Group #14644791 — subgroups

Subgroups — #14644791

Order 2816.

368 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 143 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	#13067281	C₂	1	1	yes	maximal, characteristic
2	#13067211	C₂	1	1	yes	maximal, characteristic
3	#13066905	C₂	1	2	yes	maximal
4	#13066505	C₂	1	2	yes	maximal
5	C₁₁×#2960	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#533	C₂²	1	1	yes	characteristic
7	C₁₁×#446	—	2	2	no	—
8	C₈×Q₈×C₁₁	—	2	2	no	—
9	C₁₁×#424	C₄	1	2	yes	—
10	C₁₁×#423	C₂²	1	1	yes	characteristic
11	C₁₁×#405	C₄	1	2	yes	—
12	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	#10622538	C₂²	1	2	yes	—
14	C₄×#4318	C₂²	1	2	yes	—
15	#10622185	C₄	1	4	yes	—
16	#10622181	C₄	1	4	yes	—
17	#10622093	—	2	2	no	—
18	#10622092	—	2	2	no	—
19	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
20	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
23	C₁₁×#125	C₂×C₄	1	2	yes	—
24	C₁₁×C₂²⋊Q₈	—	2	2	no	—
25	C₄×Q₈×C₁₁	—	2	2	no	—
26	C₁₁×#117	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
28	C₂×#4318	—	2	2	no	—
29	C₁₁×C₄⋊C₈	—	2	4	no	—
30	C₁₁×C₄⋊C₈	—	2	2	no	—
31	C₁₁×#97	—	2	2	no	—
32	C₄×C₈×C₁₁	—	2	2	no	—
33	C₄×C₈×C₁₁	D₄	1	2	yes	—
34	C₄×C₈×C₁₁	D₄	1	2	yes	—
35	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
36	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
37	#66867	C₂×C₄	1	4	yes	—
38	C₄×C₁₁⋊C₈	—	2	2	no	—
39	C₄×C₁₁⋊C₈	—	2	2	no	—
40	#8244	—	11	1	no	maximal, Sylow
41	C₂×Q₈×C₁₁	—	2	2	no	—
42	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₁	#41	1	2	yes	—
44	C₁₁×M₁₆	—	4	2	no	—
45	C₂×C₈×C₁₁	—	2	2	no	—
46	C₂×C₈×C₁₁	—	2	2	no	—
47	C₂×C₈×C₁₁	—	4	1	no	—
48	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
50	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
51	C₁₁×C₄⋊C₄	—	2	4	no	—
52	C₁₁×C₄⋊C₄	—	2	2	no	—
53	C₁₁×C₄⋊C₄	C₄²	1	4	yes	—
54	C₁₁×C₂²⋊C₄	—	2	2	no	—
55	C₄²×C₁₁	—	2	2	no	—
56	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
57	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
58	C₄²×C₁₁	C₂×D₄	1	2	yes	—
59	#4318	—	4	4	no	—
60	C₂×C₁₁⋊C₈	—	2	4	no	—
61	C₂×C₁₁⋊C₈	—	2	4	no	—
62	#2960	D₁₁	1	1	yes	characteristic
63	#1544	—	11	1	no	—
64	#1526	—	11	1	no	—
65	#1451	—	11	2	no	—
66	#1299	—	11	2	no	—
67	C₂³×C₁₁	#117	1	1	yes	characteristic
68	Q₈×C₁₁	—	4	4	no	—
69	C₂×C₄×C₁₁	—	2	1	no	—
70	C₂×C₄×C₁₁	—	2	1	no	—
71	C₂×C₄×C₁₁	—	2	4	no	—
72	C₂×C₄×C₁₁	—	2	4	no	—
73	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
74	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
76	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
77	C₈×C₁₁	—	2	1	no	—
78	C₈×C₁₁	—	2	2	no	—
79	C₈×C₁₁	—	4	2	no	—
80	C₈×C₁₁	#101	1	2	yes	—
81	C₁₁⋊C₈	—	4	4	no	—
82	C₁₁⋊C₈	—	4	4	no	—
83	#533	C₂×D₁₁	1	1	yes	characteristic
84	#446	—	2	2	no	—
85	C₈×Q₈	—	2	2	no	—
86	#431	—	11	2	no	—
87	#424	Dic₁₁	1	2	yes	—
88	#423	C₂×D₁₁	1	1	yes	characteristic
89	#405	Dic₁₁	1	2	yes	—
90	C₄×M₁₆	—	11	2	no	—
91	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
92	#332	—	11	4	no	—
93	#330	—	11	4	no	—
94	#322	—	22	2	no	—
95	#322	—	22	2	no	—
96	C₂²×C₁₁	—	2	1	no	—
97	C₂²×C₁₁	—	2	2	no	—
98	C₂²×C₁₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
99	C₄×C₁₁	—	2	1	no	—
100	C₄×C₁₁	—	2	2	no	—
101	C₄×C₁₁	—	4	4	no	—
102	C₄×C₁₁	C₂×#101	1	1	yes	characteristic
103	C₄×C₁₁	#413	1	1	yes	characteristic
104	C₄×C₁₁	#444	1	4	yes	—
105	C₂×M₁₆	—	22	2	no	—
106	C₂×M₁₆	C₂×Dic₁₁	1	2	yes	—
107	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
108	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
109	C₄⋊Q₈	C₄×D₁₁	1	2	yes	—
110	#125	C₄×D₁₁	1	2	yes	—
111	C₂²⋊Q₈	—	2	2	no	—
112	C₄×Q₈	—	2	2	no	—
113	#117	C₂×Dic₁₁	1	2	yes	—
114	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
115	C₄⋊C₈	—	2	4	no	—
116	C₄⋊C₈	—	2	2	no	—
117	C₄⋊C₈	—	11	4	no	—
118	C₂²⋊C₈	—	22	2	no	—
119	#97	—	2	2	no	—
120	#97	—	11	4	no	—
121	C₄×C₈	—	2	2	no	—
122	C₄×C₈	—	22	2	no	—
123	C₄×C₈	—	22	2	no	—
124	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
125	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
126	C₂×C₁₁	—	4	1	no	—
127	C₂×C₁₁	C₄×#101	1	1	yes	characteristic
128	C₂×C₁₁	#1765	1	2	yes	—
129	C₂×Q₈	—	2	2	no	—
130	C₂²×C₄	#4339	1	2	yes	—
131	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
132	M₁₆	—	4	2	no	—
133	M₁₆	—	44	4	no	—
134	C₂×C₈	—	2	2	no	—
135	C₂×C₈	—	2	2	no	—
136	C₂×C₈	—	4	1	no	—
137	C₂×C₈	—	22	4	no	—
138	C₂×C₈	—	22	4	no	—
139	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
140	C₂×C₈	C₂²⋊Dic₁₁	1	2	yes	—
141	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
142	C₄⋊C₄	—	2	4	no	—
143	C₄⋊C₄	—	2	2	no	—
144	C₄⋊C₄	C₄×Dic₁₁	1	4	yes	—
145	C₂²⋊C₄	—	2	2	no	—
146	C₄²	—	2	2	no	—
147	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
148	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
149	C₄²	C₂×C₂²⋊D₁₁	1	2	yes	—
150	C₁₁	#8244	1	1	yes	characteristic, complemented, Sylow
151	C₂³	#66979	1	1	yes	characteristic
152	Q₈	—	4	4	no	—
153	C₂×C₄	—	2	4	no	—
154	C₂×C₄	—	2	1	no	—
155	C₂×C₄	—	2	1	no	—
156	C₂×C₄	—	2	4	no	—
157	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
158	C₂×C₄	C₄×C₂²⋊D₁₁	1	2	yes	—
159	C₂×C₄	C₄×C₂²⋊D₁₁	1	2	yes	—
160	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
161	C₈	—	2	1	no	—
162	C₈	—	2	2	no	—
163	C₈	—	4	2	no	—
164	C₈	—	44	4	no	—
165	C₈	—	44	4	no	—
166	C₈	#66900	1	2	yes	—
167	C₂²	—	2	1	no	—
168	C₂²	—	2	2	no	—
169	C₂²	C₄×C₂²⋊Dic₁₁	1	1	yes	characteristic
170	C₄	—	2	1	no	—
171	C₄	—	2	2	no	—
172	C₄	—	4	4	no	—
173	C₄	#10622758	1	4	yes	—
174	C₄	C₂×#66900	1	1	yes	characteristic
175	C₄	#10622850	1	1	yes	characteristic
176	C₂	—	4	1	no	—
177	C₂	C₄×#66900	1	1	yes	characteristic
178	C₂	#13068458	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13067281

C₂

yes

maximal, characteristic

#13067211

C₂

yes

maximal, characteristic

#13066905

C₂

yes

maximal

#13066505

C₂

yes

maximal

C₁₁×#2960

C₂

yes

maximal, characteristic

C₁₁×#533

C₂²

yes

characteristic

C₁₁×#446

—

C₈×Q₈×C₁₁

—

C₁₁×#424

C₄

yes

—

C₁₁×#423

C₂²

yes

characteristic

C₁₁×#405

C₄

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

#10622538

C₂²

yes

—

C₄×#4318

C₂²

yes

—

#10622185

C₄

yes

—

#10622181

C₄

yes

—

#10622093

—

#10622092

—

C₂×C₁₁×M₁₆

C₂×C₄

yes

—

C₂²×C₈×C₁₁

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₁

C₂×C₄

yes

characteristic

C₁₁×C₄⋊Q₈

C₂×C₄

yes

—

C₁₁×#125

C₂×C₄

yes

—

C₁₁×C₂²⋊Q₈

—

C₄×Q₈×C₁₁

—

C₁₁×#117

C₂×C₄

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×#4318

—

C₁₁×C₄⋊C₈

—

C₁₁×C₄⋊C₈

—

C₁₁×#97

—

C₄×C₈×C₁₁

—

C₄×C₈×C₁₁

D₄

yes

—

C₄×C₈×C₁₁

D₄

yes

—

C₂²⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

C₂×C₄

yes

—

#66867

C₂×C₄

yes

—

C₄×C₁₁⋊C₈

—

C₄×C₁₁⋊C₈

—

#8244

—

maximal, Sylow

C₂×Q₈×C₁₁

—

C₂²×C₄×C₁₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₁

#41

yes

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₁

C₂²⋊C₄

yes

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

characteristic

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

C₄²

yes

—

C₁₁×C₂²⋊C₄

—

C₄²×C₁₁

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

—

#4318

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

#2960

D₁₁

yes

—

—

—

—

C₂³×C₁₁

#117

yes

characteristic

Q₈×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₄×D₄

yes

—

C₂×C₄×C₁₁

C₄×D₄

yes

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

#101

yes

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

#533

C₂×D₁₁

yes

characteristic

#446

—

C₈×Q₈

—

#431

—

#424

Dic₁₁

yes

—

#423

C₂×D₁₁

yes

characteristic

#405

Dic₁₁

yes

—

C₄×M₁₆

—

C₂×C₄×C₈

C₂×D₁₁

yes

—

—

—

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

C₄×C₂²⋊C₄

yes

characteristic

C₄×C₁₁

—

100

C₄×C₁₁

—

101

C₄×C₁₁

—

102

C₄×C₁₁

C₂×#101

yes

characteristic

103

C₄×C₁₁

#413

yes

characteristic

104

C₄×C₁₁

#444

yes

—

105

C₂×M₁₆

—

106

C₂×M₁₆

C₂×Dic₁₁

yes

—

107

C₂²×C₈

C₂×Dic₁₁

yes

characteristic

108

C₂²×C₈

C₂×Dic₁₁

yes

characteristic

109

C₄⋊Q₈

C₄×D₁₁

yes

—

110

#125

C₄×D₁₁

yes

—

111

C₂²⋊Q₈

—

112

C₄×Q₈

—

113

#117

C₂×Dic₁₁

yes

—

114

C₂×C₄²

C₂²×D₁₁

yes

characteristic

115

C₄⋊C₈

—

116

C₄⋊C₈

—

117

C₄⋊C₈

—

118

C₂²⋊C₈

—

119

#97

—

120

#97

—

121

C₄×C₈

—

122

C₄×C₈

—

123

C₄×C₈

—

124

C₄×C₈

C₂²⋊D₁₁

yes

—

125

C₄×C₈

C₂²⋊D₁₁

yes

—

126

C₂×C₁₁

—

127

C₂×C₁₁

C₄×#101

yes

characteristic

128

C₂×C₁₁

#1765

yes

—

129

C₂×Q₈

—

130

C₂²×C₄

#4339

yes

—

131

C₂²×C₄

C₂²×Dic₁₁

yes

characteristic

132

M₁₆

—

133

M₁₆

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

C₂²⋊Dic₁₁

yes

characteristic

140

C₂×C₈

C₂²⋊Dic₁₁

yes

—

141

C₂×C₈

C₂²⋊Dic₁₁

yes

characteristic

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄⋊C₄

C₄×Dic₁₁

yes

—

145

C₂²⋊C₄

—

146

C₄²

—

147

C₄²

C₂×C₄×D₁₁

yes

characteristic

148

C₄²

C₂×C₄×D₁₁

yes

characteristic

149

C₄²

C₂×C₂²⋊D₁₁

yes

—

150

C₁₁

#8244

yes

characteristic, complemented, Sylow

151

C₂³

#66979

yes

characteristic

152

Q₈

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

C₂×C₄×Dic₁₁

yes

characteristic

158

C₂×C₄

C₄×C₂²⋊D₁₁

yes

—

159

C₂×C₄

C₄×C₂²⋊D₁₁

yes

—

160

C₂×C₄

C₂×C₂²⋊Dic₁₁

yes

characteristic

161

C₈

—

162

C₈

—

163

C₈

—

164

C₈

—

165

C₈

—

166

C₈

#66900

yes

—

167

C₂²

—

168

C₂²

—

169

C₂²

C₄×C₂²⋊Dic₁₁

yes

characteristic

170

C₄

—

171

C₄

—

172

C₄

—

173

C₄

#10622758

yes

—

174

C₄

C₂×#66900

yes

characteristic

175

C₄

#10622850

yes

characteristic

176

C₂

—

177

C₂

C₄×#66900

yes

characteristic

178

C₂

#13068458

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₁₁
commutator	C₂×C₄×C₁₁	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#2960	C₂
socle	C₂²×C₁₁	C₄×C₂²⋊C₄
prime radical	C₂³×C₁₁	#117
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#2960	D₁₁
hypocenter	C₁₁	#8244
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2960

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊Dic₁₁

commutator

C₂×C₄×C₁₁

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#2960

C₂

socle

C₂²×C₁₁

C₄×C₂²⋊C₄

prime radical

C₂³×C₁₁

#117

cosocle

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2960

N	H ≅ G/N	type
150. C₁₁	#8244	semidirect

H ≅ G/N

type

150. C₁₁

#8244

semidirect

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

subgroup	index
#13067281	2
#13067211	2
#13066905	2
#13066505	2
C₁₁×#2960	2
#8244	11

subgroup

index

C₁₁×#2960

Subgroups — #14644791

Conjugacy classes of subgroups

Complements

Maximal subgroups