Group #14564866 — subgroups

Subgroups — #14564866

Order 2432.

402 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 95 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×#10597289	C₂	1	2	yes	maximal, complemented
2	C₂×#10597289	C₂	1	2	yes	maximal, complemented
3	#11926442	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926299	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#127	C₂	1	1	yes	maximal, characteristic
6	C₂²×D₄×C₁₉	—	2	1	no	—
7	C₂²×D₄×C₁₉	—	2	1	no	—
8	C₂²×D₄×C₁₉	C₂²	1	2	yes	—
9	C₁₉×#127	—	2	4	no	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₉⋊C₄	—	2	1	no	—
14	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
15	#10597289	—	2	4	no	—
16	#10597289	—	2	4	no	—
17	C₁₉⋊#95	—	2	1	no	—
18	C₂⁴×C₁₉	—	2	2	no	—
19	C₂×D₄×C₁₉	—	2	4	no	—
20	C₂×D₄×C₁₉	—	2	4	no	—
21	C₂×D₄×C₁₉	—	2	2	no	—
22	C₂×D₄×C₁₉	—	2	2	no	—
23	C₂×D₄×C₁₉	—	2	2	no	—
24	C₂×D₄×C₁₉	—	2	2	no	—
25	C₂×D₄×C₁₉	—	2	2	no	—
26	C₂×D₄×C₁₉	—	4	2	no	—
27	C₂×D₄×C₁₉	—	4	2	no	—
28	C₂×D₄×C₁₉	—	4	2	no	—
29	C₂×D₄×C₁₉	—	4	2	no	—
30	C₂×D₄×C₁₉	D₄	1	4	yes	—
31	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂²×Dic₁₉	—	2	1	no	—
35	C₂²×Dic₁₉	—	2	1	no	—
36	C₄²×C₁₉	—	2	2	no	—
37	C₄⋊Dic₁₉	—	2	1	no	—
38	C₄⋊Dic₁₉	—	2	2	no	—
39	C₄⋊Dic₁₉	D₄	1	2	yes	complemented
40	Dic₁₉⋊C₄	—	4	2	no	—
41	C₂×C₁₉⋊C₈	—	2	2	no	—
42	C₂×C₁₉⋊C₈	—	2	2	no	—
43	C₂×C₁₉⋊C₈	—	2	2	no	—
44	C₂³×C₁₉	—	2	4	no	—
45	C₂³×C₁₉	—	4	2	no	—
46	C₂³×C₁₉	—	4	2	no	—
47	C₂³×C₁₉	—	4	2	no	—
48	C₂³×C₁₉	—	4	2	no	—
49	C₂³×C₁₉	—	4	2	no	—
50	C₂³×C₁₉	—	4	2	no	—
51	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
52	D₄×C₁₉	—	2	4	no	—
53	D₄×C₁₉	—	2	4	no	—
54	D₄×C₁₉	—	4	8	no	—
55	D₄×C₁₉	—	4	8	no	—
56	D₄×C₁₉	—	4	2	no	—
57	D₄×C₁₉	—	4	2	no	—
58	C₂×C₄×C₁₉	—	2	1	no	—
59	C₂×C₄×C₁₉	—	2	1	no	—
60	C₂×C₄×C₁₉	—	2	1	no	—
61	C₂×C₄×C₁₉	—	2	1	no	—
62	C₂×C₄×C₁₉	D₈	1	2	yes	—
63	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
64	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
66	C₂×C₄×C₁₉	#41	1	2	yes	—
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	—	4	2	no	—
75	#2041	—	19	1	no	maximal, Sylow
76	C₂²×C₁₉	—	4	4	no	—
77	C₂²×C₁₉	—	4	4	no	—
78	C₂²×C₁₉	—	4	4	no	—
79	C₂²×C₁₉	—	8	2	no	—
80	C₂²×C₁₉	—	8	2	no	—
81	C₂²×C₁₉	—	8	2	no	—
82	C₂²×C₁₉	—	8	2	no	—
83	C₂²×C₁₉	#120	1	1	yes	characteristic
84	C₂²×C₁₉	#121	1	1	yes	characteristic
85	C₂²×C₁₉	#124	1	1	yes	characteristic
86	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
87	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
88	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
89	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
90	C₄×C₁₉	—	2	2	no	—
91	C₄×C₁₉	—	2	2	no	—
92	C₄×C₁₉	#121	1	2	yes	—
93	C₄×C₁₉	#123	1	2	yes	—
94	Dic₁₉	—	4	2	no	—
95	Dic₁₉	—	8	1	no	—
96	C₂×#127	D₁₉	1	1	yes	characteristic
97	C₂×#102	—	19	2	no	—
98	C₂×#102	—	19	2	no	—
99	#389	—	19	1	no	—
100	#336	—	19	1	no	—
101	C₂×C₁₉	—	8	4	no	—
102	C₂×C₁₉	#394	1	1	yes	characteristic
103	C₂×C₁₉	#447	1	1	yes	characteristic
104	C₂×C₁₉	#450	1	1	yes	characteristic
105	C₂×C₁₉	#459	1	1	yes	characteristic
106	C₂×C₁₉	#460	1	1	yes	characteristic
107	C₂×C₁₉	#486	1	1	yes	characteristic
108	C₂×C₁₉	#490	1	1	yes	characteristic
109	C₂²×D₄	—	2	1	no	—
110	C₂²×D₄	—	2	1	no	—
111	C₂²×D₄	C₂×D₁₉	1	2	yes	—
112	C₂²×C₈	—	19	2	no	—
113	#127	—	2	4	no	—
114	C₂×C₄⋊C₄	—	19	1	no	—
115	C₂×C₄⋊C₄	—	19	1	no	—
116	C₂×C₄⋊C₄	—	38	1	no	—
117	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
118	#102	—	38	4	no	—
119	#102	—	38	4	no	—
120	#95	—	38	1	no	—
121	C₁₉	#2041	1	1	yes	characteristic, complemented, Sylow
122	C₂⁴	—	2	2	no	—
123	C₂×D₄	—	2	4	no	—
124	C₂×D₄	—	2	4	no	—
125	C₂×D₄	—	2	2	no	—
126	C₂×D₄	—	2	2	no	—
127	C₂×D₄	—	2	2	no	—
128	C₂×D₄	—	2	2	no	—
129	C₂×D₄	—	2	2	no	—
130	C₂×D₄	—	4	2	no	—
131	C₂×D₄	—	4	2	no	—
132	C₂×D₄	—	4	2	no	—
133	C₂×D₄	—	4	2	no	—
134	C₂×D₄	C₂²⋊D₁₉	1	4	yes	—
135	C₂²×C₄	—	38	1	no	—
136	C₂²×C₄	—	38	1	no	—
137	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
138	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
139	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
140	C₂×C₈	—	38	2	no	—
141	C₂×C₈	—	38	2	no	—
142	C₂×C₈	—	38	2	no	—
143	C₄⋊C₄	—	19	2	no	—
144	C₄⋊C₄	—	38	1	no	—
145	C₄⋊C₄	—	38	2	no	—
146	C₄⋊C₄	—	76	2	no	—
147	C₄²	—	2	2	no	—
148	C₂³	—	2	4	no	—
149	C₂³	—	4	2	no	—
150	C₂³	—	4	2	no	—
151	C₂³	—	4	2	no	—
152	C₂³	—	4	2	no	—
153	C₂³	—	4	2	no	—
154	C₂³	—	4	2	no	—
155	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
156	D₄	—	2	4	no	—
157	D₄	—	2	4	no	—
158	D₄	—	4	8	no	—
159	D₄	—	4	8	no	—
160	D₄	—	4	2	no	—
161	D₄	—	4	2	no	—
162	C₂×C₄	—	2	1	no	—
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	1	no	—
166	C₂×C₄	—	38	2	no	—
167	C₂×C₄	—	76	1	no	—
168	C₂×C₄	—	76	1	no	—
169	C₂×C₄	—	76	1	no	—
170	C₂×C₄	—	76	1	no	—
171	C₂×C₄	—	76	1	no	—
172	C₂×C₄	#64525	1	2	yes	—
173	C₂×C₄	#64526	1	2	yes	—
174	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
175	C₂×C₄	#64543	1	1	yes	characteristic
176	C₂×C₄	#64543	1	2	yes	—
177	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
178	C₈	—	76	2	no	—
179	C₂²	—	4	4	no	—
180	C₂²	—	4	4	no	—
181	C₂²	—	4	4	no	—
182	C₂²	—	8	2	no	—
183	C₂²	—	8	2	no	—
184	C₂²	—	8	2	no	—
185	C₂²	—	8	2	no	—
186	C₂²	C₂×#64525	1	1	yes	characteristic
187	C₂²	#10597378	1	1	yes	characteristic
188	C₂²	#10597378	1	1	yes	characteristic
189	C₂²	C₂×#64526	1	1	yes	characteristic
190	C₂²	#10597382	1	1	yes	characteristic
191	C₂²	#10597384	1	1	yes	characteristic
192	C₂²	#10597399	1	1	yes	characteristic
193	C₄	—	2	2	no	—
194	C₄	—	2	2	no	—
195	C₄	—	76	2	no	—
196	C₄	—	152	1	no	—
197	C₄	#10597381	1	2	yes	—
198	C₄	#10597385	1	2	yes	—
199	C₂	—	8	4	no	—
200	C₂	#11926458	1	1	yes	characteristic
201	C₂	#11926678	1	1	yes	characteristic
202	C₂	#11926695	1	1	yes	characteristic
203	C₂	#11926736	1	1	yes	characteristic
204	C₂	#11926741	1	1	yes	characteristic
205	C₂	#11926890	1	1	yes	characteristic
206	C₂	#11926908	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597289

C₂

yes

maximal, complemented

C₂×#10597289

C₂

yes

maximal, complemented

#11926442

C₂

yes

maximal, characteristic, complemented

#11926299

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#127

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

C₂²

yes

—

C₁₉×#127

—

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

—

#10597289

—

#10597289

—

C₁₉⋊#95

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

complemented

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

—

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#2041

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#121

yes

—

C₄×C₁₉

#123

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×#127

D₁₉

yes

—

—

—

100

#336

—

101

C₂×C₁₉

—

102

C₂×C₁₉

#394

yes

characteristic

103

C₂×C₁₉

#447

yes

characteristic

104

C₂×C₁₉

#450

yes

characteristic

105

C₂×C₁₉

#459

yes

characteristic

106

C₂×C₁₉

#460

yes

characteristic

107

C₂×C₁₉

#486

yes

characteristic

108

C₂×C₁₉

#490

yes

characteristic

109

C₂²×D₄

—

110

C₂²×D₄

—

111

C₂²×D₄

C₂×D₁₉

yes

—

112

C₂²×C₈

—

113

#127

—

114

C₂×C₄⋊C₄

—

115

C₂×C₄⋊C₄

—

116

C₂×C₄⋊C₄

—

117

C₂×C₄²

C₂×D₁₉

yes

characteristic

118

#102

—

119

#102

—

120

#95

—

121

C₁₉

#2041

yes

characteristic, complemented, Sylow

122

C₂⁴

—

123

C₂×D₄

—

124

C₂×D₄

—

125

C₂×D₄

—

126

C₂×D₄

—

127

C₂×D₄

—

128

C₂×D₄

—

129

C₂×D₄

—

130

C₂×D₄

—

131

C₂×D₄

—

132

C₂×D₄

—

133

C₂×D₄

—

134

C₂×D₄

C₂²⋊D₁₉

yes

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

138

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

139

C₂²×C₄

C₂²×D₁₉

yes

characteristic

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

147

C₄²

—

148

C₂³

—

149

C₂³

—

150

C₂³

—

151

C₂³

—

152

C₂³

—

153

C₂³

—

154

C₂³

—

155

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

156

D₄

—

157

D₄

—

158

D₄

—

159

D₄

—

160

D₄

—

161

D₄

—

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

#64525

yes

—

173

C₂×C₄

#64526

yes

—

174

C₂×C₄

D₄×D₁₉

yes

characteristic

175

C₂×C₄

#64543

yes

characteristic

176

C₂×C₄

#64543

yes

—

177

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

178

C₈

—

179

C₂²

—

180

C₂²

—

181

C₂²

—

182

C₂²

—

183

C₂²

—

184

C₂²

—

185

C₂²

—

186

C₂²

C₂×#64525

yes

characteristic

187

C₂²

#10597378

yes

characteristic

188

C₂²

#10597378

yes

characteristic

189

C₂²

C₂×#64526

yes

characteristic

190

C₂²

#10597382

yes

characteristic

191

C₂²

#10597384

yes

characteristic

192

C₂²

#10597399

yes

characteristic

193

C₄

—

194

C₄

—

195

C₄

—

196

C₄

—

152

—

197

C₄

#10597381

yes

—

198

C₄

#10597385

yes

—

199

C₂

—

200

C₂

#11926458

yes

characteristic

201

C₂

#11926678

yes

characteristic

202

C₂

#11926695

yes

characteristic

203

C₂

#11926736

yes

characteristic

204

C₂

#11926741

yes

characteristic

205

C₂

#11926890

yes

characteristic

206

C₂

#11926908

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting, prime radical	C₂×C₁₉×#127	C₂
socle	C₂³×C₁₉	C₂×D₄
hypercenter	C₂×#127	D₁₉
hypocenter	C₁₉	#2041
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#127

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting, prime radical

C₂×C₁₉×#127

C₂

socle

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#127

N	H ≅ G/N	type
1. C₂×#10597289	C₂	semidirect
2. C₂×#10597289	C₂	semidirect
3. #11926442	C₂	semidirect
4. #11926299	C₂	semidirect
39. C₄⋊Dic₁₉	D₄	semidirect
121. C₁₉	#2041	semidirect

H ≅ G/N

type

1. C₂×#10597289

C₂

semidirect

2. C₂×#10597289

C₂

semidirect

3. #11926442

C₂

semidirect

4. #11926299

C₂

semidirect

39. C₄⋊Dic₁₉

D₄

semidirect

121. C₁₉

#2041

semidirect

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

subgroup	index
C₂×#10597289	2
#11926442	2
#11926299	2
C₂×C₁₉×#127	2
#2041	19

subgroup

index

C₂×C₁₉×#127

Subgroups — #14564866

Conjugacy classes of subgroups

Complements

Maximal subgroups