Group #14653269 — subgroups

Subgroups — #14653269

Order 2816.

390 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 123 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	#13068754	C₂	1	1	yes	maximal, characteristic
3	#13067300	C₂	1	2	yes	maximal
4	#13067296	C₂	1	2	yes	maximal
5	C₁₁×#1452	C₂	1	1	yes	maximal, characteristic
6	C₂×#66922	C₂²	1	2	yes	—
7	C₁₁×#431	C₂²	1	1	yes	characteristic
8	C₁₁×#431	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×#66882	—	2	2	no	—
11	#10622537	C₂²	1	2	yes	—
12	#10622295	—	2	2	no	—
13	#10622295	C₄	1	4	yes	—
14	C₁₁×#322	—	2	2	no	—
15	#10622190	—	2	2	no	—
16	#10622120	—	2	4	no	—
17	#10622119	—	2	4	no	—
18	C₂²×Dic₂₂	—	2	2	no	—
19	C₂²×C₈×C₁₁	D₄	1	2	yes	—
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×#4318	—	2	2	no	—
24	#66922	—	2	2	no	—
25	#66922	—	2	2	no	—
26	#66922	—	2	2	no	—
27	#66922	C₂×C₄	1	4	yes	—
28	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
29	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
30	C₁₁×C₂²⋊C₈	—	2	1	no	—
31	C₁₁×C₂²⋊C₈	—	2	1	no	—
32	C₄×C₈×C₁₁	—	2	1	no	—
33	C₄×C₈×C₁₁	—	2	1	no	—
34	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
35	C₄×C₈×C₁₁	D₄	1	2	yes	—
36	#66882	—	2	8	no	—
37	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
38	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
39	#9778	—	11	1	no	maximal, Sylow
40	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
42	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
43	C₂²×Dic₁₁	—	4	2	no	—
44	C₂×Dic₂₂	—	2	4	no	—
45	C₂×Dic₂₂	—	4	2	no	—
46	C₂×Dic₂₂	—	8	4	no	—
47	C₂×C₈×C₁₁	—	2	2	no	—
48	C₂×C₈×C₁₁	—	2	2	no	—
49	C₂×C₈×C₁₁	—	2	4	no	—
50	C₂×C₈×C₁₁	C₂²⋊C₄	1	4	yes	—
51	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
52	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
53	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
54	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
55	C₄⋊Dic₁₁	—	2	4	no	—
56	C₄⋊Dic₁₁	—	2	4	no	—
57	C₄⋊Dic₁₁	—	4	2	no	—
58	C₄⋊Dic₁₁	—	4	2	no	—
59	#4318	—	4	4	no	—
60	C₂×C₁₁⋊C₈	—	4	2	no	—
61	C₂×#500	—	11	1	no	—
62	#1837	—	11	1	no	—
63	#1549	—	11	2	no	—
64	#1548	—	11	2	no	—
65	#1452	D₁₁	1	1	yes	characteristic
66	C₂³×C₁₁	#124	1	1	yes	characteristic
67	C₂×C₄×C₁₁	—	2	2	no	—
68	C₂×C₄×C₁₁	—	2	2	no	—
69	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
71	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
72	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
73	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
74	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
75	C₂×C₄×C₁₁	#137	1	4	yes	—
76	C₂×Dic₁₁	—	4	4	no	—
77	C₂×Dic₁₁	—	8	4	no	—
78	Dic₂₂	—	8	4	no	—
79	Dic₂₂	—	8	4	no	—
80	C₈×C₁₁	—	2	4	no	—
81	C₈×C₁₁	—	4	2	no	—
82	C₈×C₁₁	—	4	2	no	—
83	C₁₁⋊C₈	—	8	2	no	—
84	C₂×C₄⋊Q₈	—	11	2	no	—
85	#500	—	11	4	no	—
86	#500	—	22	2	no	—
87	#431	C₂×D₁₁	1	1	yes	characteristic
88	#431	C₂×D₁₁	1	1	yes	characteristic
89	C₂×#107	—	22	2	no	—
90	#423	—	11	2	no	—
91	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
92	#341	—	22	2	no	—
93	#333	—	22	4	no	—
94	#332	—	22	4	no	—
95	#322	—	2	2	no	—
96	C₂²×C₁₁	—	2	1	no	—
97	C₂²×C₁₁	—	2	1	no	—
98	C₂²×C₁₁	#390	1	1	yes	characteristic
99	C₂²×C₁₁	#491	1	2	yes	—
100	C₄×C₁₁	—	2	1	no	—
101	C₄×C₁₁	—	2	1	no	—
102	C₄×C₁₁	#419	1	2	yes	—
103	C₄×C₁₁	#472	1	2	yes	—
104	C₄×C₁₁	#473	1	2	yes	—
105	C₄×C₁₁	#497	1	2	yes	—
106	Dic₁₁	—	8	4	no	—
107	C₂²×Q₈	—	22	2	no	—
108	C₂×M₁₆	—	22	2	no	—
109	C₂²×C₈	D₄₄	1	2	yes	—
110	C₄⋊Q₈	—	11	4	no	—
111	C₄⋊Q₈	—	22	2	no	—
112	C₄⋊Q₈	—	22	2	no	—
113	C₄⋊Q₈	—	22	2	no	—
114	C₂×C₄⋊C₄	—	22	2	no	—
115	C₂×C₄⋊C₄	—	22	2	no	—
116	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
117	#107	—	22	8	no	—
118	C₄⋊C₈	—	22	2	no	—
119	C₄⋊C₈	—	22	2	no	—
120	C₄⋊C₈	D₄₄	1	2	yes	—
121	C₄⋊C₈	D₄₄	1	2	yes	—
122	C₂²⋊C₈	—	2	1	no	—
123	C₂²⋊C₈	—	2	1	no	—
124	C₄×C₈	—	2	1	no	—
125	C₄×C₈	—	2	1	no	—
126	C₄×C₈	C₄×D₁₁	1	2	yes	—
127	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
128	C₂×C₁₁	—	2	2	no	—
129	C₂×C₁₁	#1960	1	1	yes	characteristic
130	C₂×C₁₁	#1978	1	1	yes	characteristic
131	C₂×C₁₁	#1979	1	1	yes	characteristic
132	C₂×Q₈	—	22	4	no	—
133	C₂×Q₈	—	44	2	no	—
134	C₂×Q₈	—	88	4	no	—
135	C₂²×C₄	—	44	2	no	—
136	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
137	C₂²×C₄	#4339	1	1	yes	characteristic
138	C₂²×C₄	#4339	1	1	yes	characteristic
139	M₁₆	—	44	4	no	—
140	C₂×C₈	—	2	4	no	—
141	C₂×C₈	—	2	2	no	—
142	C₂×C₈	—	2	2	no	—
143	C₂×C₈	—	44	2	no	—
144	C₂×C₈	(C₂×D₁₁)⋊C₄	1	4	yes	—
145	C₄⋊C₄	—	22	4	no	—
146	C₄⋊C₄	—	22	4	no	—
147	C₄⋊C₄	—	44	2	no	—
148	C₄⋊C₄	—	44	2	no	—
149	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
150	C₄²	C₂×D₄₄	1	1	yes	characteristic
151	C₄²	C₂×D₄₄	1	1	yes	characteristic
152	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
153	C₁₁	#9778	1	1	yes	characteristic, complemented, Sylow
154	C₂³	#66928	1	1	yes	characteristic
155	Q₈	—	88	4	no	—
156	Q₈	—	88	4	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	44	4	no	—
160	C₂×C₄	—	88	4	no	—
161	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
162	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
163	C₂×C₄	#66927	1	1	yes	characteristic
164	C₂×C₄	#66962	1	4	yes	—
165	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
166	C₂×C₄	#66983	1	1	yes	characteristic
167	C₂×C₄	#66983	1	1	yes	characteristic
168	C₈	—	2	4	no	—
169	C₈	—	4	2	no	—
170	C₈	—	4	2	no	—
171	C₈	—	88	2	no	—
172	C₂²	—	2	1	no	—
173	C₂²	—	2	1	no	—
174	C₂²	#10622316	1	2	yes	—
175	C₂²	#10622552	1	1	yes	characteristic
176	C₄	—	2	1	no	—
177	C₄	—	2	1	no	—
178	C₄	—	88	4	no	—
179	C₄	#10622328	1	2	yes	—
180	C₄	#10622733	1	2	yes	—
181	C₄	#10622755	1	2	yes	—
182	C₄	#10622756	1	2	yes	—
183	C₂	—	2	2	no	—
184	C₂	#13069436	1	1	yes	characteristic
185	C₂	#13069526	1	1	yes	characteristic
186	C₂	#13069531	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622295

C₂

yes

maximal, characteristic

#13068754

C₂

yes

maximal, characteristic

#13067300

C₂

yes

maximal

#13067296

C₂

yes

maximal

C₁₁×#1452

C₂

yes

maximal, characteristic

C₂×#66922

C₂²

yes

—

C₁₁×#431

C₂²

yes

characteristic

C₁₁×#431

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66882

—

#10622537

C₂²

yes

—

#10622295

—

#10622295

C₄

yes

—

C₁₁×#322

—

#10622190

—

#10622120

—

#10622119

—

C₂²×Dic₂₂

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₁

—

C₂×C₄⋊Dic₁₁

—

—

—

—

—

C₂×C₄

yes

—

C₁₁×C₄⋊C₈

D₄

yes

—

C₁₁×C₄⋊C₈

D₄

yes

—

C₁₁×C₂²⋊C₈

—

C₁₁×C₂²⋊C₈

—

C₄×C₈×C₁₁

—

C₄×C₈×C₁₁

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

D₄

yes

—

#66882

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

#9778

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

C₂²×C₄×C₁₁

yes

C₂²×C₄×C₁₁

yes

C₂²×Dic₁₁

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

#4318

—

C₂×C₁₁⋊C₈

—

—

—

—

—

D₁₁

yes

characteristic

C₂³×C₁₁

#124

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₄×D₄

yes

characteristic

C₂×C₄×C₁₁

C₄×D₄

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

Dic₂₂

—

Dic₂₂

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₂×C₄⋊Q₈

—

#500

—

#500

—

#431

C₂×D₁₁

yes

characteristic

#431

C₂×D₁₁

yes

characteristic

C₂×#107

—

#423

—

C₂×C₄×C₈

C₂×D₁₁

yes

—

—

—

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

#390

yes

characteristic

C₂²×C₁₁

#491

yes

—

100

C₄×C₁₁

—

101

C₄×C₁₁

—

102

C₄×C₁₁

#419

yes

—

103

C₄×C₁₁

#472

yes

—

104

C₄×C₁₁

#473

yes

—

105

C₄×C₁₁

#497

yes

—

106

Dic₁₁

—

107

C₂²×Q₈

—

108

C₂×M₁₆

—

109

C₂²×C₈

D₄₄

yes

—

110

C₄⋊Q₈

—

111

C₄⋊Q₈

—

112

C₄⋊Q₈

—

113

C₄⋊Q₈

—

114

C₂×C₄⋊C₄

—

115

C₂×C₄⋊C₄

—

116

C₂×C₄²

C₂²×D₁₁

yes

characteristic

117

#107

—

118

C₄⋊C₈

—

119

C₄⋊C₈

—

120

C₄⋊C₈

D₄₄

yes

—

121

C₄⋊C₈

D₄₄

yes

—

122

C₂²⋊C₈

—

123

C₂²⋊C₈

—

124

C₄×C₈

—

125

C₄×C₈

—

126

C₄×C₈

C₄×D₁₁

yes

—

127

C₄×C₈

C₂²⋊D₁₁

yes

—

128

C₂×C₁₁

—

129

C₂×C₁₁

#1960

yes

characteristic

130

C₂×C₁₁

#1978

yes

characteristic

131

C₂×C₁₁

#1979

yes

characteristic

132

C₂×Q₈

—

133

C₂×Q₈

—

134

C₂×Q₈

—

135

C₂²×C₄

—

136

C₂²×C₄

C₂×D₄₄

yes

characteristic

137

C₂²×C₄

#4339

yes

characteristic

138

C₂²×C₄

#4339

yes

characteristic

139

M₁₆

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

(C₂×D₁₁)⋊C₄

yes

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

147

C₄⋊C₄

—

148

C₄⋊C₄

—

149

C₄²

C₂×C₄×D₁₁

yes

characteristic

150

C₄²

C₂×D₄₄

yes

characteristic

151

C₄²

C₂×D₄₄

yes

characteristic

152

C₄²

C₂×C₂²⋊D₁₁

yes

characteristic

153

C₁₁

#9778

yes

characteristic, complemented, Sylow

154

C₂³

#66928

yes

characteristic

155

Q₈

—

156

Q₈

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

C₄×D₄₄

yes

characteristic

162

C₂×C₄

C₄×D₄₄

yes

characteristic

163

C₂×C₄

#66927

yes

characteristic

164

C₂×C₄

#66962

yes

—

165

C₂×C₄

C₂×(C₂×D₁₁)⋊C₄

yes

characteristic

166

C₂×C₄

#66983

yes

characteristic

167

C₂×C₄

#66983

yes

characteristic

168

C₈

—

169

C₈

—

170

C₈

—

171

C₈

—

172

C₂²

—

173

C₂²

—

174

C₂²

#10622316

yes

—

175

C₂²

#10622552

yes

characteristic

176

C₄

—

177

C₄

—

178

C₄

—

179

C₄

#10622328

yes

—

180

C₄

#10622733

yes

—

181

C₄

#10622755

yes

—

182

C₄

#10622756

yes

—

183

C₂

—

184

C₂

#13069436

yes

characteristic

185

C₂

#13069526

yes

characteristic

186

C₂

#13069531

yes

characteristic

	subgroup	G/H
center	C₂²	#10622552
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1452	C₂
socle	C₂²×C₁₁	#390
prime radical	C₂³×C₁₁	#124
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1452	D₁₁
hypocenter	C₁₁	#9778
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1452

subgroup

G/H

center

C₂²

#10622552

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1452

C₂

C₂²×C₁₁

C₂³×C₁₁

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1452

N	H ≅ G/N	type
153. C₁₁	#9778	semidirect

H ≅ G/N

type

153. C₁₁

#9778

semidirect

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

subgroup	index
C₂×#10622295	2
#13068754	2
#13067300	2
#13067296	2
C₁₁×#1452	2
#9778	11

subgroup

index

C₁₁×#1452

Subgroups — #14653269

Conjugacy classes of subgroups

Complements

Maximal subgroups