Group #14658826 — subgroups

Subgroups — #14658826

Order 2816.

442 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 165 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	#13069577	C₂	1	2	yes	maximal
2	#13069418	C₂	1	1	yes	maximal, characteristic
3	#13068776	C₂	1	1	yes	maximal, characteristic
4	#13068776	C₂	1	2	yes	maximal
5	C₁₁×#1273	C₂	1	1	yes	maximal, characteristic
6	C₂×#66922	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×#66882	—	2	4	no	—
10	C₂×#66882	—	2	2	no	—
11	C₂×#66880	—	2	2	no	—
12	#10622548	C₂²	1	2	yes	—
13	#10622548	C₂²	1	1	yes	characteristic
14	#10622189	—	2	4	no	—
15	C₂²×Dic₂₂	—	2	1	no	—
16	C₂²×C₈×C₁₁	D₄	1	2	yes	—
17	C₂²×C₈×C₁₁	D₄	1	4	yes	—
18	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
19	C₂×C₄⋊Dic₁₁	—	2	2	no	—
20	C₂×C₄⋊Dic₁₁	—	2	2	no	—
21	C₂×C₄⋊Dic₁₁	—	2	1	no	—
22	C₂×C₄⋊Dic₁₁	—	2	2	no	—
23	C₂×C₄⋊Dic₁₁	—	2	2	no	—
24	C₂×C₄⋊Dic₁₁	—	2	2	no	—
25	#66922	—	2	2	no	—
26	#66922	—	2	1	no	—
27	#66922	Q₈	1	2	yes	—
28	C₄×C₈×C₁₁	—	2	2	no	—
29	C₄×C₈×C₁₁	—	2	2	no	—
30	C₄×C₈×C₁₁	—	2	2	no	—
31	#66882	—	4	8	no	—
32	#66882	—	4	4	no	—
33	#66880	—	4	4	no	—
34	#10674	—	11	1	no	maximal, Sylow
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	2	no	—
39	C₂²×Dic₁₁	—	4	1	no	—
40	C₂×Dic₂₂	—	2	2	no	—
41	C₂×Dic₂₂	—	4	1	no	—
42	C₂×Dic₂₂	—	4	2	no	—
43	C₂×Dic₂₂	—	4	2	no	—
44	C₂×C₈×C₁₁	—	2	2	no	—
45	C₂×C₈×C₁₁	—	2	4	no	—
46	C₂×C₈×C₁₁	—	2	4	no	—
47	C₂×C₈×C₁₁	—	2	2	no	—
48	C₂×C₈×C₁₁	D₈	1	4	yes	—
49	C₂×C₈×C₁₁	Q₁₆	1	8	yes	—
50	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
51	C₄²×C₁₁	#41	1	1	yes	characteristic
52	C₄²×C₁₁	#41	1	2	yes	—
53	C₄⋊Dic₁₁	—	2	4	no	—
54	C₄⋊Dic₁₁	—	4	2	no	—
55	C₄⋊Dic₁₁	—	4	2	no	—
56	C₄⋊Dic₁₁	—	4	4	no	—
57	C₄⋊Dic₁₁	—	4	4	no	—
58	C₄⋊Dic₁₁	—	4	4	no	—
59	C₄⋊Dic₁₁	—	4	4	no	—
60	#1990	—	11	2	no	—
61	#1956	—	11	1	no	—
62	#1845	—	11	2	no	—
63	#1845	—	11	1	no	—
64	#1273	D₁₁	1	1	yes	characteristic
65	C₂³×C₁₁	#127	1	1	yes	characteristic
66	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
67	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
68	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
69	C₂×C₄×C₁₁	#123	1	2	yes	—
70	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
71	C₂×C₄×C₁₁	C₂×Q₁₆	1	4	yes	—
72	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	4	yes	—
73	C₂×C₄×C₁₁	#137	1	2	yes	—
74	C₂×Dic₁₁	—	4	2	no	—
75	C₂×Dic₁₁	—	8	1	no	—
76	C₂×Dic₁₁	—	8	1	no	—
77	C₂×Dic₁₁	—	8	1	no	—
78	C₂×Dic₁₁	—	8	2	no	—
79	C₂×Dic₁₁	—	8	2	no	—
80	C₂×Dic₁₁	—	8	2	no	—
81	C₂×Dic₁₁	—	8	2	no	—
82	Dic₂₂	—	4	4	no	—
83	Dic₂₂	—	8	2	no	—
84	C₈×C₁₁	—	2	4	no	—
85	C₈×C₁₁	—	2	8	no	—
86	C₂×C₄⋊Q₈	—	11	1	no	—
87	C₂×#107	—	22	4	no	—
88	C₂×#107	—	22	2	no	—
89	C₂×#103	—	22	2	no	—
90	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
91	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
92	#384	—	11	1	no	—
93	#384	—	11	2	no	—
94	#340	—	22	4	no	—
95	C₂²×C₁₁	#399	1	1	yes	characteristic
96	C₂²×C₁₁	#493	1	1	yes	characteristic
97	C₂²×C₁₁	#494	1	2	yes	—
98	C₂²×C₁₁	#496	1	2	yes	—
99	C₂²×C₁₁	#497	1	1	yes	characteristic
100	C₄×C₁₁	#474	1	2	yes	—
101	C₄×C₁₁	#477	1	4	yes	—
102	C₄×C₁₁	#480	1	2	yes	—
103	C₄×C₁₁	#484	1	4	yes	—
104	Dic₁₁	—	8	2	no	—
105	Dic₁₁	—	16	1	no	—
106	Dic₁₁	—	16	2	no	—
107	C₂²×Q₈	—	22	1	no	—
108	C₂²×C₈	D₄₄	1	2	yes	—
109	C₂²×C₈	D₄₄	1	4	yes	—
110	C₄⋊Q₈	—	11	2	no	—
111	C₄⋊Q₈	—	22	2	no	—
112	C₄⋊Q₈	—	22	1	no	—
113	C₂×C₄⋊C₄	—	22	2	no	—
114	C₂×C₄⋊C₄	—	22	2	no	—
115	C₂×C₄⋊C₄	—	22	1	no	—
116	C₂×C₄⋊C₄	—	22	2	no	—
117	C₂×C₄⋊C₄	—	22	2	no	—
118	C₂×C₄⋊C₄	—	22	2	no	—
119	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
120	#107	—	44	8	no	—
121	#107	—	44	4	no	—
122	#103	—	44	4	no	—
123	C₄×C₈	—	2	2	no	—
124	C₄×C₈	—	2	2	no	—
125	C₄×C₈	—	2	2	no	—
126	C₂×C₁₁	#1713	1	1	yes	characteristic
127	C₂×C₁₁	#1721	1	1	yes	characteristic
128	C₂×C₁₁	#1723	1	2	yes	—
129	C₂×C₁₁	#2093	1	1	yes	characteristic
130	C₂×C₁₁	#2095	1	2	yes	—
131	C₂×Q₈	—	22	2	no	—
132	C₂×Q₈	—	44	1	no	—
133	C₂×Q₈	—	44	2	no	—
134	C₂×Q₈	—	44	2	no	—
135	C₂²×C₄	—	44	1	no	—
136	C₂²×C₄	—	44	2	no	—
137	C₂²×C₄	—	44	1	no	—
138	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
139	C₂²×C₄	C₂×D₄₄	1	2	yes	—
140	C₂×C₈	—	2	4	no	—
141	C₂×C₈	—	2	2	no	—
142	C₂×C₈	—	2	4	no	—
143	C₂×C₈	—	2	2	no	—
144	C₂×C₈	D₈₈	1	4	yes	—
145	C₂×C₈	Dic₄₄	1	8	yes	—
146	C₄⋊C₄	—	22	4	no	—
147	C₄⋊C₄	—	44	2	no	—
148	C₄⋊C₄	—	44	2	no	—
149	C₄⋊C₄	—	44	4	no	—
150	C₄⋊C₄	—	44	4	no	—
151	C₄⋊C₄	—	44	4	no	—
152	C₄⋊C₄	—	44	4	no	—
153	C₄²	#4341	1	1	yes	characteristic
154	C₄²	#4341	1	2	yes	—
155	C₄²	Q₈×D₁₁	1	1	yes	characteristic
156	C₁₁	#10674	1	1	yes	characteristic, complemented, Sylow
157	C₂³	#66927	1	1	yes	characteristic
158	Q₈	—	44	4	no	—
159	Q₈	—	88	2	no	—
160	C₂×C₄	—	44	2	no	—
161	C₂×C₄	—	88	1	no	—
162	C₂×C₄	—	88	1	no	—
163	C₂×C₄	—	88	1	no	—
164	C₂×C₄	—	88	2	no	—
165	C₂×C₄	—	88	2	no	—
166	C₂×C₄	—	88	2	no	—
167	C₂×C₄	—	88	2	no	—
168	C₂×C₄	#66939	1	2	yes	—
169	C₂×C₄	#66939	1	1	yes	characteristic
170	C₂×C₄	#66950	1	1	yes	characteristic
171	C₂×C₄	#66950	1	2	yes	—
172	C₂×C₄	C₂×D₈₈	1	2	yes	—
173	C₂×C₄	C₂×Dic₄₄	1	4	yes	—
174	C₂×C₄	#66961	1	4	yes	—
175	C₂×C₄	#66962	1	2	yes	—
176	C₈	—	2	8	no	—
177	C₈	—	2	4	no	—
178	C₂²	#10622290	1	1	yes	characteristic
179	C₂²	#10622308	1	1	yes	characteristic
180	C₂²	#10622312	1	2	yes	—
181	C₂²	#10622325	1	2	yes	—
182	C₂²	#10622328	1	1	yes	characteristic
183	C₄	—	88	2	no	—
184	C₄	—	176	1	no	—
185	C₄	—	176	2	no	—
186	C₄	#10622335	1	4	yes	—
187	C₄	#10622349	1	2	yes	—
188	C₄	#10622459	1	2	yes	—
189	C₄	#10622463	1	4	yes	—
190	C₂	#13068234	1	1	yes	characteristic
191	C₂	#13068282	1	1	yes	characteristic
192	C₂	#13068293	1	2	yes	—
193	C₂	#13070143	1	1	yes	characteristic
194	C₂	#13070153	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13069577

C₂

yes

maximal

#13069418

C₂

yes

maximal, characteristic

#13068776

C₂

yes

maximal, characteristic

#13068776

C₂

yes

maximal

C₁₁×#1273

C₂

yes

maximal, characteristic

C₂×#66922

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₁

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

—

—

—

C₂²

yes

—

#10622548

C₂²

yes

characteristic

#10622189

—

C₂²×Dic₂₂

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₁

—

C₂×C₄⋊Dic₁₁

—

C₂×C₄⋊Dic₁₁

—

C₂×C₄⋊Dic₁₁

—

C₂×C₄⋊Dic₁₁

—

C₂×C₄⋊Dic₁₁

—

#66922

—

#66922

—

#66922

Q₈

yes

—

C₄×C₈×C₁₁

—

C₄×C₈×C₁₁

—

C₄×C₈×C₁₁

—

—

—

—

—

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×D₄

yes

—

C₂²×Dic₁₁

—

C₂²×Dic₁₁

—

C₂²×Dic₁₁

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

D₈

yes

—

C₂×C₈×C₁₁

Q₁₆

yes

—

C₄²×C₁₁

C₂×Q₈

yes

C₄²×C₁₁

yes

C₄²×C₁₁

yes

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

—

—

—

—

D₁₁

yes

characteristic

C₂³×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₁

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₁

#123

yes

characteristic

C₂×C₄×C₁₁

#123

yes

—

C₂×C₄×C₁₁

C₂×D₈

yes

—

C₂×C₄×C₁₁

C₂×Q₁₆

yes

—

C₂×C₄×C₁₁

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₁

#137

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

Dic₂₂

—

Dic₂₂

—

C₈×C₁₁

—

C₈×C₁₁

—

C₂×C₄⋊Q₈

—

C₂×#107

—

C₂×#107

—

C₂×#103

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

C₂×C₄×C₈

C₂×D₁₁

yes

—

#384

—

#384

—

#340

—

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₂²×C₁₁

yes

—

C₂²×C₁₁

#496

yes

—

C₂²×C₁₁

#497

yes

characteristic

100

C₄×C₁₁

#474

yes

—

101

C₄×C₁₁

#477

yes

—

102

C₄×C₁₁

#480

yes

—

103

C₄×C₁₁

#484

yes

—

104

Dic₁₁

—

105

Dic₁₁

—

106

Dic₁₁

—

107

C₂²×Q₈

—

108

C₂²×C₈

D₄₄

yes

—

109

C₂²×C₈

D₄₄

yes

—

110

C₄⋊Q₈

—

111

C₄⋊Q₈

—

112

C₄⋊Q₈

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄⋊C₄

—

115

C₂×C₄⋊C₄

—

116

C₂×C₄⋊C₄

—

117

C₂×C₄⋊C₄

—

118

C₂×C₄⋊C₄

—

119

C₂×C₄²

C₂²×D₁₁

yes

characteristic

120

#107

—

121

#107

—

122

#103

—

123

C₄×C₈

—

124

C₄×C₈

—

125

C₄×C₈

—

126

C₂×C₁₁

#1713

yes

characteristic

127

C₂×C₁₁

#1721

yes

characteristic

128

C₂×C₁₁

#1723

yes

—

129

C₂×C₁₁

#2093

yes

characteristic

130

C₂×C₁₁

#2095

yes

—

131

C₂×Q₈

—

132

C₂×Q₈

—

133

C₂×Q₈

—

134

C₂×Q₈

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

C₂×D₄₄

yes

characteristic

139

C₂²×C₄

C₂×D₄₄

yes

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

D₈₈

yes

—

145

C₂×C₈

Dic₄₄

yes

—

146

C₄⋊C₄

—

147

C₄⋊C₄

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄²

#4341

yes

characteristic

154

C₄²

#4341

yes

—

155

C₄²

Q₈×D₁₁

yes

characteristic

156

C₁₁

#10674

yes

characteristic, complemented, Sylow

157

C₂³

#66927

yes

characteristic

158

Q₈

—

159

Q₈

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

#66939

yes

—

169

C₂×C₄

#66939

yes

characteristic

170

C₂×C₄

#66950

yes

characteristic

171

C₂×C₄

#66950

yes

—

172

C₂×C₄

C₂×D₈₈

yes

—

173

C₂×C₄

C₂×Dic₄₄

yes

—

174

C₂×C₄

#66961

yes

—

175

C₂×C₄

#66962

yes

—

176

C₈

—

177

C₈

—

178

C₂²

#10622290

yes

characteristic

179

C₂²

#10622308

yes

characteristic

180

C₂²

#10622312

yes

—

181

C₂²

#10622325

yes

—

182

C₂²

#10622328

yes

characteristic

183

C₄

—

184

C₄

—

176

—

185

C₄

—

176

—

186

C₄

#10622335

yes

—

187

C₄

#10622349

yes

—

188

C₄

#10622459

yes

—

189

C₄

#10622463

yes

—

190

C₂

#13068234

yes

characteristic

191

C₂

#13068282

yes

characteristic

192

C₂

#13068293

yes

—

193

C₂

#13070143

yes

characteristic

194

C₂

#13070153

yes

—

	subgroup	G/H
center	C₂³	#66927
commutator, cosocle	C₂×C₄²×C₁₁	C₂³
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1273	C₂
socle, prime radical	C₂³×C₁₁	#127
hypercenter	#1273	D₁₁
hypocenter	C₁₁	#10674
LCS	G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center

C₂³

#66927

commutator, cosocle

C₂×C₄²×C₁₁

C₂³

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1273

C₂

C₂³×C₁₁

D₁₁

C₁₁

G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
156. C₁₁	#10674	semidirect

H ≅ G/N

type

156. C₁₁

#10674

semidirect

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

subgroup	index
#13069577	2
#13069418	2
#13068776	2
C₁₁×#1273	2
#10674	11

subgroup

index

C₁₁×#1273

Subgroups — #14658826

Conjugacy classes of subgroups

Complements

Maximal subgroups