Group #18087575 — subgroups

Subgroups — #18087575

Order 4864.

494 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 145 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	#14564441	C₂	1	1	yes	maximal, characteristic
2	#14564440	C₂	1	2	yes	maximal
3	#14563762	C₂	1	2	yes	maximal, complemented
4	C₁₉⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1845	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597320	C₂²	1	1	yes	characteristic
7	C₂×#10597278	—	2	2	no	—
8	C₂×#10597266	—	2	4	no	—
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
10	#11926414	C₂²	1	1	yes	characteristic
11	#11926306	—	2	4	no	—
12	C₂×C₁₉×#107	—	2	2	no	—
13	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#384	C₂²	1	2	yes	—
15	C₂²×D₇₆	—	2	2	no	—
16	C₂²×D₇₆	—	2	1	no	—
17	C₂²×C₈×C₁₉	D₄	1	2	yes	—
18	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
20	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
21	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₉	—	2	1	no	—
23	C₂×C₄⋊Dic₁₉	—	2	2	no	—
24	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
25	#10597320	—	2	2	no	—
26	#10597320	—	2	1	no	—
27	#10597320	Q₈	1	2	yes	—
28	C₁₉×#107	—	4	4	no	—
29	C₄×C₈×C₁₉	—	2	2	no	—
30	#10597278	—	4	4	no	—
31	#10597266	—	4	8	no	—
32	C₄×C₁₉⋊C₈	—	2	2	no	—
33	C₄×C₁₉⋊C₈	—	2	2	no	—
34	C₂³×D₁₉	—	4	1	no	—
35	C₂²×C₄×C₁₉	—	4	2	no	—
36	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
37	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂²×Dic₁₉	—	4	1	no	—
39	C₂×D₇₆	—	2	2	no	—
40	C₂×D₇₆	—	2	4	no	—
41	C₂×D₇₆	—	4	2	no	—
42	C₂×D₇₆	—	4	4	no	—
43	C₂×D₇₆	—	4	4	no	—
44	C₂×D₇₆	—	4	2	no	—
45	C₂×D₇₆	—	4	2	no	—
46	C₂×D₇₆	—	4	1	no	—
47	C₂×C₈×C₁₉	—	2	2	no	—
48	C₂×C₈×C₁₉	—	2	2	no	—
49	C₂×C₈×C₁₉	D₈	1	4	yes	—
50	C₄⋊C₄×C₁₉	—	4	4	no	—
51	C₄⋊C₄×C₁₉	—	4	4	no	—
52	C₄⋊C₄×C₁₉	—	4	4	no	—
53	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
54	C₄²×C₁₉	#41	1	2	yes	—
55	C₄²×C₁₉	#41	1	1	yes	characteristic
56	C₄⋊Dic₁₉	—	4	2	no	—
57	C₄⋊Dic₁₉	—	4	4	no	—
58	C₂×C₁₉⋊C₈	—	2	4	no	—
59	C₂×C₁₉⋊C₈	—	2	4	no	—
60	C₂×C₁₉⋊C₈	—	2	4	no	—
61	#10671	—	19	1	no	maximal, Sylow
62	C₂³×C₁₉	#127	1	1	yes	characteristic
63	C₂²×D₁₉	—	4	2	no	—
64	C₂²×D₁₉	—	8	1	no	—
65	C₂²×D₁₉	—	8	2	no	—
66	C₂²×D₁₉	—	8	2	no	—
67	C₂²×D₁₉	—	8	1	no	—
68	C₂×C₄×C₁₉	—	8	2	no	—
69	C₂×C₄×C₁₉	—	8	2	no	—
70	C₂×C₄×C₁₉	—	8	2	no	—
71	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
72	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
73	C₂×C₄×C₁₉	#123	1	2	yes	—
74	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
76	C₂×C₄×C₁₉	#135	1	4	yes	—
77	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
78	C₂×C₄×C₁₉	#137	1	2	yes	—
79	C₂×Dic₁₉	—	8	1	no	—
80	C₂×Dic₁₉	—	8	2	no	—
81	D₇₆	—	4	4	no	—
82	D₇₆	—	4	8	no	—
83	D₇₆	—	8	2	no	—
84	D₇₆	—	8	4	no	—
85	C₈×C₁₉	—	2	4	no	—
86	C₁₉⋊C₈	—	4	4	no	—
87	#1957	—	19	1	no	—
88	#1957	—	19	2	no	—
89	#1845	D₁₉	1	1	yes	characteristic, complemented
90	#1834	—	19	2	no	—
91	#1273	—	19	1	no	—
92	C₂²×C₁₉	#399	1	1	yes	characteristic
93	C₂²×C₁₉	#493	1	1	yes	characteristic
94	C₂²×C₁₉	#495	1	2	yes	—
95	C₂²×C₁₉	#496	1	2	yes	—
96	C₂²×C₁₉	#497	1	1	yes	characteristic
97	C₂×D₁₉	—	8	4	no	—
98	C₂×D₁₉	—	8	2	no	—
99	C₂×D₁₉	—	16	1	no	—
100	C₂×D₁₉	—	16	2	no	—
101	C₂×D₁₉	—	16	1	no	—
102	C₄×C₁₉	—	16	2	no	—
103	C₄×C₁₉	#474	1	2	yes	—
104	C₄×C₁₉	#478	1	4	yes	—
105	C₄×C₁₉	#480	1	2	yes	—
106	C₄×C₁₉	#482	1	4	yes	—
107	Dic₁₉	—	16	1	no	—
108	C₂×#127	—	19	1	no	—
109	C₂×#107	—	2	2	no	—
110	C₂×#102	—	38	4	no	—
111	C₂×#102	—	38	2	no	—
112	C₂×C₄×C₈	—	19	2	no	—
113	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
114	#384	—	19	1	no	—
115	#384	C₂×D₁₉	1	2	yes	—
116	#340	—	38	4	no	—
117	C₂×C₁₉	#1709	1	1	yes	characteristic
118	C₂×C₁₉	#1719	1	2	yes	—
119	C₂×C₁₉	#1721	1	1	yes	characteristic
120	C₂×C₁₉	#2092	1	2	yes	—
121	C₂×C₁₉	#2093	1	1	yes	characteristic
122	D₁₉	—	16	2	no	—
123	C₂²×D₄	—	38	2	no	—
124	C₂²×D₄	—	38	1	no	—
125	C₂²×C₈	—	19	4	no	—
126	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
127	#127	—	19	2	no	—
128	#127	—	38	2	no	—
129	#127	—	38	1	no	—
130	C₂×C₄⋊C₄	—	2	2	no	—
131	C₂×C₄⋊C₄	—	2	2	no	—
132	C₂×C₄⋊C₄	—	2	2	no	—
133	C₂×C₄⋊C₄	—	38	2	no	—
134	C₂×C₄⋊C₄	—	38	1	no	—
135	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
136	#107	—	4	4	no	—
137	#102	—	76	8	no	—
138	#102	—	76	4	no	—
139	C₄×C₈	—	2	2	no	—
140	C₄×C₈	—	38	2	no	—
141	C₄×C₈	—	38	2	no	—
142	C₁₉	#10671	1	1	yes	characteristic, complemented, Sylow
143	C₂⁴	—	76	1	no	—
144	C₂×D₄	—	38	2	no	—
145	C₂×D₄	—	38	4	no	—
146	C₂×D₄	—	76	2	no	—
147	C₂×D₄	—	76	2	no	—
148	C₂×D₄	—	76	2	no	—
149	C₂×D₄	—	76	4	no	—
150	C₂×D₄	—	76	4	no	—
151	C₂×D₄	—	76	1	no	—
152	C₂²×C₄	—	4	2	no	—
153	C₂²×C₄	—	76	1	no	—
154	C₂²×C₄	D₄×D₁₉	1	2	yes	—
155	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
156	C₂×C₈	—	2	2	no	—
157	C₂×C₈	—	2	2	no	—
158	C₂×C₈	—	38	4	no	—
159	C₂×C₈	—	38	4	no	—
160	C₂×C₈	—	38	4	no	—
161	C₂×C₈	#64525	1	4	yes	—
162	C₄⋊C₄	—	4	4	no	—
163	C₄⋊C₄	—	4	4	no	—
164	C₄⋊C₄	—	4	4	no	—
165	C₄⋊C₄	—	76	2	no	—
166	C₄⋊C₄	—	76	4	no	—
167	C₄²	#64541	1	2	yes	—
168	C₄²	Q₈×D₁₉	1	1	yes	characteristic
169	C₄²	#64545	1	1	yes	characteristic
170	C₂³	—	76	2	no	—
171	C₂³	—	152	1	no	—
172	C₂³	—	152	2	no	—
173	C₂³	—	152	2	no	—
174	C₂³	—	152	1	no	—
175	C₂³	#10597386	1	1	yes	characteristic
176	D₄	—	76	4	no	—
177	D₄	—	76	8	no	—
178	D₄	—	152	2	no	—
179	D₄	—	152	4	no	—
180	C₂×C₄	—	8	2	no	—
181	C₂×C₄	—	8	2	no	—
182	C₂×C₄	—	8	2	no	—
183	C₂×C₄	—	152	1	no	—
184	C₂×C₄	—	152	2	no	—
185	C₂×C₄	#10597340	1	2	yes	—
186	C₂×C₄	#10597342	1	2	yes	—
187	C₂×C₄	#10597357	1	4	yes	—
188	C₂×C₄	#10597365	1	4	yes	—
189	C₂×C₄	#10597375	1	1	yes	characteristic
190	C₂×C₄	C₂×#64525	1	2	yes	—
191	C₂×C₄	#10597388	1	2	yes	—
192	C₂×C₄	#10597392	1	1	yes	characteristic
193	C₈	—	2	4	no	—
194	C₈	—	76	4	no	—
195	C₂²	—	304	1	no	—
196	C₂²	—	304	2	no	—
197	C₂²	—	304	1	no	—
198	C₂²	—	152	4	no	—
199	C₂²	—	152	2	no	—
200	C₂²	#11926479	1	1	yes	characteristic
201	C₂²	#11926920	1	1	yes	characteristic
202	C₂²	#11926929	1	2	yes	—
203	C₂²	#11926932	1	2	yes	—
204	C₂²	#11926936	1	1	yes	characteristic
205	C₄	—	16	2	no	—
206	C₄	—	304	1	no	—
207	C₄	#11926821	1	2	yes	—
208	C₄	#11926847	1	4	yes	—
209	C₄	#11926857	1	2	yes	—
210	C₄	#11926871	1	4	yes	—
211	C₂	—	304	2	no	—
212	C₂	#14563242	1	1	yes	characteristic
213	C₂	#14563291	1	2	yes	—
214	C₂	#14563302	1	1	yes	characteristic
215	C₂	#14565153	1	2	yes	—
216	C₂	#14565164	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564441

C₂

yes

maximal, characteristic

#14564440

C₂

yes

maximal

#14563762

C₂

yes

maximal, complemented

C₁₉⋊#1273

C₂

yes

maximal, characteristic, complemented

C₁₉×#1845

C₂

yes

maximal, characteristic, complemented

C₂×#10597320

C₂²

yes

characteristic

C₂×#10597278

—

C₂×#10597266

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926414

C₂²

yes

characteristic

#11926306

—

C₂×C₁₉×#107

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#384

C₂²

yes

—

C₂²×D₇₆

—

C₂²×D₇₆

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

D₄

yes

—

#10597320

—

#10597320

—

#10597320

Q₈

yes

—

C₁₉×#107

—

C₄×C₈×C₁₉

—

#10597278

—

#10597266

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1957

—

#1957

—

#1845

D₁₉

yes

characteristic, complemented

#1834

—

#1273

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#496

yes

—

C₂²×C₁₉

#497

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

100

C₂×D₁₉

—

101

C₂×D₁₉

—

102

C₄×C₁₉

—

103

C₄×C₁₉

#474

yes

—

104

C₄×C₁₉

#478

yes

—

105

C₄×C₁₉

#480

yes

—

106

C₄×C₁₉

#482

yes

—

107

Dic₁₉

—

108

C₂×#127

—

109

C₂×#107

—

110

C₂×#102

—

111

C₂×#102

—

112

C₂×C₄×C₈

—

113

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

114

#384

—

115

#384

C₂×D₁₉

yes

—

116

#340

—

117

C₂×C₁₉

#1709

yes

characteristic

118

C₂×C₁₉

#1719

yes

—

119

C₂×C₁₉

#1721

yes

characteristic

120

C₂×C₁₉

#2092

yes

—

121

C₂×C₁₉

#2093

yes

characteristic

122

D₁₉

—

123

C₂²×D₄

—

124

C₂²×D₄

—

125

C₂²×C₈

—

126

C₂²×C₈

C₂²⋊D₁₉

yes

—

127

#127

—

128

#127

—

129

#127

—

130

C₂×C₄⋊C₄

—

131

C₂×C₄⋊C₄

—

132

C₂×C₄⋊C₄

—

133

C₂×C₄⋊C₄

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄²

C₂²×D₁₉

yes

characteristic

136

#107

—

137

#102

—

138

#102

—

139

C₄×C₈

—

140

C₄×C₈

—

141

C₄×C₈

—

142

C₁₉

#10671

yes

characteristic, complemented, Sylow

143

C₂⁴

—

144

C₂×D₄

—

145

C₂×D₄

—

146

C₂×D₄

—

147

C₂×D₄

—

148

C₂×D₄

—

149

C₂×D₄

—

150

C₂×D₄

—

151

C₂×D₄

—

152

C₂²×C₄

—

153

C₂²×C₄

—

154

C₂²×C₄

D₄×D₁₉

yes

—

155

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

#64525

yes

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄²

#64541

yes

—

168

C₄²

Q₈×D₁₉

yes

characteristic

169

C₄²

#64545

yes

characteristic

170

C₂³

—

171

C₂³

—

152

—

172

C₂³

—

152

—

173

C₂³

—

152

—

174

C₂³

—

152

—

175

C₂³

#10597386

yes

characteristic

176

D₄

—

177

D₄

—

178

D₄

—

152

—

179

D₄

—

152

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

152

—

184

C₂×C₄

—

152

—

185

C₂×C₄

#10597340

yes

—

186

C₂×C₄

#10597342

yes

—

187

C₂×C₄

#10597357

yes

—

188

C₂×C₄

#10597365

yes

—

189

C₂×C₄

#10597375

yes

characteristic

190

C₂×C₄

C₂×#64525

yes

—

191

C₂×C₄

#10597388

yes

—

192

C₂×C₄

#10597392

yes

characteristic

193

C₈

—

194

C₈

—

195

C₂²

—

304

—

196

C₂²

—

304

—

197

C₂²

—

304

—

198

C₂²

—

152

—

199

C₂²

—

152

—

200

C₂²

#11926479

yes

characteristic

201

C₂²

#11926920

yes

characteristic

202

C₂²

#11926929

yes

—

203

C₂²

#11926932

yes

—

204

C₂²

#11926936

yes

characteristic

205

C₄

—

206

C₄

—

304

—

207

C₄

#11926821

yes

—

208

C₄

#11926847

yes

—

209

C₄

#11926857

yes

—

210

C₄

#11926871

yes

—

211

C₂

—

304

—

212

C₂

#14563242

yes

characteristic

213

C₂

#14563291

yes

—

214

C₂

#14563302

yes

characteristic

215

C₂

#14565153

yes

—

216

C₂

#14565164

yes

characteristic

	subgroup	G/H
center	C₂³	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1845	C₂
socle	C₂³×C₁₉	#127
prime radical	C₂×#10597320	C₂²
hypercenter	#1845	D₁₉
hypocenter	C₁₉	#10671
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

subgroup

G/H

center

C₂³

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1845

C₂

C₂³×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

N	H ≅ G/N	type
3. #14563762	C₂	semidirect
4. C₁₉⋊#1273	C₂	semidirect
5. C₁₉×#1845	C₂	semidirect
89. #1845	D₁₉	semidirect
142. C₁₉	#10671	semidirect

H ≅ G/N

type

3. #14563762

C₂

semidirect

4. C₁₉⋊#1273

C₂

semidirect

5. C₁₉×#1845

C₂

semidirect

89. #1845

D₁₉

semidirect

142. C₁₉

#10671

semidirect

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

subgroup	index
#14564441	2
#14564440	2
#14563762	2
C₁₉⋊#1273	2
C₁₉×#1845	2
#10671	19

subgroup

index

#14564441

#14564440

#14563762

C₁₉⋊#1273

C₁₉×#1845

#10671

Subgroups — #18087575

Conjugacy classes of subgroups

Complements

Maximal subgroups