Group #14564503 — subgroups

Subgroups — #14564503

Order 2432.

304 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 99 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×#64528	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597265	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597273	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597272	C₂	1	1	yes	maximal, characteristic
5	#11926451	C₂	1	1	yes	maximal, characteristic
6	#11926449	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
8	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×#64528	—	2	2	no	—
13	C₂×#64528	—	2	2	no	—
14	C₂×#64528	C₄	1	4	yes	complemented
15	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₁₉×#103	—	2	2	no	—
19	C₁₉⋊#95	—	2	2	no	—
20	C₁₉⋊#95	—	2	2	no	—
21	#10597273	—	2	2	no	—
22	#10597272	—	2	2	no	—
23	#10597265	—	2	2	no	—
24	C₂×Q₈×C₁₉	—	2	1	no	—
25	C₂×Q₈×C₁₉	—	2	1	no	—
26	C₂×Q₈×C₁₉	—	2	1	no	—
27	C₂×Q₈×C₁₉	—	2	1	no	—
28	C₂×Q₈×C₁₉	—	2	1	no	—
29	C₂×Q₈×C₁₉	C₂×C₄	1	2	yes	—
30	C₂²×C₄×C₁₉	—	2	1	no	—
31	C₂²×C₄×C₁₉	—	2	1	no	—
32	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂²×Dic₁₉	—	2	1	no	—
34	C₂²×Dic₁₉	—	2	1	no	—
35	C₂²×Dic₁₉	D₄	1	2	yes	—
36	C₂×Dic₃₈	—	2	1	no	—
37	C₂×Dic₃₈	—	2	1	no	—
38	C₂×Dic₃₈	—	2	1	no	—
39	C₂×Dic₃₈	—	2	1	no	—
40	C₂×Dic₃₈	—	2	1	no	—
41	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
42	C₂×C₈×C₁₉	—	2	1	no	—
43	C₂×C₈×C₁₉	—	2	1	no	—
44	C₂×C₈×C₁₉	D₄	1	2	yes	—
45	C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₄⋊C₄×C₁₉	—	2	1	no	—
47	#64528	—	2	8	no	—
48	C₄⋊Dic₁₉	—	2	1	no	—
49	C₄⋊Dic₁₉	—	2	1	no	—
50	C₄×Dic₁₉	—	2	1	no	—
51	C₄×Dic₁₉	—	2	1	no	—
52	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
53	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
54	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
55	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
56	Q₈×C₁₉	—	2	2	no	—
57	Q₈×C₁₉	—	2	2	no	—
58	Q₈×C₁₉	—	4	1	no	—
59	Q₈×C₁₉	—	4	1	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	4	1	no	—
62	C₂×C₄×C₁₉	—	4	1	no	—
63	C₂×C₄×C₁₉	—	4	1	no	—
64	C₂×C₄×C₁₉	—	4	2	no	—
65	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
70	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
71	C₂×Dic₁₉	—	2	2	no	—
72	C₂×Dic₁₉	—	2	2	no	—
73	C₂×Dic₁₉	—	2	2	no	—
74	C₂×Dic₁₉	—	2	2	no	—
75	C₂×Dic₁₉	—	4	1	no	—
76	C₂×Dic₁₉	—	4	1	no	—
77	C₂×Dic₁₉	—	4	1	no	—
78	C₂×Dic₁₉	—	4	2	no	—
79	Dic₃₈	—	2	2	no	—
80	Dic₃₈	—	2	2	no	—
81	Dic₃₈	—	4	1	no	—
82	Dic₃₈	—	4	1	no	—
83	C₈×C₁₉	—	2	2	no	—
84	C₁₉⋊C₈	C₂²⋊C₄	1	4	yes	—
85	#1971	—	19	1	no	maximal, Sylow
86	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
87	C₂²×C₁₉	#121	1	1	yes	characteristic
88	C₂²×C₁₉	#127	1	1	yes	characteristic
89	C₂²×C₁₉	#137	1	2	yes	—
90	C₂²×C₁₉	#137	1	2	yes	—
91	C₄×C₁₉	—	4	2	no	—
92	C₄×C₁₉	—	8	1	no	—
93	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
95	C₄×C₁₉	#121	1	1	yes	characteristic
96	C₄×C₁₉	#124	1	1	yes	characteristic
97	Dic₁₉	—	4	2	no	—
98	Dic₁₉	—	4	2	no	—
99	Dic₁₉	—	8	1	no	—
100	C₂²×Q₁₆	—	19	1	no	—
101	C₂×#106	—	19	1	no	—
102	C₂×#103	—	19	1	no	—
103	C₂×#103	D₁₉	1	1	yes	characteristic
104	C₂×#97	—	19	1	no	—
105	#391	—	19	1	no	—
106	#391	—	19	1	no	—
107	C₂×C₁₉	#390	1	1	yes	characteristic
108	C₂×C₁₉	#441	1	2	yes	—
109	C₂×C₁₉	#470	1	2	yes	—
110	C₂×C₁₉	#497	1	1	yes	characteristic
111	C₂×C₁₉	#497	1	1	yes	characteristic
112	C₂²×Q₈	—	19	1	no	—
113	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
114	C₂×Q₁₆	—	19	4	no	—
115	C₂×Q₁₆	—	38	2	no	—
116	C₂×Q₁₆	—	38	2	no	—
117	C₂²×C₈	—	19	1	no	—
118	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
119	C₂×C₄⋊C₄	—	19	1	no	—
120	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
121	C₂×C₄²	—	19	1	no	—
122	#106	—	38	2	no	—
123	#103	—	2	2	no	—
124	#103	—	38	2	no	—
125	#97	—	38	2	no	—
126	#95	—	38	2	no	—
127	#95	—	38	2	no	—
128	C₁₉	#1971	1	1	yes	characteristic, complemented, Sylow
129	C₂×Q₈	—	2	1	no	—
130	C₂×Q₈	—	2	1	no	—
131	C₂×Q₈	—	2	1	no	—
132	C₂×Q₈	—	2	1	no	—
133	C₂×Q₈	—	2	1	no	—
134	C₂×Q₈	—	19	2	no	—
135	C₂×Q₈	—	38	1	no	—
136	C₂×Q₈	—	38	1	no	—
137	C₂×Q₈	—	38	1	no	—
138	C₂×Q₈	—	38	1	no	—
139	C₂×Q₈	—	38	1	no	—
140	C₂×Q₈	C₄×D₁₉	1	2	yes	—
141	C₂²×C₄	—	2	1	no	—
142	C₂²×C₄	—	2	1	no	—
143	C₂²×C₄	—	19	2	no	—
144	C₂²×C₄	—	38	1	no	—
145	C₂²×C₄	—	38	1	no	—
146	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
147	Q₁₆	—	38	8	no	—
148	C₂×C₈	—	2	1	no	—
149	C₂×C₈	—	2	1	no	—
150	C₂×C₈	—	19	2	no	—
151	C₂×C₈	—	19	2	no	—
152	C₂×C₈	—	19	2	no	—
153	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
154	C₄⋊C₄	—	2	1	no	—
155	C₄⋊C₄	—	2	1	no	—
156	C₄⋊C₄	—	38	1	no	—
157	C₄⋊C₄	—	38	1	no	—
158	C₄²	—	38	1	no	—
159	C₄²	—	38	1	no	—
160	C₂³	D₄×D₁₉	1	1	yes	characteristic
161	Q₈	—	2	2	no	—
162	Q₈	—	2	2	no	—
163	Q₈	—	4	1	no	—
164	Q₈	—	4	1	no	—
165	Q₈	—	38	2	no	—
166	Q₈	—	38	2	no	—
167	Q₈	—	76	1	no	—
168	Q₈	—	76	1	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	4	1	no	—
171	C₂×C₄	—	4	1	no	—
172	C₂×C₄	—	4	1	no	—
173	C₂×C₄	—	4	2	no	—
174	C₂×C₄	—	38	2	no	—
175	C₂×C₄	—	38	2	no	—
176	C₂×C₄	—	38	2	no	—
177	C₂×C₄	—	38	2	no	—
178	C₂×C₄	—	76	1	no	—
179	C₂×C₄	—	76	1	no	—
180	C₂×C₄	—	76	1	no	—
181	C₂×C₄	—	76	2	no	—
182	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
183	C₂×C₄	#64541	1	1	yes	characteristic
184	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
185	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
186	C₂×C₄	#64543	1	1	yes	characteristic
187	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
188	C₈	—	2	2	no	—
189	C₈	—	19	4	no	—
190	C₂²	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
191	C₂²	#10597330	1	1	yes	characteristic
192	C₂²	#10597361	1	2	yes	—
193	C₂²	#10597364	1	2	yes	—
194	C₂²	#10597386	1	1	yes	characteristic
195	C₄	—	4	2	no	—
196	C₄	—	8	1	no	—
197	C₄	—	76	2	no	—
198	C₄	—	76	2	no	—
199	C₄	—	152	1	no	—
200	C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
201	C₄	#10597331	1	1	yes	characteristic
202	C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
203	C₄	#10597385	1	1	yes	characteristic
204	C₂	#11926444	1	1	yes	characteristic
205	C₂	#11926648	1	2	yes	—
206	C₂	#11926801	1	2	yes	—
207	C₂	#11926935	1	1	yes	characteristic
208	C₂	#11926937	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64528

C₂

yes

maximal, characteristic

C₂×#10597265

C₂

yes

maximal, characteristic

C₂×#10597273

C₂

yes

maximal, characteristic

C₂×#10597272

C₂

yes

maximal, characteristic

#11926451

C₂

yes

maximal, characteristic

#11926449

C₂

yes

maximal, characteristic

C₂×C₁₉×#103

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

—

C₄

yes

complemented

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#103

—

C₁₉⋊#95

—

C₁₉⋊#95

—

#10597273

—

#10597272

—

#10597265

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂×C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

#64528

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×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

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

C₂²⋊C₄

yes

—

#1971

—

maximal, Sylow

C₂²×C₁₉

C₄×D₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#137

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

100

C₂²×Q₁₆

—

101

C₂×#106

—

102

C₂×#103

—

103

C₂×#103

D₁₉

yes

characteristic

104

C₂×#97

—

105

#391

—

106

#391

—

107

C₂×C₁₉

#390

yes

characteristic

108

C₂×C₁₉

#441

yes

—

109

C₂×C₁₉

#470

yes

—

110

C₂×C₁₉

#497

yes

characteristic

111

C₂×C₁₉

#497

yes

characteristic

112

C₂²×Q₈

—

113

C₂²×Q₈

C₂×D₁₉

yes

characteristic

114

C₂×Q₁₆

—

115

C₂×Q₁₆

—

116

C₂×Q₁₆

—

117

C₂²×C₈

—

118

C₂²×C₈

C₂×D₁₉

yes

characteristic

119

C₂×C₄⋊C₄

—

120

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

121

C₂×C₄²

—

122

#106

—

123

#103

—

124

#103

—

125

#97

—

126

#95

—

127

#95

—

128

C₁₉

#1971

yes

characteristic, complemented, Sylow

129

C₂×Q₈

—

130

C₂×Q₈

—

131

C₂×Q₈

—

132

C₂×Q₈

—

133

C₂×Q₈

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂×Q₈

—

137

C₂×Q₈

—

138

C₂×Q₈

—

139

C₂×Q₈

—

140

C₂×Q₈

C₄×D₁₉

yes

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

C₂²×D₁₉

yes

characteristic

147

Q₁₆

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

C₂²⋊D₁₉

yes

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄²

—

159

C₄²

—

160

C₂³

D₄×D₁₉

yes

characteristic

161

Q₈

—

162

Q₈

—

163

Q₈

—

164

Q₈

—

165

Q₈

—

166

Q₈

—

167

Q₈

—

168

Q₈

—

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

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

183

C₂×C₄

#64541

yes

characteristic

184

C₂×C₄

D₄×D₁₉

yes

characteristic

185

C₂×C₄

D₄×D₁₉

yes

characteristic

186

C₂×C₄

#64543

yes

characteristic

187

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

188

C₈

—

189

C₈

—

190

C₂²

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

191

C₂²

#10597330

yes

characteristic

192

C₂²

#10597361

yes

—

193

C₂²

#10597364

yes

—

194

C₂²

#10597386

yes

characteristic

195

C₄

—

196

C₄

—

197

C₄

—

198

C₄

—

199

C₄

—

152

—

200

C₄

C₂²⋊C₄×D₁₉

yes

characteristic

201

C₄

#10597331

yes

characteristic

202

C₄

C₄×C₂²⋊D₁₉

yes

characteristic

203

C₄

#10597385

yes

characteristic

204

C₂

#11926444

yes

characteristic

205

C₂

#11926648

yes

—

206

C₂

#11926801

yes

—

207

C₂

#11926935

yes

characteristic

208

C₂

#11926937

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#103	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#103	D₁₉
hypocenter	C₁₉	#1971
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#103

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

N	H ≅ G/N	type
14. C₂×#64528	C₄	semidirect
128. C₁₉	#1971	semidirect

H ≅ G/N

type

14. C₂×#64528

C₄

semidirect

128. C₁₉

#1971

semidirect

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

subgroup	index
C₂²×#64528	2
C₂×#10597265	2
C₂×#10597273	2
C₂×#10597272	2
#11926451	2
#11926449	2
C₂×C₁₉×#103	2
#1971	19

subgroup

index

C₂²×#64528

C₂×C₁₉×#103

Subgroups — #14564503

Conjugacy classes of subgroups

Complements

Maximal subgroups