Group #15762946 — subgroups

Subgroups — #15762946

Order 3328.

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

normal subgroups only

This group has 434 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	C₄×#88124	C₂	1	1	yes	maximal, characteristic
2	#13114953	C₂	1	1	yes	maximal, characteristic
3	#13112676	C₂	1	4	yes	maximal
4	C₁₃×#1744	C₂	1	1	yes	maximal, characteristic
5	C₂×#88124	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
7	C₄³×C₁₃	C₂²	1	1	yes	characteristic
8	#11718597	C₄	1	1	yes	characteristic
9	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	—
10	#11718594	—	2	2	no	—
11	C₄×#6101	—	2	2	no	—
12	#11718589	C₄	1	2	yes	—
13	C₂×C₄⋊#1055	C₂²	1	2	yes	—
14	C₁₃×#336	—	2	2	no	—
15	#11718116	—	2	2	no	—
16	C₂²×C₈×C₁₃	—	2	2	no	—
17	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₃	D₄	1	2	yes	—
20	C₂×C₄²×C₁₃	D₄	1	2	yes	—
21	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
23	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
24	C₂×#6101	—	2	2	no	—
25	C₂×#6101	—	2	2	no	—
26	C₂×C₄×Dic₁₃	—	2	2	no	—
27	C₂²×#1055	—	2	2	no	—
28	#88124	—	2	4	no	—
29	C₄×C₈×C₁₃	—	2	2	no	—
30	C₄×C₈×C₁₃	Q₈	1	4	yes	—
31	#88071	—	2	2	no	—
32	#88071	—	2	2	no	—
33	#88071	—	2	2	no	—
34	C₄⋊#1055	—	2	4	no	—
35	#9875	—	13	1	no	maximal, Sylow
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	C₂²×Dic₁₃	—	2	2	no	—
42	C₂²×Dic₁₃	—	2	2	no	—
43	C₂×C₈×C₁₃	—	2	4	no	—
44	C₂×C₈×C₁₃	—	4	4	no	—
45	C₄²×C₁₃	—	2	2	no	—
46	C₄²×C₁₃	—	2	2	no	—
47	C₄²×C₁₃	—	2	4	no	—
48	C₄²×C₁₃	—	4	2	no	—
49	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
50	C₄²×C₁₃	#41	1	2	yes	—
51	C₄⋊Dic₁₃	—	2	2	no	—
52	C₄⋊Dic₁₃	—	2	4	no	—
53	C₄⋊Dic₁₃	M₁₆	1	4	yes	—
54	#6101	—	2	8	no	—
55	#6101	—	4	4	no	—
56	C₄×Dic₁₃	—	4	4	no	—
57	C₂×#1055	—	4	2	no	—
58	C₂×#1055	—	4	4	no	—
59	C₄×#125	—	13	1	no	—
60	#1831	—	13	1	no	—
61	#1744	D₁₃	1	1	yes	characteristic
62	#1279	—	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	—	2	2	no	—
71	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
72	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
73	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
74	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
75	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
76	C₂×C₄×C₁₃	#131	1	2	yes	—
77	C₂×C₄×C₁₃	#135	1	4	yes	—
78	C₂×Dic₁₃	—	2	4	no	—
79	C₂×Dic₁₃	—	4	2	no	—
80	C₂×Dic₁₃	—	4	2	no	—
81	C₂×Dic₁₃	—	4	2	no	—
82	C₂×Dic₁₃	—	4	2	no	—
83	C₂×Dic₁₃	—	4	2	no	—
84	C₈×C₁₃	—	4	4	no	—
85	#1055	—	8	2	no	—
86	C₂×#125	—	13	1	no	—
87	C₂×C₄⋊C₈	—	13	2	no	—
88	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
89	#389	—	13	2	no	—
90	#387	—	26	2	no	—
91	#382	—	13	1	no	—
92	C₄×C₄⋊C₄	—	13	2	no	—
93	C₄×C₄⋊C₄	—	26	2	no	—
94	C₄³	C₂×D₁₃	1	1	yes	characteristic
95	#336	—	2	2	no	—
96	#336	—	26	2	no	—
97	C₂²×C₁₃	#391	1	1	yes	characteristic
98	C₂²×C₁₃	#407	1	1	yes	characteristic
99	C₂²×C₁₃	#408	1	1	yes	characteristic
100	C₂²×C₁₃	#416	1	2	yes	—
101	C₂²×C₁₃	#421	1	2	yes	—
102	C₄×C₁₃	—	2	2	no	—
103	C₄×C₁₃	—	4	2	no	—
104	C₄×C₁₃	—	4	2	no	—
105	C₄×C₁₃	#446	1	4	yes	—
106	C₄×C₁₃	#488	1	2	yes	—
107	C₄×C₁₃	#499	1	2	yes	—
108	Dic₁₃	—	4	4	no	—
109	Dic₁₃	—	8	2	no	—
110	C₂²×C₈	—	2	2	no	—
111	C₂²×C₈	—	26	2	no	—
112	#125	—	26	4	no	—
113	C₂×C₄⋊C₄	—	13	2	no	—
114	C₂×C₄⋊C₄	—	13	2	no	—
115	C₂×C₄⋊C₄	—	26	2	no	—
116	C₂×C₄⋊C₄	—	26	2	no	—
117	C₂×C₄²	—	26	2	no	—
118	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
119	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
120	C₂×C₄²	D₅₂	1	2	yes	—
121	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
122	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
123	C₄⋊C₈	—	26	4	no	—
124	C₄×C₈	—	2	2	no	—
125	C₄×C₈	Dic₂₆	1	4	yes	—
126	#95	—	26	2	no	—
127	#95	—	26	2	no	—
128	#95	—	26	2	no	—
129	C₂×C₁₃	#1482	1	2	yes	—
130	C₂×C₁₃	#1488	1	2	yes	—
131	C₂×C₁₃	#1985	1	1	yes	characteristic
132	C₂×C₁₃	#1991	1	1	yes	characteristic
133	C₂×C₁₃	#1995	1	1	yes	characteristic
134	C₂²×C₄	—	26	2	no	—
135	C₂²×C₄	—	26	2	no	—
136	C₂²×C₄	#6103	1	2	yes	—
137	C₂²×C₄	#6103	1	2	yes	—
138	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
139	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
140	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
141	C₂×C₈	—	2	4	no	—
142	C₂×C₈	—	4	4	no	—
143	C₂×C₈	—	52	2	no	—
144	C₂×C₈	—	52	4	no	—
145	C₄⋊C₄	—	13	4	no	—
146	C₄⋊C₄	—	26	8	no	—
147	C₄⋊C₄	—	26	2	no	—
148	C₄⋊C₄	—	26	4	no	—
149	C₄⋊C₄	—	52	4	no	—
150	C₄²	—	2	4	no	—
151	C₄²	—	2	2	no	—
152	C₄²	—	2	2	no	—
153	C₄²	—	4	2	no	—
154	C₄²	—	52	4	no	—
155	C₄²	C₂×Dic₂₆	1	2	yes	—
156	C₄²	#6127	1	2	yes	—
157	C₁₃	#9875	1	1	yes	characteristic, complemented, Sylow
158	C₂³	C₂×#6103	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	—	2	2	no	—
166	C₂×C₄	—	26	4	no	—
167	C₂×C₄	—	52	2	no	—
168	C₂×C₄	—	52	2	no	—
169	C₂×C₄	—	52	2	no	—
170	C₂×C₄	—	52	2	no	—
171	C₂×C₄	—	52	2	no	—
172	C₂×C₄	C₄×Dic₂₆	1	2	yes	—
173	C₂×C₄	#88123	1	1	yes	characteristic
174	C₂×C₄	#88129	1	1	yes	characteristic
175	C₂×C₄	#88158	1	4	yes	—
176	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
177	C₂×C₄	#88161	1	2	yes	—
178	C₂×C₄	#88178	1	2	yes	—
179	C₈	—	4	4	no	—
180	C₈	—	104	2	no	—
181	C₂²	#11718590	1	1	yes	characteristic
182	C₂²	#11718666	1	2	yes	—
183	C₂²	#11718774	1	2	yes	—
184	C₂²	#11718787	1	1	yes	characteristic
185	C₂²	#11718790	1	1	yes	characteristic
186	C₄	—	2	2	no	—
187	C₄	—	4	2	no	—
188	C₄	—	4	2	no	—
189	C₄	—	52	4	no	—
190	C₄	—	104	2	no	—
191	C₄	#11718344	1	2	yes	—
192	C₄	#11718358	1	2	yes	—
193	C₄	#11718362	1	4	yes	—
194	C₂	#13113245	1	2	yes	—
195	C₂	#13113271	1	2	yes	—
196	C₂	#13115776	1	1	yes	characteristic
197	C₂	#13115801	1	1	yes	characteristic
198	C₂	#13115817	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#88124

C₂

yes

maximal, characteristic

#13114953

C₂

yes

maximal, characteristic

#13112676

C₂

yes

maximal

C₁₃×#1744

C₂

yes

maximal, characteristic

C₂×#88124

C₄

yes

characteristic

C₂×C₄×C₈×C₁₃

C₂²

yes

—

C₄³×C₁₃

C₂²

yes

characteristic

#11718597

C₄

yes

characteristic

C₄×C₄⋊Dic₁₃

C₂²

yes

—

#11718594

—

C₄×#6101

—

#11718589

C₄

yes

—

C₂×C₄⋊#1055

C₂²

yes

—

C₁₃×#336

—

#11718116

—

C₂²×C₈×C₁₃

—

C₂×C₄²×C₁₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₃

C₂×C₄

yes

—

C₂×C₄⋊Dic₁₃

C₂×C₄

yes

—

C₂×#6101

—

C₂×#6101

—

C₂×C₄×Dic₁₃

—

C₂²×#1055

—

#88124

—

C₄×C₈×C₁₃

—

C₄×C₈×C₁₃

Q₈

yes

—

—

—

—

—

—

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

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×Q₈

yes

—

C₄²×C₁₃

#41

yes

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

M₁₆

yes

—

#6101

—

#6101

—

C₄×Dic₁₃

—

—

—

—

—

D₁₃

yes

characteristic

#1279

—

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

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×M₁₆

yes

—

C₂×C₄×C₁₃

#131

yes

—

C₂×C₄×C₁₃

#135

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₈×C₁₃

—

#1055

—

C₂×#125

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

C₂×D₁₃

yes

—

#389

—

#387

—

#382

—

C₄×C₄⋊C₄

—

C₄×C₄⋊C₄

—

C₄³

C₂×D₁₃

yes

characteristic

#336

—

#336

—

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

100

C₂²×C₁₃

#416

yes

—

101

C₂²×C₁₃

#421

yes

—

102

C₄×C₁₃

—

103

C₄×C₁₃

—

104

C₄×C₁₃

—

105

C₄×C₁₃

#446

yes

—

106

C₄×C₁₃

#488

yes

—

107

C₄×C₁₃

#499

yes

—

108

Dic₁₃

—

109

Dic₁₃

—

110

C₂²×C₈

—

111

C₂²×C₈

—

112

#125

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄⋊C₄

—

115

C₂×C₄⋊C₄

—

116

C₂×C₄⋊C₄

—

117

C₂×C₄²

—

118

C₂×C₄²

C₄×D₁₃

yes

characteristic

119

C₂×C₄²

C₄×D₁₃

yes

characteristic

120

C₂×C₄²

D₅₂

yes

—

121

C₂×C₄²

C₂²⋊D₁₃

yes

—

122

C₂×C₄²

C₂²×D₁₃

yes

characteristic

123

C₄⋊C₈

—

124

C₄×C₈

—

125

C₄×C₈

Dic₂₆

yes

—

126

#95

—

127

#95

—

128

#95

—

129

C₂×C₁₃

#1482

yes

—

130

C₂×C₁₃

#1488

yes

—

131

C₂×C₁₃

#1985

yes

characteristic

132

C₂×C₁₃

#1991

yes

characteristic

133

C₂×C₁₃

#1995

yes

characteristic

134

C₂²×C₄

—

135

C₂²×C₄

—

136

C₂²×C₄

#6103

yes

—

137

C₂²×C₄

#6103

yes

—

138

C₂²×C₄

C₂×C₄×D₁₃

yes

characteristic

139

C₂²×C₄

C₂×D₅₂

yes

characteristic

140

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

147

C₄⋊C₄

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄²

—

151

C₄²

—

152

C₄²

—

153

C₄²

—

154

C₄²

—

155

C₄²

C₂×Dic₂₆

yes

—

156

C₄²

#6127

yes

—

157

C₁₃

#9875

yes

characteristic, complemented, Sylow

158

C₂³

C₂×#6103

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

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

C₄×Dic₂₆

yes

—

173

C₂×C₄

#88123

yes

characteristic

174

C₂×C₄

#88129

yes

characteristic

175

C₂×C₄

#88158

yes

—

176

C₂×C₄

M₁₆×D₁₃

yes

—

177

C₂×C₄

#88161

yes

—

178

C₂×C₄

#88178

yes

—

179

C₈

—

180

C₈

—

104

—

181

C₂²

#11718590

yes

characteristic

182

C₂²

#11718666

yes

—

183

C₂²

#11718774

yes

—

184

C₂²

#11718787

yes

characteristic

185

C₂²

#11718790

yes

characteristic

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

—

190

C₄

—

104

—

191

C₄

#11718344

yes

—

192

C₄

#11718358

yes

—

193

C₄

#11718362

yes

—

194

C₂

#13113245

yes

—

195

C₂

#13113271

yes

—

196

C₂

#13115776

yes

characteristic

197

C₂

#13115801

yes

characteristic

198

C₂

#13115817

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₅₂
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1744	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1744	D₁₃
hypocenter	C₁₃	#9875
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1744

subgroup

G/H

center

C₂²×C₄

C₂×D₅₂

commutator

C₂²×C₄×C₁₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1744

C₂

socle, prime radical

C₂³×C₁₃

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1744

N	H ≅ G/N	type
157. C₁₃	#9875	semidirect

H ≅ G/N

type

157. C₁₃

#9875

semidirect

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

subgroup	index
C₄×#88124	2
#13114953	2
#13112676	2
C₁₃×#1744	2
#9875	13

subgroup

index

C₁₃×#1744

Subgroups — #15762946

Conjugacy classes of subgroups

Complements

Maximal subgroups