Group #18076029 — subgroups

Subgroups — #18076029

Order 4864.

450 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 107 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	#14561969	C₂	1	2	yes	maximal
2	#14561491	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2296	C₂	1	1	yes	maximal, characteristic
4	#11926601	C₂²	1	4	yes	—
5	#11926270	—	2	2	no	—
6	#11926268	—	2	2	no	—
7	C₂×C₁₉×#117	C₄	1	1	yes	characteristic
8	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₁₉	C₄	1	1	yes	characteristic
10	C₁₉×#389	—	2	2	no	—
11	C₁₉×#385	—	2	2	no	—
12	C₄×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
13	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂³×C₄×C₁₉	—	2	1	no	—
15	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₁₉×#117	—	2	4	no	—
17	C₁₉×#117	—	4	2	no	—
18	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
20	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
21	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
22	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
23	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
24	C₂×C₄²×C₁₉	—	2	1	no	—
25	C₂×C₄²×C₁₉	—	4	2	no	—
26	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₁₉×#95	—	2	2	no	—
31	C₁₉×#95	—	2	2	no	—
32	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
33	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
34	#10597260	—	2	4	no	—
35	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	—	2	2	no	—
37	C₂²×C₄×C₁₉	—	2	2	no	—
38	C₂²×C₄×C₁₉	—	2	2	no	—
39	C₂²×C₄×C₁₉	—	2	2	no	—
40	C₂²×C₄×C₁₉	—	2	2	no	—
41	C₂²×C₄×C₁₉	—	4	4	no	—
42	C₂²×C₄×C₁₉	—	4	2	no	—
43	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
45	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
47	C₄⋊C₄×C₁₉	—	2	4	no	—
48	C₄⋊C₄×C₁₉	—	4	4	no	—
49	C₄⋊C₄×C₁₉	—	4	4	no	—
50	C₄⋊C₄×C₁₉	—	4	2	no	—
51	C₂²⋊C₄×C₁₉	—	2	4	no	—
52	C₂²⋊C₄×C₁₉	—	4	2	no	—
53	C₄²×C₁₉	—	2	2	no	—
54	C₄²×C₁₉	—	4	2	no	—
55	C₄²×C₁₉	—	4	2	no	—
56	C₄²×C₁₉	—	4	2	no	—
57	C₄²×C₁₉	#41	1	4	yes	—
58	C₂×C₁₉⋊C₈	—	4	4	no	—
59	#8743	—	19	1	no	maximal, Sylow
60	C₂³×C₁₉	—	2	1	no	—
61	C₂³×C₁₉	—	2	1	no	—
62	C₂³×C₁₉	—	4	2	no	—
63	C₂³×C₁₉	#101	1	2	yes	—
64	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₉	—	2	8	no	—
66	C₂×C₄×C₁₉	—	2	1	no	—
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	1	no	—
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	—	2	4	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	4	2	no	—
73	C₂×C₄×C₁₉	—	4	2	no	—
74	C₂×C₄×C₁₉	—	4	8	no	—
75	C₂×C₄×C₁₉	—	4	2	no	—
76	C₂×C₄×C₁₉	—	4	2	no	—
77	C₂×C₄×C₁₉	—	4	2	no	—
78	C₂×C₄×C₁₉	—	4	2	no	—
79	C₂×C₄×C₁₉	—	4	2	no	—
80	C₂×C₄×C₁₉	#100	1	2	yes	—
81	C₂×C₄×C₁₉	#117	1	2	yes	—
82	C₂×C₄×C₁₉	#123	1	4	yes	—
83	C₁₉⋊C₈	—	8	4	no	—
84	#2296	D₁₉	1	1	yes	characteristic
85	#1464	—	19	2	no	—
86	#1285	—	19	4	no	—
87	C₂²×C₁₉	—	2	2	no	—
88	C₂²×C₁₉	—	2	2	no	—
89	C₂²×C₁₉	—	4	2	no	—
90	C₂²×C₁₉	—	4	2	no	—
91	C₂²×C₁₉	—	4	2	no	—
92	C₂²×C₁₉	#381	1	1	yes	characteristic
93	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
94	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
95	C₄×C₁₉	—	2	2	no	—
96	C₄×C₁₉	—	2	2	no	—
97	C₄×C₁₉	—	2	4	no	—
98	C₄×C₁₉	—	4	4	no	—
99	C₄×C₁₉	—	4	2	no	—
100	C₄×C₁₉	—	8	2	no	—
101	C₂×#117	Dic₁₉	1	1	yes	characteristic
102	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
103	C₂²×C₄²	Dic₁₉	1	1	yes	characteristic
104	#432	—	19	4	no	—
105	#389	—	2	2	no	—
106	#385	—	2	2	no	—
107	C₄×C₄⋊C₄	Dic₁₉	1	2	yes	—
108	C₄×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
109	#324	—	38	2	no	—
110	#323	—	38	2	no	—
111	C₂×C₁₉	—	2	1	no	—
112	C₂×C₁₉	—	2	1	no	—
113	C₂×C₁₉	—	4	2	no	—
114	C₂×C₁₉	#1821	1	1	yes	characteristic
115	C₂×C₁₉	#1827	1	2	yes	—
116	C₂³×C₄	—	2	1	no	—
117	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
118	#117	—	2	4	no	—
119	#117	—	4	2	no	—
120	C₂×C₄⋊C₄	—	2	1	no	—
121	C₂×C₄⋊C₄	—	2	2	no	—
122	C₂×C₄⋊C₄	—	2	2	no	—
123	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
124	C₂×C₂²⋊C₄	—	2	1	no	—
125	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	2	yes	—
126	C₂×C₄²	—	2	1	no	—
127	C₂×C₄²	—	4	2	no	—
128	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
129	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
130	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
131	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
132	C₄⋊C₈	—	38	4	no	—
133	C₂²⋊C₈	—	38	4	no	—
134	#97	—	38	4	no	—
135	#95	—	2	2	no	—
136	#95	—	2	2	no	—
137	C₁₉	#8743	1	1	yes	characteristic, complemented, Sylow
138	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
139	C₂²×C₄	—	2	2	no	—
140	C₂²×C₄	—	2	2	no	—
141	C₂²×C₄	—	2	2	no	—
142	C₂²×C₄	—	2	2	no	—
143	C₂²×C₄	—	2	2	no	—
144	C₂²×C₄	—	4	4	no	—
145	C₂²×C₄	—	4	2	no	—
146	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
147	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
148	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
149	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
150	C₂×C₈	—	76	4	no	—
151	C₄⋊C₄	—	2	4	no	—
152	C₄⋊C₄	—	4	4	no	—
153	C₄⋊C₄	—	4	4	no	—
154	C₄⋊C₄	—	4	2	no	—
155	C₂²⋊C₄	—	2	4	no	—
156	C₂²⋊C₄	—	4	2	no	—
157	C₄²	—	2	2	no	—
158	C₄²	—	4	2	no	—
159	C₄²	—	4	2	no	—
160	C₄²	—	4	2	no	—
161	C₄²	#64541	1	4	yes	—
162	C₂³	—	2	1	no	—
163	C₂³	—	2	1	no	—
164	C₂³	—	4	2	no	—
165	C₂³	#10597293	1	2	yes	—
166	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
167	C₂×C₄	—	2	8	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	—	2	1	no	—
170	C₂×C₄	—	2	1	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	2	4	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	4	2	no	—
175	C₂×C₄	—	4	2	no	—
176	C₂×C₄	—	4	8	no	—
177	C₂×C₄	—	4	2	no	—
178	C₂×C₄	—	4	2	no	—
179	C₂×C₄	—	4	2	no	—
180	C₂×C₄	—	4	2	no	—
181	C₂×C₄	—	4	2	no	—
182	C₂×C₄	#10597290	1	2	yes	—
183	C₂×C₄	#10597372	1	2	yes	—
184	C₂×C₄	#10597375	1	4	yes	—
185	C₈	—	152	4	no	—
186	C₂²	—	2	2	no	—
187	C₂²	—	2	2	no	—
188	C₂²	—	4	2	no	—
189	C₂²	—	4	2	no	—
190	C₂²	—	4	2	no	—
191	C₂²	#11926407	1	1	yes	characteristic
192	C₂²	C₂×#10597290	1	1	yes	characteristic
193	C₂²	C₂×#10597293	1	1	yes	characteristic
194	C₄	—	2	2	no	—
195	C₄	—	2	2	no	—
196	C₄	—	2	4	no	—
197	C₄	—	4	4	no	—
198	C₄	—	4	2	no	—
199	C₄	—	8	2	no	—
200	C₂	—	2	1	no	—
201	C₂	—	2	1	no	—
202	C₂	—	4	2	no	—
203	C₂	#14563715	1	1	yes	characteristic
204	C₂	#14563739	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14561969

C₂

yes

maximal

#14561491

C₂

yes

maximal, complemented

C₁₉×#2296

C₂

yes

maximal, characteristic

#11926601

C₂²

yes

—

#11926270

—

#11926268

—

C₂×C₁₉×#117

C₄

yes

characteristic

C₂×C₁₉×#117

C₂²

yes

characteristic

C₂²×C₄²×C₁₉

C₄

yes

characteristic

C₁₉×#389

—

C₁₉×#385

—

C₄×C₄⋊C₄×C₁₉

C₄

yes

—

C₄×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#95

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

#8743

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#101

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

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×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#100

yes

—

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₁₉⋊C₈

—

#2296

D₁₉

yes

characteristic

#1464

—

#1285

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

100

C₄×C₁₉

—

101

C₂×#117

Dic₁₉

yes

characteristic

102

C₂×#117

C₂×D₁₉

yes

characteristic

103

C₂²×C₄²

Dic₁₉

yes

characteristic

104

#432

—

105

#389

—

106

#385

—

107

C₄×C₄⋊C₄

Dic₁₉

yes

—

108

C₄×C₄⋊C₄

C₂×D₁₉

yes

—

109

#324

—

110

#323

—

111

C₂×C₁₉

—

112

C₂×C₁₉

—

113

C₂×C₁₉

—

114

C₂×C₁₉

#1821

yes

characteristic

115

C₂×C₁₉

#1827

yes

—

116

C₂³×C₄

—

117

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

118

#117

—

119

#117

—

120

C₂×C₄⋊C₄

—

121

C₂×C₄⋊C₄

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

124

C₂×C₂²⋊C₄

—

125

C₂×C₂²⋊C₄

C₂²⋊D₁₉

yes

—

126

C₂×C₄²

—

127

C₂×C₄²

—

128

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

129

C₂×C₄²

C₂×Dic₁₉

yes

—

130

C₂×C₄²

C₂×Dic₁₉

yes

—

131

C₂×C₄²

C₂²×D₁₉

yes

characteristic

132

C₄⋊C₈

—

133

C₂²⋊C₈

—

134

#97

—

135

#95

—

136

#95

—

137

C₁₉

#8743

yes

characteristic, complemented, Sylow

138

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

147

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

148

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

149

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

150

C₂×C₈

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₂²⋊C₄

—

156

C₂²⋊C₄

—

157

C₄²

—

158

C₄²

—

159

C₄²

—

160

C₄²

—

161

C₄²

#64541

yes

—

162

C₂³

—

163

C₂³

—

164

C₂³

—

165

C₂³

#10597293

yes

—

166

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

#10597290

yes

—

183

C₂×C₄

#10597372

yes

—

184

C₂×C₄

#10597375

yes

—

185

C₈

—

152

—

186

C₂²

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

—

191

C₂²

#11926407

yes

characteristic

192

C₂²

C₂×#10597290

yes

characteristic

193

C₂²

C₂×#10597293

yes

characteristic

194

C₄

—

195

C₄

—

196

C₄

—

197

C₄

—

198

C₄

—

199

C₄

—

200

C₂

—

201

C₂

—

202

C₂

—

203

C₂

#14563715

yes

characteristic

204

C₂

#14563739

yes

—

	subgroup	G/H
center	C₂²	#11926407
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2296	C₂
socle	C₂²×C₁₉	#381
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2296	D₁₉
hypocenter	C₁₉	#8743
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2296

subgroup

G/H

center

C₂²

#11926407

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2296

C₂

socle

C₂²×C₁₉

#381

prime radical

C₂⁴×C₁₉

C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2296

N	H ≅ G/N	type
2. #14561491	C₂	semidirect
137. C₁₉	#8743	semidirect

H ≅ G/N

type

2. #14561491

C₂

semidirect

137. C₁₉

#8743

semidirect

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

subgroup	index
#14561969	2
#14561491	2
C₁₉×#2296	2
#8743	19

subgroup

index

#14561969

#14561491

C₁₉×#2296

#8743

Subgroups — #18076029

Conjugacy classes of subgroups

Complements

Maximal subgroups