Group #14653239 — subgroups

Subgroups — #14653239

Order 2816.

582 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 151 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×#10622308	C₂	1	1	yes	maximal, characteristic
2	#13067285	C₂	1	4	yes	maximal, complemented
3	#13066899	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1848	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₈₈	—	2	2	no	—
6	C₂×#66927	C₂²	1	2	yes	—
7	C₂×C₁₁×#108	—	2	2	no	—
8	C₁₁×#423	C₂²	1	2	yes	—
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	#10622538	C₂²	1	2	yes	—
11	#10622308	—	2	1	no	—
12	#10622308	—	2	1	no	—
13	#10622308	C₄	1	4	yes	—
14	#10622123	—	2	8	no	—
15	#10622093	—	2	1	no	—
16	C₈×C₁₁⋊C₈	—	2	1	no	—
17	C₂²×D₄₄	—	2	2	no	—
18	C₂²×D₄₄	—	2	4	no	—
19	C₂×C₁₁×M₁₆	—	2	2	no	—
20	C₂²×C₈×C₁₁	D₄	1	2	yes	—
21	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
22	C₂×D₈₈	—	2	4	no	—
23	C₂×D₈₈	—	2	4	no	—
24	C₂×D₈₈	—	4	4	no	—
25	C₂×D₈₈	—	4	4	no	—
26	#66927	—	2	2	no	—
27	#66927	—	2	4	no	—
28	#66927	C₂×C₄	1	4	yes	—
29	C₁₁×#108	—	4	4	no	—
30	C₁₁×C₄⋊C₈	—	2	4	no	—
31	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
32	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
33	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
34	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
35	C₄⋊(C₁₁⋊C₈)	D₄	1	4	yes	—
36	C₄×C₁₁⋊C₈	—	2	2	no	—
37	#9773	—	11	1	no	maximal, Sylow
38	C₂³×D₁₁	—	4	2	no	—
39	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₁	#41	1	2	yes	—
41	C₂×D₄₄	—	2	4	no	—
42	C₂×D₄₄	—	2	8	no	—
43	C₂×D₄₄	—	4	4	no	—
44	C₂×D₄₄	—	4	2	no	—
45	C₂×D₄₄	—	4	4	no	—
46	C₂×D₄₄	—	4	4	no	—
47	C₂×D₄₄	—	8	8	no	—
48	C₁₁×M₁₆	—	4	4	no	—
49	C₂×C₈×C₁₁	—	4	2	no	—
50	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
51	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
52	C₂×C₈×C₁₁	D₈	1	4	yes	—
53	C₂×C₈×C₁₁	SD₁₆	1	4	yes	—
54	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
55	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
56	C₄²×C₁₁	C₂×D₄	1	2	yes	—
57	C₂×C₁₁⋊C₈	—	2	4	no	—
58	D₈₈	—	4	8	no	—
59	D₈₈	—	4	8	no	—
60	C₂×#493	—	11	1	no	—
61	#1848	D₁₁	1	1	yes	characteristic, complemented
62	#1545	—	11	4	no	—
63	#1450	—	11	1	no	—
64	C₂³×C₁₁	#124	1	1	yes	characteristic
65	C₂²×D₁₁	—	4	4	no	—
66	C₂²×D₁₁	—	8	8	no	—
67	C₂²×D₁₁	—	8	4	no	—
68	C₂×C₄×C₁₁	—	2	4	no	—
69	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
71	C₂×C₄×C₁₁	#121	1	2	yes	—
72	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
73	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
74	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
75	D₄₄	—	4	8	no	—
76	D₄₄	—	8	8	no	—
77	D₄₄	—	8	8	no	—
78	D₄₄	—	8	2	no	—
79	D₄₄	—	8	2	no	—
80	C₈×C₁₁	—	8	2	no	—
81	C₈×C₁₁	#102	1	4	yes	—
82	C₈×C₁₁	#102	1	4	yes	—
83	C₁₁⋊C₈	—	4	4	no	—
84	C₂²×D₈	—	22	2	no	—
85	C₂×#127	—	11	2	no	—
86	#493	—	11	4	no	—
87	#493	—	22	1	no	—
88	#493	—	22	1	no	—
89	#431	—	11	2	no	—
90	C₂×#108	—	2	2	no	—
91	#423	C₂×D₁₁	1	2	yes	—
92	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
93	#331	—	22	8	no	—
94	#322	—	22	1	no	—
95	C₈²	—	22	1	no	—
96	C₂²×C₁₁	—	2	2	no	—
97	C₂²×C₁₁	#390	1	1	yes	characteristic
98	C₂²×C₁₁	#486	1	2	yes	—
99	C₂×D₁₁	—	8	4	no	—
100	C₂×D₁₁	—	8	8	no	—
101	C₂×D₁₁	—	16	8	no	—
102	C₄×C₁₁	—	2	2	no	—
103	C₄×C₁₁	C₂×#102	1	2	yes	—
104	C₄×C₁₁	#472	1	4	yes	—
105	C₄×C₁₁	#492	1	1	yes	characteristic
106	C₄×C₁₁	#493	1	1	yes	characteristic
107	C₂²×D₄	—	22	4	no	—
108	C₂²×D₄	—	22	2	no	—
109	C₂×D₈	—	22	4	no	—
110	C₂×D₈	—	22	4	no	—
111	C₂×D₈	—	44	4	no	—
112	C₂×D₈	—	44	4	no	—
113	C₂×M₁₆	—	2	2	no	—
114	C₂²×C₈	C₂²⋊D₁₁	1	2	yes	—
115	#127	—	11	4	no	—
116	#127	—	22	2	no	—
117	#127	—	22	4	no	—
118	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
119	#108	—	4	4	no	—
120	C₄⋊C₈	—	2	4	no	—
121	C₄⋊C₈	—	11	4	no	—
122	C₂²⋊C₈	—	22	2	no	—
123	C₄×C₈	—	22	2	no	—
124	C₄×C₈	C₄×D₁₁	1	2	yes	—
125	C₄×C₈	D₄₄	1	1	yes	characteristic
126	C₄×C₈	D₄₄	1	1	yes	characteristic
127	C₂×C₁₁	—	2	2	no	—
128	C₂×C₁₁	#1957	1	1	yes	characteristic
129	C₂×C₁₁	#1978	1	2	yes	—
130	D₁₁	—	16	4	no	—
131	C₂⁴	—	44	2	no	—
132	C₂×D₄	—	22	8	no	—
133	C₂×D₄	—	22	4	no	—
134	C₂×D₄	—	44	4	no	—
135	C₂×D₄	—	44	4	no	—
136	C₂×D₄	—	44	2	no	—
137	C₂×D₄	—	44	4	no	—
138	C₂×D₄	—	88	8	no	—
139	C₂²×C₄	#4343	1	2	yes	—
140	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
141	D₈	—	44	8	no	—
142	D₈	—	44	8	no	—
143	M₁₆	—	4	4	no	—
144	C₂×C₈	—	4	2	no	—
145	C₂×C₈	—	22	4	no	—
146	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
147	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
148	C₂×C₈	#4323	1	4	yes	—
149	C₂×C₈	#4325	1	4	yes	—
150	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
151	C₄²	C₂×D₄₄	1	1	yes	characteristic
152	C₄²	D₄×D₁₁	1	2	yes	—
153	C₁₁	#9773	1	1	yes	characteristic, complemented, Sylow
154	C₂³	—	44	4	no	—
155	C₂³	—	88	8	no	—
156	C₂³	—	88	4	no	—
157	C₂³	#67000	1	1	yes	characteristic
158	D₄	—	44	8	no	—
159	D₄	—	88	8	no	—
160	D₄	—	88	8	no	—
161	D₄	—	88	2	no	—
162	D₄	—	88	2	no	—
163	C₂×C₄	—	2	4	no	—
164	C₂×C₄	#66946	1	2	yes	—
165	C₂×C₄	#66948	1	2	yes	—
166	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
167	C₂×C₄	C₂×#4323	1	2	yes	—
168	C₂×C₄	#66993	1	1	yes	characteristic
169	C₂×C₄	C₂×#4325	1	2	yes	—
170	C₈	—	8	2	no	—
171	C₈	—	44	4	no	—
172	C₈	#66873	1	4	yes	—
173	C₈	#66873	1	4	yes	—
174	C₂²	—	2	2	no	—
175	C₂²	—	88	4	no	—
176	C₂²	—	88	8	no	—
177	C₂²	—	176	8	no	—
178	C₂²	#10622601	1	1	yes	characteristic
179	C₂²	#10622701	1	2	yes	—
180	C₄	—	2	2	no	—
181	C₄	#10622510	1	4	yes	—
182	C₄	C₂×#66873	1	2	yes	—
183	C₄	#10622686	1	1	yes	characteristic
184	C₄	#10622698	1	1	yes	characteristic
185	C₂	—	2	2	no	—
186	C₂	—	176	4	no	—
187	C₂	#13069421	1	1	yes	characteristic
188	C₂	#13069524	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622308

C₂

yes

maximal, characteristic

#13067285

C₂

yes

maximal, complemented

#13066899

C₂

yes

maximal, characteristic, complemented

C₁₁×#1848

C₂

yes

maximal, characteristic, complemented

C₂²×D₈₈

—

C₂×#66927

C₂²

yes

—

C₂×C₁₁×#108

—

C₁₁×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

#10622538

C₂²

yes

—

#10622308

—

#10622308

—

#10622308

C₄

yes

—

#10622123

—

#10622093

—

C₈×C₁₁⋊C₈

—

C₂²×D₄₄

—

C₂²×D₄₄

—

C₂×C₁₁×M₁₆

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×D₈₈

—

C₂×D₈₈

—

C₂×D₈₈

—

C₂×D₈₈

—

#66927

—

#66927

—

#66927

C₂×C₄

yes

—

C₁₁×#108

—

C₁₁×C₄⋊C₈

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

D₄

yes

characteristic

C₄×C₈×C₁₁

D₄

yes

characteristic

C₂²⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

D₄

yes

—

C₄×C₁₁⋊C₈

—

#9773

—

maximal, Sylow

C₂³×D₁₁

—

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

#41

yes

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×D₄₄

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

—

C₂×C₈×C₁₁

D₈

yes

—

C₂×C₈×C₁₁

SD₁₆

yes

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

—

C₂×C₁₁⋊C₈

—

D₈₈

—

D₈₈

—

C₂×#493

—

#1848

D₁₁

yes

characteristic, complemented

#1545

—

#1450

—

C₂³×C₁₁

#124

yes

characteristic

C₂²×D₁₁

—

C₂²×D₁₁

—

C₂²×D₁₁

—

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

C₂×D₈

yes

—

C₂×C₄×C₁₁

C₂×SD₁₆

yes

—

D₄₄

—

D₄₄

—

D₄₄

—

D₄₄

—

D₄₄

—

C₈×C₁₁

—

C₈×C₁₁

#102

yes

—

C₈×C₁₁

#102

yes

—

C₁₁⋊C₈

—

C₂²×D₈

—

—

—

—

—

—

—

C₂×D₁₁

yes

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

#331

—

#322

—

C₈²

—

C₂²×C₁₁

—

C₂²×C₁₁

#390

yes

characteristic

C₂²×C₁₁

#486

yes

—

C₂×D₁₁

—

100

C₂×D₁₁

—

101

C₂×D₁₁

—

102

C₄×C₁₁

—

103

C₄×C₁₁

C₂×#102

yes

—

104

C₄×C₁₁

#472

yes

—

105

C₄×C₁₁

#492

yes

characteristic

106

C₄×C₁₁

#493

yes

characteristic

107

C₂²×D₄

—

108

C₂²×D₄

—

109

C₂×D₈

—

110

C₂×D₈

—

111

C₂×D₈

—

112

C₂×D₈

—

113

C₂×M₁₆

—

114

C₂²×C₈

C₂²⋊D₁₁

yes

—

115

#127

—

116

#127

—

117

#127

—

118

C₂×C₄²

C₂²×D₁₁

yes

characteristic

119

#108

—

120

C₄⋊C₈

—

121

C₄⋊C₈

—

122

C₂²⋊C₈

—

123

C₄×C₈

—

124

C₄×C₈

C₄×D₁₁

yes

—

125

C₄×C₈

D₄₄

yes

characteristic

126

C₄×C₈

D₄₄

yes

characteristic

127

C₂×C₁₁

—

128

C₂×C₁₁

#1957

yes

characteristic

129

C₂×C₁₁

#1978

yes

—

130

D₁₁

—

131

C₂⁴

—

132

C₂×D₄

—

133

C₂×D₄

—

134

C₂×D₄

—

135

C₂×D₄

—

136

C₂×D₄

—

137

C₂×D₄

—

138

C₂×D₄

—

139

C₂²×C₄

#4343

yes

—

140

C₂²×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

141

D₈

—

142

D₈

—

143

M₁₆

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

(C₂×D₁₁)⋊C₄

yes

—

147

C₂×C₈

(C₂×D₁₁)⋊C₄

yes

—

148

C₂×C₈

#4323

yes

—

149

C₂×C₈

#4325

yes

—

150

C₄²

C₂×C₄×D₁₁

yes

characteristic

151

C₄²

C₂×D₄₄

yes

characteristic

152

C₄²

D₄×D₁₁

yes

—

153

C₁₁

#9773

yes

characteristic, complemented, Sylow

154

C₂³

—

155

C₂³

—

156

C₂³

—

157

C₂³

#67000

yes

characteristic

158

D₄

—

159

D₄

—

160

D₄

—

161

D₄

—

162

D₄

—

163

C₂×C₄

—

164

C₂×C₄

#66946

yes

—

165

C₂×C₄

#66948

yes

—

166

C₂×C₄

C₂×(C₂×D₁₁)⋊C₄

yes

characteristic

167

C₂×C₄

C₂×#4323

yes

—

168

C₂×C₄

#66993

yes

characteristic

169

C₂×C₄

C₂×#4325

yes

—

170

C₈

—

171

C₈

—

172

C₈

#66873

yes

—

173

C₈

#66873

yes

—

174

C₂²

—

175

C₂²

—

176

C₂²

—

177

C₂²

—

176

—

178

C₂²

#10622601

yes

characteristic

179

C₂²

#10622701

yes

—

180

C₄

—

181

C₄

#10622510

yes

—

182

C₄

C₂×#66873

yes

—

183

C₄

#10622686

yes

characteristic

184

C₄

#10622698

yes

characteristic

185

C₂

—

186

C₂

—

176

—

187

C₂

#13069421

yes

characteristic

188

C₂

#13069524

yes

—

	subgroup	G/H
center	C₂²	#10622601
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1848	C₂
socle	C₂²×C₁₁	#390
prime radical	C₂×#10622308	C₂
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1848	D₁₁
hypocenter	C₁₁	#9773
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1848

subgroup

G/H

center

C₂²

#10622601

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1848

C₂

C₂²×C₁₁

C₂

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1848

N	H ≅ G/N	type
2. #13067285	C₂	semidirect
3. #13066899	C₂	semidirect
4. C₁₁×#1848	C₂	semidirect
61. #1848	D₁₁	semidirect
153. C₁₁	#9773	semidirect

H ≅ G/N

type

2. #13067285

C₂

semidirect

3. #13066899

C₂

semidirect

4. C₁₁×#1848

C₂

semidirect

61. #1848

D₁₁

semidirect

153. C₁₁

#9773

semidirect

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

subgroup	index
C₂×#10622308	2
#13067285	2
#13066899	2
C₁₁×#1848	2
#9773	11

subgroup

index

C₁₁×#1848

Subgroups — #14653239

Conjugacy classes of subgroups

Complements

Maximal subgroups