Group #14653902 — subgroups

Subgroups — #14653902

Order 2816.

430 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 163 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	#13076979	C₂	1	1	yes	maximal, characteristic
2	#13068733	C₂	1	1	yes	maximal, characteristic
3	#13066500	C₂	1	4	yes	maximal
4	C₄×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂×#66923	—	2	1	no	—
6	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₁	—	2	1	no	—
8	C₄³×C₁₁	C₂²	1	1	yes	characteristic
9	#10622549	—	2	1	no	—
10	#10622548	C₂²	1	2	yes	—
11	#10622541	—	2	2	no	—
12	#10622541	C₄	1	4	yes	—
13	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
14	C₁₁×#336	—	2	1	no	—
15	#10622162	—	2	2	no	—
16	C₂²×C₈×C₁₁	—	2	2	no	—
17	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₁₁	D₄	1	2	yes	—
19	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₁	—	2	2	no	—
23	C₂×C₄⋊Dic₁₁	—	2	2	no	—
24	C₂×C₄⋊Dic₁₁	C₂×C₄	1	4	yes	—
25	C₂×Dic₁₁⋊C₄	—	2	4	no	—
26	C₂²×C₁₁⋊C₈	—	2	2	no	—
27	#66923	—	4	2	no	—
28	#66923	—	4	2	no	—
29	C₁₁×C₄⋊C₈	—	2	2	no	—
30	C₁₁×C₄⋊C₈	Q₈	1	4	yes	—
31	C₄×C₈×C₁₁	—	4	2	no	—
32	C₁₁⋊#95	—	2	4	no	—
33	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
34	#9899	—	11	1	no	maximal, Sylow
35	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
36	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
37	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
40	C₂²×Dic₁₁	—	2	4	no	—
41	C₂×C₈×C₁₁	—	2	4	no	—
42	C₂×C₈×C₁₁	—	4	2	no	—
43	C₂×C₈×C₁₁	—	4	2	no	—
44	C₄²×C₁₁	—	2	4	no	—
45	C₄²×C₁₁	—	2	2	no	—
46	C₄²×C₁₁	—	4	2	no	—
47	C₄²×C₁₁	D₈	1	2	yes	—
48	C₄²×C₁₁	SD₁₆	1	2	yes	—
49	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
50	C₄²×C₁₁	#41	1	2	yes	—
51	C₄⋊Dic₁₁	—	4	4	no	—
52	C₄⋊Dic₁₁	—	4	2	no	—
53	C₄⋊Dic₁₁	—	4	2	no	—
54	C₄⋊Dic₁₁	—	4	4	no	—
55	Dic₁₁⋊C₄	—	4	8	no	—
56	C₂×C₁₁⋊C₈	—	4	2	no	—
57	C₂×C₁₁⋊C₈	—	4	4	no	—
58	#2859	—	11	1	no	—
59	#1831	—	11	1	no	—
60	C₄×C₄⋊C₈	D₁₁	1	1	yes	characteristic
61	#1296	—	11	4	no	—
62	C₂³×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₄×C₁₁	—	2	2	no	—
64	C₂×C₄×C₁₁	—	2	2	no	—
65	C₂×C₄×C₁₁	—	2	2	no	—
66	C₂×C₄×C₁₁	—	2	2	no	—
67	C₂×C₄×C₁₁	—	2	2	no	—
68	C₂×C₄×C₁₁	—	2	2	no	—
69	C₂×C₄×C₁₁	#102	1	4	yes	—
70	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
71	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
72	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
73	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
74	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
75	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
76	C₂×C₄×C₁₁	#135	1	4	yes	—
77	C₂×C₄×C₁₁	#137	1	2	yes	—
78	C₂×Dic₁₁	—	4	4	no	—
79	C₂×Dic₁₁	—	4	4	no	—
80	C₂×Dic₁₁	—	4	4	no	—
81	C₈×C₁₁	—	4	4	no	—
82	C₁₁⋊C₈	—	8	2	no	—
83	C₂×#125	—	22	1	no	—
84	C₂×C₄⋊C₈	—	11	2	no	—
85	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
86	C₂×C₄×C₈	—	2	1	no	—
87	#389	—	11	4	no	—
88	#389	—	22	2	no	—
89	#384	—	11	2	no	—
90	#382	—	22	1	no	—
91	C₄³	C₂×D₁₁	1	1	yes	characteristic
92	#336	—	2	1	no	—
93	#336	—	22	2	no	—
94	C₂²×C₁₁	#391	1	1	yes	characteristic
95	C₂²×C₁₁	#413	1	2	yes	—
96	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
97	C₂²×C₁₁	#416	1	2	yes	—
98	C₂²×C₁₁	#419	1	1	yes	characteristic
99	C₄×C₁₁	—	2	4	no	—
100	C₄×C₁₁	—	2	2	no	—
101	C₄×C₁₁	—	4	2	no	—
102	C₄×C₁₁	#474	1	2	yes	—
103	C₄×C₁₁	#475	1	2	yes	—
104	C₄×C₁₁	#488	1	2	yes	—
105	C₄×C₁₁	#499	1	2	yes	—
106	Dic₁₁	—	8	4	no	—
107	C₂²×C₈	—	2	2	no	—
108	C₂²×C₈	—	22	2	no	—
109	#125	—	44	2	no	—
110	#125	—	44	2	no	—
111	C₂×C₄⋊C₄	—	11	4	no	—
112	C₂×C₄⋊C₄	—	22	4	no	—
113	C₂×C₄⋊C₄	—	22	2	no	—
114	C₂×C₄⋊C₄	—	22	2	no	—
115	C₂×C₄²	C₄×D₁₁	1	2	yes	—
116	C₂×C₄²	D₄₄	1	2	yes	—
117	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
118	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
119	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
120	C₄⋊C₈	—	2	2	no	—
121	C₄⋊C₈	—	22	4	no	—
122	C₄⋊C₈	Dic₂₂	1	4	yes	—
123	C₄×C₈	—	4	2	no	—
124	#95	—	22	4	no	—
125	C₂×C₁₁	#1540	1	2	yes	—
126	C₂×C₁₁	#1554	1	2	yes	—
127	C₂×C₁₁	#1988	1	1	yes	characteristic
128	C₂×C₁₁	#1991	1	1	yes	characteristic
129	C₂×C₁₁	#1998	1	1	yes	characteristic
130	C₂²×C₄	—	22	4	no	—
131	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
132	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
133	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
134	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
135	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
136	C₂×C₈	—	2	4	no	—
137	C₂×C₈	—	4	2	no	—
138	C₂×C₈	—	4	2	no	—
139	C₂×C₈	—	44	2	no	—
140	C₂×C₈	—	44	4	no	—
141	C₄⋊C₄	—	44	4	no	—
142	C₄⋊C₄	—	44	8	no	—
143	C₄⋊C₄	—	44	4	no	—
144	C₄⋊C₄	—	44	2	no	—
145	C₄⋊C₄	—	44	2	no	—
146	C₄²	—	2	4	no	—
147	C₄²	—	2	2	no	—
148	C₄²	—	4	2	no	—
149	C₄²	#4323	1	2	yes	—
150	C₄²	#4325	1	2	yes	—
151	C₄²	C₂×Dic₂₂	1	2	yes	—
152	C₄²	#4339	1	2	yes	—
153	C₁₁	#9899	1	1	yes	characteristic, complemented, Sylow
154	C₂³	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	44	4	no	—
162	C₂×C₄	—	44	4	no	—
163	C₂×C₄	—	44	4	no	—
164	C₂×C₄	#66873	1	4	yes	—
165	C₂×C₄	C₄×Dic₂₂	1	2	yes	—
166	C₂×C₄	#66922	1	1	yes	characteristic
167	C₂×C₄	#66928	1	1	yes	characteristic
168	C₂×C₄	#66957	1	4	yes	—
169	C₂×C₄	#66977	1	2	yes	—
170	C₂×C₄	C₂×#4323	1	1	yes	characteristic
171	C₂×C₄	C₂×#4325	1	1	yes	characteristic
172	C₂×C₄	#67004	1	2	yes	—
173	C₈	—	4	4	no	—
174	C₈	—	88	2	no	—
175	C₂²	#10622542	1	1	yes	characteristic
176	C₂²	C₂×#66873	1	1	yes	characteristic
177	C₂²	#10622617	1	1	yes	characteristic
178	C₂²	#10622726	1	2	yes	—
179	C₂²	#10622745	1	2	yes	—
180	C₄	—	2	4	no	—
181	C₄	—	2	2	no	—
182	C₄	—	4	2	no	—
183	C₄	—	88	4	no	—
184	C₄	#10622296	1	2	yes	—
185	C₄	#10622310	1	2	yes	—
186	C₄	#10622620	1	2	yes	—
187	C₄	#10622633	1	2	yes	—
188	C₂	#13067266	1	2	yes	—
189	C₂	#13067324	1	2	yes	—
190	C₂	#13069568	1	1	yes	characteristic
191	C₂	#13069581	1	1	yes	characteristic
192	C₂	#13069609	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13076979

C₂

yes

maximal, characteristic

#13068733

C₂

yes

maximal, characteristic

#13066500

C₂

yes

maximal

C₄×C₁₁×C₄⋊C₈

C₂

yes

maximal, characteristic

C₂×#66923

—

C₂×C₁₁×C₄⋊C₈

C₂²

yes

—

C₂×C₄×C₈×C₁₁

—

C₄³×C₁₁

C₂²

yes

characteristic

#10622549

—

#10622548

C₂²

yes

—

#10622541

—

#10622541

C₄

yes

—

C₂×C₄⋊(C₁₁⋊C₈)

C₂²

yes

—

C₁₁×#336

—

#10622162

—

C₂²×C₈×C₁₁

—

C₂×C₄²×C₁₁

C₂×C₄

yes

—

C₂×C₄²×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

D₄

yes

characteristic

C₂×C₄²×C₁₁

D₄

yes

characteristic

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₁

—

C₂×C₄⋊Dic₁₁

—

C₂×C₄⋊Dic₁₁

C₂×C₄

yes

—

C₂×Dic₁₁⋊C₄

—

C₂²×C₁₁⋊C₈

—

#66923

—

#66923

—

C₁₁×C₄⋊C₈

—

C₁₁×C₄⋊C₈

Q₈

yes

—

C₄×C₈×C₁₁

—

C₁₁⋊#95

—

C₄⋊(C₁₁⋊C₈)

—

#9899

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×Dic₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

D₈

yes

—

C₄²×C₁₁

SD₁₆

yes

—

C₄²×C₁₁

C₂×Q₈

yes

—

C₄²×C₁₁

#41

yes

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

Dic₁₁⋊C₄

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

#2859

—

#1831

—

C₄×C₄⋊C₈

D₁₁

yes

characteristic

#1296

—

C₂³×C₁₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#102

yes

—

C₂×C₄×C₁₁

C₄×Q₈

yes

—

C₂×C₄×C₁₁

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₁

#124

yes

characteristic

C₂×C₄×C₁₁

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

C₂×C₄×C₁₁

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₁

#135

yes

—

C₂×C₄×C₁₁

#137

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₂×#125

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

C₂×D₁₁

yes

—

C₂×C₄×C₈

—

—

—

—

—

C₄³

C₂×D₁₁

yes

characteristic

#336

—

#336

—

C₂²×C₁₁

#391

yes

characteristic

C₂²×C₁₁

#413

yes

—

C₂²×C₁₁

C₂×#102

yes

characteristic

C₂²×C₁₁

#416

yes

—

C₂²×C₁₁

#419

yes

characteristic

C₄×C₁₁

—

100

C₄×C₁₁

—

101

C₄×C₁₁

—

102

C₄×C₁₁

#474

yes

—

103

C₄×C₁₁

#475

yes

—

104

C₄×C₁₁

#488

yes

—

105

C₄×C₁₁

#499

yes

—

106

Dic₁₁

—

107

C₂²×C₈

—

108

C₂²×C₈

—

109

#125

—

110

#125

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄⋊C₄

—

115

C₂×C₄²

C₄×D₁₁

yes

—

116

C₂×C₄²

D₄₄

yes

—

117

C₂×C₄²

C₂²⋊D₁₁

yes

characteristic

118

C₂×C₄²

C₂²⋊D₁₁

yes

characteristic

119

C₂×C₄²

C₂²×D₁₁

yes

characteristic

120

C₄⋊C₈

—

121

C₄⋊C₈

—

122

C₄⋊C₈

Dic₂₂

yes

—

123

C₄×C₈

—

124

#95

—

125

C₂×C₁₁

#1540

yes

—

126

C₂×C₁₁

#1554

yes

—

127

C₂×C₁₁

#1988

yes

characteristic

128

C₂×C₁₁

#1991

yes

characteristic

129

C₂×C₁₁

#1998

yes

characteristic

130

C₂²×C₄

—

131

C₂²×C₄

(C₂×D₁₁)⋊C₄

yes

—

132

C₂²×C₄

(C₂×D₁₁)⋊C₄

yes

—

133

C₂²×C₄

C₂×C₄×D₁₁

yes

characteristic

134

C₂²×C₄

C₂×D₄₄

yes

characteristic

135

C₂²×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₄⋊C₄

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₄²

—

147

C₄²

—

148

C₄²

—

149

C₄²

#4323

yes

—

150

C₄²

#4325

yes

—

151

C₄²

C₂×Dic₂₂

yes

—

152

C₄²

#4339

yes

—

153

C₁₁

#9899

yes

characteristic, complemented, Sylow

154

C₂³

C₂×(C₂×D₁₁)⋊C₄

yes

characteristic

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

#66873

yes

—

165

C₂×C₄

C₄×Dic₂₂

yes

—

166

C₂×C₄

#66922

yes

characteristic

167

C₂×C₄

#66928

yes

characteristic

168

C₂×C₄

#66957

yes

—

169

C₂×C₄

#66977

yes

—

170

C₂×C₄

C₂×#4323

yes

characteristic

171

C₂×C₄

C₂×#4325

yes

characteristic

172

C₂×C₄

#67004

yes

—

173

C₈

—

174

C₈

—

175

C₂²

#10622542

yes

characteristic

176

C₂²

C₂×#66873

yes

characteristic

177

C₂²

#10622617

yes

characteristic

178

C₂²

#10622726

yes

—

179

C₂²

#10622745

yes

—

180

C₄

—

181

C₄

—

182

C₄

—

183

C₄

—

184

C₄

#10622296

yes

—

185

C₄

#10622310

yes

—

186

C₄

#10622620

yes

—

187

C₄

#10622633

yes

—

188

C₂

#13067266

yes

—

189

C₂

#13067324

yes

—

190

C₂

#13069568

yes

characteristic

191

C₂

#13069581

yes

characteristic

192

C₂

#13069609

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₁)⋊C₄
commutator	C₂²×C₄×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₄×C₁₁×C₄⋊C₈	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₄×C₄⋊C₈	D₁₁
hypocenter	C₁₁	#9899
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×C₄⋊C₈

subgroup

G/H

center

C₂³

C₂×(C₂×D₁₁)⋊C₄

commutator

C₂²×C₄×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₄×C₁₁×C₄⋊C₈

C₂

socle, prime radical

C₂³×C₁₁

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₁

C₂³

hypercenter

C₄×C₄⋊C₈

D₁₁

hypocenter

C₁₁

#9899

LCS

G ▷ C₂²×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×C₄⋊C₈

N	H ≅ G/N	type
153. C₁₁	#9899	semidirect

H ≅ G/N

type

153. C₁₁

#9899

semidirect

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

subgroup	index
#13076979	2
#13068733	2
#13066500	2
C₄×C₁₁×C₄⋊C₈	2
#9899	11

subgroup

index

C₄×C₁₁×C₄⋊C₈

Subgroups — #14653902

Conjugacy classes of subgroups

Complements

Maximal subgroups