Group #14564450 — subgroups

Subgroups — #14564450

Order 2432.

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

normal subgroups only

This group has 344 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	C₂×#10597382	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597273	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597267	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10597289	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597272	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926413	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#102	C₂	1	1	yes	maximal, characteristic
8	C₂²×D₄×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×C₂²⋊Dic₁₉	—	2	2	no	—
13	#10597382	—	2	2	no	—
14	#10597382	C₄	1	4	yes	complemented
15	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₉⋊C₄	—	2	2	no	—
17	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₁₉×#102	—	2	2	no	—
20	#10597289	—	2	2	no	—
21	#10597273	—	2	2	no	—
22	#10597272	—	2	2	no	—
23	#10597267	—	2	2	no	—
24	C₂⁴×C₁₉	—	2	1	no	—
25	C₂×D₄×C₁₉	—	2	1	no	—
26	C₂×D₄×C₁₉	—	2	1	no	—
27	C₂×D₄×C₁₉	—	2	1	no	—
28	C₂×D₄×C₁₉	—	2	1	no	—
29	C₂×D₄×C₁₉	—	2	1	no	—
30	C₂×D₄×C₁₉	C₂×C₄	1	2	yes	—
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	C₂²⋊Dic₁₉	—	2	8	no	—
48	C₄⋊Dic₁₉	—	2	1	no	—
49	C₄⋊Dic₁₉	—	2	1	no	—
50	Dic₁₉⋊C₄	—	4	4	no	—
51	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
52	C₄×Dic₁₉	D₄	1	2	yes	—
53	C₂×C₁₉⋊C₈	—	2	1	no	—
54	C₂×C₁₉⋊C₈	—	2	1	no	—
55	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
56	C₂³×C₁₉	—	2	2	no	—
57	C₂³×C₁₉	—	4	1	no	—
58	C₂³×C₁₉	—	4	1	no	—
59	C₂³×C₁₉	—	4	2	no	—
60	C₂³×C₁₉	—	4	2	no	—
61	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
62	D₄×C₁₉	—	2	2	no	—
63	D₄×C₁₉	—	2	2	no	—
64	D₄×C₁₉	—	4	1	no	—
65	D₄×C₁₉	—	4	1	no	—
66	C₂×C₄×C₁₉	—	4	1	no	—
67	C₂×C₄×C₁₉	—	4	2	no	—
68	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
73	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
74	C₂×Dic₁₉	—	2	2	no	—
75	C₂×Dic₁₉	—	2	2	no	—
76	C₂×Dic₁₉	—	2	2	no	—
77	C₂×Dic₁₉	—	4	1	no	—
78	C₂×Dic₁₉	—	4	1	no	—
79	C₂×Dic₁₉	—	4	1	no	—
80	C₂×Dic₁₉	—	4	2	no	—
81	C₂×Dic₁₉	C₂²⋊C₄	1	4	yes	—
82	Dic₃₈	—	2	2	no	—
83	Dic₃₈	—	2	2	no	—
84	Dic₃₈	—	4	1	no	—
85	Dic₃₈	—	4	1	no	—
86	C₈×C₁₉	—	2	2	no	—
87	C₁₉⋊C₈	—	2	2	no	—
88	#1959	—	19	1	no	maximal, Sylow
89	C₂²×C₁₉	—	4	2	no	—
90	C₂²×C₁₉	—	4	4	no	—
91	C₂²×C₁₉	—	8	2	no	—
92	C₂²×C₁₉	—	8	1	no	—
93	C₂²×C₁₉	—	8	1	no	—
94	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₁₉	#124	1	1	yes	characteristic
96	C₂²×C₁₉	#127	1	1	yes	characteristic
97	C₂²×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
98	C₂²×C₁₉	#137	1	2	yes	—
99	C₄×C₁₉	—	8	1	no	—
100	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
101	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
102	C₄×C₁₉	#121	1	1	yes	characteristic
103	C₄×C₁₉	#121	1	1	yes	characteristic
104	Dic₁₉	—	2	4	no	—
105	Dic₁₉	—	4	2	no	—
106	Dic₁₉	—	8	1	no	—
107	C₂×#124	—	19	1	no	—
108	C₂×#103	—	19	1	no	—
109	C₂×#103	—	19	1	no	—
110	C₂×#102	—	19	1	no	—
111	C₂×#102	D₁₉	1	1	yes	characteristic
112	C₂×#97	—	19	1	no	—
113	#384	—	19	1	no	—
114	C₂×C₁₉	—	8	2	no	—
115	C₂×C₁₉	#390	1	1	yes	characteristic
116	C₂×C₁₉	#417	1	2	yes	—
117	C₂×C₁₉	#489	1	2	yes	—
118	C₂×C₁₉	#496	1	1	yes	characteristic
119	C₂×C₁₉	#497	1	1	yes	characteristic
120	C₂²×Q₈	—	19	1	no	—
121	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
122	C₂²×C₈	—	19	1	no	—
123	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
124	#124	—	19	4	no	—
125	#124	—	38	2	no	—
126	C₂×C₄⋊C₄	—	19	1	no	—
127	C₂×C₄⋊C₄	—	38	2	no	—
128	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
129	C₂×C₂²⋊C₄	—	38	2	no	—
130	C₂×C₄²	—	19	1	no	—
131	#103	—	38	2	no	—
132	#103	—	38	2	no	—
133	#102	—	2	2	no	—
134	#102	—	38	2	no	—
135	#97	—	38	2	no	—
136	C₁₉	#1959	1	1	yes	characteristic, complemented, Sylow
137	C₂⁴	—	2	1	no	—
138	C₂×Q₈	—	19	2	no	—
139	C₂×Q₈	—	38	1	no	—
140	C₂×Q₈	—	38	1	no	—
141	C₂×Q₈	—	38	1	no	—
142	C₂×Q₈	—	38	1	no	—
143	C₂×Q₈	—	38	1	no	—
144	C₂×D₄	—	2	1	no	—
145	C₂×D₄	—	2	1	no	—
146	C₂×D₄	—	2	1	no	—
147	C₂×D₄	—	2	1	no	—
148	C₂×D₄	—	2	1	no	—
149	C₂×D₄	C₄×D₁₉	1	2	yes	—
150	C₂²×C₄	—	2	1	no	—
151	C₂²×C₄	—	19	2	no	—
152	C₂²×C₄	—	38	1	no	—
153	C₂²×C₄	—	38	1	no	—
154	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
155	C₂×C₈	—	2	1	no	—
156	C₂×C₈	—	2	1	no	—
157	C₂×C₈	—	19	2	no	—
158	C₂×C₈	—	38	1	no	—
159	C₂×C₈	—	38	1	no	—
160	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
161	C₄⋊C₄	—	2	1	no	—
162	C₄⋊C₄	—	2	1	no	—
163	C₄⋊C₄	—	38	1	no	—
164	C₄⋊C₄	—	38	1	no	—
165	C₄⋊C₄	—	76	4	no	—
166	C₂²⋊C₄	—	38	8	no	—
167	C₄²	—	19	2	no	—
168	C₄²	—	19	2	no	—
169	C₂³	—	2	2	no	—
170	C₂³	—	4	1	no	—
171	C₂³	—	4	1	no	—
172	C₂³	—	4	2	no	—
173	C₂³	—	4	2	no	—
174	C₂³	D₄×D₁₉	1	1	yes	characteristic
175	Q₈	—	38	2	no	—
176	Q₈	—	38	2	no	—
177	Q₈	—	76	1	no	—
178	Q₈	—	76	1	no	—
179	D₄	—	2	2	no	—
180	D₄	—	2	2	no	—
181	D₄	—	4	1	no	—
182	D₄	—	4	1	no	—
183	C₂×C₄	—	4	1	no	—
184	C₂×C₄	—	4	2	no	—
185	C₂×C₄	—	19	4	no	—
186	C₂×C₄	—	38	2	no	—
187	C₂×C₄	—	38	2	no	—
188	C₂×C₄	—	38	2	no	—
189	C₂×C₄	—	76	1	no	—
190	C₂×C₄	—	76	1	no	—
191	C₂×C₄	—	76	1	no	—
192	C₂×C₄	—	76	2	no	—
193	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
194	C₂×C₄	#64541	1	1	yes	characteristic
195	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
196	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
197	C₂×C₄	#64543	1	1	yes	characteristic
198	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
199	C₈	—	2	2	no	—
200	C₈	—	38	2	no	—
201	C₂²	—	4	4	no	—
202	C₂²	—	4	2	no	—
203	C₂²	—	8	2	no	—
204	C₂²	—	8	1	no	—
205	C₂²	—	8	1	no	—
206	C₂²	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
207	C₂²	#10597331	1	1	yes	characteristic
208	C₂²	#10597357	1	2	yes	—
209	C₂²	#10597361	1	2	yes	—
210	C₂²	#10597386	1	1	yes	characteristic
211	C₄	—	8	1	no	—
212	C₄	—	38	4	no	—
213	C₄	—	76	2	no	—
214	C₄	—	152	1	no	—
215	C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
216	C₄	#10597330	1	1	yes	characteristic
217	C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
218	C₄	#10597385	1	1	yes	characteristic
219	C₂	—	8	2	no	—
220	C₂	#11926444	1	1	yes	characteristic
221	C₂	#11926542	1	2	yes	—
222	C₂	#11926902	1	2	yes	—
223	C₂	#11926932	1	1	yes	characteristic
224	C₂	#11926935	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597382

C₂

yes

maximal, characteristic

C₂×#10597273

C₂

yes

maximal, characteristic, complemented

C₂×#10597267

C₂

yes

maximal, characteristic, complemented

C₂×#10597289

C₂

yes

maximal, characteristic

C₂×#10597272

C₂

yes

maximal, characteristic, complemented

#11926413

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#102

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

#10597382

—

#10597382

C₄

yes

complemented

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#102

—

—

—

—

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂×C₄

yes

—

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

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

C₂×C₄

yes

—

C₄×Dic₁₉

D₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

C₂²⋊C₄

yes

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1959

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#137

yes

—

C₄×C₁₉

—

100

C₄×C₁₉

C₄×D₄

yes

characteristic

101

C₄×C₁₉

C₄×D₄

yes

characteristic

102

C₄×C₁₉

#121

yes

characteristic

103

C₄×C₁₉

#121

yes

characteristic

104

Dic₁₉

—

105

Dic₁₉

—

106

Dic₁₉

—

107

C₂×#124

—

108

C₂×#103

—

109

C₂×#103

—

110

C₂×#102

—

111

C₂×#102

D₁₉

yes

characteristic

112

C₂×#97

—

113

#384

—

114

C₂×C₁₉

—

115

C₂×C₁₉

#390

yes

characteristic

116

C₂×C₁₉

#417

yes

—

117

C₂×C₁₉

#489

yes

—

118

C₂×C₁₉

#496

yes

characteristic

119

C₂×C₁₉

#497

yes

characteristic

120

C₂²×Q₈

—

121

C₂²×D₄

C₂×D₁₉

yes

characteristic

122

C₂²×C₈

—

123

C₂²×C₈

C₂×D₁₉

yes

characteristic

124

#124

—

125

#124

—

126

C₂×C₄⋊C₄

—

127

C₂×C₄⋊C₄

—

128

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

129

C₂×C₂²⋊C₄

—

130

C₂×C₄²

—

131

#103

—

132

#103

—

133

#102

—

134

#102

—

135

#97

—

136

C₁₉

#1959

yes

characteristic, complemented, Sylow

137

C₂⁴

—

138

C₂×Q₈

—

139

C₂×Q₈

—

140

C₂×Q₈

—

141

C₂×Q₈

—

142

C₂×Q₈

—

143

C₂×Q₈

—

144

C₂×D₄

—

145

C₂×D₄

—

146

C₂×D₄

—

147

C₂×D₄

—

148

C₂×D₄

—

149

C₂×D₄

C₄×D₁₉

yes

—

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

—

153

C₂²×C₄

—

154

C₂²×C₄

C₂²×D₁₉

yes

characteristic

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

C₂²⋊D₁₉

yes

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₂²⋊C₄

—

167

C₄²

—

168

C₄²

—

169

C₂³

—

170

C₂³

—

171

C₂³

—

172

C₂³

—

173

C₂³

—

174

C₂³

D₄×D₁₉

yes

characteristic

175

Q₈

—

176

Q₈

—

177

Q₈

—

178

Q₈

—

179

D₄

—

180

D₄

—

181

D₄

—

182

D₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

194

C₂×C₄

#64541

yes

characteristic

195

C₂×C₄

D₄×D₁₉

yes

characteristic

196

C₂×C₄

D₄×D₁₉

yes

characteristic

197

C₂×C₄

#64543

yes

characteristic

198

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

199

C₈

—

200

C₈

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

204

C₂²

—

205

C₂²

—

206

C₂²

C₂²⋊C₄×D₁₉

yes

characteristic

207

C₂²

#10597331

yes

characteristic

208

C₂²

#10597357

yes

—

209

C₂²

#10597361

yes

—

210

C₂²

#10597386

yes

characteristic

211

C₄

—

212

C₄

—

213

C₄

—

214

C₄

—

152

—

215

C₄

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

216

C₄

#10597330

yes

characteristic

217

C₄

C₄×C₂²⋊D₁₉

yes

characteristic

218

C₄

#10597385

yes

characteristic

219

C₂

—

220

C₂

#11926444

yes

characteristic

221

C₂

#11926542

yes

—

222

C₂

#11926902

yes

—

223

C₂

#11926932

yes

characteristic

224

C₂

#11926935

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#102	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂²×D₄×C₁₉	C₂²
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#102	D₁₉
hypocenter	C₁₉	#1959
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#102

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#102

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂²×D₄×C₁₉

C₂²

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#102

N	H ≅ G/N	type
2. C₂×#10597273	C₂	semidirect
3. C₂×#10597267	C₂	semidirect
5. C₂×#10597272	C₂	semidirect
6. #11926413	C₂	semidirect
14. #10597382	C₄	semidirect
136. C₁₉	#1959	semidirect

H ≅ G/N

type

2. C₂×#10597273

C₂

semidirect

3. C₂×#10597267

C₂

semidirect

5. C₂×#10597272

C₂

semidirect

6. #11926413

C₂

semidirect

14. #10597382

C₄

semidirect

136. C₁₉

#1959

semidirect

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

subgroup	index
C₂×#10597382	2
C₂×#10597273	2
C₂×#10597267	2
C₂×#10597289	2
C₂×#10597272	2
#11926413	2
C₂×C₁₉×#102	2
#1959	19

subgroup

index

C₂×C₁₉×#102

Subgroups — #14564450

Conjugacy classes of subgroups

Complements

Maximal subgroups