Group #18087283 — subgroups

Subgroups — #18087283

Order 4864.

350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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	#14563763	C₂	1	1	yes	maximal, characteristic
2	#14563640	C₂	1	2	yes	maximal
3	#14561519	C₂	1	2	yes	maximal
4	#14561470	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1984	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×#10597292	—	2	2	no	—
8	#11926414	C₂²	1	2	yes	—
9	#11926307	—	2	2	no	—
10	#11926306	—	2	2	no	—
11	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#336	—	2	2	no	—
15	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	—	2	1	no	—
17	C₂²×C₈×C₁₉	D₄	1	2	yes	—
18	C₄×Q₈×C₁₉	—	2	2	no	—
19	C₄×Q₈×C₁₉	—	2	2	no	—
20	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
21	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₄²×C₁₉	—	2	1	no	—
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉	—	2	2	no	—
25	C₂×C₄⋊Dic₁₉	—	2	2	no	—
26	C₂×C₄⋊Dic₁₉	—	2	2	no	—
27	C₂²×C₁₉⋊C₈	—	2	2	no	—
28	C₁₉×C₄⋊C₈	—	2	2	no	—
29	C₄×C₈×C₁₉	—	2	2	no	—
30	#10597292	—	4	4	no	—
31	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
32	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
33	C₂×Q₈×C₁₉	—	2	1	no	—
34	C₂×Q₈×C₁₉	—	2	2	no	—
35	C₂×Q₈×C₁₉	—	2	2	no	—
36	C₂×Q₈×C₁₉	D₈	1	2	yes	—
37	C₂²×C₄×C₁₉	—	2	1	no	—
38	C₂²×C₄×C₁₉	—	2	1	no	—
39	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
42	C₂²×Dic₁₉	—	4	2	no	—
43	C₂×C₈×C₁₉	—	2	2	no	—
44	C₂×C₈×C₁₉	—	2	2	no	—
45	C₂×C₈×C₁₉	—	2	2	no	—
46	C₂×C₈×C₁₉	—	4	1	no	—
47	C₂×C₈×C₁₉	—	4	2	no	—
48	C₄⋊C₄×C₁₉	—	2	2	no	—
49	C₄⋊C₄×C₁₉	—	4	2	no	—
50	C₄²×C₁₉	—	4	1	no	—
51	C₄²×C₁₉	—	4	1	no	—
52	C₄²×C₁₉	#41	1	2	yes	—
53	C₄²×C₁₉	#41	1	2	yes	—
54	C₄⋊Dic₁₉	—	4	2	no	—
55	C₄⋊Dic₁₉	—	4	2	no	—
56	C₄⋊Dic₁₉	—	4	2	no	—
57	C₄⋊Dic₁₉	—	4	2	no	—
58	C₄⋊Dic₁₉	—	8	2	no	—
59	C₂×C₁₉⋊C₈	—	4	2	no	—
60	C₂×C₁₉⋊C₈	—	4	2	no	—
61	C₂×C₁₉⋊C₈	—	4	2	no	—
62	#10623	—	19	1	no	maximal, Sylow
63	C₂³×C₁₉	#121	1	1	yes	characteristic
64	Q₈×C₁₉	—	2	4	no	—
65	Q₈×C₁₉	—	4	2	no	—
66	C₂×C₄×C₁₉	—	2	2	no	—
67	C₂×C₄×C₁₉	—	2	2	no	—
68	C₂×C₄×C₁₉	—	4	1	no	—
69	C₂×C₄×C₁₉	—	4	1	no	—
70	C₂×C₄×C₁₉	—	4	1	no	—
71	C₂×C₄×C₁₉	—	4	2	no	—
72	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
73	C₂×C₄×C₁₉	#123	1	2	yes	—
74	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
75	C₂×C₄×C₁₉	#126	1	2	yes	—
76	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
77	C₂×C₄×C₁₉	#135	1	2	yes	—
78	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
79	C₂×C₄×C₁₉	#137	1	2	yes	—
80	C₂×C₄×C₁₉	#137	1	2	yes	—
81	C₂×Dic₁₉	—	8	2	no	—
82	C₂×Dic₁₉	—	8	2	no	—
83	C₂×Dic₁₉	—	8	2	no	—
84	C₈×C₁₉	—	4	2	no	—
85	C₈×C₁₉	—	8	1	no	—
86	C₁₉⋊C₈	—	8	2	no	—
87	#1984	D₁₉	1	1	yes	characteristic
88	#1834	—	19	1	no	—
89	#1803	—	19	2	no	—
90	#1296	—	19	2	no	—
91	#1277	—	19	1	no	—
92	C₂²×C₁₉	#397	1	1	yes	characteristic
93	C₂²×C₁₉	#464	1	2	yes	—
94	C₂²×C₁₉	#466	1	1	yes	characteristic
95	C₂²×C₁₉	#470	1	1	yes	characteristic
96	C₂²×C₁₉	#471	1	2	yes	—
97	C₄×C₁₉	—	2	2	no	—
98	C₄×C₁₉	—	4	2	no	—
99	C₄×C₁₉	—	8	1	no	—
100	C₄×C₁₉	#480	1	2	yes	—
101	C₄×C₁₉	#485	1	2	yes	—
102	C₄×C₁₉	#485	1	2	yes	—
103	C₄×C₁₉	#488	1	1	yes	characteristic
104	C₄×C₁₉	#491	1	1	yes	characteristic
105	Dic₁₉	—	16	2	no	—
106	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
107	C₂×C₄⋊C₈	—	19	2	no	—
108	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
109	C₂×#103	—	38	2	no	—
110	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
111	#384	—	19	2	no	—
112	#340	—	38	2	no	—
113	#340	—	38	2	no	—
114	#336	—	2	2	no	—
115	C₂×C₁₉	#1682	1	2	yes	—
116	C₂×C₁₉	#1704	1	2	yes	—
117	C₂×C₁₉	#2074	1	1	yes	characteristic
118	C₂×C₁₉	#2075	1	1	yes	characteristic
119	C₂×C₁₉	#2079	1	1	yes	characteristic
120	C₂²×Q₈	D₇₆	1	1	yes	characteristic
121	C₂²×C₈	—	2	1	no	—
122	C₂²×C₈	—	38	2	no	—
123	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
124	C₄×Q₈	—	2	2	no	—
125	C₄×Q₈	—	2	2	no	—
126	C₂×C₄⋊C₄	—	2	1	no	—
127	C₂×C₄⋊C₄	—	38	2	no	—
128	C₂×C₄⋊C₄	—	38	2	no	—
129	C₂×C₄⋊C₄	—	38	2	no	—
130	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
131	C₂×C₄²	—	2	1	no	—
132	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
133	C₄⋊C₈	—	2	2	no	—
134	C₄⋊C₈	—	38	2	no	—
135	C₄⋊C₈	—	38	2	no	—
136	#103	—	76	4	no	—
137	C₄×C₈	—	2	2	no	—
138	C₁₉	#10623	1	1	yes	characteristic, complemented, Sylow
139	C₂×Q₈	—	2	1	no	—
140	C₂×Q₈	—	2	2	no	—
141	C₂×Q₈	—	2	2	no	—
142	C₂×Q₈	D₁₅₂	1	2	yes	—
143	C₂²×C₄	—	2	1	no	—
144	C₂²×C₄	—	2	1	no	—
145	C₂²×C₄	—	76	2	no	—
146	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
147	C₂²×C₄	#64541	1	1	yes	characteristic
148	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
149	C₂×C₈	—	2	2	no	—
150	C₂×C₈	—	2	2	no	—
151	C₂×C₈	—	2	2	no	—
152	C₂×C₈	—	4	1	no	—
153	C₂×C₈	—	4	2	no	—
154	C₂×C₈	—	76	2	no	—
155	C₂×C₈	—	76	2	no	—
156	C₂×C₈	—	76	2	no	—
157	C₄⋊C₄	—	2	2	no	—
158	C₄⋊C₄	—	4	2	no	—
159	C₄⋊C₄	—	76	2	no	—
160	C₄⋊C₄	—	76	2	no	—
161	C₄⋊C₄	—	76	2	no	—
162	C₄⋊C₄	—	76	2	no	—
163	C₄⋊C₄	—	152	2	no	—
164	C₄²	—	4	1	no	—
165	C₄²	—	4	1	no	—
166	C₄²	#64543	1	2	yes	—
167	C₄²	#64543	1	2	yes	—
168	C₂³	#10597376	1	1	yes	characteristic
169	Q₈	—	2	4	no	—
170	Q₈	—	4	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	4	1	no	—
174	C₂×C₄	—	4	1	no	—
175	C₂×C₄	—	4	2	no	—
176	C₂×C₄	—	4	1	no	—
177	C₂×C₄	—	152	2	no	—
178	C₂×C₄	—	152	2	no	—
179	C₂×C₄	—	152	2	no	—
180	C₂×C₄	#10597325	1	2	yes	—
181	C₂×C₄	#10597332	1	2	yes	—
182	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
183	C₂×C₄	#10597350	1	1	yes	characteristic
184	C₂×C₄	#10597355	1	2	yes	—
185	C₂×C₄	#10597381	1	1	yes	characteristic
186	C₂×C₄	#10597382	1	1	yes	characteristic
187	C₂×C₄	#10597388	1	2	yes	—
188	C₂×C₄	#10597396	1	2	yes	—
189	C₈	—	4	2	no	—
190	C₈	—	8	1	no	—
191	C₈	—	152	2	no	—
192	C₂²	#11926469	1	1	yes	characteristic
193	C₂²	#11926766	1	2	yes	—
194	C₂²	#11926780	1	1	yes	characteristic
195	C₂²	#11926802	1	1	yes	characteristic
196	C₂²	#11926807	1	2	yes	—
197	C₄	—	2	2	no	—
198	C₄	—	4	2	no	—
199	C₄	—	8	1	no	—
200	C₄	—	304	2	no	—
201	C₄	#11926858	1	2	yes	—
202	C₄	#11926882	1	2	yes	—
203	C₄	#11926886	1	2	yes	—
204	C₄	#11926898	1	1	yes	characteristic
205	C₄	#11926912	1	1	yes	characteristic
206	C₂	#14563079	1	2	yes	—
207	C₂	#14563217	1	2	yes	—
208	C₂	#14565053	1	1	yes	characteristic
209	C₂	#14565058	1	1	yes	characteristic
210	C₂	#14565080	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563763

C₂

yes

maximal, characteristic

#14563640

C₂

yes

maximal

#14561519

C₂

yes

maximal

#14561470

C₂

yes

maximal, characteristic

C₁₉×#1984

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×#10597292

—

#11926414

C₂²

yes

—

#11926307

—

#11926306

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

—

#10597292

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

#126

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#135

yes

characteristic

C₂×C₄×C₁₉

#137

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1984

D₁₉

yes

—

—

—

—

C₂²×C₁₉

#397

yes

characteristic

C₂²×C₁₉

#464

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

100

C₄×C₁₉

#480

yes

—

101

C₄×C₁₉

#485

yes

—

102

C₄×C₁₉

#485

yes

—

103

C₄×C₁₉

#488

yes

characteristic

104

C₄×C₁₉

#491

yes

characteristic

105

Dic₁₉

—

106

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

107

C₂×C₄⋊C₈

—

108

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

109

C₂×#103

—

110

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

111

#384

—

112

#340

—

113

#340

—

114

#336

—

115

C₂×C₁₉

#1682

yes

—

116

C₂×C₁₉

#1704

yes

—

117

C₂×C₁₉

#2074

yes

characteristic

118

C₂×C₁₉

#2075

yes

characteristic

119

C₂×C₁₉

#2079

yes

characteristic

120

C₂²×Q₈

D₇₆

yes

characteristic

121

C₂²×C₈

—

122

C₂²×C₈

—

123

C₂²×C₈

C₂²⋊D₁₉

yes

—

124

C₄×Q₈

—

125

C₄×Q₈

—

126

C₂×C₄⋊C₄

—

127

C₂×C₄⋊C₄

—

128

C₂×C₄⋊C₄

—

129

C₂×C₄⋊C₄

—

130

C₂×C₄⋊C₄

D₇₆

yes

characteristic

131

C₂×C₄²

—

132

C₂×C₄²

C₂²×D₁₉

yes

characteristic

133

C₄⋊C₈

—

134

C₄⋊C₈

—

135

C₄⋊C₈

—

136

#103

—

137

C₄×C₈

—

138

C₁₉

#10623

yes

characteristic, complemented, Sylow

139

C₂×Q₈

—

140

C₂×Q₈

—

141

C₂×Q₈

—

142

C₂×Q₈

D₁₅₂

yes

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

C₂×D₇₆

yes

characteristic

147

C₂²×C₄

#64541

yes

characteristic

148

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄⋊C₄

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

152

—

164

C₄²

—

165

C₄²

—

166

C₄²

#64543

yes

—

167

C₄²

#64543

yes

—

168

C₂³

#10597376

yes

characteristic

169

Q₈

—

170

Q₈

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

152

—

178

C₂×C₄

—

152

—

179

C₂×C₄

—

152

—

180

C₂×C₄

#10597325

yes

—

181

C₂×C₄

#10597332

yes

—

182

C₂×C₄

C₂×D₁₅₂

yes

characteristic

183

C₂×C₄

#10597350

yes

characteristic

184

C₂×C₄

#10597355

yes

—

185

C₂×C₄

#10597381

yes

characteristic

186

C₂×C₄

#10597382

yes

characteristic

187

C₂×C₄

#10597388

yes

—

188

C₂×C₄

#10597396

yes

—

189

C₈

—

190

C₈

—

191

C₈

—

152

—

192

C₂²

#11926469

yes

characteristic

193

C₂²

#11926766

yes

—

194

C₂²

#11926780

yes

characteristic

195

C₂²

#11926802

yes

characteristic

196

C₂²

#11926807

yes

—

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

—

304

—

201

C₄

#11926858

yes

—

202

C₄

#11926882

yes

—

203

C₄

#11926886

yes

—

204

C₄

#11926898

yes

characteristic

205

C₄

#11926912

yes

characteristic

206

C₂

#14563079

yes

—

207

C₂

#14563217

yes

—

208

C₂

#14565053

yes

characteristic

209

C₂

#14565058

yes

characteristic

210

C₂

#14565080

yes

characteristic

	subgroup	G/H
center	C₂³	#10597376
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1984	C₂
socle, prime radical	C₂³×C₁₉	#121
hypercenter	#1984	D₁₉
hypocenter	C₁₉	#10623
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1984

subgroup

G/H

center

C₂³

#10597376

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1984

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1984

N	H ≅ G/N	type
138. C₁₉	#10623	semidirect

H ≅ G/N

type

138. C₁₉

#10623

semidirect

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

subgroup	index
#14563763	2
#14563640	2
#14561519	2
#14561470	2
C₁₉×#1984	2
#10623	19

subgroup

index

C₁₉×#1984

Subgroups — #18087283

Conjugacy classes of subgroups

Complements

Maximal subgroups