Group #15763063 — subgroups

Subgroups — #15763063

Order 3328.

438 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 167 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	#13114988	C₂	1	1	yes	maximal, characteristic
2	#13114689	C₂	1	1	yes	maximal, characteristic
3	#13112719	C₂	1	4	yes	maximal
4	C₁₃×#2859	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#125	—	2	1	no	—
6	C₁₃×#389	—	2	2	no	—
7	C₁₃×#389	C₄	1	4	yes	—
8	C₁₃×#384	C₂²	1	2	yes	—
9	C₁₃×#382	—	2	1	no	—
10	C₄³×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊#1055	—	2	2	no	—
12	C₂×C₄⋊#1055	C₂²	1	2	yes	—
13	C₂×C₄⋊#1055	C₂²	1	2	yes	—
14	C₂×#88043	—	2	1	no	—
15	#11718116	—	2	1	no	—
16	C₁₃×#125	—	4	4	no	—
17	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
18	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
19	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
20	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
21	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₃	D₄	1	2	yes	—
23	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
26	C₂²×#1055	—	2	2	no	—
27	C₂²×#1055	—	2	2	no	—
28	C₁₃×#95	—	2	4	no	—
29	C₄⋊#1055	—	2	2	no	—
30	C₄⋊#1055	—	2	4	no	—
31	C₄⋊#1055	—	4	4	no	—
32	C₄⋊#1055	Q₈	1	4	yes	—
33	#88043	—	4	2	no	—
34	#9902	—	13	1	no	maximal, Sylow
35	C₂²×C₄×C₁₃	—	2	4	no	—
36	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
37	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
38	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
41	C₁₃×C₄⋊C₄	—	4	4	no	—
42	C₁₃×C₄⋊C₄	—	4	8	no	—
43	C₁₃×C₄⋊C₄	—	4	2	no	—
44	C₁₃×C₄⋊C₄	—	4	4	no	—
45	C₁₃×C₄⋊C₄	—	4	2	no	—
46	C₄²×C₁₃	—	2	2	no	—
47	C₄²×C₁₃	—	2	2	no	—
48	C₄²×C₁₃	—	2	2	no	—
49	C₄²×C₁₃	—	4	2	no	—
50	C₄²×C₁₃	SD₁₆	1	2	yes	—
51	C₄²×C₁₃	Q₁₆	1	2	yes	—
52	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
53	C₄²×C₁₃	#41	1	2	yes	—
54	C₂×#1055	—	2	4	no	—
55	C₂×#1055	—	4	2	no	—
56	C₂×#1055	—	4	2	no	—
57	C₂×#1055	—	4	2	no	—
58	C₂×#1055	—	4	4	no	—
59	#2859	D₁₃	1	1	yes	characteristic
60	#1842	—	13	1	no	—
61	#1767	—	13	1	no	—
62	#1296	—	13	4	no	—
63	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₄×C₁₃	—	2	2	no	—
65	C₂×C₄×C₁₃	—	2	2	no	—
66	C₂×C₄×C₁₃	—	2	2	no	—
67	C₂×C₄×C₁₃	—	2	2	no	—
68	C₂×C₄×C₁₃	—	2	2	no	—
69	C₂×C₄×C₁₃	—	2	2	no	—
70	C₂×C₄×C₁₃	—	4	4	no	—
71	C₂×C₄×C₁₃	—	4	4	no	—
72	C₂×C₄×C₁₃	—	4	4	no	—
73	C₂×C₄×C₁₃	#103	1	4	yes	—
74	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
75	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
76	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
77	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
80	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
81	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
82	C₂×C₄×C₁₃	#137	1	2	yes	—
83	#1055	—	4	4	no	—
84	#1055	—	8	2	no	—
85	C₂×#125	—	2	1	no	—
86	C₂×C₄⋊C₈	—	13	2	no	—
87	C₂×C₄⋊C₈	—	13	2	no	—
88	C₂×C₄⋊C₈	—	26	2	no	—
89	C₂×#97	—	26	1	no	—
90	#389	—	2	2	no	—
91	#389	Dic₁₃	1	4	yes	—
92	#384	C₂×D₁₃	1	2	yes	—
93	#382	—	2	1	no	—
94	C₄³	C₂×D₁₃	1	1	yes	characteristic
95	#336	—	26	1	no	—
96	C₂²×C₁₃	#391	1	1	yes	characteristic
97	C₂²×C₁₃	#413	1	2	yes	—
98	C₂²×C₁₃	C₂×#103	1	1	yes	characteristic
99	C₂²×C₁₃	#417	1	2	yes	—
100	C₂²×C₁₃	#418	1	1	yes	characteristic
101	C₄×C₁₃	—	2	4	no	—
102	C₄×C₁₃	—	2	2	no	—
103	C₄×C₁₃	—	4	2	no	—
104	C₄×C₁₃	—	8	4	no	—
105	C₄×C₁₃	#476	1	2	yes	—
106	C₄×C₁₃	#477	1	2	yes	—
107	C₄×C₁₃	#490	1	1	yes	characteristic
108	C₄×C₁₃	#491	1	1	yes	characteristic
109	C₄×C₁₃	#501	1	2	yes	—
110	C₂²×C₈	—	26	2	no	—
111	C₂²×C₈	—	26	2	no	—
112	#125	—	4	4	no	—
113	C₂×C₄⋊C₄	—	2	4	no	—
114	C₂×C₄⋊C₄	—	2	2	no	—
115	C₂×C₄⋊C₄	—	2	2	no	—
116	C₂×C₄⋊C₄	C₂×Dic₁₃	1	4	yes	—
117	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
118	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
119	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
120	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
121	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
122	C₄⋊C₈	—	13	4	no	—
123	C₄⋊C₈	—	26	2	no	—
124	C₄⋊C₈	—	26	4	no	—
125	C₄⋊C₈	—	52	4	no	—
126	#97	—	52	2	no	—
127	#95	—	2	4	no	—
128	C₂×C₁₃	#1550	1	2	yes	—
129	C₂×C₁₃	#1557	1	2	yes	—
130	C₂×C₁₃	#1987	1	1	yes	characteristic
131	C₂×C₁₃	#1992	1	1	yes	characteristic
132	C₂×C₁₃	#1998	1	1	yes	characteristic
133	C₂²×C₄	—	2	4	no	—
134	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
135	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
136	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
137	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
138	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
139	C₂×C₈	—	26	4	no	—
140	C₂×C₈	—	52	2	no	—
141	C₂×C₈	—	52	2	no	—
142	C₂×C₈	—	52	2	no	—
143	C₂×C₈	—	52	4	no	—
144	C₄⋊C₄	—	4	4	no	—
145	C₄⋊C₄	—	4	8	no	—
146	C₄⋊C₄	—	4	4	no	—
147	C₄⋊C₄	—	4	2	no	—
148	C₄⋊C₄	—	4	2	no	—
149	C₄²	—	2	2	no	—
150	C₄²	—	2	2	no	—
151	C₄²	—	2	2	no	—
152	C₄²	—	4	2	no	—
153	C₄²	#6106	1	2	yes	—
154	C₄²	#6107	1	2	yes	—
155	C₄²	Q₈×D₁₃	1	2	yes	—
156	C₄²	#6131	1	2	yes	—
157	C₁₃	#9902	1	1	yes	characteristic, complemented, Sylow
158	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	4	4	no	—
166	C₂×C₄	—	4	4	no	—
167	C₂×C₄	—	4	4	no	—
168	C₂×C₄	#88075	1	4	yes	—
169	C₂×C₄	#88186	1	2	yes	—
170	C₂×C₄	C₂×#6106	1	1	yes	characteristic
171	C₂×C₄	C₂×#6107	1	1	yes	characteristic
172	C₂×C₄	#88198	1	1	yes	characteristic
173	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
174	C₂×C₄	#88200	1	2	yes	—
175	C₂×C₄	#88201	1	1	yes	characteristic
176	C₂×C₄	#88203	1	2	yes	—
177	C₂×C₄	#88205	1	2	yes	—
178	C₈	—	52	4	no	—
179	C₈	—	104	2	no	—
180	C₂²	#11718876	1	1	yes	characteristic
181	C₂²	C₂×#88075	1	1	yes	characteristic
182	C₂²	#11718891	1	1	yes	characteristic
183	C₂²	#11718893	1	2	yes	—
184	C₂²	#11718898	1	2	yes	—
185	C₄	—	2	4	no	—
186	C₄	—	2	2	no	—
187	C₄	—	4	2	no	—
188	C₄	—	8	4	no	—
189	C₄	#11718726	1	2	yes	—
190	C₄	#11718728	1	1	yes	characteristic
191	C₄	#11718730	1	1	yes	characteristic
192	C₄	#11718745	1	2	yes	—
193	C₄	#11718752	1	2	yes	—
194	C₂	#13113526	1	2	yes	—
195	C₂	#13113558	1	2	yes	—
196	C₂	#13115785	1	1	yes	characteristic
197	C₂	#13115806	1	1	yes	characteristic
198	C₂	#13115830	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13114988

C₂

yes

maximal, characteristic

#13114689

C₂

yes

maximal, characteristic

#13112719

C₂

yes

maximal

C₁₃×#2859

C₂

yes

maximal, characteristic

C₂×C₁₃×#125

—

C₁₃×#389

—

C₁₃×#389

C₄

yes

—

C₁₃×#384

C₂²

yes

—

C₁₃×#382

—

C₄³×C₁₃

C₂²

yes

characteristic

C₂×C₄⋊#1055

—

C₂×C₄⋊#1055

C₂²

yes

—

C₂×C₄⋊#1055

C₂²

yes

—

C₂×#88043

—

#11718116

—

C₁₃×#125

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

D₄

yes

characteristic

C₂×C₄²×C₁₃

D₄

yes

characteristic

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂²×#1055

—

C₂²×#1055

—

C₁₃×#95

—

—

—

—

Q₈

yes

—

#88043

—

#9902

—

maximal, Sylow

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

SD₁₆

yes

—

C₄²×C₁₃

Q₁₆

yes

—

C₄²×C₁₃

C₂×Q₈

yes

—

C₄²×C₁₃

#41

yes

—

—

—

—

—

—

D₁₃

yes

—

—

—

C₂³×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#103

yes

—

C₂×C₄×C₁₃

C₄×Q₈

yes

—

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₃

#124

yes

characteristic

C₂×C₄×C₁₃

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₃

#137

yes

—

#1055

—

#1055

—

C₂×#125

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×#97

—

#389

—

#389

Dic₁₃

yes

—

#384

C₂×D₁₃

yes

—

#382

—

C₄³

C₂×D₁₃

yes

characteristic

#336

—

C₂²×C₁₃

#391

yes

characteristic

C₂²×C₁₃

#413

yes

—

C₂²×C₁₃

C₂×#103

yes

characteristic

C₂²×C₁₃

#417

yes

—

100

C₂²×C₁₃

#418

yes

characteristic

101

C₄×C₁₃

—

102

C₄×C₁₃

—

103

C₄×C₁₃

—

104

C₄×C₁₃

—

105

C₄×C₁₃

#476

yes

—

106

C₄×C₁₃

#477

yes

—

107

C₄×C₁₃

#490

yes

characteristic

108

C₄×C₁₃

#491

yes

characteristic

109

C₄×C₁₃

#501

yes

—

110

C₂²×C₈

—

111

C₂²×C₈

—

112

#125

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄⋊C₄

—

115

C₂×C₄⋊C₄

—

116

C₂×C₄⋊C₄

C₂×Dic₁₃

yes

—

117

C₂×C₄²

C₂×Dic₁₃

yes

—

118

C₂×C₄²

C₂²⋊D₁₃

yes

characteristic

119

C₂×C₄²

C₂²⋊D₁₃

yes

—

120

C₂×C₄²

C₂²⋊D₁₃

yes

characteristic

121

C₂×C₄²

C₂²×D₁₃

yes

characteristic

122

C₄⋊C₈

—

123

C₄⋊C₈

—

124

C₄⋊C₈

—

125

C₄⋊C₈

—

126

#97

—

127

#95

—

128

C₂×C₁₃

#1550

yes

—

129

C₂×C₁₃

#1557

yes

—

130

C₂×C₁₃

#1987

yes

characteristic

131

C₂×C₁₃

#1992

yes

characteristic

132

C₂×C₁₃

#1998

yes

characteristic

133

C₂²×C₄

—

134

C₂²×C₄

C₂²⋊Dic₁₃

yes

—

135

C₂²×C₄

C₂²⋊Dic₁₃

yes

—

136

C₂²×C₄

C₂²×Dic₁₃

yes

characteristic

137

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

138

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

147

C₄⋊C₄

—

148

C₄⋊C₄

—

149

C₄²

—

150

C₄²

—

151

C₄²

—

152

C₄²

—

153

C₄²

#6106

yes

—

154

C₄²

#6107

yes

—

155

C₄²

Q₈×D₁₃

yes

—

156

C₄²

#6131

yes

—

157

C₁₃

#9902

yes

characteristic, complemented, Sylow

158

C₂³

C₂×C₂²⋊Dic₁₃

yes

characteristic

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

#88075

yes

—

169

C₂×C₄

#88186

yes

—

170

C₂×C₄

C₂×#6106

yes

characteristic

171

C₂×C₄

C₂×#6107

yes

characteristic

172

C₂×C₄

#88198

yes

characteristic

173

C₂×C₄

Q₈×Dic₁₃

yes

—

174

C₂×C₄

#88200

yes

—

175

C₂×C₄

#88201

yes

characteristic

176

C₂×C₄

#88203

yes

—

177

C₂×C₄

#88205

yes

—

178

C₈

—

179

C₈

—

104

—

180

C₂²

#11718876

yes

characteristic

181

C₂²

C₂×#88075

yes

characteristic

182

C₂²

#11718891

yes

characteristic

183

C₂²

#11718893

yes

—

184

C₂²

#11718898

yes

—

185

C₄

—

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

#11718726

yes

—

190

C₄

#11718728

yes

characteristic

191

C₄

#11718730

yes

characteristic

192

C₄

#11718745

yes

—

193

C₄

#11718752

yes

—

194

C₂

#13113526

yes

—

195

C₂

#13113558

yes

—

196

C₂

#13115785

yes

characteristic

197

C₂

#13115806

yes

characteristic

198

C₂

#13115830

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₃
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#2859	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#2859	D₁₃
hypocenter	C₁₃	#9902
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2859

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₃

commutator

C₂²×C₄×C₁₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#2859

C₂

socle, prime radical

C₂³×C₁₃

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂²×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #2859

N	H ≅ G/N	type
157. C₁₃	#9902	semidirect

H ≅ G/N

type

157. C₁₃

#9902

semidirect

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

subgroup	index
#13114988	2
#13114689	2
#13112719	2
C₁₃×#2859	2
#9902	13

subgroup

index

C₁₃×#2859

Subgroups — #15763063

Conjugacy classes of subgroups

Complements

Maximal subgroups