Group #14564061 — subgroups

Subgroups — #14564061

Order 2432.

432 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 121 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	C₂³×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597376	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597266	C₂	1	2	yes	maximal, complemented
4	#11926306	C₂	1	2	yes	maximal, complemented
5	C₁₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₂²⋊D₁₉	—	2	1	no	—
8	C₂²×D₇₆	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
10	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
11	#10597376	—	2	2	no	—
12	#10597376	C₄	1	4	yes	complemented
13	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
14	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₁₉⋊C₈	—	2	2	no	—
16	C₂²×C₁₉⋊C₈	—	2	4	no	—
17	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
18	C₁₉×#95	—	2	1	no	—
19	#10597266	—	2	4	no	—
20	C₂⁴×C₁₉	D₄	1	1	yes	characteristic
21	C₂³×D₁₉	—	2	1	no	—
22	C₂²×C₄×C₁₉	—	2	2	no	—
23	C₂²×C₄×C₁₉	—	2	2	no	—
24	C₂²×C₄×C₁₉	—	2	2	no	—
25	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₁₉	D₄	1	2	yes	—
27	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₂²⋊D₁₉	—	2	4	no	—
30	C₂×C₂²⋊D₁₉	—	4	2	no	—
31	C₂×C₂²⋊D₁₉	—	4	2	no	—
32	C₂²×Dic₁₉	—	2	1	no	—
33	C₂×D₇₆	—	2	2	no	—
34	C₂×D₇₆	—	2	2	no	—
35	C₂×D₇₆	—	2	1	no	—
36	C₂×D₇₆	C₂×C₄	1	2	yes	—
37	C₄⋊C₄×C₁₉	—	2	2	no	—
38	C₄⋊C₄×C₁₉	—	2	2	no	—
39	C₂²⋊C₄×C₁₉	—	4	2	no	—
40	(C₂×D₁₉)⋊C₄	—	2	4	no	—
41	C₄⋊Dic₁₉	—	2	1	no	—
42	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
43	C₂×C₁₉⋊C₈	—	2	8	no	—
44	C₂×C₁₉⋊C₈	—	2	2	no	—
45	C₂×C₁₉⋊C₈	—	2	2	no	—
46	C₂×C₁₉⋊C₈	D₄	1	4	yes	complemented
47	C₂³×C₁₉	—	2	2	no	—
48	C₂³×C₁₉	—	2	2	no	—
49	C₂³×C₁₉	C₂²⋊C₄	1	2	yes	—
50	C₂³×C₁₉	D₈	1	2	yes	—
51	C₂³×C₁₉	SD₁₆	1	2	yes	—
52	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×D₁₉	—	2	2	no	—
54	C₂²×D₁₉	—	4	2	no	—
55	C₂²×D₁₉	—	4	1	no	—
56	C₂²×D₁₉	—	4	1	no	—
57	C₂²×D₁₉	—	4	2	no	—
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	—	2	4	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	—	4	2	no	—
63	C₂×C₄×C₁₉	—	4	2	no	—
64	C₂×C₄×C₁₉	—	4	2	no	—
65	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
66	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
69	C₂×C₄×C₁₉	#41	1	2	yes	—
70	C₂²⋊D₁₉	—	4	8	no	—
71	C₂×Dic₁₉	—	2	2	no	—
72	C₂×Dic₁₉	—	4	1	no	—
73	C₂×Dic₁₉	—	4	1	no	—
74	D₇₆	—	2	4	no	—
75	D₇₆	—	4	1	no	—
76	D₇₆	—	4	1	no	—
77	C₁₉⋊C₈	—	2	4	no	—
78	#1893	—	19	1	no	maximal, Sylow
79	C₂²×C₁₉	—	2	2	no	—
80	C₂²×C₁₉	—	2	2	no	—
81	C₂²×C₁₉	—	2	4	no	—
82	C₂²×C₁₉	—	2	4	no	—
83	C₂²×C₁₉	#102	1	4	yes	complemented
84	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₁₉	#121	1	2	yes	—
86	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
87	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
88	C₂²×C₁₉	#135	1	2	yes	—
89	C₂×D₁₉	—	4	2	no	—
90	C₂×D₁₉	—	4	2	no	—
91	C₂×D₁₉	—	4	2	no	—
92	C₂×D₁₉	—	8	2	no	—
93	C₂×D₁₉	—	8	2	no	—
94	C₄×C₁₉	—	2	2	no	—
95	C₄×C₁₉	—	8	2	no	—
96	C₄×C₁₉	C₄×D₄	1	2	yes	—
97	C₄×C₁₉	#120	1	1	yes	characteristic
98	C₄×C₁₉	#123	1	1	yes	characteristic
99	Dic₁₉	—	4	2	no	—
100	C₂³×C₈	—	19	1	no	—
101	C₂×#121	—	19	1	no	—
102	C₂×#102	—	19	2	no	—
103	#380	D₁₉	1	1	yes	characteristic, complemented
104	#340	—	19	2	no	—
105	C₂×C₁₉	—	2	4	no	—
106	C₂×C₁₉	#386	1	1	yes	characteristic
107	C₂×C₁₉	C₂×#102	1	1	yes	characteristic
108	C₂×C₁₉	#416	1	1	yes	characteristic
109	C₂×C₁₉	#465	1	2	yes	—
110	C₂×C₁₉	#466	1	2	yes	—
111	D₁₉	—	8	2	no	—
112	C₂²×D₄	—	19	1	no	—
113	C₂²×D₄	—	38	1	no	—
114	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
115	C₂²×C₈	—	19	2	no	—
116	C₂²×C₈	—	38	4	no	—
117	C₂²×C₈	—	38	2	no	—
118	#121	—	19	4	no	—
119	#121	—	38	2	no	—
120	C₂×C₄⋊C₄	—	19	1	no	—
121	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
122	C₂×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₂²⋊C₄	—	38	1	no	—
124	#102	—	38	4	no	—
125	#95	—	2	1	no	—
126	C₁₉	#1893	1	1	yes	characteristic, complemented, Sylow
127	C₂⁴	—	38	1	no	—
128	C₂⁴	C₂²⋊D₁₉	1	1	yes	characteristic
129	C₂×D₄	—	19	2	no	—
130	C₂×D₄	—	38	4	no	—
131	C₂×D₄	—	38	1	no	—
132	C₂×D₄	—	38	2	no	—
133	C₂×D₄	—	38	2	no	—
134	C₂×D₄	—	76	2	no	—
135	C₂×D₄	—	76	2	no	—
136	C₂²×C₄	—	2	2	no	—
137	C₂²×C₄	—	2	2	no	—
138	C₂²×C₄	—	2	2	no	—
139	C₂²×C₄	—	38	1	no	—
140	C₂²×C₄	C₄×D₁₉	1	2	yes	—
141	C₂²×C₄	D₇₆	1	2	yes	—
142	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
143	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
144	C₂×C₈	—	19	4	no	—
145	C₂×C₈	—	38	8	no	—
146	C₂×C₈	—	38	2	no	—
147	C₂×C₈	—	38	2	no	—
148	C₄⋊C₄	—	2	2	no	—
149	C₄⋊C₄	—	2	2	no	—
150	C₄⋊C₄	—	19	2	no	—
151	C₄⋊C₄	—	38	1	no	—
152	C₂²⋊C₄	—	4	2	no	—
153	C₂²⋊C₄	—	38	4	no	—
154	C₂³	—	2	2	no	—
155	C₂³	—	2	2	no	—
156	C₂³	—	38	2	no	—
157	C₂³	—	76	1	no	—
158	C₂³	—	76	2	no	—
159	C₂³	—	76	1	no	—
160	C₂³	—	76	2	no	—
161	C₂³	(C₂×D₁₉)⋊C₄	1	2	yes	—
162	C₂³	#64525	1	2	yes	—
163	C₂³	#64527	1	2	yes	—
164	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
165	D₄	—	38	4	no	—
166	D₄	—	76	8	no	—
167	D₄	—	76	1	no	—
168	D₄	—	76	1	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	4	2	no	—
174	C₂×C₄	—	4	2	no	—
175	C₂×C₄	—	4	2	no	—
176	C₂×C₄	—	38	2	no	—
177	C₂×C₄	—	76	1	no	—
178	C₂×C₄	—	76	1	no	—
179	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
180	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
181	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
182	C₂×C₄	D₄×D₁₉	1	2	yes	—
183	C₂×C₄	#64543	1	2	yes	—
184	C₈	—	38	4	no	—
185	C₂²	—	2	2	no	—
186	C₂²	—	2	2	no	—
187	C₂²	—	2	4	no	—
188	C₂²	—	2	4	no	—
189	C₂²	—	76	2	no	—
190	C₂²	—	76	2	no	—
191	C₂²	—	76	2	no	—
192	C₂²	—	152	2	no	—
193	C₂²	—	152	2	no	—
194	C₂²	#10597266	1	4	yes	complemented
195	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
196	C₂²	C₂×#64525	1	1	yes	characteristic
197	C₂²	#10597385	1	2	yes	—
198	C₂²	C₂×#64527	1	1	yes	characteristic
199	C₂²	#10597396	1	2	yes	—
200	C₄	—	2	2	no	—
201	C₄	—	8	2	no	—
202	C₄	—	76	2	no	—
203	C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
204	C₄	#10597328	1	1	yes	characteristic
205	C₄	#10597332	1	1	yes	characteristic
206	C₂	—	2	4	no	—
207	C₂	—	152	2	no	—
208	C₂	#11926421	1	1	yes	characteristic
209	C₂	C₂×#10597266	1	1	yes	characteristic
210	C₂	#11926538	1	1	yes	characteristic
211	C₂	#11926775	1	2	yes	—
212	C₂	#11926778	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×C₁₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₂×#10597376

C₂

yes

maximal, characteristic

C₂×#10597266

C₂

yes

maximal, complemented

#11926306

C₂

yes

maximal, complemented

C₁₉×#380

C₂

yes

maximal, characteristic, complemented

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂²×C₂²⋊D₁₉

—

C₂²×D₇₆

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

—

#10597376

—

#10597376

C₄

yes

complemented

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₁₉×#95

—

#10597266

—

C₂⁴×C₁₉

D₄

yes

characteristic

C₂³×D₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×C₂²⋊D₁₉

—

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂×C₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

complemented

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₄

yes

—

C₂³×C₁₉

D₈

yes

—

C₂³×C₁₉

SD₁₆

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

C₁₉⋊C₈

—

#1893

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#102

yes

complemented

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

#121

yes

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₂²×C₁₉

#135

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

100

C₂³×C₈

—

101

C₂×#121

—

102

C₂×#102

—

103

#380

D₁₉

yes

characteristic, complemented

104

#340

—

105

C₂×C₁₉

—

106

C₂×C₁₉

#386

yes

characteristic

107

C₂×C₁₉

C₂×#102

yes

characteristic

108

C₂×C₁₉

#416

yes

characteristic

109

C₂×C₁₉

#465

yes

—

110

C₂×C₁₉

#466

yes

—

111

D₁₉

—

112

C₂²×D₄

—

113

C₂²×D₄

—

114

C₂³×C₄

C₂×D₁₉

yes

characteristic

115

C₂²×C₈

—

116

C₂²×C₈

—

117

C₂²×C₈

—

118

#121

—

119

#121

—

120

C₂×C₄⋊C₄

—

121

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

122

C₂×C₂²⋊C₄

—

123

C₂×C₂²⋊C₄

—

124

#102

—

125

#95

—

126

C₁₉

#1893

yes

characteristic, complemented, Sylow

127

C₂⁴

—

128

C₂⁴

C₂²⋊D₁₉

yes

characteristic

129

C₂×D₄

—

130

C₂×D₄

—

131

C₂×D₄

—

132

C₂×D₄

—

133

C₂×D₄

—

134

C₂×D₄

—

135

C₂×D₄

—

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

C₄×D₁₉

yes

—

141

C₂²×C₄

D₇₆

yes

—

142

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

143

C₂²×C₄

C₂²×D₁₉

yes

characteristic

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₂²⋊C₄

—

153

C₂²⋊C₄

—

154

C₂³

—

155

C₂³

—

156

C₂³

—

157

C₂³

—

158

C₂³

—

159

C₂³

—

160

C₂³

—

161

C₂³

(C₂×D₁₉)⋊C₄

yes

—

162

C₂³

#64525

yes

—

163

C₂³

#64527

yes

—

164

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

165

D₄

—

166

D₄

—

167

D₄

—

168

D₄

—

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

(C₂×D₁₉)⋊C₄

yes

—

180

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

181

C₂×C₄

C₂×D₇₆

yes

characteristic

182

C₂×C₄

D₄×D₁₉

yes

—

183

C₂×C₄

#64543

yes

—

184

C₈

—

185

C₂²

—

186

C₂²

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

—

191

C₂²

—

192

C₂²

—

152

—

193

C₂²

—

152

—

194

C₂²

#10597266

yes

complemented

195

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

196

C₂²

C₂×#64525

yes

characteristic

197

C₂²

#10597385

yes

—

198

C₂²

C₂×#64527

yes

characteristic

199

C₂²

#10597396

yes

—

200

C₄

—

201

C₄

—

202

C₄

—

203

C₄

(C₂²⋊D₁₉)⋊C₄

yes

—

204

C₄

#10597328

yes

characteristic

205

C₄

#10597332

yes

characteristic

206

C₂

—

207

C₂

—

152

—

208

C₂

#11926421

yes

characteristic

209

C₂

C₂×#10597266

yes

characteristic

210

C₂

#11926538

yes

characteristic

211

C₂

#11926775

yes

—

212

C₂

#11926778

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#380	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂×#10597376	C₂
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#380	D₁₉
hypocenter	C₁₉	#1893
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ #380

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#380

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂×#10597376

C₂

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ #380

N	H ≅ G/N	type
1. C₂³×C₁₉⋊C₈	C₂	semidirect
3. C₂×#10597266	C₂	semidirect
4. #11926306	C₂	semidirect
5. C₁₉×#380	C₂	semidirect
12. #10597376	C₄	semidirect
46. C₂×C₁₉⋊C₈	D₄	semidirect
83. C₂²×C₁₉	#102	semidirect
103. #380	D₁₉	semidirect
126. C₁₉	#1893	semidirect
194. C₂²	#10597266	semidirect

H ≅ G/N

type

1. C₂³×C₁₉⋊C₈

C₂

semidirect

3. C₂×#10597266

C₂

semidirect

4. #11926306

C₂

semidirect

5. C₁₉×#380

C₂

semidirect

12. #10597376

C₄

semidirect

46. C₂×C₁₉⋊C₈

D₄

semidirect

83. C₂²×C₁₉

#102

semidirect

103. #380

D₁₉

semidirect

126. C₁₉

#1893

semidirect

194. C₂²

#10597266

semidirect

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

subgroup	index
C₂³×C₁₉⋊C₈	2
C₂×#10597376	2
C₂×#10597266	2
#11926306	2
C₁₉×#380	2
#1893	19

subgroup

index

C₂³×C₁₉⋊C₈

C₁₉×#380

Subgroups — #14564061

Conjugacy classes of subgroups

Complements

Maximal subgroups