Group #14564544 — subgroups

Subgroups — #14564544

Order 2432.

316 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 83 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	C₂²×#64525	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597279	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926548	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10597290	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10597280	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926500	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#418	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×D₇₆	C₂²	1	1	yes	characteristic
10	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#117	C₂²	1	1	yes	characteristic
12	C₂×#64525	—	2	1	no	—
13	C₂×#64525	—	2	1	no	—
14	C₂×#64525	—	2	2	no	—
15	C₂×#64525	C₄	1	4	yes	complemented
16	C₂×#64520	C₂²	1	1	yes	characteristic
17	C₂×#64520	C₂²	1	1	yes	characteristic
18	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₁₉×#102	—	2	2	no	—
20	#10597290	—	2	2	no	—
21	#10597280	—	2	2	no	—
22	#10597279	—	2	2	no	—
23	#10597266	—	2	2	no	—
24	#10597260	—	2	1	no	—
25	C₄×C₁₉⋊C₈	—	2	1	no	—
26	C₂⁴×C₁₉	—	2	1	no	—
27	C₂³×D₁₉	—	2	1	no	—
28	C₂×D₄×C₁₉	—	2	1	no	—
29	C₂×D₄×C₁₉	—	2	1	no	—
30	C₂×D₄×C₁₉	—	2	1	no	—
31	C₂×D₄×C₁₉	—	2	1	no	—
32	C₂×D₄×C₁₉	—	2	1	no	—
33	C₂×D₄×C₁₉	C₂×C₄	1	2	yes	—
34	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×D₇₆	—	2	1	no	—
36	C₂×D₇₆	—	2	1	no	—
37	C₂×D₇₆	—	2	1	no	—
38	C₂×D₇₆	—	2	1	no	—
39	C₂×D₇₆	—	2	1	no	—
40	C₂×D₇₆	C₂×C₄	1	2	yes	—
41	M₁₆×C₁₉	—	2	1	no	—
42	M₁₆×C₁₉	—	2	1	no	—
43	C₂×C₈×C₁₉	—	2	1	no	—
44	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
45	C₂²⋊C₄×C₁₉	—	2	1	no	—
46	C₄²×C₁₉	—	2	1	no	—
47	#64525	—	2	4	no	—
48	#64525	—	2	4	no	—
49	#64520	—	2	1	no	—
50	#64520	—	2	1	no	—
51	#64520	—	2	1	no	—
52	#64520	D₄	1	2	yes	—
53	C₂×C₁₉⋊C₈	—	2	1	no	—
54	C₂×C₁₉⋊C₈	—	2	1	no	—
55	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
56	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
57	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
58	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
59	C₂³×C₁₉	—	2	2	no	—
60	C₂³×C₁₉	—	4	1	no	—
61	C₂³×C₁₉	—	4	1	no	—
62	C₂³×C₁₉	—	8	2	no	—
63	C₂³×C₁₉	#41	1	1	yes	characteristic
64	C₂²×D₁₉	—	2	2	no	—
65	C₂²×D₁₉	—	4	1	no	—
66	C₂²×D₁₉	—	4	1	no	—
67	C₂²×D₁₉	—	8	2	no	—
68	D₄×C₁₉	—	2	2	no	—
69	D₄×C₁₉	—	2	2	no	—
70	D₄×C₁₉	—	4	1	no	—
71	D₄×C₁₉	—	4	1	no	—
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
79	D₇₆	—	2	2	no	—
80	D₇₆	—	2	2	no	—
81	D₇₆	—	4	1	no	—
82	D₇₆	—	4	1	no	—
83	C₈×C₁₉	—	4	1	no	—
84	C₁₉⋊C₈	—	2	2	no	—
85	C₁₉⋊C₈	—	4	1	no	—
86	C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
87	C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
88	#1978	—	19	1	no	maximal, Sylow
89	C₂²×C₁₉	—	2	2	no	—
90	C₂²×C₁₉	—	4	2	no	—
91	C₂²×C₁₉	—	8	2	no	—
92	C₂²×C₁₉	—	8	2	no	—
93	C₂²×C₁₉	—	8	2	no	—
94	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
95	C₂²×C₁₉	#121	1	1	yes	characteristic
96	C₂²×C₁₉	#124	1	1	yes	characteristic
97	C₂×D₁₉	—	4	2	no	—
98	C₂×D₁₉	—	8	2	no	—
99	C₂×D₁₉	—	8	2	no	—
100	C₂×D₁₉	—	8	2	no	—
101	C₄×C₁₉	—	4	2	no	—
102	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
104	C₄×C₁₉	#121	1	1	yes	characteristic
105	C₄×C₁₉	#127	1	1	yes	characteristic
106	C₂²×D₈	—	19	1	no	—
107	C₂×#108	—	19	1	no	—
108	#418	—	19	1	no	—
109	#418	D₁₉	1	1	yes	characteristic, complemented
110	C₂×#100	—	19	1	no	—
111	C₂×#100	—	19	1	no	—
112	#405	—	19	1	no	—
113	C₂×C₁₉	—	2	1	no	—
114	C₂×C₁₉	—	2	1	no	—
115	C₂×C₁₉	—	8	2	no	—
116	C₂×C₁₉	#390	1	1	yes	characteristic
117	C₂×C₁₉	#472	1	2	yes	—
118	D₁₉	—	8	2	no	—
119	C₂²×D₄	—	19	1	no	—
120	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
121	C₂×D₈	—	19	4	no	—
122	C₂×D₈	—	38	1	no	—
123	C₂×D₈	—	38	1	no	—
124	C₂×D₈	—	38	2	no	—
125	C₂×M₁₆	—	19	1	no	—
126	C₂×M₁₆	—	19	1	no	—
127	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
128	C₂²×C₈	—	19	1	no	—
129	#117	C₂×D₁₉	1	1	yes	characteristic
130	#108	—	38	2	no	—
131	#102	—	2	2	no	—
132	#102	—	38	2	no	—
133	#100	—	38	2	no	—
134	#100	—	38	2	no	—
135	#97	—	38	1	no	—
136	C₄×C₈	—	38	1	no	—
137	C₁₉	#1978	1	1	yes	characteristic, complemented, Sylow
138	C₂⁴	—	2	1	no	—
139	C₂⁴	—	38	1	no	—
140	C₂×D₄	—	2	1	no	—
141	C₂×D₄	—	2	1	no	—
142	C₂×D₄	—	2	1	no	—
143	C₂×D₄	—	2	1	no	—
144	C₂×D₄	—	2	1	no	—
145	C₂×D₄	—	19	2	no	—
146	C₂×D₄	—	38	1	no	—
147	C₂×D₄	—	38	1	no	—
148	C₂×D₄	—	38	1	no	—
149	C₂×D₄	—	38	1	no	—
150	C₂×D₄	—	38	1	no	—
151	C₂×D₄	C₄×D₁₉	1	2	yes	—
152	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
153	D₈	—	38	4	no	—
154	D₈	—	38	4	no	—
155	M₁₆	—	2	1	no	—
156	M₁₆	—	2	1	no	—
157	M₁₆	—	19	2	no	—
158	M₁₆	—	38	1	no	—
159	M₁₆	—	38	1	no	—
160	M₁₆	—	38	1	no	—
161	C₂×C₈	—	2	1	no	—
162	C₂×C₈	—	19	2	no	—
163	C₂×C₈	—	19	1	no	—
164	C₂×C₈	—	19	1	no	—
165	C₂×C₈	—	19	2	no	—
166	C₂×C₈	—	38	1	no	—
167	C₂×C₈	—	38	1	no	—
168	C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
169	C₂²⋊C₄	—	2	1	no	—
170	C₄²	—	2	1	no	—
171	C₂³	—	2	2	no	—
172	C₂³	—	4	1	no	—
173	C₂³	—	4	1	no	—
174	C₂³	—	8	2	no	—
175	C₂³	—	38	2	no	—
176	C₂³	—	76	1	no	—
177	C₂³	—	76	1	no	—
178	C₂³	—	152	2	no	—
179	C₂³	#64543	1	1	yes	characteristic
180	D₄	—	2	2	no	—
181	D₄	—	2	2	no	—
182	D₄	—	4	1	no	—
183	D₄	—	4	1	no	—
184	D₄	—	38	2	no	—
185	D₄	—	38	2	no	—
186	D₄	—	76	1	no	—
187	D₄	—	76	1	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
190	C₂×C₄	#64541	1	1	yes	characteristic
191	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
192	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
193	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
194	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
195	C₈	—	4	1	no	—
196	C₈	—	19	2	no	—
197	C₈	—	19	2	no	—
198	C₈	—	38	2	no	—
199	C₈	—	76	1	no	—
200	C₂²	—	2	2	no	—
201	C₂²	—	4	2	no	—
202	C₂²	—	8	2	no	—
203	C₂²	—	8	2	no	—
204	C₂²	—	8	2	no	—
205	C₂²	—	76	2	no	—
206	C₂²	—	152	2	no	—
207	C₂²	—	152	2	no	—
208	C₂²	—	152	2	no	—
209	C₂²	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
210	C₂²	#10597331	1	1	yes	characteristic
211	C₂²	#10597385	1	1	yes	characteristic
212	C₄	—	4	2	no	—
213	C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
214	C₄	#10597330	1	1	yes	characteristic
215	C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
216	C₄	#10597386	1	1	yes	characteristic
217	C₂	—	2	1	no	—
218	C₂	—	2	1	no	—
219	C₂	—	8	2	no	—
220	C₂	—	152	2	no	—
221	C₂	#11926444	1	1	yes	characteristic
222	C₂	#11926812	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64525

C₂

yes

maximal, characteristic

C₂×#10597279

C₂

yes

maximal, characteristic, complemented

#11926548

C₂

yes

maximal, characteristic, complemented

C₂×#10597290

C₂

yes

maximal, characteristic, complemented

C₂×#10597280

C₂

yes

maximal, characteristic, complemented

#11926500

C₂

yes

maximal, characteristic, complemented

C₁₉×#418

C₂

yes

maximal, characteristic, complemented

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂²×D₇₆

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

—

—

—

C₄

yes

complemented

C₂×#64520

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#102

—

—

—

—

—

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

—

C₂³×D₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂×C₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

—

—

—

—

—

D₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#41

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₁₉⋊C₈

C₂²⋊C₄

yes

—

#1978

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₄×D₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

100

C₂×D₁₉

—

101

C₄×C₁₉

—

102

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

103

C₄×C₁₉

C₄×D₄

yes

characteristic

104

C₄×C₁₉

#121

yes

characteristic

105

C₄×C₁₉

#127

yes

characteristic

106

C₂²×D₈

—

107

C₂×#108

—

108

#418

—

109

#418

D₁₉

yes

characteristic, complemented

110

C₂×#100

—

111

C₂×#100

—

112

#405

—

113

C₂×C₁₉

—

114

C₂×C₁₉

—

115

C₂×C₁₉

—

116

C₂×C₁₉

#390

yes

characteristic

117

C₂×C₁₉

#472

yes

—

118

D₁₉

—

119

C₂²×D₄

—

120

C₂²×D₄

C₂×D₁₉

yes

characteristic

121

C₂×D₈

—

122

C₂×D₈

—

123

C₂×D₈

—

124

C₂×D₈

—

125

C₂×M₁₆

—

126

C₂×M₁₆

—

127

C₂×M₁₆

C₂×D₁₉

yes

characteristic

128

C₂²×C₈

—

129

#117

C₂×D₁₉

yes

characteristic

130

#108

—

131

#102

—

132

#102

—

133

#100

—

134

#100

—

135

#97

—

136

C₄×C₈

—

137

C₁₉

#1978

yes

characteristic, complemented, Sylow

138

C₂⁴

—

139

C₂⁴

—

140

C₂×D₄

—

141

C₂×D₄

—

142

C₂×D₄

—

143

C₂×D₄

—

144

C₂×D₄

—

145

C₂×D₄

—

146

C₂×D₄

—

147

C₂×D₄

—

148

C₂×D₄

—

149

C₂×D₄

—

150

C₂×D₄

—

151

C₂×D₄

C₄×D₁₉

yes

—

152

C₂²×C₄

C₂²×D₁₉

yes

characteristic

153

D₈

—

154

D₈

—

155

M₁₆

—

156

M₁₆

—

157

M₁₆

—

158

M₁₆

—

159

M₁₆

—

160

M₁₆

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₄⋊C₄

C₂²⋊D₁₉

yes

—

169

C₂²⋊C₄

—

170

C₄²

—

171

C₂³

—

172

C₂³

—

173

C₂³

—

174

C₂³

—

175

C₂³

—

176

C₂³

—

177

C₂³

—

178

C₂³

—

152

—

179

C₂³

#64543

yes

characteristic

180

D₄

—

181

D₄

—

182

D₄

—

183

D₄

—

184

D₄

—

185

D₄

—

186

D₄

—

187

D₄

—

188

C₂×C₄

—

189

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

190

C₂×C₄

#64541

yes

characteristic

191

C₂×C₄

D₄×D₁₉

yes

characteristic

192

C₂×C₄

D₄×D₁₉

yes

characteristic

193

C₂×C₄

D₄×D₁₉

yes

characteristic

194

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

195

C₈

—

196

C₈

—

197

C₈

—

198

C₈

—

199

C₈

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

204

C₂²

—

205

C₂²

—

206

C₂²

—

152

—

207

C₂²

—

152

—

208

C₂²

—

152

—

209

C₂²

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

210

C₂²

#10597331

yes

characteristic

211

C₂²

#10597385

yes

characteristic

212

C₄

—

213

C₄

C₂²⋊C₄×D₁₉

yes

characteristic

214

C₄

#10597330

yes

characteristic

215

C₄

C₄×C₂²⋊D₁₉

yes

characteristic

216

C₄

#10597386

yes

characteristic

217

C₂

—

218

C₂

—

219

C₂

—

220

C₂

—

152

—

221

C₂

#11926444

yes

characteristic

222

C₂

#11926812

yes

—

	subgroup	G/H
center	C₂²	#10597385
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#418	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂²×#64525	C₂
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#418	D₁₉
hypocenter	C₁₉	#1978
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #418

subgroup

G/H

center

C₂²

#10597385

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#418

C₂

socle

C₂²×C₁₉

#121

prime radical

C₂²×#64525

C₂

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #418

N	H ≅ G/N	type
2. C₂×#10597279	C₂	semidirect
3. #11926548	C₂	semidirect
4. C₂×#10597290	C₂	semidirect
5. C₂×#10597280	C₂	semidirect
6. #11926500	C₂	semidirect
7. C₁₉×#418	C₂	semidirect
15. C₂×#64525	C₄	semidirect
109. #418	D₁₉	semidirect
137. C₁₉	#1978	semidirect

H ≅ G/N

type

2. C₂×#10597279

C₂

semidirect

3. #11926548

C₂

semidirect

4. C₂×#10597290

C₂

semidirect

5. C₂×#10597280

C₂

semidirect

6. #11926500

C₂

semidirect

7. C₁₉×#418

C₂

semidirect

15. C₂×#64525

C₄

semidirect

109. #418

D₁₉

semidirect

137. C₁₉

#1978

semidirect

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

subgroup	index
C₂²×#64525	2
C₂×#10597279	2
#11926548	2
C₂×#10597290	2
C₂×#10597280	2
#11926500	2
C₁₉×#418	2
#1978	19

subgroup

index

C₂²×#64525

C₁₉×#418

Subgroups — #14564544

Conjugacy classes of subgroups

Complements

Maximal subgroups