yes

characteristic

199

C₄

#10622312

yes

characteristic

200

C₄

C₂×#66880

yes

—

201

C₄

#10622755

yes

—

202

C₄

#10622756

yes

—

203

C₂

—

204

C₂

#13069418

yes

characteristic

205

C₂

#13069526

yes

characteristic

206

C₂

#13069531

yes

characteristic

	subgroup	G/H
center	C₂²	#10622552
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1450	C₂
socle	C₂²×C₁₁	#390
prime radical	C₂³×C₁₁	#124
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1450	D₁₁
hypocenter	C₁₁	#9771
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1450

subgroup

G/H

center

C₂²

#10622552

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1450

C₂

C₂²×C₁₁

C₂³×C₁₁

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1450

N	H ≅ G/N	type
170. C₁₁	#9771	semidirect

H ≅ G/N

type

170. C₁₁

#9771

semidirect

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

subgroup	index
C₂×#10622295	2
#13068788	2
#13067300	2
#13067296	2
C₁₁×#1450	2
#9771	11

subgroup

index

C₁₁×#1450

Subgroups — #14653232

Conjugacy classes of subgroups

Complements

Maximal subgroups