Group #14564073 — subgroups

Subgroups — #14564073

Order 2432.

412 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 109 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×#10597376	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597278	C₂	1	2	yes	maximal, complemented
3	#11926404	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926307	C₂	1	2	yes	maximal, complemented
5	C₂²×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₂²⋊D₁₉	—	2	1	no	—
8	C₂²×D₇₆	C₂²	1	1	yes	characteristic
9	C₂×M₁₆×C₁₉	—	2	2	no	—
10	C₂×M₁₆×C₁₉	—	2	4	no	—
11	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
12	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
13	#10597376	—	2	2	no	—
14	#10597376	C₄	1	4	yes	complemented
15	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
16	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
17	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
18	C₁₉⋊#95	—	2	1	no	—
19	#10597278	—	2	4	no	—
20	C₂⁴×C₁₉	D₄	1	1	yes	characteristic
21	C₂³×D₁₉	—	2	1	no	—
22	C₂²×C₄×C₁₉	—	2	2	no	—
23	C₂²×C₄×C₁₉	—	2	2	no	—
24	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
25	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	D₄	1	2	yes	—
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₂²⋊D₁₉	—	2	4	no	—
29	C₂×C₂²⋊D₁₉	—	4	4	no	—
30	C₂²×Dic₁₉	—	2	1	no	—
31	C₂²×Dic₁₉	—	2	2	no	—
32	C₂×D₇₆	—	2	2	no	—
33	C₂×D₇₆	—	2	2	no	—
34	C₂×D₇₆	—	2	1	no	—
35	C₂×D₇₆	C₂×C₄	1	2	yes	—
36	M₁₆×C₁₉	—	2	8	no	—
37	C₂×C₈×C₁₉	—	2	2	no	—
38	C₂×C₈×C₁₉	—	2	2	no	—
39	C₂×C₈×C₁₉	D₄	1	4	yes	complemented
40	C₂²⋊Dic₁₉	—	4	2	no	—
41	(C₂×D₁₉)⋊C₄	—	2	4	no	—
42	C₄⋊Dic₁₉	—	2	1	no	—
43	C₄⋊Dic₁₉	—	2	2	no	—
44	C₄⋊Dic₁₉	—	2	2	no	—
45	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
46	C₂³×C₁₉	—	2	2	no	—
47	C₂³×C₁₉	—	2	1	no	—
48	C₂³×C₁₉	—	2	2	no	—
49	C₂³×C₁₉	—	2	1	no	—
50	C₂³×C₁₉	C₂²⋊C₄	1	2	yes	—
51	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×D₁₉	—	2	2	no	—
53	C₂²×D₁₉	—	4	2	no	—
54	C₂²×D₁₉	—	4	2	no	—
55	C₂²×D₁₉	—	4	1	no	—
56	C₂²×D₁₉	—	4	1	no	—
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	2	4	no	—
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
62	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
64	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#41	1	2	yes	—
66	C₂²⋊D₁₉	—	4	8	no	—
67	C₂×Dic₁₉	—	2	2	no	—
68	C₂×Dic₁₉	—	4	2	no	—
69	C₂×Dic₁₉	—	4	2	no	—
70	C₂×Dic₁₉	—	4	2	no	—
71	C₂×Dic₁₉	—	4	2	no	—
72	D₇₆	—	2	4	no	—
73	D₇₆	—	4	1	no	—
74	D₇₆	—	4	1	no	—
75	C₈×C₁₉	—	2	4	no	—
76	#1895	—	19	1	no	maximal, Sylow
77	C₂²×C₁₉	—	2	2	no	—
78	C₂²×C₁₉	—	2	2	no	—
79	C₂²×C₁₉	—	2	2	no	—
80	C₂²×C₁₉	—	4	2	no	—
81	C₂²×C₁₉	—	4	2	no	—
82	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₁₉	#121	1	2	yes	—
84	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
85	C₂²×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
86	C₂²×C₁₉	#137	1	1	yes	characteristic
87	C₂×D₁₉	—	4	2	no	—
88	C₂×D₁₉	—	4	2	no	—
89	C₂×D₁₉	—	4	2	no	—
90	C₂×D₁₉	—	8	2	no	—
91	C₂×D₁₉	—	8	2	no	—
92	C₄×C₁₉	—	2	2	no	—
93	C₄×C₁₉	C₄×D₄	1	2	yes	—
94	C₄×C₁₉	#120	1	1	yes	characteristic
95	C₄×C₁₉	#123	1	1	yes	characteristic
96	Dic₁₉	—	4	2	no	—
97	Dic₁₉	—	8	2	no	—
98	C₂²×M₁₆	D₁₉	1	1	yes	characteristic, complemented
99	C₂×#121	—	19	1	no	—
100	C₂×#102	—	19	2	no	—
101	#380	—	19	1	no	—
102	#340	—	19	2	no	—
103	C₂×C₁₉	—	4	2	no	—
104	C₂×C₁₉	#386	1	1	yes	characteristic
105	C₂×C₁₉	#417	1	1	yes	characteristic
106	C₂×C₁₉	#418	1	1	yes	characteristic
107	C₂×C₁₉	#468	1	2	yes	—
108	C₂×C₁₉	#469	1	2	yes	—
109	D₁₉	—	8	2	no	—
110	C₂²×D₄	—	19	1	no	—
111	C₂²×D₄	—	38	1	no	—
112	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
113	C₂×M₁₆	—	2	2	no	—
114	C₂×M₁₆	—	2	4	no	—
115	C₂²×C₈	C₂×D₁₉	1	2	yes	—
116	#121	—	19	4	no	—
117	#121	—	38	2	no	—
118	C₂×C₄⋊C₄	—	19	1	no	—
119	C₂×C₄⋊C₄	—	19	2	no	—
120	C₂×C₂²⋊C₄	—	38	1	no	—
121	C₂×C₂²⋊C₄	—	38	1	no	—
122	#102	—	38	4	no	—
123	#95	—	38	1	no	—
124	C₁₉	#1895	1	1	yes	characteristic, complemented, Sylow
125	C₂⁴	—	38	1	no	—
126	C₂⁴	D₇₆	1	1	yes	characteristic
127	C₂×D₄	—	19	2	no	—
128	C₂×D₄	—	38	4	no	—
129	C₂×D₄	—	38	2	no	—
130	C₂×D₄	—	38	2	no	—
131	C₂×D₄	—	38	1	no	—
132	C₂×D₄	—	76	4	no	—
133	C₂²×C₄	—	2	2	no	—
134	C₂²×C₄	—	2	2	no	—
135	C₂²×C₄	—	38	1	no	—
136	C₂²×C₄	—	38	2	no	—
137	C₂²×C₄	C₄×D₁₉	1	2	yes	—
138	C₂²×C₄	D₇₆	1	1	yes	characteristic
139	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
140	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
141	M₁₆	—	2	8	no	—
142	C₂×C₈	—	2	2	no	—
143	C₂×C₈	—	2	2	no	—
144	C₂×C₈	C₂²⋊D₁₉	1	4	yes	complemented
145	C₄⋊C₄	—	19	2	no	—
146	C₄⋊C₄	—	38	1	no	—
147	C₄⋊C₄	—	38	2	no	—
148	C₄⋊C₄	—	38	2	no	—
149	C₂²⋊C₄	—	38	4	no	—
150	C₂²⋊C₄	—	76	2	no	—
151	C₂³	—	2	2	no	—
152	C₂³	—	2	1	no	—
153	C₂³	—	2	2	no	—
154	C₂³	—	2	1	no	—
155	C₂³	—	38	2	no	—
156	C₂³	—	76	2	no	—
157	C₂³	—	76	2	no	—
158	C₂³	—	76	1	no	—
159	C₂³	—	76	1	no	—
160	C₂³	(C₂×D₁₉)⋊C₄	1	2	yes	—
161	C₂³	C₂×D₇₆	1	1	yes	characteristic
162	D₄	—	38	4	no	—
163	D₄	—	76	8	no	—
164	D₄	—	76	1	no	—
165	D₄	—	76	1	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	4	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	38	2	no	—
171	C₂×C₄	—	76	2	no	—
172	C₂×C₄	—	76	2	no	—
173	C₂×C₄	—	76	2	no	—
174	C₂×C₄	—	76	2	no	—
175	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
176	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
177	C₂×C₄	#64541	1	2	yes	—
178	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
179	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
180	C₈	—	2	4	no	—
181	C₂²	—	2	2	no	—
182	C₂²	—	2	2	no	—
183	C₂²	—	2	2	no	—
184	C₂²	—	4	2	no	—
185	C₂²	—	4	2	no	—
186	C₂²	—	76	2	no	—
187	C₂²	—	76	2	no	—
188	C₂²	—	76	2	no	—
189	C₂²	—	152	2	no	—
190	C₂²	—	152	2	no	—
191	C₂²	#10597354	1	2	yes	—
192	C₂²	#10597354	1	1	yes	characteristic
193	C₂²	#10597355	1	1	yes	characteristic
194	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
195	C₂²	#10597376	1	2	yes	—
196	C₄	—	2	2	no	—
197	C₄	—	76	2	no	—
198	C₄	—	152	2	no	—
199	C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
200	C₄	#10597375	1	1	yes	characteristic
201	C₄	#10597399	1	1	yes	characteristic
202	C₂	—	4	2	no	—
203	C₂	—	152	2	no	—
204	C₂	#11926423	1	1	yes	characteristic
205	C₂	#11926546	1	1	yes	characteristic
206	C₂	#11926550	1	1	yes	characteristic
207	C₂	#11926790	1	2	yes	—
208	C₂	#11926797	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597376

C₂

yes

maximal, characteristic

C₂×#10597278

C₂

yes

maximal, complemented

#11926404

C₂

yes

maximal, characteristic, complemented

#11926307

C₂

yes

maximal, complemented

C₂²×M₁₆×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂²×C₂²⋊D₁₉

—

C₂²×D₇₆

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

—

#10597376

—

#10597376

C₄

yes

complemented

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₁₉⋊#95

—

#10597278

—

C₂⁴×C₁₉

D₄

yes

characteristic

C₂³×D₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂×C₄

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

complemented

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

#1895

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

#121

yes

—

C₂²×C₁₉

AGL(1,ℤ/8)

yes

characteristic

C₂²×C₁₉

AGL(1,ℤ/8)

yes

—

C₂²×C₁₉

#137

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₂²×M₁₆

D₁₉

yes

characteristic, complemented

C₂×#121

—

100

C₂×#102

—

101

#380

—

102

#340

—

103

C₂×C₁₉

—

104

C₂×C₁₉

#386

yes

characteristic

105

C₂×C₁₉

#417

yes

characteristic

106

C₂×C₁₉

#418

yes

characteristic

107

C₂×C₁₉

#468

yes

—

108

C₂×C₁₉

#469

yes

—

109

D₁₉

—

110

C₂²×D₄

—

111

C₂²×D₄

—

112

C₂³×C₄

C₂×D₁₉

yes

characteristic

113

C₂×M₁₆

—

114

C₂×M₁₆

—

115

C₂²×C₈

C₂×D₁₉

yes

—

116

#121

—

117

#121

—

118

C₂×C₄⋊C₄

—

119

C₂×C₄⋊C₄

—

120

C₂×C₂²⋊C₄

—

121

C₂×C₂²⋊C₄

—

122

#102

—

123

#95

—

124

C₁₉

#1895

yes

characteristic, complemented, Sylow

125

C₂⁴

—

126

C₂⁴

D₇₆

yes

characteristic

127

C₂×D₄

—

128

C₂×D₄

—

129

C₂×D₄

—

130

C₂×D₄

—

131

C₂×D₄

—

132

C₂×D₄

—

133

C₂²×C₄

—

134

C₂²×C₄

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

C₄×D₁₉

yes

—

138

C₂²×C₄

D₇₆

yes

characteristic

139

C₂²×C₄

C₂²⋊D₁₉

yes

—

140

C₂²×C₄

C₂²×D₁₉

yes

characteristic

141

M₁₆

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

C₂²⋊D₁₉

yes

complemented

145

C₄⋊C₄

—

146

C₄⋊C₄

—

147

C₄⋊C₄

—

148

C₄⋊C₄

—

149

C₂²⋊C₄

—

150

C₂²⋊C₄

—

151

C₂³

—

152

C₂³

—

153

C₂³

—

154

C₂³

—

155

C₂³

—

156

C₂³

—

157

C₂³

—

158

C₂³

—

159

C₂³

—

160

C₂³

(C₂×D₁₉)⋊C₄

yes

—

161

C₂³

C₂×D₇₆

yes

characteristic

162

D₄

—

163

D₄

—

164

D₄

—

165

D₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

176

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

177

C₂×C₄

#64541

yes

—

178

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

179

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

180

C₈

—

181

C₂²

—

182

C₂²

—

183

C₂²

—

184

C₂²

—

185

C₂²

—

186

C₂²

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

152

—

190

C₂²

—

152

—

191

C₂²

#10597354

yes

—

192

C₂²

#10597354

yes

characteristic

193

C₂²

#10597355

yes

characteristic

194

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

195

C₂²

#10597376

yes

—

196

C₄

—

197

C₄

—

198

C₄

—

152

—

199

C₄

C₄×C₂²⋊D₁₉

yes

—

200

C₄

#10597375

yes

characteristic

201

C₄

#10597399

yes

characteristic

202

C₂

—

203

C₂

—

152

—

204

C₂

#11926423

yes

characteristic

205

C₂

#11926546

yes

characteristic

206

C₂

#11926550

yes

characteristic

207

C₂

#11926790

yes

—

208

C₂

#11926797

yes

—

	subgroup	G/H
center	C₂³	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂²×M₁₆×C₁₉	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂×#10597376	C₂
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂²×M₁₆	D₁₉
hypocenter	C₁₉	#1895
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂²×M₁₆

subgroup

G/H

center

C₂³

C₂×D₇₆

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂²×M₁₆×C₁₉

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂×#10597376

C₂

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₂²×M₁₆

D₁₉

hypocenter

C₁₉

#1895

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂²×M₁₆

N	H ≅ G/N	type
2. C₂×#10597278	C₂	semidirect
3. #11926404	C₂	semidirect
4. #11926307	C₂	semidirect
5. C₂²×M₁₆×C₁₉	C₂	semidirect
14. #10597376	C₄	semidirect
39. C₂×C₈×C₁₉	D₄	semidirect
98. C₂²×M₁₆	D₁₉	semidirect
124. C₁₉	#1895	semidirect
144. C₂×C₈	C₂²⋊D₁₉	semidirect

H ≅ G/N

type

2. C₂×#10597278

C₂

semidirect

3. #11926404

C₂

semidirect

4. #11926307

C₂

semidirect

5. C₂²×M₁₆×C₁₉

C₂

semidirect

14. #10597376

C₄

semidirect

39. C₂×C₈×C₁₉

D₄

semidirect

98. C₂²×M₁₆

D₁₉

semidirect

124. C₁₉

#1895

semidirect

144. C₂×C₈

C₂²⋊D₁₉

semidirect

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

subgroup	index
C₂×#10597376	2
C₂×#10597278	2
#11926404	2
#11926307	2
C₂²×M₁₆×C₁₉	2
#1895	19

subgroup

index

C₂²×M₁₆×C₁₉

Subgroups — #14564073

Conjugacy classes of subgroups

Complements

Maximal subgroups