Group #14656399 — subgroups

Subgroups — #14656399

Order 2816.

510 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 139 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	C₂×#10622463	C₂	1	2	yes	maximal
3	#13069552	C₂	1	1	yes	maximal, characteristic
4	C₂×#10622119	C₂	1	2	yes	maximal
5	C₁₁×#1277	C₂	1	1	yes	maximal, characteristic
6	C₂×#66922	C₂²	1	2	yes	—
7	C₂×C₄×Dic₂₂	C₂²	1	1	yes	characteristic
8	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×#66882	—	2	2	no	—
11	C₂×#66882	—	2	2	no	—
12	C₂×#66880	—	2	2	no	—
13	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
14	#10622463	—	2	4	no	—
15	#10622463	—	2	4	no	—
16	#10622295	—	2	4	no	—
17	#10622188	—	2	2	no	—
18	#10622119	—	2	4	no	—
19	C₂²×Dic₂₂	—	2	2	no	—
20	C₂²×Dic₂₂	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₁	—	2	2	no	—
22	C₂²×C₈×C₁₁	D₄	1	2	yes	—
23	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₁	—	2	2	no	—
25	C₂×C₄⋊Dic₁₁	—	2	2	no	—
26	C₂×C₄⋊Dic₁₁	D₄	1	1	yes	characteristic
27	C₂×Dic₁₁⋊C₄	—	2	1	no	—
28	C₂×C₄×Dic₁₁	—	2	1	no	—
29	C₂²×C₁₁⋊C₈	—	2	1	no	—
30	#66922	—	2	2	no	—
31	#66922	—	2	2	no	—
32	#66922	—	2	2	no	—
33	#66922	D₄	1	4	yes	—
34	C₄×Dic₂₂	—	2	2	no	—
35	C₄×Dic₂₂	—	2	2	no	—
36	C₁₁×C₄⋊C₈	—	2	2	no	—
37	C₁₁×C₄⋊C₈	D₄	1	4	yes	—
38	C₄×C₈×C₁₁	—	2	2	no	—
39	#66882	—	2	8	no	—
40	#66882	—	2	8	no	—
41	#66880	—	2	8	no	—
42	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
43	#10279	—	11	1	no	maximal, Sylow
44	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
47	C₂²×Dic₁₁	—	2	1	no	—
48	C₂²×Dic₁₁	—	2	1	no	—
49	C₂²×Dic₁₁	—	4	2	no	—
50	C₂×Dic₂₂	—	2	2	no	—
51	C₂×Dic₂₂	—	2	4	no	—
52	C₂×Dic₂₂	—	2	1	no	—
53	C₂×Dic₂₂	—	2	2	no	—
54	C₂×Dic₂₂	—	4	2	no	—
55	C₂×Dic₂₂	—	8	4	no	—
56	C₂×Dic₂₂	Q₁₆	1	2	yes	—
57	C₂×C₈×C₁₁	—	2	2	no	—
58	C₂×C₈×C₁₁	—	2	4	no	—
59	C₂×C₈×C₁₁	—	2	2	no	—
60	C₂×C₈×C₁₁	—	4	2	no	—
61	C₂×C₈×C₁₁	—	4	2	no	—
62	C₂×C₈×C₁₁	Q₁₆	1	4	yes	—
63	C₄²×C₁₁	C₂×D₄	1	2	yes	—
64	C₄²×C₁₁	C₂×D₄	1	2	yes	—
65	C₄⋊Dic₁₁	—	2	4	no	—
66	C₄⋊Dic₁₁	—	2	2	no	—
67	C₄⋊Dic₁₁	—	2	4	no	—
68	C₄⋊Dic₁₁	—	4	2	no	—
69	C₄⋊Dic₁₁	—	4	2	no	—
70	Dic₁₁⋊C₄	—	4	2	no	—
71	C₄×Dic₁₁	—	4	1	no	—
72	C₄×Dic₁₁	—	4	1	no	—
73	C₂×C₁₁⋊C₈	—	4	1	no	—
74	C₂×C₁₁⋊C₈	—	4	2	no	—
75	C₂×#500	—	11	1	no	—
76	C₂×#477	—	11	2	no	—
77	#1984	—	11	1	no	—
78	C₂×#333	—	11	2	no	—
79	#1277	D₁₁	1	1	yes	characteristic
80	C₂³×C₁₁	#121	1	1	yes	characteristic
81	C₂×C₄×C₁₁	—	2	2	no	—
82	C₂×C₄×C₁₁	#120	1	1	yes	characteristic
83	C₂×C₄×C₁₁	#120	1	2	yes	—
84	C₂×C₄×C₁₁	#121	1	2	yes	—
85	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
86	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
87	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
88	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
89	C₂×C₄×C₁₁	#137	1	2	yes	—
90	C₂×C₄×C₁₁	#137	1	2	yes	—
91	C₂×Dic₁₁	—	2	2	no	—
92	C₂×Dic₁₁	—	4	1	no	—
93	C₂×Dic₁₁	—	4	1	no	—
94	C₂×Dic₁₁	—	4	1	no	—
95	C₂×Dic₁₁	—	4	4	no	—
96	C₂×Dic₁₁	—	4	2	no	—
97	C₂×Dic₁₁	—	8	4	no	—
98	Dic₂₂	—	2	4	no	—
99	Dic₂₂	—	4	2	no	—
100	Dic₂₂	—	8	4	no	—
101	Dic₂₂	—	8	4	no	—
102	C₈×C₁₁	—	2	4	no	—
103	C₈×C₁₁	—	4	4	no	—
104	C₁₁⋊C₈	—	8	1	no	—
105	C₂×C₄⋊Q₈	—	11	2	no	—
106	C₂×C₄×Q₈	—	11	1	no	—
107	#500	—	22	4	no	—
108	#477	—	22	4	no	—
109	#477	—	22	4	no	—
110	C₂×#107	—	22	2	no	—
111	C₂×#107	—	22	2	no	—
112	C₂×C₄⋊C₈	—	11	1	no	—
113	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
114	C₂×#103	—	22	2	no	—
115	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
116	#336	—	22	2	no	—
117	#333	—	22	4	no	—
118	C₂²×C₁₁	#392	1	1	yes	characteristic
119	C₂²×C₁₁	#462	1	2	yes	—
120	C₂²×C₁₁	#467	1	1	yes	characteristic
121	C₂²×C₁₁	#470	1	1	yes	characteristic
122	C₂²×C₁₁	#472	1	2	yes	—
123	C₄×C₁₁	—	2	2	no	—
124	C₄×C₁₁	#451	1	2	yes	—
125	C₄×C₁₁	#451	1	2	yes	—
126	C₄×C₁₁	#452	1	2	yes	—
127	C₄×C₁₁	#494	1	1	yes	characteristic
128	C₄×C₁₁	#497	1	1	yes	characteristic
129	Dic₁₁	—	4	2	no	—
130	Dic₁₁	—	8	4	no	—
131	Dic₁₁	—	8	1	no	—
132	C₂²×Q₈	—	11	1	no	—
133	C₂²×Q₈	—	22	2	no	—
134	C₂²×C₈	—	2	2	no	—
135	C₂²×C₈	—	22	1	no	—
136	C₂²×C₈	D₄₄	1	2	yes	—
137	C₄⋊Q₈	—	11	4	no	—
138	C₄⋊Q₈	—	22	2	no	—
139	C₄⋊Q₈	—	22	2	no	—
140	C₄⋊Q₈	—	22	2	no	—
141	C₄×Q₈	—	22	2	no	—
142	C₄×Q₈	—	22	2	no	—
143	C₂×C₄⋊C₄	—	11	1	no	—
144	C₂×C₄⋊C₄	—	22	2	no	—
145	C₂×C₄⋊C₄	—	22	2	no	—
146	C₂×C₄⋊C₄	—	22	1	no	—
147	C₂×C₄²	—	22	1	no	—
148	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
149	#107	—	22	8	no	—
150	#107	—	22	8	no	—
151	C₄⋊C₈	—	2	2	no	—
152	C₄⋊C₈	—	22	2	no	—
153	C₄⋊C₈	D₄₄	1	4	yes	—
154	#103	—	22	8	no	—
155	C₄×C₈	—	2	2	no	—
156	C₂×C₁₁	#1676	1	2	yes	—
157	C₂×C₁₁	#1696	1	2	yes	—
158	C₂×C₁₁	#2001	1	1	yes	characteristic
159	C₂×C₁₁	#2016	1	1	yes	characteristic
160	C₂×C₁₁	#2018	1	1	yes	characteristic
161	C₂×Q₈	—	11	2	no	—
162	C₂×Q₈	—	22	1	no	—
163	C₂×Q₈	—	22	2	no	—
164	C₂×Q₈	—	22	4	no	—
165	C₂×Q₈	—	22	2	no	—
166	C₂×Q₈	—	44	2	no	—
167	C₂×Q₈	—	88	4	no	—
168	C₂²×C₄	—	22	1	no	—
169	C₂²×C₄	—	22	1	no	—
170	C₂²×C₄	—	44	2	no	—
171	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
172	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
173	C₂²×C₄	#4343	1	1	yes	characteristic
174	C₂×C₈	—	2	2	no	—
175	C₂×C₈	—	2	2	no	—
176	C₂×C₈	—	2	4	no	—
177	C₂×C₈	—	4	2	no	—
178	C₂×C₈	—	4	2	no	—
179	C₂×C₈	—	44	1	no	—
180	C₂×C₈	—	44	2	no	—
181	C₂×C₈	Dic₄₄	1	4	yes	—
182	C₄⋊C₄	—	22	4	no	—
183	C₄⋊C₄	—	22	2	no	—
184	C₄⋊C₄	—	22	4	no	—
185	C₄⋊C₄	—	44	2	no	—
186	C₄⋊C₄	—	44	2	no	—
187	C₄⋊C₄	—	44	2	no	—
188	C₄²	—	44	1	no	—
189	C₄²	—	44	1	no	—
190	C₄²	C₂×D₄₄	1	2	yes	—
191	C₄²	D₄×D₁₁	1	2	yes	—
192	C₁₁	#10279	1	1	yes	characteristic, complemented, Sylow
193	C₂³	#66948	1	1	yes	characteristic
194	Q₈	—	22	4	no	—
195	Q₈	—	44	2	no	—
196	Q₈	—	88	4	no	—
197	Q₈	—	88	4	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	22	2	no	—
200	C₂×C₄	—	44	1	no	—
201	C₂×C₄	—	44	1	no	—
202	C₂×C₄	—	44	2	no	—
203	C₂×C₄	—	44	1	no	—
204	C₂×C₄	—	44	4	no	—
205	C₂×C₄	—	88	4	no	—
206	C₂×C₄	#66927	1	1	yes	characteristic
207	C₂×C₄	#66935	1	1	yes	characteristic
208	C₂×C₄	#66935	1	2	yes	—
209	C₂×C₄	#66948	1	2	yes	—
210	C₂×C₄	C₂×Dic₄₄	1	2	yes	—
211	C₂×C₄	#66962	1	2	yes	—
212	C₂×C₄	#66965	1	1	yes	characteristic
213	C₂×C₄	#66968	1	2	yes	—
214	C₂×C₄	Q₁₆×D₁₁	1	1	yes	characteristic
215	C₈	—	2	4	no	—
216	C₈	—	4	4	no	—
217	C₈	—	88	1	no	—
218	C₂²	#10622284	1	1	yes	characteristic
219	C₂²	#10622462	1	2	yes	—
220	C₂²	#10622481	1	1	yes	characteristic
221	C₂²	#10622500	1	1	yes	characteristic
222	C₂²	#10622510	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	44	2	no	—
225	C₄	—	88	1	no	—
226	C₄	—	88	4	no	—
227	C₄	#10622312	1	1	yes	characteristic
228	C₄	#10622328	1	1	yes	characteristic
229	C₄	#10622352	1	2	yes	—
230	C₄	#10622396	1	2	yes	—
231	C₄	#10622421	1	2	yes	—
232	C₂	#13068021	1	2	yes	—
233	C₂	#13068145	1	2	yes	—
234	C₂	#13069627	1	1	yes	characteristic
235	C₂	#13069718	1	1	yes	characteristic
236	C₂	#13069726	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622295

C₂

yes

maximal, characteristic

C₂×#10622463

C₂

yes

maximal

#13069552

C₂

yes

maximal, characteristic

C₂×#10622119

C₂

yes

maximal

C₁₁×#1277

C₂

yes

maximal, characteristic

C₂×#66922

C₂²

yes

—

C₂×C₄×Dic₂₂

C₂²

yes

characteristic

C₂×C₁₁×C₄⋊C₈

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

—

—

—

C₂×C₄⋊(C₁₁⋊C₈)

C₂²

yes

—

—

—

—

—

C₂²×Dic₂₂

—

C₂²×Dic₂₂

D₄

yes

characteristic

C₂²×C₈×C₁₁

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₁

—

C₂×C₄⋊Dic₁₁

—

C₂×C₄⋊Dic₁₁

D₄

yes

characteristic

C₂×Dic₁₁⋊C₄

—

C₂×C₄×Dic₁₁

—

C₂²×C₁₁⋊C₈

—

—

—

—

D₄

yes

—

C₄×Dic₂₂

—

C₄×Dic₂₂

—

C₁₁×C₄⋊C₈

—

C₁₁×C₄⋊C₈

D₄

yes

—

C₄×C₈×C₁₁

—

#66882

—

#66882

—

#66880

—

C₄⋊(C₁₁⋊C₈)

—

#10279

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

#41

yes

characteristic

C₂²×Dic₁₁

—

C₂²×Dic₁₁

—

C₂²×Dic₁₁

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

Q₁₆

yes

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

Q₁₆

yes

—

C₄²×C₁₁

C₂×D₄

yes

—

C₄²×C₁₁

C₂×D₄

yes

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

Dic₁₁⋊C₄

—

C₄×Dic₁₁

—

C₄×Dic₁₁

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

—

—

—

—

D₁₁

yes

characteristic

C₂³×C₁₁

#121

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#120

yes

characteristic

C₂×C₄×C₁₁

#120

yes

—

C₂×C₄×C₁₁

#121

yes

—

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

C₂×Q₁₆

yes

—

C₂×C₄×C₁₁

C₂×Q₁₆

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

—

C₂×C₄×C₁₁

#137

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

Dic₂₂

—

Dic₂₂

—

100

Dic₂₂

—

101

Dic₂₂

—

102

C₈×C₁₁

—

103

C₈×C₁₁

—

104

C₁₁⋊C₈

—

105

C₂×C₄⋊Q₈

—

106

C₂×C₄×Q₈

—

107

#500

—

108

#477

—

109

#477

—

110

C₂×#107

—

111

C₂×#107

—

112

C₂×C₄⋊C₈

—

113

C₂×C₄⋊C₈

C₂×D₁₁

yes

—

114

C₂×#103

—

115

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

116

#336

—

117

#333

—

118

C₂²×C₁₁

#392

yes

characteristic

119

C₂²×C₁₁

#462

yes

—

120

C₂²×C₁₁

#467

yes

characteristic

121

C₂²×C₁₁

#470

yes

characteristic

122

C₂²×C₁₁

#472

yes

—

123

C₄×C₁₁

—

124

C₄×C₁₁

#451

yes

—

125

C₄×C₁₁

#451

yes

—

126

C₄×C₁₁

#452

yes

—

127

C₄×C₁₁

#494

yes

characteristic

128

C₄×C₁₁

#497

yes

characteristic

129

Dic₁₁

—

130

Dic₁₁

—

131

Dic₁₁

—

132

C₂²×Q₈

—

133

C₂²×Q₈

—

134

C₂²×C₈

—

135

C₂²×C₈

—

136

C₂²×C₈

D₄₄

yes

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

—

139

C₄⋊Q₈

—

140

C₄⋊Q₈

—

141

C₄×Q₈

—

142

C₄×Q₈

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄²

—

148

C₂×C₄²

C₂²×D₁₁

yes

characteristic

149

#107

—

150

#107

—

151

C₄⋊C₈

—

152

C₄⋊C₈

—

153

C₄⋊C₈

D₄₄

yes

—

154

#103

—

155

C₄×C₈

—

156

C₂×C₁₁

#1676

yes

—

157

C₂×C₁₁

#1696

yes

—

158

C₂×C₁₁

#2001

yes

characteristic

159

C₂×C₁₁

#2016

yes

characteristic

160

C₂×C₁₁

#2018

yes

characteristic

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

C₂×D₄₄

yes

characteristic

172

C₂²×C₄

D₄×D₁₁

yes

characteristic

173

C₂²×C₄

#4343

yes

characteristic

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

Dic₄₄

yes

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄²

—

189

C₄²

—

190

C₄²

C₂×D₄₄

yes

—

191

C₄²

D₄×D₁₁

yes

—

192

C₁₁

#10279

yes

characteristic, complemented, Sylow

193

C₂³

#66948

yes

characteristic

194

Q₈

—

195

Q₈

—

196

Q₈

—

197

Q₈

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

#66927

yes

characteristic

207

C₂×C₄

#66935

yes

characteristic

208

C₂×C₄

#66935

yes

—

209

C₂×C₄

#66948

yes

—

210

C₂×C₄

C₂×Dic₄₄

yes

—

211

C₂×C₄

#66962

yes

—

212

C₂×C₄

#66965

yes

characteristic

213

C₂×C₄

#66968

yes

—

214

C₂×C₄

Q₁₆×D₁₁

yes

characteristic

215

C₈

—

216

C₈

—

217

C₈

—

218

C₂²

#10622284

yes

characteristic

219

C₂²

#10622462

yes

—

220

C₂²

#10622481

yes

characteristic

221

C₂²

#10622500

yes

characteristic

222

C₂²

#10622510

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

#10622312

yes

characteristic

228

C₄

#10622328

yes

characteristic

229

C₄

#10622352

yes

—

230

C₄

#10622396

yes

—

231

C₄

#10622421

yes

—

232

C₂

#13068021

yes

—

233

C₂

#13068145

yes

—

234

C₂

#13069627

yes

characteristic

235

C₂

#13069718

yes

characteristic

236

C₂

#13069726

yes

characteristic

	subgroup	G/H
center	C₂³	#66948
commutator, cosocle	C₂×C₄²×C₁₁	C₂³
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1277	C₂
socle, prime radical	C₂³×C₁₁	#121
hypercenter	#1277	D₁₁
hypocenter	C₁₁	#10279
LCS	G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1277

subgroup

G/H

center

C₂³

#66948

commutator, cosocle

C₂×C₄²×C₁₁

C₂³

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1277

C₂

C₂³×C₁₁

D₁₁

C₁₁

G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1277

N	H ≅ G/N	type
192. C₁₁	#10279	semidirect

H ≅ G/N

type

192. C₁₁

#10279

semidirect

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

subgroup	index
C₂×#10622295	2
C₂×#10622463	2
#13069552	2
C₂×#10622119	2
C₁₁×#1277	2
#10279	11

subgroup

index

C₁₁×#1277

Subgroups — #14656399

Conjugacy classes of subgroups

Complements

Maximal subgroups