Group #15762741 — subgroups

Subgroups — #15762741

Order 3328.

494 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 163 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×#11718343	C₂	1	1	yes	maximal, characteristic
2	#13115796	C₂	1	2	yes	maximal
3	#13115637	C₂	1	2	yes	maximal
4	C₂×#11718046	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1834	C₂	1	1	yes	maximal, characteristic
6	C₂×#88123	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×#384	C₂²	1	2	yes	—
9	C₂×#88058	—	2	2	no	—
10	C₂×#88050	—	2	4	no	—
11	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
12	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
13	#11718343	—	2	2	no	—
14	#11718343	C₄	1	4	yes	complemented
15	C₁₃×#340	—	2	2	no	—
16	#11718121	—	2	4	no	—
17	#11718046	—	2	2	no	—
18	C₂²×Dic₂₆	—	2	2	no	—
19	C₂²×C₈×C₁₃	D₄	1	2	yes	—
20	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
21	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
22	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
23	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₃	—	2	2	no	—
25	C₂×C₄⋊Dic₁₃	—	2	2	no	—
26	C₂²×#1055	D₄	1	2	yes	—
27	C₂²×#1055	D₄	1	2	yes	—
28	#88123	—	2	2	no	—
29	#88123	—	2	2	no	—
30	#88123	—	2	2	no	—
31	#88123	C₂×C₄	1	4	yes	—
32	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
33	C₄×C₈×C₁₃	D₄	1	2	yes	—
34	#88058	—	2	8	no	—
35	#88050	—	4	8	no	—
36	C₄×#1055	—	2	1	no	—
37	C₄×#1055	—	2	1	no	—
38	C₄×#1055	—	2	1	no	—
39	C₄×#1055	—	2	1	no	—
40	#9834	—	13	1	no	maximal, Sylow
41	C₂²×C₄×C₁₃	—	4	2	no	—
42	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
45	C₂²×Dic₁₃	—	4	2	no	—
46	C₂×Dic₂₆	—	2	4	no	—
47	C₂×Dic₂₆	—	4	4	no	—
48	C₂×Dic₂₆	—	4	4	no	—
49	C₂×Dic₂₆	—	4	2	no	—
50	C₂×C₈×C₁₃	—	2	4	no	—
51	C₂×C₈×C₁₃	C₂²⋊C₄	1	4	yes	—
52	C₁₃×C₄⋊C₄	—	4	4	no	—
53	C₁₃×C₄⋊C₄	—	4	4	no	—
54	C₁₃×C₄⋊C₄	—	4	4	no	—
55	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
56	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₄²×C₁₃	#41	1	1	yes	characteristic
58	C₄²×C₁₃	#41	1	1	yes	characteristic
59	C₄⋊Dic₁₃	—	2	4	no	—
60	C₄⋊Dic₁₃	—	2	4	no	—
61	C₄⋊Dic₁₃	—	4	2	no	—
62	C₄⋊Dic₁₃	—	4	2	no	—
63	C₂×#1055	—	2	2	no	—
64	C₂×#1055	—	2	2	no	—
65	C₂×#1055	—	2	2	no	—
66	C₂×#1055	—	2	4	no	—
67	C₂×#1055	Q₁₆	1	4	yes	—
68	C₂×#500	—	13	1	no	—
69	#1990	—	13	2	no	—
70	#1956	—	13	2	no	—
71	#1834	D₁₃	1	1	yes	characteristic
72	C₂×#322	—	13	1	no	—
73	C₂³×C₁₃	#127	1	1	yes	characteristic
74	C₂×C₄×C₁₃	—	8	2	no	—
75	C₂×C₄×C₁₃	—	8	2	no	—
76	C₂×C₄×C₁₃	—	8	2	no	—
77	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
80	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
81	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
82	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
83	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
84	C₂×C₄×C₁₃	#135	1	2	yes	—
85	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
86	C₂×C₄×C₁₃	#137	1	4	yes	—
87	C₂×Dic₁₃	—	4	4	no	—
88	C₂×Dic₁₃	—	8	2	no	—
89	C₂×Dic₁₃	—	8	2	no	—
90	Dic₂₆	—	4	8	no	—
91	Dic₂₆	—	8	4	no	—
92	C₈×C₁₃	—	2	4	no	—
93	#1055	—	2	4	no	—
94	#1055	—	4	2	no	—
95	C₂×C₄⋊Q₈	—	13	2	no	—
96	#500	—	13	4	no	—
97	#500	—	26	2	no	—
98	C₂×#107	—	26	2	no	—
99	C₂×#103	—	26	4	no	—
100	C₂×C₄×C₈	—	13	1	no	—
101	C₂×C₄×C₈	—	13	1	no	—
102	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
103	#384	C₂×D₁₃	1	2	yes	—
104	#340	—	2	2	no	—
105	#340	—	26	4	no	—
106	#322	—	26	2	no	—
107	C₂²×C₁₃	#390	1	1	yes	characteristic
108	C₂²×C₁₃	#494	1	1	yes	characteristic
109	C₂²×C₁₃	#495	1	1	yes	characteristic
110	C₂²×C₁₃	#496	1	2	yes	—
111	C₂²×C₁₃	#497	1	2	yes	—
112	C₄×C₁₃	—	16	2	no	—
113	C₄×C₁₃	#419	1	2	yes	—
114	C₄×C₁₃	C₄×Q₁₆	1	2	yes	—
115	C₄×C₁₃	#442	1	2	yes	—
116	C₄×C₁₃	#467	1	2	yes	—
117	C₄×C₁₃	#469	1	2	yes	—
118	C₄×C₁₃	#491	1	2	yes	—
119	Dic₁₃	—	8	4	no	—
120	C₂²×Q₈	—	26	2	no	—
121	C₂²×C₈	—	13	2	no	—
122	C₂²×C₈	—	13	2	no	—
123	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
124	C₄⋊Q₈	—	13	4	no	—
125	C₄⋊Q₈	—	26	2	no	—
126	C₄⋊Q₈	—	26	2	no	—
127	C₄⋊Q₈	—	26	2	no	—
128	C₂×C₄⋊C₄	—	2	2	no	—
129	C₂×C₄⋊C₄	—	2	2	no	—
130	C₂×C₄⋊C₄	—	2	2	no	—
131	C₂×C₄⋊C₄	—	26	2	no	—
132	C₂×C₄⋊C₄	—	26	2	no	—
133	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
134	#107	—	26	8	no	—
135	#103	—	52	8	no	—
136	C₄×C₈	—	26	1	no	—
137	C₄×C₈	—	26	1	no	—
138	C₄×C₈	—	26	1	no	—
139	C₄×C₈	—	26	1	no	—
140	C₄×C₈	C₄×D₁₃	1	2	yes	—
141	C₄×C₈	D₅₂	1	2	yes	—
142	C₂×C₁₃	#1719	1	2	yes	—
143	C₂×C₁₃	#1723	1	2	yes	—
144	C₂×C₁₃	#1960	1	1	yes	characteristic
145	C₂×C₁₃	#1969	1	1	yes	characteristic
146	C₂×C₁₃	#1972	1	1	yes	characteristic
147	C₂×Q₈	—	26	4	no	—
148	C₂×Q₈	—	52	2	no	—
149	C₂×Q₈	—	52	4	no	—
150	C₂×Q₈	—	52	4	no	—
151	C₂²×C₄	—	4	2	no	—
152	C₂²×C₄	—	52	2	no	—
153	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
154	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
155	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
156	C₂×C₈	—	2	4	no	—
157	C₂×C₈	—	13	4	no	—
158	C₂×C₈	—	26	2	no	—
159	C₂×C₈	—	26	2	no	—
160	C₂×C₈	—	26	2	no	—
161	C₂×C₈	—	26	4	no	—
162	C₂×C₈	#6103	1	4	yes	—
163	C₄⋊C₄	—	4	4	no	—
164	C₄⋊C₄	—	4	4	no	—
165	C₄⋊C₄	—	4	4	no	—
166	C₄⋊C₄	—	26	4	no	—
167	C₄⋊C₄	—	26	4	no	—
168	C₄⋊C₄	—	52	2	no	—
169	C₄⋊C₄	—	52	2	no	—
170	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
171	C₄²	C₂×D₅₂	1	1	yes	characteristic
172	C₄²	#6131	1	1	yes	characteristic
173	C₄²	#6131	1	1	yes	characteristic
174	C₁₃	#9834	1	1	yes	characteristic, complemented, Sylow
175	C₂³	#88194	1	1	yes	characteristic
176	Q₈	—	52	8	no	—
177	Q₈	—	104	4	no	—
178	C₂×C₄	—	8	2	no	—
179	C₂×C₄	—	8	2	no	—
180	C₂×C₄	—	8	2	no	—
181	C₂×C₄	—	52	4	no	—
182	C₂×C₄	—	104	2	no	—
183	C₂×C₄	—	104	2	no	—
184	C₂×C₄	#88147	1	1	yes	characteristic
185	C₂×C₄	#88147	1	1	yes	characteristic
186	C₂×C₄	#88149	1	1	yes	characteristic
187	C₂×C₄	#88149	1	1	yes	characteristic
188	C₂×C₄	#88166	1	2	yes	—
189	C₂×C₄	#88168	1	4	yes	—
190	C₂×C₄	Q₁₆×D₁₃	1	2	yes	—
191	C₂×C₄	C₂×#6103	1	1	yes	characteristic
192	C₂×C₄	#88201	1	1	yes	characteristic
193	C₂×C₄	#88205	1	4	yes	—
194	C₈	—	2	4	no	—
195	C₈	—	26	4	no	—
196	C₈	—	52	2	no	—
197	C₂²	#11718649	1	1	yes	characteristic
198	C₂²	#11718721	1	2	yes	—
199	C₂²	#11718816	1	1	yes	characteristic
200	C₂²	#11718837	1	2	yes	—
201	C₂²	#11718842	1	1	yes	characteristic
202	C₄	—	16	2	no	—
203	C₄	—	104	4	no	—
204	C₄	#11718526	1	2	yes	—
205	C₄	#11718530	1	2	yes	—
206	C₄	#11718534	1	2	yes	—
207	C₄	#11718548	1	2	yes	—
208	C₄	#11718665	1	2	yes	—
209	C₄	#11718730	1	2	yes	—
210	C₂	#13114488	1	2	yes	—
211	C₂	#13114516	1	2	yes	—
212	C₂	#13115655	1	1	yes	characteristic
213	C₂	#13115695	1	1	yes	characteristic
214	C₂	#13115710	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718343

C₂

yes

maximal, characteristic

#13115796

C₂

yes

maximal

#13115637

C₂

yes

maximal

C₂×#11718046

C₂

yes

maximal, characteristic

C₁₃×#1834

C₂

yes

maximal, characteristic

C₂×#88123

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#384

C₂²

yes

—

C₂×#88058

—

C₂×#88050

—

C₂×C₄×#1055

C₂²

yes

characteristic

C₂×C₄×#1055

C₂²

yes

characteristic

#11718343

—

#11718343

C₄

yes

complemented

C₁₃×#340

—

#11718121

—

#11718046

—

C₂²×Dic₂₆

—

C₂²×C₈×C₁₃

D₄

yes

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

—

C₂²×#1055

D₄

yes

—

C₂²×#1055

D₄

yes

—

—

—

—

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

D₄

yes

—

—

—

—

—

—

—

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×Dic₁₃

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂²⋊C₄

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂²×C₄

yes

characteristic

C₄²×C₁₃

C₂×D₄

yes

C₄²×C₁₃

yes

C₄²×C₁₃

yes

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

—

—

—

—

Q₁₆

yes

—

—

—

—

D₁₃

yes

characteristic

C₂×#322

—

C₂³×C₁₃

#127

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₄×D₄

yes

characteristic

C₂×C₄×C₁₃

C₄×D₄

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

C₂×Q₁₆

yes

—

C₂×C₄×C₁₃

#135

yes

—

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₃

#137

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

Dic₂₆

—

Dic₂₆

—

C₈×C₁₃

—

#1055

—

#1055

—

C₂×C₄⋊Q₈

—

—

—

—

—

100

C₂×C₄×C₈

—

101

C₂×C₄×C₈

—

102

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

103

#384

C₂×D₁₃

yes

—

104

#340

—

105

#340

—

106

#322

—

107

C₂²×C₁₃

#390

yes

characteristic

108

C₂²×C₁₃

#494

yes

characteristic

109

C₂²×C₁₃

#495

yes

characteristic

110

C₂²×C₁₃

#496

yes

—

111

C₂²×C₁₃

#497

yes

—

112

C₄×C₁₃

—

113

C₄×C₁₃

#419

yes

—

114

C₄×C₁₃

C₄×Q₁₆

yes

—

115

C₄×C₁₃

#442

yes

—

116

C₄×C₁₃

#467

yes

—

117

C₄×C₁₃

#469

yes

—

118

C₄×C₁₃

#491

yes

—

119

Dic₁₃

—

120

C₂²×Q₈

—

121

C₂²×C₈

—

122

C₂²×C₈

—

123

C₂²×C₈

C₂²⋊D₁₃

yes

—

124

C₄⋊Q₈

—

125

C₄⋊Q₈

—

126

C₄⋊Q₈

—

127

C₄⋊Q₈

—

128

C₂×C₄⋊C₄

—

129

C₂×C₄⋊C₄

—

130

C₂×C₄⋊C₄

—

131

C₂×C₄⋊C₄

—

132

C₂×C₄⋊C₄

—

133

C₂×C₄²

C₂²×D₁₃

yes

characteristic

134

#107

—

135

#103

—

136

C₄×C₈

—

137

C₄×C₈

—

138

C₄×C₈

—

139

C₄×C₈

—

140

C₄×C₈

C₄×D₁₃

yes

—

141

C₄×C₈

D₅₂

yes

—

142

C₂×C₁₃

#1719

yes

—

143

C₂×C₁₃

#1723

yes

—

144

C₂×C₁₃

#1960

yes

characteristic

145

C₂×C₁₃

#1969

yes

characteristic

146

C₂×C₁₃

#1972

yes

characteristic

147

C₂×Q₈

—

148

C₂×Q₈

—

149

C₂×Q₈

—

150

C₂×Q₈

—

151

C₂²×C₄

—

152

C₂²×C₄

—

153

C₂²×C₄

D₄×D₁₃

yes

characteristic

154

C₂²×C₄

D₄×D₁₃

yes

characteristic

155

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

#6103

yes

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄²

C₂×C₄×D₁₃

yes

characteristic

171

C₄²

C₂×D₅₂

yes

characteristic

172

C₄²

#6131

yes

characteristic

173

C₄²

#6131

yes

characteristic

174

C₁₃

#9834

yes

characteristic, complemented, Sylow

175

C₂³

#88194

yes

characteristic

176

Q₈

—

177

Q₈

—

104

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

104

—

183

C₂×C₄

—

104

—

184

C₂×C₄

#88147

yes

characteristic

185

C₂×C₄

#88147

yes

characteristic

186

C₂×C₄

#88149

yes

characteristic

187

C₂×C₄

#88149

yes

characteristic

188

C₂×C₄

#88166

yes

—

189

C₂×C₄

#88168

yes

—

190

C₂×C₄

Q₁₆×D₁₃

yes

—

191

C₂×C₄

C₂×#6103

yes

characteristic

192

C₂×C₄

#88201

yes

characteristic

193

C₂×C₄

#88205

yes

—

194

C₈

—

195

C₈

—

196

C₈

—

197

C₂²

#11718649

yes

characteristic

198

C₂²

#11718721

yes

—

199

C₂²

#11718816

yes

characteristic

200

C₂²

#11718837

yes

—

201

C₂²

#11718842

yes

characteristic

202

C₄

—

203

C₄

—

104

—

204

C₄

#11718526

yes

—

205

C₄

#11718530

yes

—

206

C₄

#11718534

yes

—

207

C₄

#11718548

yes

—

208

C₄

#11718665

yes

—

209

C₄

#11718730

yes

—

210

C₂

#13114488

yes

—

211

C₂

#13114516

yes

—

212

C₂

#13115655

yes

characteristic

213

C₂

#13115695

yes

characteristic

214

C₂

#13115710

yes

characteristic

	subgroup	G/H
center	C₂³	#88194
commutator	C₄²×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1834	C₂
socle, prime radical	C₂³×C₁₃	#127
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1834	D₁₃
hypocenter	C₁₃	#9834
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

subgroup

G/H

center

C₂³

#88194

commutator

C₄²×C₁₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1834

C₂

socle, prime radical

C₂³×C₁₃

#127

cosocle

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

N	H ≅ G/N	type
14. #11718343	C₄	semidirect
174. C₁₃	#9834	semidirect

H ≅ G/N

type

14. #11718343

C₄

semidirect

174. C₁₃

#9834

semidirect

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

subgroup	index
C₂×#11718343	2
#13115796	2
#13115637	2
C₂×#11718046	2
C₁₃×#1834	2
#9834	13

subgroup

index

C₁₃×#1834

Subgroups — #15762741

Conjugacy classes of subgroups

Complements

Maximal subgroups