Group #14564970 — subgroups

Subgroups — #14564970

Order 2432.

250 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 91 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×#10597264	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597265	C₂	1	1	yes	maximal, characteristic
3	#11926442	C₂	1	1	yes	maximal, characteristic
4	#11926306	C₂	1	1	yes	maximal, characteristic
5	#11926306	C₂	1	1	yes	maximal, characteristic
6	#11926299	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#125	—	2	2	no	—
9	C₁₉×#125	—	2	2	no	—
10	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
11	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
12	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₉⋊C₄	—	2	1	no	—
18	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₁₉⋊#95	—	2	1	no	—
21	#10597265	—	2	2	no	—
22	#10597264	—	2	2	no	—
23	C₂²×C₄×C₁₉	—	2	1	no	—
24	C₂²×C₄×C₁₉	—	2	1	no	—
25	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×Dic₁₉	—	2	1	no	—
29	C₂²×Dic₁₉	—	2	1	no	—
30	C₄⋊C₄×C₁₉	—	2	4	no	—
31	C₄⋊C₄×C₁₉	—	2	4	no	—
32	C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
35	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
36	C₄²×C₁₉	—	2	1	no	—
37	C₄²×C₁₉	—	2	1	no	—
38	C₄⋊Dic₁₉	—	2	1	no	—
39	C₄⋊Dic₁₉	—	2	1	no	—
40	C₄⋊Dic₁₉	—	2	1	no	—
41	C₄⋊Dic₁₉	Q₈	1	2	yes	—
42	Dic₁₉⋊C₄	—	4	2	no	—
43	C₂×C₁₉⋊C₈	—	2	1	no	—
44	C₂×C₁₉⋊C₈	—	2	1	no	—
45	C₂×C₁₉⋊C₈	—	2	1	no	—
46	C₂×C₁₉⋊C₈	—	2	1	no	—
47	C₂×C₁₉⋊C₈	Q₈	1	2	yes	—
48	C₂×C₁₉⋊C₈	Q₈	1	2	yes	—
49	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	1	no	—
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
57	C₂×C₄×C₁₉	—	2	1	no	—
58	C₂×C₄×C₁₉	—	4	1	no	—
59	C₂×C₄×C₁₉	—	4	1	no	—
60	C₂×C₄×C₁₉	—	4	1	no	—
61	C₂×C₄×C₁₉	—	4	1	no	—
62	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
65	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
66	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
68	C₂×Dic₁₉	—	2	2	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	—	4	1	no	—
74	C₁₉⋊C₈	—	2	2	no	—
75	C₁₉⋊C₈	—	2	2	no	—
76	#2059	—	19	1	no	maximal, Sylow
77	C₂²×C₁₉	#120	1	1	yes	characteristic
78	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
79	C₂²×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
80	C₂²×C₁₉	#135	1	1	yes	characteristic
81	C₂²×C₁₉	#135	1	1	yes	characteristic
82	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
83	C₂²×C₁₉	#137	1	1	yes	characteristic
84	C₄×C₁₉	—	4	1	no	—
85	C₄×C₁₉	—	4	2	no	—
86	C₄×C₁₉	—	4	1	no	—
87	C₄×C₁₉	—	4	2	no	—
88	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
89	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
90	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
91	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
92	Dic₁₉	—	4	2	no	—
93	Dic₁₉	—	8	1	no	—
94	C₂×#125	D₁₉	1	1	yes	characteristic
95	C₂×#107	—	19	1	no	—
96	C₂×#106	—	19	1	no	—
97	#389	—	19	1	no	—
98	#340	—	19	1	no	—
99	#340	—	19	1	no	—
100	#336	—	19	1	no	—
101	C₂×C₁₉	#395	1	1	yes	characteristic
102	C₂×C₁₉	#449	1	1	yes	characteristic
103	C₂×C₁₉	#452	1	1	yes	characteristic
104	C₂×C₁₉	#478	1	1	yes	characteristic
105	C₂×C₁₉	#479	1	1	yes	characteristic
106	C₂×C₁₉	#499	1	1	yes	characteristic
107	C₂×C₁₉	#501	1	1	yes	characteristic
108	C₂²×C₈	—	19	1	no	—
109	C₂²×C₈	—	19	1	no	—
110	#125	—	2	2	no	—
111	#125	—	2	2	no	—
112	C₂×C₄⋊C₄	—	2	1	no	—
113	C₂×C₄⋊C₄	—	2	1	no	—
114	C₂×C₄⋊C₄	—	19	1	no	—
115	C₂×C₄⋊C₄	—	19	1	no	—
116	C₂×C₄⋊C₄	—	38	1	no	—
117	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
118	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
119	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
120	#107	—	38	2	no	—
121	#106	—	38	2	no	—
122	#95	—	38	1	no	—
123	C₁₉	#2059	1	1	yes	characteristic, complemented, Sylow
124	C₂²×C₄	—	2	1	no	—
125	C₂²×C₄	—	2	1	no	—
126	C₂²×C₄	—	38	1	no	—
127	C₂²×C₄	—	38	1	no	—
128	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
129	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
130	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
131	C₂×C₈	—	19	2	no	—
132	C₂×C₈	—	19	2	no	—
133	C₂×C₈	—	38	1	no	—
134	C₂×C₈	—	38	1	no	—
135	C₂×C₈	—	38	1	no	—
136	C₂×C₈	—	38	1	no	—
137	C₄⋊C₄	—	2	4	no	—
138	C₄⋊C₄	—	2	4	no	—
139	C₄⋊C₄	—	2	1	no	—
140	C₄⋊C₄	—	2	1	no	—
141	C₄⋊C₄	—	19	2	no	—
142	C₄⋊C₄	—	38	1	no	—
143	C₄⋊C₄	—	38	1	no	—
144	C₄⋊C₄	—	38	1	no	—
145	C₄⋊C₄	—	76	2	no	—
146	C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
147	C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
148	C₄²	—	2	1	no	—
149	C₄²	—	2	1	no	—
150	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
151	C₂×C₄	—	2	1	no	—
152	C₂×C₄	—	2	1	no	—
153	C₂×C₄	—	2	1	no	—
154	C₂×C₄	—	2	1	no	—
155	C₂×C₄	—	2	1	no	—
156	C₂×C₄	—	2	1	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	4	1	no	—
160	C₂×C₄	—	4	1	no	—
161	C₂×C₄	—	4	1	no	—
162	C₂×C₄	—	4	1	no	—
163	C₂×C₄	—	38	2	no	—
164	C₂×C₄	—	76	1	no	—
165	C₂×C₄	—	76	1	no	—
166	C₂×C₄	—	76	1	no	—
167	C₂×C₄	—	76	1	no	—
168	C₂×C₄	—	76	1	no	—
169	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
170	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
171	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
172	C₂×C₄	#64545	1	1	yes	characteristic
173	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
174	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
175	C₈	—	38	2	no	—
176	C₈	—	38	2	no	—
177	C₂²	#10597390	1	1	yes	characteristic
178	C₂²	#10597392	1	1	yes	characteristic
179	C₂²	#10597395	1	1	yes	characteristic
180	C₂²	#10597396	1	1	yes	characteristic
181	C₂²	#10597396	1	1	yes	characteristic
182	C₂²	#10597397	1	1	yes	characteristic
183	C₂²	#10597399	1	1	yes	characteristic
184	C₄	—	4	1	no	—
185	C₄	—	4	2	no	—
186	C₄	—	4	1	no	—
187	C₄	—	4	2	no	—
188	C₄	—	76	2	no	—
189	C₄	—	152	1	no	—
190	C₄	#10597390	1	1	yes	characteristic
191	C₄	#10597390	1	1	yes	characteristic
192	C₄	#10597392	1	1	yes	characteristic
193	C₄	#10597392	1	1	yes	characteristic
194	C₂	#11926463	1	1	yes	characteristic
195	C₂	#11926689	1	1	yes	characteristic
196	C₂	#11926706	1	1	yes	characteristic
197	C₂	#11926841	1	1	yes	characteristic
198	C₂	#11926848	1	1	yes	characteristic
199	C₂	#11926943	1	1	yes	characteristic
200	C₂	#11926954	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597264

C₂

yes

maximal, characteristic

C₂×#10597265

C₂

yes

maximal, characteristic

#11926442

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal, characteristic

#11926299

C₂

yes

maximal, characteristic

C₂×C₁₉×#125

C₂

yes

maximal, characteristic

C₁₉×#125

—

C₁₉×#125

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉⋊#95

—

#10597265

—

#10597264

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

Q₈

yes

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

Q₈

yes

—

C₂×C₁₉⋊C₈

Q₈

yes

—

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×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

C₄⋊Q₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₄×C₁₉

C₄⋊Q₈

yes

characteristic

Dic₁₉

—

Dic₁₉

—

C₂×#125

D₁₉

yes

—

—

—

—

—

100

#336

—

101

C₂×C₁₉

#395

yes

characteristic

102

C₂×C₁₉

#449

yes

characteristic

103

C₂×C₁₉

#452

yes

characteristic

104

C₂×C₁₉

#478

yes

characteristic

105

C₂×C₁₉

#479

yes

characteristic

106

C₂×C₁₉

#499

yes

characteristic

107

C₂×C₁₉

#501

yes

characteristic

108

C₂²×C₈

—

109

C₂²×C₈

—

110

#125

—

111

#125

—

112

C₂×C₄⋊C₄

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄⋊C₄

—

115

C₂×C₄⋊C₄

—

116

C₂×C₄⋊C₄

—

117

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

118

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

119

C₂×C₄²

C₂×D₁₉

yes

characteristic

120

#107

—

121

#106

—

122

#95

—

123

C₁₉

#2059

yes

characteristic, complemented, Sylow

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

—

127

C₂²×C₄

—

128

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

129

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

130

C₂²×C₄

C₂²×D₁₉

yes

characteristic

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₄⋊C₄

—

138

C₄⋊C₄

—

139

C₄⋊C₄

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₄⋊C₄

C₂²⋊D₁₉

yes

—

147

C₄⋊C₄

C₂²⋊D₁₉

yes

—

148

C₄²

—

149

C₄²

—

150

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

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

Q₈×D₁₉

yes

characteristic

170

C₂×C₄

Q₈×D₁₉

yes

characteristic

171

C₂×C₄

Q₈×D₁₉

yes

characteristic

172

C₂×C₄

#64545

yes

characteristic

173

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

174

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

175

C₈

—

176

C₈

—

177

C₂²

#10597390

yes

characteristic

178

C₂²

#10597392

yes

characteristic

179

C₂²

#10597395

yes

characteristic

180

C₂²

#10597396

yes

characteristic

181

C₂²

#10597396

yes

characteristic

182

C₂²

#10597397

yes

characteristic

183

C₂²

#10597399

yes

characteristic

184

C₄

—

185

C₄

—

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

—

152

—

190

C₄

#10597390

yes

characteristic

191

C₄

#10597390

yes

characteristic

192

C₄

#10597392

yes

characteristic

193

C₄

#10597392

yes

characteristic

194

C₂

#11926463

yes

characteristic

195

C₂

#11926689

yes

characteristic

196

C₂

#11926706

yes

characteristic

197

C₂

#11926841

yes

characteristic

198

C₂

#11926848

yes

characteristic

199

C₂

#11926943

yes

characteristic

200

C₂

#11926954

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#125	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	C₂×#125	D₁₉
hypocenter	C₁₉	#2059
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#125

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

N	H ≅ G/N	type
123. C₁₉	#2059	semidirect

H ≅ G/N

type

123. C₁₉

#2059

semidirect

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

subgroup	index
C₂×#10597264	2
C₂×#10597265	2
#11926442	2
#11926306	2
#11926299	2
C₂×C₁₉×#125	2
#2059	19

subgroup

index

C₂×C₁₉×#125

Subgroups — #14564970

Conjugacy classes of subgroups

Complements

Maximal subgroups