Group #14673653 — subgroups

Subgroups — #14673653

Order 2816.

284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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×#10622143	C₂	1	1	yes	maximal, characteristic, complemented
2	#13070229	C₂	1	1	yes	maximal, characteristic
3	#13068677	C₂	1	2	yes	maximal
4	#13066726	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1381	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#66954	C₂²	1	1	yes	characteristic
7	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₁₁×#108	C₂²	1	2	yes	—
9	#10622746	—	2	2	no	—
10	C₂×#66882	C₂²	1	2	yes	—
11	C₂×#66876	C₂²	1	1	yes	characteristic
12	#10622192	—	2	2	no	—
13	(C₂×D₁₁)⋊C₁₆	—	2	2	no	—
14	#10622143	—	2	2	no	—
15	C₂×#4339	D₄	1	1	yes	characteristic
16	C₂×C₁₁×M₁₆	—	2	2	no	—
17	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
18	C₂×C₄⋊Dic₁₁	—	2	2	no	—
19	C₂×#4318	D₄	1	1	yes	characteristic
20	#66954	—	2	2	no	—
21	#66954	—	2	2	no	—
22	C₂×#4313	—	2	1	no	—
23	C₂×C₈×D₁₁	—	2	1	no	—
24	C₂×C₁₁×C₁₆	—	2	2	no	—
25	C₂×C₁₁×C₁₆	D₄	1	2	yes	—
26	C₁₁×#108	—	2	2	no	—
27	C₁₁×#108	—	2	2	no	—
28	#66885	—	4	2	no	—
29	#66882	—	2	2	no	—
30	#66882	—	2	2	no	—
31	#66880	—	4	2	no	—
32	#66876	—	2	2	no	—
33	C₂×C₁₁⋊C₁₆	—	2	1	no	—
34	#13496	—	11	1	no	maximal, Sylow
35	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
36	C₂×C₂²⋊D₁₁	—	2	1	no	—
37	C₂²×Dic₁₁	—	4	2	no	—
38	#4339	—	2	2	no	—
39	#4339	—	2	2	no	—
40	C₂×D₄₄	D₈	1	1	yes	characteristic
41	C₂×C₄×D₁₁	—	2	1	no	—
42	C₂×Dic₂₂	D₈	1	1	yes	characteristic
43	C₁₁×M₁₆	—	4	2	no	—
44	C₁₁×M₁₆	—	4	2	no	—
45	C₂×C₈×C₁₁	—	4	2	no	—
46	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
47	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
48	C₂×C₈×C₁₁	#41	1	2	yes	—
49	C₂×C₈×C₁₁	#41	1	2	yes	—
50	C₄⋊Dic₁₁	—	4	2	no	—
51	C₄⋊Dic₁₁	—	4	2	no	—
52	#4318	—	2	2	no	—
53	C₂×C₁₁⋊C₈	—	2	1	no	—
54	#4313	—	4	2	no	—
55	C₈×D₁₁	—	4	1	no	—
56	C₈×D₁₁	—	4	1	no	—
57	C₁₁×C₁₆	—	2	2	no	—
58	C₁₁⋊C₁₆	—	4	1	no	—
59	C₂×#367	—	11	1	no	—
60	#2113	—	11	1	no	—
61	#1816	—	11	2	no	—
62	#1387	—	11	2	no	—
63	#1381	D₁₁	1	1	yes	characteristic, complemented
64	C₂³×C₁₁	#135	1	1	yes	characteristic
65	C₂²×D₁₁	—	2	1	no	—
66	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
67	C₂×C₄×C₁₁	#123	1	2	yes	—
68	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
69	C₂×C₄×C₁₁	#137	1	2	yes	—
70	C₂²⋊D₁₁	—	4	2	no	—
71	C₂×Dic₁₁	—	2	1	no	—
72	C₂×Dic₁₁	—	8	2	no	—
73	C₂×Dic₁₁	—	16	2	no	—
74	D₄₄	—	2	2	no	—
75	C₄×D₁₁	—	4	1	no	—
76	C₄×D₁₁	—	4	1	no	—
77	Dic₂₂	—	2	2	no	—
78	C₈×C₁₁	—	8	2	no	—
79	C₈×C₁₁	#123	1	1	yes	characteristic
80	C₈×C₁₁	#124	1	1	yes	characteristic
81	C₈×C₁₁	#126	1	2	yes	—
82	C₁₁⋊C₈	—	4	1	no	—
83	C₂×#131	—	11	1	no	—
84	C₂×M₃₂	—	11	1	no	—
85	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
86	C₂×#108	C₂×D₁₁	1	2	yes	—
87	C₂×#107	—	11	2	no	—
88	#417	—	22	2	no	—
89	#367	—	22	2	no	—
90	C₂²⋊C₁₆	—	22	2	no	—
91	#343	—	22	2	no	—
92	C₂²×C₁₁	—	2	2	no	—
93	C₂²×C₁₁	#466	1	1	yes	characteristic
94	C₂²×C₁₁	#485	1	2	yes	—
95	C₂×D₁₁	—	4	1	no	—
96	C₂×D₁₁	—	4	2	no	—
97	C₄×C₁₁	#397	1	1	yes	characteristic
98	C₄×C₁₁	#470	1	1	yes	characteristic
99	C₄×C₁₁	#480	1	2	yes	—
100	Dic₁₁	—	4	1	no	—
101	Dic₁₁	—	16	2	no	—
102	C₂×#41	—	11	1	no	—
103	#131	—	22	2	no	—
104	#131	—	22	2	no	—
105	C₂×M₁₆	—	2	2	no	—
106	C₂×M₁₆	—	11	1	no	—
107	C₂×M₁₆	—	22	1	no	—
108	C₂²×C₈	—	22	1	no	—
109	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
110	C₂×C₄⋊C₄	—	22	2	no	—
111	M₃₂	—	22	2	no	—
112	C₂×C₁₆	—	2	2	no	—
113	C₂×C₁₆	—	22	1	no	—
114	C₂×C₁₆	D₄₄	1	2	yes	—
115	#108	—	2	2	no	—
116	#108	—	2	2	no	—
117	#107	—	22	2	no	—
118	#107	—	22	2	no	—
119	#103	—	44	2	no	—
120	#102	—	44	2	no	—
121	C₂×C₁₁	—	2	2	no	—
122	C₂×C₁₁	#2075	1	1	yes	characteristic
123	C₂×C₁₁	#2223	1	2	yes	—
124	D₁₁	—	8	1	no	—
125	#41	—	22	2	no	—
126	#41	—	22	2	no	—
127	C₂×Q₈	—	11	1	no	—
128	C₂×D₄	—	11	1	no	—
129	C₂×D₄	—	22	1	no	—
130	C₂²×C₄	—	22	1	no	—
131	C₂²×C₄	—	44	2	no	—
132	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
133	M₁₆	—	4	2	no	—
134	M₁₆	—	4	2	no	—
135	M₁₆	—	22	2	no	—
136	M₁₆	—	44	2	no	—
137	C₂×C₈	—	4	2	no	—
138	C₂×C₈	—	22	1	no	—
139	C₂×C₈	—	44	1	no	—
140	C₂×C₈	—	44	1	no	—
141	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
142	C₂×C₈	#4339	1	2	yes	—
143	C₂×C₈	#4341	1	2	yes	—
144	C₂×C₈	#4343	1	1	yes	characteristic
145	C₄⋊C₄	—	44	2	no	—
146	C₄⋊C₄	—	44	2	no	—
147	C₁₆	—	2	2	no	—
148	C₁₆	—	44	1	no	—
149	C₁₁	#13496	1	1	yes	characteristic, complemented, Sylow
150	C₂³	—	22	1	no	—
151	C₂³	#66972	1	1	yes	characteristic
152	Q₈	—	22	2	no	—
153	D₄	—	22	2	no	—
154	D₄	—	44	2	no	—
155	C₂×C₄	—	22	1	no	—
156	C₂×C₄	—	44	1	no	—
157	C₂×C₄	—	44	1	no	—
158	C₂×C₄	—	88	2	no	—
159	C₂×C₄	—	176	2	no	—
160	C₂×C₄	#66936	1	2	yes	—
161	C₂×C₄	#66948	1	1	yes	characteristic
162	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
163	C₂×C₄	#66968	1	2	yes	—
164	C₈	—	8	2	no	—
165	C₈	—	44	1	no	—
166	C₈	#66928	1	1	yes	characteristic
167	C₈	#66939	1	1	yes	characteristic
168	C₈	#66951	1	2	yes	—
169	C₂²	—	2	2	no	—
170	C₂²	—	44	2	no	—
171	C₂²	—	44	1	no	—
172	C₂²	#10622427	1	2	yes	—
173	C₂²	#10622496	1	1	yes	characteristic
174	C₄	—	44	1	no	—
175	C₄	—	176	2	no	—
176	C₄	#10622287	1	1	yes	characteristic
177	C₄	#10622387	1	2	yes	—
178	C₄	#10622481	1	1	yes	characteristic
179	C₂	—	2	2	no	—
180	C₂	—	88	1	no	—
181	C₂	#13070041	1	1	yes	characteristic
182	C₂	#13070747	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622143

C₂

yes

maximal, characteristic, complemented

#13070229

C₂

yes

maximal, characteristic

#13068677

C₂

yes

maximal

#13066726

C₂

yes

maximal, complemented

C₁₁×#1381

C₂

yes

maximal, characteristic, complemented

C₂×#66954

C₂²

yes

characteristic

C₂²×C₁₁×C₁₆

C₂²

yes

characteristic

C₂×C₁₁×#108

C₂²

yes

—

#10622746

—

C₂×#66882

C₂²

yes

—

C₂×#66876

C₂²

yes

characteristic

#10622192

—

(C₂×D₁₁)⋊C₁₆

—

#10622143

—

C₂×#4339

D₄

yes

characteristic

C₂×C₁₁×M₁₆

—

C₂²×C₈×C₁₁

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₁

—

C₂×#4318

D₄

yes

—

—

—

C₂×C₈×D₁₁

—

C₂×C₁₁×C₁₆

—

C₂×C₁₁×C₁₆

D₄

yes

—

C₁₁×#108

—

C₁₁×#108

—

—

—

—

—

—

C₂×C₁₁⋊C₁₆

—

#13496

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₁₁

—

C₂²×Dic₁₁

—

#4339

—

#4339

—

C₂×D₄₄

D₈

yes

characteristic

C₂×C₄×D₁₁

—

C₂×Dic₂₂

D₈

yes

characteristic

C₁₁×M₁₆

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂×D₄

yes

C₂×C₈×C₁₁

yes

C₂×C₈×C₁₁

yes

—

C₂×C₈×C₁₁

#41

yes

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

#4318

—

C₂×C₁₁⋊C₈

—

#4313

—

C₈×D₁₁

—

C₈×D₁₁

—

C₁₁×C₁₆

—

C₁₁⋊C₁₆

—

—

—

—

—

D₁₁

yes

characteristic, complemented

C₂³×C₁₁

#135

yes

characteristic

C₂²×D₁₁

—

C₂×C₄×C₁₁

#121

yes

characteristic

C₂×C₄×C₁₁

#123

yes

—

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

C₂×C₄×C₁₁

#137

yes

—

C₂²⋊D₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

D₄₄

—

C₄×D₁₁

—

C₄×D₁₁

—

Dic₂₂

—

C₈×C₁₁

—

C₈×C₁₁

yes

C₈×C₁₁

yes

C₈×C₁₁

yes

—

C₁₁⋊C₈

—

C₂×#131

—

C₂×M₃₂

—

C₂²×C₁₆

C₂×D₁₁

yes

characteristic

C₂×#108

C₂×D₁₁

yes

—

C₂×#107

—

#417

—

#367

—

C₂²⋊C₁₆

—

#343

—

C₂²×C₁₁

—

C₂²×C₁₁

#466

yes

characteristic

C₂²×C₁₁

#485

yes

—

C₂×D₁₁

—

C₂×D₁₁

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

—

100

Dic₁₁

—

101

Dic₁₁

—

102

C₂×#41

—

103

#131

—

104

#131

—

105

C₂×M₁₆

—

106

C₂×M₁₆

—

107

C₂×M₁₆

—

108

C₂²×C₈

—

109

C₂²×C₈

C₂²×D₁₁

yes

characteristic

110

C₂×C₄⋊C₄

—

111

M₃₂

—

112

C₂×C₁₆

—

113

C₂×C₁₆

—

114

C₂×C₁₆

D₄₄

yes

—

115

#108

—

116

#108

—

117

#107

—

118

#107

—

119

#103

—

120

#102

—

121

C₂×C₁₁

—

122

C₂×C₁₁

#2075

yes

characteristic

123

C₂×C₁₁

#2223

yes

—

124

D₁₁

—

125

#41

—

126

#41

—

127

C₂×Q₈

—

128

C₂×D₄

—

129

C₂×D₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

D₄×D₁₁

yes

characteristic

133

M₁₆

—

134

M₁₆

—

135

M₁₆

—

136

M₁₆

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

C₂×D₄₄

yes

characteristic

142

C₂×C₈

#4339

yes

—

143

C₂×C₈

#4341

yes

—

144

C₂×C₈

#4343

yes

characteristic

145

C₄⋊C₄

—

146

C₄⋊C₄

—

147

C₁₆

—

148

C₁₆

—

149

C₁₁

#13496

yes

characteristic, complemented, Sylow

150

C₂³

—

151

C₂³

#66972

yes

characteristic

152

Q₈

—

153

D₄

—

154

D₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

176

—

160

C₂×C₄

#66936

yes

—

161

C₂×C₄

#66948

yes

characteristic

162

C₂×C₄

D₈×D₁₁

yes

characteristic

163

C₂×C₄

#66968

yes

—

164

C₈

—

165

C₈

—

166

C₈

#66928

yes

characteristic

167

C₈

#66939

yes

characteristic

168

C₈

#66951

yes

—

169

C₂²

—

170

C₂²

—

171

C₂²

—

172

C₂²

#10622427

yes

—

173

C₂²

#10622496

yes

characteristic

174

C₄

—

175

C₄

—

176

—

176

C₄

#10622287

yes

characteristic

177

C₄

#10622387

yes

—

178

C₄

#10622481

yes

characteristic

179

C₂

—

180

C₂

—

181

C₂

#13070041

yes

characteristic

182

C₂

#13070747

yes

—

	subgroup	G/H
center	C₂²	#10622496
commutator, cosocle	C₂²×C₈×C₁₁	C₂³
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#1381	C₂
socle	C₂²×C₁₁	#466
prime radical	C₂×#4339	D₄
hypercenter	#1381	D₁₁
hypocenter	C₁₁	#13496
LCS	G ▷ C₂²×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1381

subgroup

G/H

center

C₂²

#10622496

commutator, cosocle

C₂²×C₈×C₁₁

C₂³

Frattini

C₂²×C₈

C₂²×D₁₁

Fitting

C₁₁×#1381

C₂

C₂²×C₁₁

D₄

D₁₁

C₁₁

G ▷ C₂²×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1381

N	H ≅ G/N	type
1. C₂×#10622143	C₂	semidirect
4. #13066726	C₂	semidirect
5. C₁₁×#1381	C₂	semidirect
63. #1381	D₁₁	semidirect
149. C₁₁	#13496	semidirect

H ≅ G/N

type

1. C₂×#10622143

C₂

semidirect

4. #13066726

C₂

semidirect

5. C₁₁×#1381

C₂

semidirect

63. #1381

D₁₁

semidirect

149. C₁₁

#13496

semidirect

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

subgroup	index
C₂×#10622143	2
#13070229	2
#13068677	2
#13066726	2
C₁₁×#1381	2
#13496	11

subgroup

index

C₁₁×#1381

Subgroups — #14673653

Conjugacy classes of subgroups

Complements

Maximal subgroups