Group #14670250 — subgroups

Subgroups — #14670250

Order 2816.

374 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 147 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	#13081719	C₂	1	1	yes	maximal, characteristic
2	#13070375	C₂	1	2	yes	maximal, complemented
3	#13070230	C₂	1	1	yes	maximal, characteristic
4	#13066702	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1757	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
7	C₁₁×#413	C₄	1	1	yes	characteristic
8	C₁₁×#410	C₄	1	1	yes	characteristic
9	C₁₁×#405	C₂²	1	2	yes	—
10	#10622753	—	2	4	no	—
11	C₂×#66876	—	2	2	no	—
12	C₂×#66876	C₂²	1	1	yes	characteristic
13	C₂×#66876	C₂²	1	2	yes	—
14	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
15	C₁₁×#344	C₄	1	2	yes	—
16	C₂²⋊(C₁₁⋊C₁₆)	—	2	2	no	—
17	C₄⋊(C₁₁⋊C₁₆)	—	2	4	no	—
18	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
19	C₁₁×#131	—	2	2	no	—
20	C₁₁×#131	—	2	2	no	—
21	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
22	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
23	C₂×C₁₁×M₁₆	Q₈	1	2	yes	—
24	C₂²×C₈×C₁₁	D₄	1	2	yes	—
25	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
26	C₁₁×#117	C₂×C₄	1	2	yes	—
27	C₁₁×#101	—	2	1	no	—
28	C₁₁×#100	—	2	1	no	—
29	C₁₁×#99	C₈	1	4	yes	—
30	C₁₁×#97	—	2	2	no	—
31	C₄×C₈×C₁₁	—	2	2	no	—
32	#66876	—	2	4	no	—
33	#66876	—	2	2	no	—
34	#66876	—	2	2	no	—
35	#66876	—	2	2	no	—
36	C₂×C₁₁⋊C₁₆	—	2	4	no	—
37	C₂×C₁₁⋊C₁₆	—	2	2	no	—
38	C₂×C₁₁⋊C₁₆	—	2	1	no	—
39	C₂×C₁₁⋊C₁₆	—	2	1	no	—
40	C₂×C₁₁⋊C₁₆	D₄	1	4	yes	—
41	#12915	—	11	1	no	maximal, Sylow
42	C₁₁×#41	—	2	2	no	—
43	C₁₁×#41	—	2	2	no	—
44	C₂×Q₈×C₁₁	M₁₆	1	1	yes	characteristic
45	C₂×D₄×C₁₁	C₂×C₈	1	2	yes	—
46	C₂×D₄×C₁₁	M₁₆	1	1	yes	characteristic
47	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
48	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
49	C₁₁×M₁₆	—	2	4	no	—
50	C₁₁×M₁₆	—	2	2	no	—
51	C₁₁×M₁₆	—	2	2	no	—
52	C₁₁×M₁₆	—	2	2	no	—
53	C₂×C₈×C₁₁	—	2	2	no	—
54	C₂×C₈×C₁₁	—	2	2	no	—
55	C₂×C₈×C₁₁	—	2	2	no	—
56	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
57	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
58	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
59	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
60	C₂×C₈×C₁₁	#41	1	2	yes	—
61	C₁₁×C₄⋊C₄	—	2	2	no	—
62	C₁₁×C₂²⋊C₄	C₂×C₈	1	4	yes	—
63	C₄²×C₁₁	—	2	2	no	—
64	C₁₁⋊C₁₆	—	2	4	no	—
65	C₁₁⋊C₁₆	—	4	1	no	—
66	C₁₁⋊C₁₆	—	4	1	no	—
67	#3407	—	11	1	no	—
68	#2151	—	11	2	no	—
69	#2113	—	11	1	no	—
70	#1757	D₁₁	1	1	yes	characteristic
71	#1378	—	11	2	no	—
72	C₂³×C₁₁	C₄⋊C₈	1	2	yes	—
73	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
74	Q₈×C₁₁	—	2	2	no	—
75	D₄×C₁₁	—	2	4	no	—
76	D₄×C₁₁	—	2	2	no	—
77	C₂×C₄×C₁₁	—	2	2	no	—
78	C₂×C₄×C₁₁	—	2	2	no	—
79	C₂×C₄×C₁₁	—	2	4	no	—
80	C₂×C₄×C₁₁	C₄⋊C₈	1	2	yes	—
81	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
83	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
84	C₂×C₄×C₁₁	#131	1	2	yes	—
85	C₈×C₁₁	—	2	2	no	—
86	C₈×C₁₁	—	4	2	no	—
87	C₈×C₁₁	#120	1	1	yes	characteristic
88	C₈×C₁₁	C₂²⋊Q₈	1	2	yes	—
89	C₈×C₁₁	#123	1	1	yes	characteristic
90	C₂×#131	C₂×D₁₁	1	1	yes	characteristic
91	#504	—	22	4	no	—
92	C₂×M₃₂	—	11	2	no	—
93	C₂×M₃₂	—	11	1	no	—
94	C₂×M₃₂	—	22	2	no	—
95	C₂²×C₁₆	—	11	1	no	—
96	#413	Dic₁₁	1	1	yes	characteristic
97	#410	Dic₁₁	1	1	yes	characteristic
98	#405	C₂×D₁₁	1	2	yes	—
99	C₄⋊C₁₆	—	22	4	no	—
100	C₂²⋊C₁₆	—	22	2	no	—
101	#344	Dic₁₁	1	2	yes	—
102	C₂²×C₁₁	—	2	2	no	—
103	C₂²×C₁₁	—	4	1	no	—
104	C₂²×C₁₁	—	4	2	no	—
105	C₂²×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
106	C₂²×C₁₁	C₈×D₄	1	2	yes	—
107	C₄×C₁₁	—	2	2	no	—
108	C₄×C₁₁	—	4	4	no	—
109	C₄×C₁₁	#385	1	1	yes	characteristic
110	C₄×C₁₁	#424	1	1	yes	characteristic
111	C₄×C₁₁	#435	1	2	yes	—
112	C₂×#41	C₂×Dic₁₁	1	1	yes	characteristic
113	#131	—	2	2	no	—
114	#131	—	2	2	no	—
115	C₂×M₁₆	Dic₂₂	1	2	yes	—
116	C₂×M₁₆	C₂×Dic₁₁	1	2	yes	—
117	C₂×M₁₆	C₂×Dic₁₁	1	1	yes	characteristic
118	C₂²×C₈	D₄₄	1	2	yes	—
119	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
120	#117	C₂×Dic₁₁	1	2	yes	—
121	M₃₂	—	22	4	no	—
122	M₃₂	—	22	2	no	—
123	M₃₂	—	22	2	no	—
124	M₃₂	—	22	2	no	—
125	C₂×C₁₆	—	11	4	no	—
126	C₂×C₁₆	—	22	4	no	—
127	C₂×C₁₆	—	22	1	no	—
128	C₂×C₁₆	—	22	1	no	—
129	C₂×C₁₆	—	22	2	no	—
130	#101	—	2	1	no	—
131	#100	—	2	1	no	—
132	#99	C₁₁⋊C₈	1	4	yes	—
133	#97	—	2	2	no	—
134	C₄×C₈	—	2	2	no	—
135	C₂×C₁₁	—	2	2	no	—
136	C₂×C₁₁	—	2	1	no	—
137	C₂×C₁₁	—	4	2	no	—
138	C₂×C₁₁	#1850	1	1	yes	characteristic
139	#41	—	2	2	no	—
140	#41	—	2	2	no	—
141	C₂×Q₈	#4318	1	1	yes	characteristic
142	C₂×D₄	C₂×C₁₁⋊C₈	1	2	yes	—
143	C₂×D₄	#4318	1	1	yes	characteristic
144	C₂²×C₄	C₄⋊Dic₁₁	1	2	yes	—
145	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
146	M₁₆	—	2	2	no	—
147	M₁₆	—	2	4	no	—
148	M₁₆	—	2	2	no	—
149	M₁₆	—	2	2	no	—
150	C₂×C₈	—	2	2	no	—
151	C₂×C₈	—	2	2	no	—
152	C₂×C₈	—	2	2	no	—
153	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
154	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
155	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
156	C₂×C₈	D₄×D₁₁	1	2	yes	—
157	C₂×C₈	#4341	1	2	yes	—
158	C₄⋊C₄	—	2	2	no	—
159	C₂²⋊C₄	C₂×C₁₁⋊C₈	1	4	yes	—
160	C₄²	—	2	2	no	—
161	C₁₆	—	22	4	no	—
162	C₁₆	—	44	1	no	—
163	C₁₆	—	44	1	no	—
164	C₁₁	#12915	1	1	yes	characteristic, complemented, Sylow
165	C₂³	C₄⋊(C₁₁⋊C₈)	1	2	yes	—
166	C₂³	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
167	Q₈	—	2	2	no	—
168	D₄	—	2	4	no	—
169	D₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	4	no	—
173	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	2	yes	—
174	C₂×C₄	C₂×#4318	1	1	yes	characteristic
175	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
176	C₂×C₄	D₄×Dic₁₁	1	2	yes	—
177	C₂×C₄	#67001	1	2	yes	—
178	C₈	—	2	2	no	—
179	C₈	—	4	2	no	—
180	C₈	#66931	1	2	yes	—
181	C₈	#66935	1	1	yes	characteristic
182	C₈	#66939	1	1	yes	characteristic
183	C₂²	—	2	2	no	—
184	C₂²	—	4	1	no	—
185	C₂²	—	4	2	no	—
186	C₂²	C₂×C₄⋊(C₁₁⋊C₈)	1	1	yes	characteristic
187	C₂²	D₄×C₁₁⋊C₈	1	2	yes	—
188	C₄	—	2	2	no	—
189	C₄	—	4	4	no	—
190	C₄	#10622563	1	1	yes	characteristic
191	C₄	#10622612	1	1	yes	characteristic
192	C₄	#10622624	1	2	yes	—
193	C₂	—	2	2	no	—
194	C₂	—	2	1	no	—
195	C₂	—	4	2	no	—
196	C₂	#13068796	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13081719

C₂

yes

maximal, characteristic

#13070375

C₂

yes

maximal, complemented

#13070230

C₂

yes

maximal, characteristic

#13066702

C₂

yes

maximal, complemented

C₁₁×#1757

C₂

yes

maximal, characteristic

C₂×C₁₁×#131

C₂²

yes

characteristic

C₁₁×#413

C₄

yes

characteristic

C₁₁×#410

C₄

yes

characteristic

C₁₁×#405

C₂²

yes

—

#10622753

—

C₂×#66876

—

C₂×#66876

C₂²

yes

characteristic

C₂×#66876

C₂²

yes

—

C₂²×C₁₁⋊C₁₆

C₂²

yes

characteristic

C₁₁×#344

C₄

yes

—

C₂²⋊(C₁₁⋊C₁₆)

—

C₄⋊(C₁₁⋊C₁₆)

—

C₂×C₁₁×#41

C₂×C₄

yes

characteristic

C₁₁×#131

—

C₁₁×#131

—

C₂×C₁₁×M₁₆

C₂×C₄

yes

—

C₂×C₁₁×M₁₆

C₂×C₄

yes

characteristic

C₂×C₁₁×M₁₆

Q₈

yes

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂²×C₈×C₁₁

C₂³

yes

characteristic

C₁₁×#117

C₂×C₄

yes

—

C₁₁×#101

—

C₁₁×#100

—

C₁₁×#99

C₈

yes

—

C₁₁×#97

—

C₄×C₈×C₁₁

—

—

—

—

—

C₂×C₁₁⋊C₁₆

—

C₂×C₁₁⋊C₁₆

—

C₂×C₁₁⋊C₁₆

—

C₂×C₁₁⋊C₁₆

—

C₂×C₁₁⋊C₁₆

D₄

yes

—

#12915

—

maximal, Sylow

C₁₁×#41

—

C₁₁×#41

—

C₂×Q₈×C₁₁

M₁₆

yes

characteristic

C₂×D₄×C₁₁

C₂×C₈

yes

—

C₂×D₄×C₁₁

M₁₆

yes

characteristic

C₂²×C₄×C₁₁

C₄⋊C₄

yes

—

C₂²×C₄×C₁₁

C₂²×C₄

yes

characteristic

C₁₁×M₁₆

—

C₁₁×M₁₆

—

C₁₁×M₁₆

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

C₂×D₄

yes

characteristic

C₂×C₈×C₁₁

C₂×D₄

yes

—

C₂×C₈×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₁

#41

yes

—

C₁₁×C₄⋊C₄

—

C₁₁×C₂²⋊C₄

C₂×C₈

yes

—

C₄²×C₁₁

—

C₁₁⋊C₁₆

—

C₁₁⋊C₁₆

—

C₁₁⋊C₁₆

—

—

—

—

D₁₁

yes

characteristic

#1378

—

C₂³×C₁₁

C₄⋊C₈

yes

—

C₂³×C₁₁

C₂²×C₈

yes

characteristic

Q₈×C₁₁

—

D₄×C₁₁

—

D₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₄⋊C₈

yes

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₄×D₄

yes

—

C₂×C₄×C₁₁

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₁

#131

yes

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

#120

yes

characteristic

C₈×C₁₁

C₂²⋊Q₈

yes

—

C₈×C₁₁

#123

yes

characteristic

C₂×#131

C₂×D₁₁

yes

characteristic

#504

—

C₂×M₃₂

—

C₂×M₃₂

—

C₂×M₃₂

—

C₂²×C₁₆

—

#413

Dic₁₁

yes

characteristic

#410

Dic₁₁

yes

characteristic

#405

C₂×D₁₁

yes

—

C₄⋊C₁₆

—

100

C₂²⋊C₁₆

—

101

#344

Dic₁₁

yes

—

102

C₂²×C₁₁

—

103

C₂²×C₁₁

—

104

C₂²×C₁₁

—

105

C₂²×C₁₁

C₂×C₄⋊C₈

yes

characteristic

106

C₂²×C₁₁

C₈×D₄

yes

—

107

C₄×C₁₁

—

108

C₄×C₁₁

—

109

C₄×C₁₁

#385

yes

characteristic

110

C₄×C₁₁

#424

yes

characteristic

111

C₄×C₁₁

#435

yes

—

112

C₂×#41

C₂×Dic₁₁

yes

characteristic

113

#131

—

114

#131

—

115

C₂×M₁₆

Dic₂₂

yes

—

116

C₂×M₁₆

C₂×Dic₁₁

yes

—

117

C₂×M₁₆

C₂×Dic₁₁

yes

characteristic

118

C₂²×C₈

D₄₄

yes

—

119

C₂²×C₈

C₂²×D₁₁

yes

characteristic

120

#117

C₂×Dic₁₁

yes

—

121

M₃₂

—

122

M₃₂

—

123

M₃₂

—

124

M₃₂

—

125

C₂×C₁₆

—

126

C₂×C₁₆

—

127

C₂×C₁₆

—

128

C₂×C₁₆

—

129

C₂×C₁₆

—

130

#101

—

131

#100

—

132

#99

C₁₁⋊C₈

yes

—

133

#97

—

134

C₄×C₈

—

135

C₂×C₁₁

—

136

C₂×C₁₁

—

137

C₂×C₁₁

—

138

C₂×C₁₁

#1850

yes

characteristic

139

#41

—

140

#41

—

141

C₂×Q₈

#4318

yes

characteristic

142

C₂×D₄

C₂×C₁₁⋊C₈

yes

—

143

C₂×D₄

#4318

yes

characteristic

144

C₂²×C₄

C₄⋊Dic₁₁

yes

—

145

C₂²×C₄

C₂²×Dic₁₁

yes

characteristic

146

M₁₆

—

147

M₁₆

—

148

M₁₆

—

149

M₁₆

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

C₄⋊Dic₁₁

yes

—

154

C₂×C₈

C₂×Dic₂₂

yes

characteristic

155

C₂×C₈

C₂×D₄₄

yes

characteristic

156

C₂×C₈

D₄×D₁₁

yes

—

157

C₂×C₈

#4341

yes

—

158

C₄⋊C₄

—

159

C₂²⋊C₄

C₂×C₁₁⋊C₈

yes

—

160

C₄²

—

161

C₁₆

—

162

C₁₆

—

163

C₁₆

—

164

C₁₁

#12915

yes

characteristic, complemented, Sylow

165

C₂³

C₄⋊(C₁₁⋊C₈)

yes

—

166

C₂³

C₂²×C₁₁⋊C₈

yes

characteristic

167

Q₈

—

168

D₄

—

169

D₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

C₄⋊(C₁₁⋊C₈)

yes

—

174

C₂×C₄

C₂×#4318

yes

characteristic

175

C₂×C₄

C₂×C₄⋊Dic₁₁

yes

characteristic

176

C₂×C₄

D₄×Dic₁₁

yes

—

177

C₂×C₄

#67001

yes

—

178

C₈

—

179

C₈

—

180

C₈

#66931

yes

—

181

C₈

#66935

yes

characteristic

182

C₈

#66939

yes

characteristic

183

C₂²

—

184

C₂²

—

185

C₂²

—

186

C₂²

C₂×C₄⋊(C₁₁⋊C₈)

yes

characteristic

187

C₂²

D₄×C₁₁⋊C₈

yes

—

188

C₄

—

189

C₄

—

190

C₄

#10622563

yes

characteristic

191

C₄

#10622612

yes

characteristic

192

C₄

#10622624

yes

—

193

C₂

—

194

C₂

—

195

C₂

—

196

C₂

#13068796

yes

characteristic

	subgroup	G/H
center	C₈	#66935
commutator	C₂³×C₁₁	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#1757	C₂
socle	C₂×C₁₁	#1850
prime radical	C₂×C₁₁×#41	C₂×C₄
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#1757	D₁₁
hypocenter	C₁₁	#12915
LCS	G ▷ C₂³×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #1757

subgroup

G/H

center

C₈

#66935

commutator

C₂³×C₁₁

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₁₁

Fitting

C₁₁×#1757

C₂

socle

C₂×C₁₁

#1850

prime radical

C₂×C₁₁×#41

C₂×C₄

cosocle

C₂²×C₈×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂³×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #1757

N	H ≅ G/N	type
2. #13070375	C₂	semidirect
4. #13066702	C₂	semidirect
164. C₁₁	#12915	semidirect

H ≅ G/N

type

2. #13070375

C₂

semidirect

4. #13066702

C₂

semidirect

164. C₁₁

#12915

semidirect

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

subgroup	index
#13081719	2
#13070375	2
#13070230	2
#13066702	2
C₁₁×#1757	2
#12915	11

subgroup

index

C₁₁×#1757

Subgroups — #14670250

Conjugacy classes of subgroups

Complements

Maximal subgroups