Group #18076208 — subgroups

Subgroups — #18076208

Order 4864.

362 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 147 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	#14563786	C₂	1	2	yes	maximal
2	#14563380	C₂	1	1	yes	maximal, characteristic
3	#14561470	C₂	1	1	yes	maximal, characteristic
4	#14561469	C₂	1	2	yes	maximal
5	C₁₉×#1277	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×Dic₁₉⋊C₈	—	2	2	no	—
8	C₂×Dic₁₉⋊C₈	—	2	2	no	—
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
11	#11926298	C₄	1	2	yes	—
12	#11926298	C₄	1	2	yes	—
13	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	—	2	2	no	—
16	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
18	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
19	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
20	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
21	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
22	C₂²×C₁₉⋊C₈	—	2	2	no	—
23	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₁₉×C₄⋊C₈	—	2	2	no	—
26	C₁₉×C₄⋊C₈	—	2	2	no	—
27	C₄×C₈×C₁₉	—	2	2	no	—
28	Dic₁₉⋊C₈	—	4	4	no	—
29	Dic₁₉⋊C₈	—	4	4	no	—
30	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
31	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
32	C₄×C₁₉⋊C₈	—	2	2	no	—
33	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
36	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
37	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
38	C₂×C₈×C₁₉	—	2	2	no	—
39	C₂×C₈×C₁₉	—	2	2	no	—
40	C₂×C₈×C₁₉	—	2	2	no	—
41	C₂×C₈×C₁₉	—	4	2	no	—
42	C₂×C₈×C₁₉	—	4	2	no	—
43	C₂×C₈×C₁₉	—	4	2	no	—
44	C₄²×C₁₉	#41	1	2	yes	—
45	C₄²×C₁₉	#41	1	2	yes	—
46	C₄×Dic₁₉	—	2	2	no	—
47	C₄×Dic₁₉	—	2	2	no	—
48	C₄×Dic₁₉	—	4	2	no	—
49	C₄×Dic₁₉	D₈	1	2	yes	—
50	C₄×Dic₁₉	SD₁₆	1	4	yes	—
51	C₄×Dic₁₉	Q₁₆	1	2	yes	—
52	C₂×C₁₉⋊C₈	—	2	1	no	—
53	C₂×C₁₉⋊C₈	—	2	1	no	—
54	C₂×C₁₉⋊C₈	—	2	2	no	—
55	C₂×C₁₉⋊C₈	—	2	2	no	—
56	C₂×C₁₉⋊C₈	—	4	2	no	—
57	C₂×C₁₉⋊C₈	—	4	2	no	—
58	C₂×C₁₉⋊C₈	—	4	2	no	—
59	#8787	—	19	1	no	maximal, Sylow
60	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#124	1	2	yes	—
65	C₂×C₄×C₁₉	#125	1	2	yes	—
66	C₂×C₄×C₁₉	#131	1	2	yes	—
67	C₂×C₄×C₁₉	#131	1	2	yes	—
68	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
70	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
71	C₂×Dic₁₉	—	2	2	no	—
72	C₂×Dic₁₉	—	2	2	no	—
73	C₂×Dic₁₉	—	2	2	no	—
74	C₂×Dic₁₉	—	2	2	no	—
75	C₂×Dic₁₉	#106	1	4	yes	—
76	C₂×Dic₁₉	#107	1	4	yes	—
77	C₈×C₁₉	—	4	2	no	—
78	C₈×C₁₉	—	8	2	no	—
79	C₁₉⋊C₈	—	4	1	no	—
80	C₁₉⋊C₈	—	4	1	no	—
81	C₁₉⋊C₈	—	8	2	no	—
82	#1842	—	19	2	no	—
83	#1744	—	19	1	no	—
84	#1277	—	19	2	no	—
85	#1277	—	19	1	no	—
86	#1277	D₁₉	1	1	yes	characteristic
87	C₂²×C₁₉	#382	1	1	yes	characteristic
88	C₂²×C₁₉	#424	1	2	yes	—
89	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
90	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
91	C₂²×C₁₉	#430	1	2	yes	—
92	C₄×C₁₉	—	2	2	no	—
93	C₄×C₁₉	#433	1	2	yes	—
94	C₄×C₁₉	#433	1	1	yes	characteristic
95	C₄×C₁₉	#433	1	1	yes	characteristic
96	C₄×C₁₉	#486	1	2	yes	—
97	C₄×C₁₉	#487	1	2	yes	—
98	Dic₁₉	—	2	4	no	—
99	Dic₁₉	—	2	4	no	—
100	C₂×C₄⋊C₈	—	19	2	no	—
101	C₂×C₄⋊C₈	—	38	2	no	—
102	C₂×C₄⋊C₈	—	38	2	no	—
103	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
104	C₂×C₄×C₈	—	19	1	no	—
105	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
106	C₄³	—	19	1	no	—
107	#336	—	19	2	no	—
108	#336	—	19	2	no	—
109	C₂×C₁₉	#1570	1	2	yes	—
110	C₂×C₁₉	#1571	1	2	yes	—
111	C₂×C₁₉	#1832	1	1	yes	characteristic
112	C₂×C₁₉	#1834	1	1	yes	characteristic
113	C₂×C₁₉	#1838	1	1	yes	characteristic
114	C₂²×C₈	—	2	2	no	—
115	C₂²×C₈	—	19	1	no	—
116	C₂²×C₈	—	19	1	no	—
117	C₂²×C₈	—	38	2	no	—
118	C₂²×C₈	C₄×D₁₉	1	2	yes	—
119	C₂×C₄²	—	19	1	no	—
120	C₂×C₄²	—	19	1	no	—
121	C₂×C₄²	—	19	2	no	—
122	C₂×C₄²	—	19	2	no	—
123	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
124	C₄⋊C₈	—	2	2	no	—
125	C₄⋊C₈	—	2	2	no	—
126	C₄⋊C₈	—	38	2	no	—
127	C₄⋊C₈	—	38	2	no	—
128	C₄⋊C₈	—	76	4	no	—
129	C₄⋊C₈	—	76	4	no	—
130	C₄×C₈	—	2	2	no	—
131	C₄×C₈	—	38	2	no	—
132	C₁₉	#8787	1	1	yes	characteristic, complemented, Sylow
133	C₂²×C₄	—	19	2	no	—
134	C₂²×C₄	—	19	2	no	—
135	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
136	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
137	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
138	C₂×C₈	—	2	2	no	—
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	—	2	2	no	—
141	C₂×C₈	—	4	2	no	—
142	C₂×C₈	—	4	2	no	—
143	C₂×C₈	—	4	2	no	—
144	C₂×C₈	—	38	1	no	—
145	C₂×C₈	—	38	1	no	—
146	C₂×C₈	—	38	2	no	—
147	C₂×C₈	—	38	2	no	—
148	C₂×C₈	—	76	2	no	—
149	C₂×C₈	—	76	2	no	—
150	C₂×C₈	—	76	2	no	—
151	C₄²	—	19	2	no	—
152	C₄²	—	19	4	no	—
153	C₄²	—	19	2	no	—
154	C₄²	—	38	2	no	—
155	C₄²	—	38	2	no	—
156	C₄²	—	76	2	no	—
157	C₄²	#64541	1	2	yes	—
158	C₄²	#64543	1	2	yes	—
159	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	19	4	no	—
162	C₂×C₄	—	19	4	no	—
163	C₂×C₄	—	38	2	no	—
164	C₂×C₄	—	38	2	no	—
165	C₂×C₄	—	38	2	no	—
166	C₂×C₄	—	38	2	no	—
167	C₂×C₄	#10597318	1	1	yes	characteristic
168	C₂×C₄	#10597323	1	1	yes	characteristic
169	C₂×C₄	#10597331	1	2	yes	—
170	C₂×C₄	#10597335	1	2	yes	—
171	C₂×C₄	#10597347	1	2	yes	—
172	C₂×C₄	#10597353	1	2	yes	—
173	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
174	C₂×C₄	SD₁₆×D₁₉	1	2	yes	—
175	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
176	C₈	—	4	2	no	—
177	C₈	—	8	2	no	—
178	C₈	—	76	1	no	—
179	C₈	—	76	1	no	—
180	C₈	—	152	2	no	—
181	C₂²	#11926408	1	1	yes	characteristic
182	C₂²	#11926569	1	2	yes	—
183	C₂²	#106×D₁₉	1	1	yes	characteristic
184	C₂²	#107×D₁₉	1	1	yes	characteristic
185	C₂²	#11926591	1	2	yes	—
186	C₄	—	2	2	no	—
187	C₄	—	38	4	no	—
188	C₄	—	38	4	no	—
189	C₄	#11926602	1	2	yes	—
190	C₄	#11926603	1	1	yes	characteristic
191	C₄	#11926606	1	1	yes	characteristic
192	C₄	#11926889	1	2	yes	—
193	C₄	#11926893	1	2	yes	—
194	C₂	#14562404	1	2	yes	—
195	C₂	#14562408	1	2	yes	—
196	C₂	#14563753	1	1	yes	characteristic
197	C₂	#14563761	1	1	yes	characteristic
198	C₂	#14563774	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563786

C₂

yes

maximal

#14563380

C₂

yes

maximal, characteristic

#14561470

C₂

yes

maximal, characteristic

#14561469

C₂

yes

maximal

C₁₉×#1277

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×Dic₁₉⋊C₈

—

C₂×Dic₁₉⋊C₈

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₄²×Dic₁₉

C₂²

yes

characteristic

#11926298

C₄

yes

—

#11926298

C₄

yes

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

—

C₂×C₄×Dic₁₉

D₄

yes

characteristic

C₂×C₄×Dic₁₉

D₄

yes

characteristic

C₂×C₄×Dic₁₉

Q₈

yes

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

—

Dic₁₉⋊C₈

—

Dic₁₉⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×Dic₁₉

C₄⋊C₄

yes

—

C₂²×Dic₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₈

yes

—

C₄×Dic₁₉

SD₁₆

yes

—

C₄×Dic₁₉

Q₁₆

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8787

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#125

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

#106

yes

—

C₂×Dic₁₉

#107

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

—

—

—

D₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

#433

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₄×C₁₉

#487

yes

—

Dic₁₉

—

Dic₁₉

—

100

C₂×C₄⋊C₈

—

101

C₂×C₄⋊C₈

—

102

C₂×C₄⋊C₈

—

103

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

104

C₂×C₄×C₈

—

105

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

106

C₄³

—

107

#336

—

108

#336

—

109

C₂×C₁₉

#1570

yes

—

110

C₂×C₁₉

#1571

yes

—

111

C₂×C₁₉

#1832

yes

characteristic

112

C₂×C₁₉

#1834

yes

characteristic

113

C₂×C₁₉

#1838

yes

characteristic

114

C₂²×C₈

—

115

C₂²×C₈

—

116

C₂²×C₈

—

117

C₂²×C₈

—

118

C₂²×C₈

C₄×D₁₉

yes

—

119

C₂×C₄²

—

120

C₂×C₄²

—

121

C₂×C₄²

—

122

C₂×C₄²

—

123

C₂×C₄²

C₂²×D₁₉

yes

characteristic

124

C₄⋊C₈

—

125

C₄⋊C₈

—

126

C₄⋊C₈

—

127

C₄⋊C₈

—

128

C₄⋊C₈

—

129

C₄⋊C₈

—

130

C₄×C₈

—

131

C₄×C₈

—

132

C₁₉

#8787

yes

characteristic, complemented, Sylow

133

C₂²×C₄

—

134

C₂²×C₄

—

135

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

136

C₂²×C₄

D₄×D₁₉

yes

characteristic

137

C₂²×C₄

Q₈×D₁₉

yes

characteristic

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₄²

—

152

C₄²

—

153

C₄²

—

154

C₄²

—

155

C₄²

—

156

C₄²

—

157

C₄²

#64541

yes

—

158

C₄²

#64543

yes

—

159

C₂³

C₄⋊C₄×D₁₉

yes

characteristic

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

#10597318

yes

characteristic

168

C₂×C₄

#10597323

yes

characteristic

169

C₂×C₄

#10597331

yes

—

170

C₂×C₄

#10597335

yes

—

171

C₂×C₄

#10597347

yes

—

172

C₂×C₄

#10597353

yes

—

173

C₂×C₄

D₈×D₁₉

yes

characteristic

174

C₂×C₄

SD₁₆×D₁₉

yes

—

175

C₂×C₄

Q₁₆×D₁₉

yes

characteristic

176

C₈

—

177

C₈

—

178

C₈

—

179

C₈

—

180

C₈

—

152

—

181

C₂²

#11926408

yes

characteristic

182

C₂²

#11926569

yes

—

183

C₂²

#106×D₁₉

yes

characteristic

184

C₂²

#107×D₁₉

yes

characteristic

185

C₂²

#11926591

yes

—

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

#11926602

yes

—

190

C₄

#11926603

yes

characteristic

191

C₄

#11926606

yes

characteristic

192

C₄

#11926889

yes

—

193

C₄

#11926893

yes

—

194

C₂

#14562404

yes

—

195

C₂

#14562408

yes

—

196

C₂

#14563753

yes

characteristic

197

C₂

#14563761

yes

characteristic

198

C₂

#14563774

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1277	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1277	D₁₉
hypocenter	C₁₉	#8787
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

subgroup

G/H

center

C₂²×C₄

D₄×D₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1277

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

N	H ≅ G/N	type
132. C₁₉	#8787	semidirect

H ≅ G/N

type

132. C₁₉

#8787

semidirect

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

subgroup	index
#14563786	2
#14563380	2
#14561470	2
#14561469	2
C₁₉×#1277	2
#8787	19

subgroup

index

C₁₉×#1277

Subgroups — #18076208

Conjugacy classes of subgroups

Complements

Maximal subgroups