Group #14565047 — subgroups

Subgroups — #14565047

Order 2432.

238 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 81 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×#10597273	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597267	C₂	1	1	yes	maximal, characteristic
3	#11926449	C₂	1	1	yes	maximal, characteristic
4	#11926413	C₂	1	1	yes	maximal, characteristic
5	#11926306	C₂	1	1	yes	maximal, characteristic
6	#11926298	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#340	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₉⋊C₄	—	2	1	no	—
14	C₂×Dic₁₉⋊C₄	—	2	1	no	—
15	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₁₉⋊#95	—	2	1	no	—
18	C₁₉⋊#95	—	2	1	no	—
19	#10597273	—	2	2	no	—
20	#10597267	—	2	2	no	—
21	C₂²×C₄×C₁₉	—	2	1	no	—
22	C₂²×C₄×C₁₉	—	2	1	no	—
23	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂²×Dic₁₉	—	2	1	no	—
25	C₂²×Dic₁₉	—	2	1	no	—
26	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
27	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
28	C₂×Dic₃₈	—	2	1	no	—
29	C₂×Dic₃₈	—	2	1	no	—
30	C₂×Dic₃₈	—	2	1	no	—
31	C₂×Dic₃₈	—	2	1	no	—
32	C₂×Dic₃₈	—	2	1	no	—
33	C₂×Dic₃₈	D₄	1	2	yes	—
34	C₂×C₈×C₁₉	—	2	1	no	—
35	C₂×C₈×C₁₉	—	2	1	no	—
36	C₂×C₈×C₁₉	—	2	1	no	—
37	C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₄⋊C₄×C₁₉	—	2	1	no	—
41	C₄⋊Dic₁₉	—	2	1	no	—
42	C₄⋊Dic₁₉	—	2	1	no	—
43	Dic₁₉⋊C₄	—	4	2	no	—
44	Dic₁₉⋊C₄	—	4	2	no	—
45	C₄×Dic₁₉	—	2	1	no	—
46	C₄×Dic₁₉	—	2	1	no	—
47	C₂×C₁₉⋊C₈	—	2	1	no	—
48	C₂×C₁₉⋊C₈	—	2	1	no	—
49	C₂×C₁₉⋊C₈	—	2	1	no	—
50	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	—	4	1	no	—
53	C₂×C₄×C₁₉	—	4	1	no	—
54	C₂×C₄×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	—	4	1	no	—
56	C₂×C₄×C₁₉	—	4	1	no	—
57	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
59	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
60	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
61	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
62	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
63	C₂×Dic₁₉	—	2	1	no	—
64	C₂×Dic₁₉	—	2	1	no	—
65	C₂×Dic₁₉	—	2	1	no	—
66	C₂×Dic₁₉	—	2	1	no	—
67	C₂×Dic₁₉	—	2	2	no	—
68	C₂×Dic₁₉	—	4	1	no	—
69	C₂×Dic₁₉	—	4	1	no	—
70	C₂×Dic₁₉	—	4	1	no	—
71	C₂×Dic₁₉	—	4	1	no	—
72	C₂×Dic₁₉	—	4	1	no	—
73	C₂×Dic₁₉	SD₁₆	1	2	yes	—
74	C₂×Dic₁₉	Q₁₆	1	2	yes	—
75	Dic₃₈	—	2	2	no	—
76	Dic₃₈	—	2	2	no	—
77	Dic₃₈	—	4	1	no	—
78	Dic₃₈	—	4	1	no	—
79	C₈×C₁₉	—	4	1	no	—
80	C₁₉⋊C₈	—	4	1	no	—
81	#2072	—	19	1	no	maximal, Sylow
82	C₂²×C₁₉	#121	1	1	yes	characteristic
83	C₂²×C₁₉	#123	1	1	yes	characteristic
84	C₂²×C₁₉	#124	1	1	yes	characteristic
85	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
86	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
87	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
88	C₂²×C₁₉	#137	1	1	yes	characteristic
89	C₄×C₁₉	—	8	1	no	—
90	C₄×C₁₉	—	8	1	no	—
91	C₄×C₁₉	#123	1	1	yes	characteristic
92	C₄×C₁₉	#123	1	1	yes	characteristic
93	C₄×C₁₉	#126	1	1	yes	characteristic
94	C₄×C₁₉	#126	1	1	yes	characteristic
95	Dic₁₉	—	2	2	no	—
96	Dic₁₉	—	2	2	no	—
97	Dic₁₉	—	4	2	no	—
98	Dic₁₉	—	8	1	no	—
99	C₂×#103	—	19	1	no	—
100	C₂×#103	—	19	1	no	—
101	#391	—	19	1	no	—
102	#384	—	19	1	no	—
103	#340	—	19	1	no	—
104	#340	D₁₉	1	1	yes	characteristic
105	#336	—	19	1	no	—
106	C₂×C₁₉	#397	1	1	yes	characteristic
107	C₂×C₁₉	#460	1	1	yes	characteristic
108	C₂×C₁₉	#462	1	1	yes	characteristic
109	C₂×C₁₉	#483	1	1	yes	characteristic
110	C₂×C₁₉	#484	1	1	yes	characteristic
111	C₂×C₁₉	#487	1	1	yes	characteristic
112	C₂×C₁₉	#489	1	1	yes	characteristic
113	C₂²×Q₈	—	19	1	no	—
114	C₂²×C₈	—	19	1	no	—
115	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
116	C₂×C₄⋊C₄	—	19	1	no	—
117	C₂×C₄⋊C₄	—	38	1	no	—
118	C₂×C₄⋊C₄	—	38	1	no	—
119	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
120	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
121	C₂×C₄²	—	19	1	no	—
122	#103	—	38	2	no	—
123	#103	—	38	2	no	—
124	#95	—	38	1	no	—
125	#95	—	38	1	no	—
126	C₁₉	#2072	1	1	yes	characteristic, complemented, Sylow
127	C₂×Q₈	—	19	2	no	—
128	C₂×Q₈	—	38	1	no	—
129	C₂×Q₈	—	38	1	no	—
130	C₂×Q₈	—	38	1	no	—
131	C₂×Q₈	—	38	1	no	—
132	C₂×Q₈	—	38	1	no	—
133	C₂²×C₄	—	2	1	no	—
134	C₂²×C₄	—	2	1	no	—
135	C₂²×C₄	—	19	1	no	—
136	C₂²×C₄	—	19	1	no	—
137	C₂²×C₄	—	38	1	no	—
138	C₂²×C₄	—	38	1	no	—
139	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
140	C₂×C₈	—	2	1	no	—
141	C₂×C₈	—	2	1	no	—
142	C₂×C₈	—	2	1	no	—
143	C₂×C₈	—	38	1	no	—
144	C₂×C₈	—	38	1	no	—
145	C₂×C₈	—	38	1	no	—
146	C₄⋊C₄	—	2	1	no	—
147	C₄⋊C₄	—	2	1	no	—
148	C₄⋊C₄	—	2	1	no	—
149	C₄⋊C₄	—	2	1	no	—
150	C₄⋊C₄	—	38	1	no	—
151	C₄⋊C₄	—	38	1	no	—
152	C₄⋊C₄	—	76	2	no	—
153	C₄⋊C₄	—	76	2	no	—
154	C₄²	—	38	1	no	—
155	C₄²	—	38	1	no	—
156	C₂³	D₄×D₁₉	1	1	yes	characteristic
157	Q₈	—	38	2	no	—
158	Q₈	—	38	2	no	—
159	Q₈	—	76	1	no	—
160	Q₈	—	76	1	no	—
161	C₂×C₄	—	4	1	no	—
162	C₂×C₄	—	4	1	no	—
163	C₂×C₄	—	4	1	no	—
164	C₂×C₄	—	4	1	no	—
165	C₂×C₄	—	4	1	no	—
166	C₂×C₄	—	4	1	no	—
167	C₂×C₄	—	19	2	no	—
168	C₂×C₄	—	19	2	no	—
169	C₂×C₄	—	38	1	no	—
170	C₂×C₄	—	38	1	no	—
171	C₂×C₄	—	38	1	no	—
172	C₂×C₄	—	38	1	no	—
173	C₂×C₄	—	38	2	no	—
174	C₂×C₄	—	76	1	no	—
175	C₂×C₄	—	76	1	no	—
176	C₂×C₄	—	76	1	no	—
177	C₂×C₄	—	76	1	no	—
178	C₂×C₄	—	76	1	no	—
179	C₂×C₄	#64541	1	1	yes	characteristic
180	C₂×C₄	#64541	1	1	yes	characteristic
181	C₂×C₄	#64541	1	1	yes	characteristic
182	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
183	C₂×C₄	#64543	1	1	yes	characteristic
184	C₂×C₄	#64545	1	1	yes	characteristic
185	C₈	—	4	1	no	—
186	C₈	—	76	1	no	—
187	C₂²	#10597330	1	1	yes	characteristic
188	C₂²	#10597331	1	1	yes	characteristic
189	C₂²	#10597340	1	1	yes	characteristic
190	C₂²	#10597357	1	1	yes	characteristic
191	C₂²	SD₁₆×D₁₉	1	1	yes	characteristic
192	C₂²	#10597361	1	1	yes	characteristic
193	C₂²	Q₁₆×D₁₉	1	1	yes	characteristic
194	C₄	—	8	1	no	—
195	C₄	—	8	1	no	—
196	C₄	—	38	2	no	—
197	C₄	—	38	2	no	—
198	C₄	—	76	2	no	—
199	C₄	—	152	1	no	—
200	C₄	#10597322	1	1	yes	characteristic
201	C₄	#10597329	1	1	yes	characteristic
202	C₄	#10597340	1	1	yes	characteristic
203	C₄	#10597344	1	1	yes	characteristic
204	C₂	#11926473	1	1	yes	characteristic
205	C₂	#11926743	1	1	yes	characteristic
206	C₂	#11926753	1	1	yes	characteristic
207	C₂	#11926876	1	1	yes	characteristic
208	C₂	#11926881	1	1	yes	characteristic
209	C₂	#11926893	1	1	yes	characteristic
210	C₂	#11926902	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597273

C₂

yes

maximal, characteristic

C₂×#10597267

C₂

yes

maximal, characteristic

#11926449

C₂

yes

maximal, characteristic

#11926413

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal, characteristic

#11926298

C₂

yes

maximal, characteristic

C₁₉×#340

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉⋊#95

—

C₁₉⋊#95

—

#10597273

—

#10597267

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

characteristic

C₂²×Dic₁₉

D₄

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

SD₁₆

yes

—

C₂×Dic₁₉

Q₁₆

yes

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₂²×C₁₉

C₂×Q₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×#103

—

100

C₂×#103

—

101

#391

—

102

#384

—

103

#340

—

104

#340

D₁₉

yes

characteristic

105

#336

—

106

C₂×C₁₉

#397

yes

characteristic

107

C₂×C₁₉

#460

yes

characteristic

108

C₂×C₁₉

#462

yes

characteristic

109

C₂×C₁₉

#483

yes

characteristic

110

C₂×C₁₉

#484

yes

characteristic

111

C₂×C₁₉

#487

yes

characteristic

112

C₂×C₁₉

#489

yes

characteristic

113

C₂²×Q₈

—

114

C₂²×C₈

—

115

C₂²×C₈

C₂×D₁₉

yes

characteristic

116

C₂×C₄⋊C₄

—

117

C₂×C₄⋊C₄

—

118

C₂×C₄⋊C₄

—

119

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

120

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

121

C₂×C₄²

—

122

#103

—

123

#103

—

124

#95

—

125

#95

—

126

C₁₉

#2072

yes

characteristic, complemented, Sylow

127

C₂×Q₈

—

128

C₂×Q₈

—

129

C₂×Q₈

—

130

C₂×Q₈

—

131

C₂×Q₈

—

132

C₂×Q₈

—

133

C₂²×C₄

—

134

C₂²×C₄

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

C₂²×D₁₉

yes

characteristic

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₄⋊C₄

—

147

C₄⋊C₄

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄⋊C₄

—

154

C₄²

—

155

C₄²

—

156

C₂³

D₄×D₁₉

yes

characteristic

157

Q₈

—

158

Q₈

—

159

Q₈

—

160

Q₈

—

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

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

#64541

yes

characteristic

180

C₂×C₄

#64541

yes

characteristic

181

C₂×C₄

#64541

yes

characteristic

182

C₂×C₄

D₄×D₁₉

yes

characteristic

183

C₂×C₄

#64543

yes

characteristic

184

C₂×C₄

#64545

yes

characteristic

185

C₈

—

186

C₈

—

187

C₂²

#10597330

yes

characteristic

188

C₂²

#10597331

yes

characteristic

189

C₂²

#10597340

yes

characteristic

190

C₂²

#10597357

yes

characteristic

191

C₂²

SD₁₆×D₁₉

yes

characteristic

192

C₂²

#10597361

yes

characteristic

193

C₂²

Q₁₆×D₁₉

yes

characteristic

194

C₄

—

195

C₄

—

196

C₄

—

197

C₄

—

198

C₄

—

199

C₄

—

152

—

200

C₄

#10597322

yes

characteristic

201

C₄

#10597329

yes

characteristic

202

C₄

#10597340

yes

characteristic

203

C₄

#10597344

yes

characteristic

204

C₂

#11926473

yes

characteristic

205

C₂

#11926743

yes

characteristic

206

C₂

#11926753

yes

characteristic

207

C₂

#11926876

yes

characteristic

208

C₂

#11926881

yes

characteristic

209

C₂

#11926893

yes

characteristic

210

C₂

#11926902

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#340	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#340	D₁₉
hypocenter	C₁₉	#2072
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#340

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
126. C₁₉	#2072	semidirect

H ≅ G/N

type

126. C₁₉

#2072

semidirect

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

subgroup	index
C₂×#10597273	2
C₂×#10597267	2
#11926449	2
#11926413	2
#11926306	2
#11926298	2
C₁₉×#340	2
#2072	19

subgroup

index

C₁₉×#340

Subgroups — #14565047

Conjugacy classes of subgroups

Complements

Maximal subgroups