Group #14653257 — subgroups

Subgroups — #14653257

Order 2816.

390 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 119 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×#10622293	C₂	1	1	yes	maximal, characteristic
2	#13067302	C₂	1	2	yes	maximal
3	#13067298	C₂	1	2	yes	maximal
4	#13066908	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1837	C₂	1	1	yes	maximal, characteristic
6	C₂×#66922	C₂²	1	2	yes	—
7	C₁₁×#423	C₂²	1	1	yes	characteristic
8	C₁₁×#423	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×#66881	—	2	2	no	—
11	#10622538	C₂²	1	2	yes	—
12	#10622293	—	2	2	no	—
13	#10622293	C₄	1	4	yes	—
14	C₁₁×#341	—	2	2	no	—
15	#10622124	—	2	4	no	—
16	#10622119	—	2	4	no	—
17	#10622092	—	2	2	no	—
18	C₂²×Dic₂₂	—	2	2	no	—
19	C₂×C₁₁×M₁₆	—	2	1	no	—
20	C₂×C₁₁×M₁₆	—	2	1	no	—
21	C₂²×C₈×C₁₁	D₄	1	2	yes	—
22	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
23	C₂×C₄⋊Dic₁₁	—	2	2	no	—
24	C₂×C₄⋊Dic₁₁	—	2	2	no	—
25	#66922	—	2	2	no	—
26	#66922	—	2	2	no	—
27	#66922	—	2	2	no	—
28	#66922	C₂×C₄	1	4	yes	—
29	C₁₁×C₄⋊C₈	—	2	2	no	—
30	C₁₁×C₄⋊C₈	—	2	2	no	—
31	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
32	C₄×C₈×C₁₁	D₄	1	2	yes	—
33	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
34	#66881	—	2	8	no	—
35	C₄⋊(C₁₁⋊C₈)	D₄	1	4	yes	—
36	C₄×C₁₁⋊C₈	—	2	2	no	—
37	#9776	—	11	1	no	maximal, Sylow
38	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₁	#41	1	2	yes	—
40	C₂²×Dic₁₁	—	4	2	no	—
41	C₂×Dic₂₂	—	2	4	no	—
42	C₂×Dic₂₂	—	4	2	no	—
43	C₂×Dic₂₂	—	8	4	no	—
44	C₁₁×M₁₆	—	4	2	no	—
45	C₁₁×M₁₆	—	4	2	no	—
46	C₂×C₈×C₁₁	—	2	2	no	—
47	C₂×C₈×C₁₁	—	2	2	no	—
48	C₂×C₈×C₁₁	—	4	1	no	—
49	C₂×C₈×C₁₁	—	4	1	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	2	yes	—
54	C₄⋊Dic₁₁	—	2	4	no	—
55	C₄⋊Dic₁₁	—	2	4	no	—
56	C₄⋊Dic₁₁	—	4	2	no	—
57	C₄⋊Dic₁₁	—	4	2	no	—
58	C₂×C₁₁⋊C₈	—	2	4	no	—
59	C₂×#498	—	11	1	no	—
60	#1837	D₁₁	1	1	yes	characteristic
61	#1549	—	11	2	no	—
62	#1548	—	11	2	no	—
63	#1452	—	11	1	no	—
64	C₂³×C₁₁	#124	1	1	yes	characteristic
65	C₂×C₄×C₁₁	—	2	4	no	—
66	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
68	C₂×C₄×C₁₁	#121	1	2	yes	—
69	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
70	C₂×C₄×C₁₁	#137	1	2	yes	—
71	C₂×C₄×C₁₁	#137	1	2	yes	—
72	C₂×Dic₁₁	—	4	4	no	—
73	C₂×Dic₁₁	—	8	4	no	—
74	Dic₂₂	—	8	4	no	—
75	Dic₂₂	—	8	4	no	—
76	C₈×C₁₁	—	2	4	no	—
77	C₈×C₁₁	—	8	1	no	—
78	C₈×C₁₁	—	8	1	no	—
79	C₁₁⋊C₈	—	4	4	no	—
80	C₂×C₄⋊Q₈	—	11	2	no	—
81	#498	—	11	4	no	—
82	#498	—	22	2	no	—
83	#431	—	11	2	no	—
84	C₂×#106	—	22	2	no	—
85	#423	C₂×D₁₁	1	1	yes	characteristic
86	#423	C₂×D₁₁	1	1	yes	characteristic
87	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
88	#341	—	2	2	no	—
89	#333	—	22	4	no	—
90	#332	—	22	4	no	—
91	#322	—	22	2	no	—
92	C₂²×C₁₁	—	2	2	no	—
93	C₂²×C₁₁	#390	1	1	yes	characteristic
94	C₂²×C₁₁	#491	1	2	yes	—
95	C₄×C₁₁	—	2	2	no	—
96	C₄×C₁₁	#419	1	2	yes	—
97	C₄×C₁₁	#471	1	4	yes	—
98	C₄×C₁₁	#497	1	1	yes	characteristic
99	C₄×C₁₁	#497	1	1	yes	characteristic
100	Dic₁₁	—	8	4	no	—
101	C₂²×Q₈	—	22	2	no	—
102	C₂×M₁₆	—	2	1	no	—
103	C₂×M₁₆	—	2	1	no	—
104	C₂²×C₈	C₂²⋊D₁₁	1	2	yes	—
105	C₄⋊Q₈	—	11	4	no	—
106	C₄⋊Q₈	—	22	2	no	—
107	C₄⋊Q₈	—	22	2	no	—
108	C₄⋊Q₈	—	22	2	no	—
109	C₂×C₄⋊C₄	—	22	2	no	—
110	C₂×C₄⋊C₄	—	22	2	no	—
111	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
112	#106	—	22	8	no	—
113	C₄⋊C₈	—	2	2	no	—
114	C₄⋊C₈	—	2	2	no	—
115	C₄⋊C₈	—	11	4	no	—
116	C₂²⋊C₈	—	22	2	no	—
117	C₄×C₈	—	22	2	no	—
118	C₄×C₈	C₄×D₁₁	1	2	yes	—
119	C₄×C₈	D₄₄	1	2	yes	—
120	C₂×C₁₁	—	2	2	no	—
121	C₂×C₁₁	#1960	1	1	yes	characteristic
122	C₂×C₁₁	#1977	1	2	yes	—
123	C₂×Q₈	—	22	4	no	—
124	C₂×Q₈	—	44	2	no	—
125	C₂×Q₈	—	88	4	no	—
126	C₂²×C₄	—	44	2	no	—
127	C₂²×C₄	#4343	1	2	yes	—
128	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
129	M₁₆	—	4	2	no	—
130	M₁₆	—	4	2	no	—
131	C₂×C₈	—	2	2	no	—
132	C₂×C₈	—	2	2	no	—
133	C₂×C₈	—	4	1	no	—
134	C₂×C₈	—	4	1	no	—
135	C₂×C₈	—	22	4	no	—
136	C₂×C₈	(C₂×D₁₁)⋊C₄	1	4	yes	—
137	C₄⋊C₄	—	22	4	no	—
138	C₄⋊C₄	—	22	4	no	—
139	C₄⋊C₄	—	44	2	no	—
140	C₄⋊C₄	—	44	2	no	—
141	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
142	C₄²	C₂×D₄₄	1	1	yes	characteristic
143	C₄²	D₄×D₁₁	1	2	yes	—
144	C₁₁	#9776	1	1	yes	characteristic, complemented, Sylow
145	C₂³	#67000	1	1	yes	characteristic
146	Q₈	—	88	4	no	—
147	Q₈	—	88	4	no	—
148	C₂×C₄	—	2	4	no	—
149	C₂×C₄	—	44	4	no	—
150	C₂×C₄	—	88	4	no	—
151	C₂×C₄	#66946	1	2	yes	—
152	C₂×C₄	#66948	1	2	yes	—
153	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
154	C₂×C₄	#66993	1	1	yes	characteristic
155	C₂×C₄	#67004	1	2	yes	—
156	C₂×C₄	#67004	1	2	yes	—
157	C₈	—	2	4	no	—
158	C₈	—	8	1	no	—
159	C₈	—	8	1	no	—
160	C₈	—	44	4	no	—
161	C₂²	—	2	2	no	—
162	C₂²	#10622601	1	1	yes	characteristic
163	C₂²	#10622682	1	2	yes	—
164	C₄	—	2	2	no	—
165	C₄	—	88	4	no	—
166	C₄	#10622511	1	4	yes	—
167	C₄	#10622617	1	2	yes	—
168	C₄	#10622673	1	1	yes	characteristic
169	C₄	#10622673	1	1	yes	characteristic
170	C₂	—	2	2	no	—
171	C₂	#13069435	1	1	yes	characteristic
172	C₂	#13069517	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622293

C₂

yes

maximal, characteristic

#13067302

C₂

yes

maximal

#13067298

C₂

yes

maximal

#13066908

C₂

yes

maximal, characteristic

C₁₁×#1837

C₂

yes

maximal, characteristic

C₂×#66922

C₂²

yes

—

C₁₁×#423

C₂²

yes

characteristic

C₁₁×#423

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66881

—

#10622538

C₂²

yes

—

#10622293

—

#10622293

C₄

yes

—

C₁₁×#341

—

#10622124

—

#10622119

—

#10622092

—

C₂²×Dic₂₂

—

C₂×C₁₁×M₁₆

—

C₂×C₁₁×M₁₆

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₁

—

C₂×C₄⋊Dic₁₁

—

—

—

—

C₂×C₄

yes

—

C₁₁×C₄⋊C₈

—

C₁₁×C₄⋊C₈

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

D₄

yes

—

C₂²⋊(C₁₁⋊C₈)

—

#66881

—

C₄⋊(C₁₁⋊C₈)

D₄

yes

—

C₄×C₁₁⋊C₈

—

#9776

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

#41

yes

—

C₂²×Dic₁₁

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₁₁×M₁₆

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

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

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₂×C₁₁⋊C₈

—

C₂×#498

—

#1837

D₁₁

yes

—

—

—

C₂³×C₁₁

#124

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₄×D₄

yes

—

C₂×C₄×C₁₁

#121

yes

—

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

#137

yes

—

C₂×C₄×C₁₁

#137

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

Dic₂₂

—

Dic₂₂

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₂×C₄⋊Q₈

—

—

—

—

—

C₂×D₁₁

yes

characteristic

#423

C₂×D₁₁

yes

characteristic

C₂×C₄×C₈

C₂×D₁₁

yes

—

—

—

—

C₂²×C₁₁

—

C₂²×C₁₁

#390

yes

characteristic

C₂²×C₁₁

#491

yes

—

C₄×C₁₁

—

C₄×C₁₁

#419

yes

—

C₄×C₁₁

#471

yes

—

C₄×C₁₁

yes

C₄×C₁₁

yes

100

Dic₁₁

—

101

C₂²×Q₈

—

102

C₂×M₁₆

—

103

C₂×M₁₆

—

104

C₂²×C₈

C₂²⋊D₁₁

yes

—

105

C₄⋊Q₈

—

106

C₄⋊Q₈

—

107

C₄⋊Q₈

—

108

C₄⋊Q₈

—

109

C₂×C₄⋊C₄

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄²

C₂²×D₁₁

yes

characteristic

112

#106

—

113

C₄⋊C₈

—

114

C₄⋊C₈

—

115

C₄⋊C₈

—

116

C₂²⋊C₈

—

117

C₄×C₈

—

118

C₄×C₈

C₄×D₁₁

yes

—

119

C₄×C₈

D₄₄

yes

—

120

C₂×C₁₁

—

121

C₂×C₁₁

#1960

yes

characteristic

122

C₂×C₁₁

#1977

yes

—

123

C₂×Q₈

—

124

C₂×Q₈

—

125

C₂×Q₈

—

126

C₂²×C₄

—

127

C₂²×C₄

#4343

yes

—

128

C₂²×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

129

M₁₆

—

130

M₁₆

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

(C₂×D₁₁)⋊C₄

yes

—

137

C₄⋊C₄

—

138

C₄⋊C₄

—

139

C₄⋊C₄

—

140

C₄⋊C₄

—

141

C₄²

C₂×C₄×D₁₁

yes

characteristic

142

C₄²

C₂×D₄₄

yes

characteristic

143

C₄²

D₄×D₁₁

yes

—

144

C₁₁

#9776

yes

characteristic, complemented, Sylow

145

C₂³

#67000

yes

characteristic

146

Q₈

—

147

Q₈

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

#66946

yes

—

152

C₂×C₄

#66948

yes

—

153

C₂×C₄

C₂×(C₂×D₁₁)⋊C₄

yes

characteristic

154

C₂×C₄

#66993

yes

characteristic

155

C₂×C₄

#67004

yes

—

156

C₂×C₄

#67004

yes

—

157

C₈

—

158

C₈

—

159

C₈

—

160

C₈

—

161

C₂²

—

162

C₂²

#10622601

yes

characteristic

163

C₂²

#10622682

yes

—

164

C₄

—

165

C₄

—

166

C₄

#10622511

yes

—

167

C₄

#10622617

yes

—

168

C₄

#10622673

yes

characteristic

169

C₄

#10622673

yes

characteristic

170

C₂

—

171

C₂

#13069435

yes

characteristic

172

C₂

#13069517

yes

—

	subgroup	G/H
center	C₂²	#10622601
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1837	C₂
socle	C₂²×C₁₁	#390
prime radical	C₂³×C₁₁	#124
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1837	D₁₁
hypocenter	C₁₁	#9776
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1837

subgroup

G/H

center

C₂²

#10622601

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1837

C₂

C₂²×C₁₁

C₂³×C₁₁

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1837

N	H ≅ G/N	type
144. C₁₁	#9776	semidirect

H ≅ G/N

type

144. C₁₁

#9776

semidirect

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

subgroup	index
C₂×#10622293	2
#13067302	2
#13067298	2
#13066908	2
C₁₁×#1837	2
#9776	11

subgroup

index

C₁₁×#1837

Subgroups — #14653257

Conjugacy classes of subgroups

Complements

Maximal subgroups