Group #14658836 — subgroups

Subgroups — #14658836

Order 2816.

410 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 145 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	#13069576	C₂	1	2	yes	maximal
2	#13069418	C₂	1	1	yes	maximal, characteristic
3	#13068743	C₂	1	2	yes	maximal
4	C₁₁⋊#1273	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1845	C₂	1	1	yes	maximal, characteristic
6	C₂×#66922	C₂²	1	1	yes	characteristic
7	C₂×C₁₁×#107	—	2	2	no	—
8	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₁₁×#384	C₂²	1	2	yes	—
10	C₂×#66880	—	2	2	no	—
11	#10622548	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
13	#10622167	—	2	4	no	—
14	#10622167	—	2	4	no	—
15	C₂²×Dic₂₂	—	2	1	no	—
16	C₂²×C₈×C₁₁	D₄	1	2	yes	—
17	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
18	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
19	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
20	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
21	C₂×C₄⋊Dic₁₁	—	2	2	no	—
22	C₂×C₄⋊Dic₁₁	—	2	2	no	—
23	C₂×C₄⋊Dic₁₁	—	2	1	no	—
24	C₂²×C₁₁⋊C₈	D₄	1	4	yes	—
25	#66922	—	2	2	no	—
26	#66922	—	2	1	no	—
27	#66922	Q₈	1	2	yes	—
28	C₁₁×#107	—	4	4	no	—
29	C₄×C₈×C₁₁	—	2	2	no	—
30	#66880	—	4	4	no	—
31	C₄×C₁₁⋊C₈	—	2	2	no	—
32	C₄×C₁₁⋊C₈	—	2	2	no	—
33	#10676	—	11	1	no	maximal, Sylow
34	C₂²×C₄×C₁₁	—	4	2	no	—
35	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
37	C₂²×Dic₁₁	—	4	1	no	—
38	C₂²×Dic₁₁	—	4	1	no	—
39	C₂×Dic₂₂	—	2	2	no	—
40	C₂×Dic₂₂	—	4	1	no	—
41	C₂×Dic₂₂	—	4	2	no	—
42	C₂×Dic₂₂	—	4	2	no	—
43	C₂×C₈×C₁₁	—	2	2	no	—
44	C₂×C₈×C₁₁	—	2	2	no	—
45	C₂×C₈×C₁₁	D₈	1	4	yes	—
46	C₁₁×C₄⋊C₄	—	4	4	no	—
47	C₁₁×C₄⋊C₄	—	4	4	no	—
48	C₁₁×C₄⋊C₄	—	4	4	no	—
49	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
50	C₄²×C₁₁	#41	1	2	yes	—
51	C₄²×C₁₁	#41	1	1	yes	characteristic
52	C₄⋊Dic₁₁	—	2	4	no	—
53	C₄⋊Dic₁₁	—	4	2	no	—
54	C₄⋊Dic₁₁	—	4	2	no	—
55	C₄⋊Dic₁₁	—	4	4	no	—
56	C₂×C₁₁⋊C₈	—	2	4	no	—
57	C₂×C₁₁⋊C₈	—	2	4	no	—
58	C₂×C₁₁⋊C₈	—	2	4	no	—
59	#1990	—	11	2	no	—
60	#1956	—	11	1	no	—
61	#1845	D₁₁	1	1	yes	characteristic
62	#1834	—	11	2	no	—
63	#1273	—	11	1	no	—
64	C₂³×C₁₁	#127	1	1	yes	characteristic
65	C₂×C₄×C₁₁	—	8	2	no	—
66	C₂×C₄×C₁₁	—	8	2	no	—
67	C₂×C₄×C₁₁	—	8	2	no	—
68	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
69	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
70	C₂×C₄×C₁₁	#123	1	2	yes	—
71	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
72	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
73	C₂×C₄×C₁₁	#135	1	4	yes	—
74	C₂×C₄×C₁₁	#137	1	4	yes	—
75	C₂×C₄×C₁₁	#137	1	2	yes	—
76	C₂×Dic₁₁	—	4	2	no	—
77	C₂×Dic₁₁	—	8	1	no	—
78	C₂×Dic₁₁	—	8	1	no	—
79	C₂×Dic₁₁	—	8	1	no	—
80	C₂×Dic₁₁	—	8	2	no	—
81	Dic₂₂	—	4	4	no	—
82	Dic₂₂	—	8	2	no	—
83	C₈×C₁₁	—	2	4	no	—
84	C₁₁⋊C₈	—	4	4	no	—
85	C₂×C₄⋊Q₈	—	11	1	no	—
86	C₂×#107	—	2	2	no	—
87	C₂×#103	—	22	2	no	—
88	C₂×C₄×C₈	—	11	2	no	—
89	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
90	#384	—	11	1	no	—
91	#384	C₂×D₁₁	1	2	yes	—
92	#340	—	22	4	no	—
93	#340	—	22	4	no	—
94	C₂²×C₁₁	#399	1	1	yes	characteristic
95	C₂²×C₁₁	#493	1	1	yes	characteristic
96	C₂²×C₁₁	#495	1	2	yes	—
97	C₂²×C₁₁	#497	1	2	yes	—
98	C₂²×C₁₁	#497	1	1	yes	characteristic
99	C₄×C₁₁	—	16	2	no	—
100	C₄×C₁₁	#474	1	2	yes	—
101	C₄×C₁₁	#479	1	4	yes	—
102	C₄×C₁₁	#480	1	2	yes	—
103	C₄×C₁₁	#485	1	4	yes	—
104	Dic₁₁	—	8	2	no	—
105	Dic₁₁	—	16	1	no	—
106	C₂²×Q₈	—	22	1	no	—
107	C₂²×C₈	—	11	4	no	—
108	C₂²×C₈	C₂²⋊D₁₁	1	2	yes	—
109	C₄⋊Q₈	—	11	2	no	—
110	C₄⋊Q₈	—	22	2	no	—
111	C₄⋊Q₈	—	22	1	no	—
112	C₂×C₄⋊C₄	—	2	2	no	—
113	C₂×C₄⋊C₄	—	2	2	no	—
114	C₂×C₄⋊C₄	—	2	2	no	—
115	C₂×C₄⋊C₄	—	22	2	no	—
116	C₂×C₄⋊C₄	—	22	2	no	—
117	C₂×C₄⋊C₄	—	22	1	no	—
118	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
119	#107	—	4	4	no	—
120	#103	—	44	4	no	—
121	C₄×C₈	—	2	2	no	—
122	C₄×C₈	—	22	2	no	—
123	C₄×C₈	—	22	2	no	—
124	C₂×C₁₁	#1709	1	1	yes	characteristic
125	C₂×C₁₁	#1718	1	2	yes	—
126	C₂×C₁₁	#1722	1	1	yes	characteristic
127	C₂×C₁₁	#2093	1	1	yes	characteristic
128	C₂×C₁₁	#2097	1	2	yes	—
129	C₂×Q₈	—	22	2	no	—
130	C₂×Q₈	—	44	1	no	—
131	C₂×Q₈	—	44	2	no	—
132	C₂×Q₈	—	44	2	no	—
133	C₂²×C₄	—	4	2	no	—
134	C₂²×C₄	—	44	1	no	—
135	C₂²×C₄	—	44	1	no	—
136	C₂²×C₄	D₄×D₁₁	1	2	yes	—
137	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
138	C₂×C₈	—	2	2	no	—
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	—	22	4	no	—
141	C₂×C₈	—	22	4	no	—
142	C₂×C₈	—	22	4	no	—
143	C₂×C₈	#4323	1	4	yes	—
144	C₄⋊C₄	—	4	4	no	—
145	C₄⋊C₄	—	4	4	no	—
146	C₄⋊C₄	—	4	4	no	—
147	C₄⋊C₄	—	22	4	no	—
148	C₄⋊C₄	—	44	2	no	—
149	C₄⋊C₄	—	44	4	no	—
150	C₄⋊C₄	—	44	2	no	—
151	C₄²	#4339	1	2	yes	—
152	C₄²	Q₈×D₁₁	1	1	yes	characteristic
153	C₄²	#4343	1	1	yes	characteristic
154	C₁₁	#10676	1	1	yes	characteristic, complemented, Sylow
155	C₂³	#66993	1	1	yes	characteristic
156	Q₈	—	44	4	no	—
157	Q₈	—	88	2	no	—
158	C₂×C₄	—	8	2	no	—
159	C₂×C₄	—	8	2	no	—
160	C₂×C₄	—	8	2	no	—
161	C₂×C₄	—	44	2	no	—
162	C₂×C₄	—	88	1	no	—
163	C₂×C₄	—	88	1	no	—
164	C₂×C₄	—	88	2	no	—
165	C₂×C₄	—	88	1	no	—
166	C₂×C₄	#66947	1	2	yes	—
167	C₂×C₄	#66949	1	2	yes	—
168	C₂×C₄	#66965	1	4	yes	—
169	C₂×C₄	#66971	1	4	yes	—
170	C₂×C₄	#66982	1	1	yes	characteristic
171	C₂×C₄	C₂×#4323	1	2	yes	—
172	C₂×C₄	#66995	1	2	yes	—
173	C₂×C₄	#66999	1	1	yes	characteristic
174	C₈	—	2	4	no	—
175	C₈	—	44	4	no	—
176	C₂²	#10622605	1	1	yes	characteristic
177	C₂²	#10622686	1	1	yes	characteristic
178	C₂²	#10622699	1	1	yes	characteristic
179	C₂²	#10622768	1	2	yes	—
180	C₂²	#10622803	1	2	yes	—
181	C₄	—	16	2	no	—
182	C₄	—	88	2	no	—
183	C₄	—	176	1	no	—
184	C₄	#10622490	1	4	yes	—
185	C₄	#10622501	1	4	yes	—
186	C₄	#10622580	1	2	yes	—
187	C₄	#10622700	1	2	yes	—
188	C₂	#13068221	1	1	yes	characteristic
189	C₂	#13068261	1	2	yes	—
190	C₂	#13068288	1	1	yes	characteristic
191	C₂	#13070145	1	1	yes	characteristic
192	C₂	#13070161	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13069576

C₂

yes

maximal

#13069418

C₂

yes

maximal, characteristic

#13068743

C₂

yes

maximal

C₁₁⋊#1273

C₂

yes

maximal, characteristic

C₁₁×#1845

C₂

yes

maximal, characteristic

C₂×#66922

C₂²

yes

characteristic

C₂×C₁₁×#107

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₁₁×#384

C₂²

yes

—

C₂×#66880

—

#10622548

C₂²

yes

characteristic

C₂×C₄×C₁₁⋊C₈

C₂²

yes

—

#10622167

—

#10622167

—

C₂²×Dic₂₂

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂×C₁₁×C₄⋊C₄

—

C₂×C₁₁×C₄⋊C₄

—

C₂×C₁₁×C₄⋊C₄

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₁

—

C₂×C₄⋊Dic₁₁

—

C₂×C₄⋊Dic₁₁

—

C₂²×C₁₁⋊C₈

D₄

yes

—

#66922

—

#66922

—

#66922

Q₈

yes

—

C₁₁×#107

—

C₄×C₈×C₁₁

—

#66880

—

C₄×C₁₁⋊C₈

—

C₄×C₁₁⋊C₈

—

#10676

—

maximal, Sylow

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×D₄

yes

—

C₂²×Dic₁₁

—

C₂²×Dic₁₁

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

D₈

yes

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₄²×C₁₁

C₂×Q₈

yes

characteristic

C₄²×C₁₁

#41

yes

—

C₄²×C₁₁

#41

yes

characteristic

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

#1990

—

#1956

—

#1845

D₁₁

yes

characteristic

#1834

—

#1273

—

C₂³×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₁

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₁

#123

yes

—

C₂×C₄×C₁₁

#123

yes

characteristic

C₂×C₄×C₁₁

C₂×D₈

yes

—

C₂×C₄×C₁₁

#135

yes

—

C₂×C₄×C₁₁

#137

yes

—

C₂×C₄×C₁₁

#137

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

Dic₂₂

—

Dic₂₂

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₂×C₄⋊Q₈

—

C₂×#107

—

C₂×#103

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

#384

—

#384

C₂×D₁₁

yes

—

#340

—

#340

—

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₂²×C₁₁

yes

—

C₂²×C₁₁

#497

yes

—

C₂²×C₁₁

#497

yes

characteristic

C₄×C₁₁

—

100

C₄×C₁₁

#474

yes

—

101

C₄×C₁₁

#479

yes

—

102

C₄×C₁₁

#480

yes

—

103

C₄×C₁₁

#485

yes

—

104

Dic₁₁

—

105

Dic₁₁

—

106

C₂²×Q₈

—

107

C₂²×C₈

—

108

C₂²×C₈

C₂²⋊D₁₁

yes

—

109

C₄⋊Q₈

—

110

C₄⋊Q₈

—

111

C₄⋊Q₈

—

112

C₂×C₄⋊C₄

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄⋊C₄

—

115

C₂×C₄⋊C₄

—

116

C₂×C₄⋊C₄

—

117

C₂×C₄⋊C₄

—

118

C₂×C₄²

C₂²×D₁₁

yes

characteristic

119

#107

—

120

#103

—

121

C₄×C₈

—

122

C₄×C₈

—

123

C₄×C₈

—

124

C₂×C₁₁

#1709

yes

characteristic

125

C₂×C₁₁

#1718

yes

—

126

C₂×C₁₁

#1722

yes

characteristic

127

C₂×C₁₁

#2093

yes

characteristic

128

C₂×C₁₁

#2097

yes

—

129

C₂×Q₈

—

130

C₂×Q₈

—

131

C₂×Q₈

—

132

C₂×Q₈

—

133

C₂²×C₄

—

134

C₂²×C₄

—

135

C₂²×C₄

—

136

C₂²×C₄

D₄×D₁₁

yes

—

137

C₂²×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

#4323

yes

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

147

C₄⋊C₄

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₄²

#4339

yes

—

152

C₄²

Q₈×D₁₁

yes

characteristic

153

C₄²

#4343

yes

characteristic

154

C₁₁

#10676

yes

characteristic, complemented, Sylow

155

C₂³

#66993

yes

characteristic

156

Q₈

—

157

Q₈

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

#66947

yes

—

167

C₂×C₄

#66949

yes

—

168

C₂×C₄

#66965

yes

—

169

C₂×C₄

#66971

yes

—

170

C₂×C₄

#66982

yes

characteristic

171

C₂×C₄

C₂×#4323

yes

—

172

C₂×C₄

#66995

yes

—

173

C₂×C₄

#66999

yes

characteristic

174

C₈

—

175

C₈

—

176

C₂²

#10622605

yes

characteristic

177

C₂²

#10622686

yes

characteristic

178

C₂²

#10622699

yes

characteristic

179

C₂²

#10622768

yes

—

180

C₂²

#10622803

yes

—

181

C₄

—

182

C₄

—

183

C₄

—

176

—

184

C₄

#10622490

yes

—

185

C₄

#10622501

yes

—

186

C₄

#10622580

yes

—

187

C₄

#10622700

yes

—

188

C₂

#13068221

yes

characteristic

189

C₂

#13068261

yes

—

190

C₂

#13068288

yes

characteristic

191

C₂

#13070145

yes

characteristic

192

C₂

#13070161

yes

—

	subgroup	G/H
center	C₂³	#66993
commutator, cosocle	C₂×C₄²×C₁₁	C₂³
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1845	C₂
socle, prime radical	C₂³×C₁₁	#127
hypercenter	#1845	D₁₁
hypocenter	C₁₁	#10676
LCS	G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

subgroup

G/H

center

C₂³

#66993

commutator, cosocle

C₂×C₄²×C₁₁

C₂³

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1845

C₂

C₂³×C₁₁

D₁₁

C₁₁

G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

N	H ≅ G/N	type
154. C₁₁	#10676	semidirect

H ≅ G/N

type

154. C₁₁

#10676

semidirect

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

subgroup	index
#13069576	2
#13069418	2
#13068743	2
C₁₁⋊#1273	2
C₁₁×#1845	2
#10676	11

subgroup

index

#13069576

#13069418

#13068743

C₁₁⋊#1273

C₁₁×#1845

#10676

Subgroups — #14658836

Conjugacy classes of subgroups

Complements

Maximal subgroups