Group #14565161 — subgroups

Subgroups — #14565161

Order 2432.

290 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 89 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	C₂×#10597275	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597264	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597289	C₂	1	1	yes	maximal, characteristic
4	#11926447	C₂	1	1	yes	maximal, characteristic
5	#11926413	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926298	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#102	C₂	1	1	yes	maximal, characteristic
8	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
12	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	C₂×Dic₁₉⋊C₄	—	2	2	no	—
15	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₁₉×#102	—	2	2	no	—
18	#10597289	—	2	2	no	—
19	#10597275	—	2	2	no	—
20	#10597264	—	2	2	no	—
21	C₂⁴×C₁₉	—	2	1	no	—
22	C₂×D₄×C₁₉	—	2	1	no	—
23	C₂×D₄×C₁₉	—	2	1	no	—
24	C₂×D₄×C₁₉	—	2	1	no	—
25	C₂×D₄×C₁₉	—	2	1	no	—
26	C₂×D₄×C₁₉	—	2	1	no	—
27	C₂×D₄×C₁₉	Q₈	1	2	yes	—
28	C₂²×C₄×C₁₉	—	2	1	no	—
29	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂²×Dic₁₉	—	2	1	no	—
31	C₂²×Dic₁₉	—	2	1	no	—
32	C₂²×Dic₁₉	D₄	1	2	yes	—
33	C₂×C₈×C₁₉	—	2	1	no	—
34	C₂×C₈×C₁₉	—	2	1	no	—
35	C₂×C₈×C₁₉	D₄	1	2	yes	—
36	C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂²⋊Dic₁₉	—	4	4	no	—
39	C₄⋊Dic₁₉	—	2	1	no	—
40	C₄⋊Dic₁₉	—	2	1	no	—
41	C₄⋊Dic₁₉	—	2	1	no	—
42	C₄⋊Dic₁₉	—	2	1	no	—
43	Dic₁₉⋊C₄	—	4	4	no	—
44	C₄×Dic₁₉	—	2	1	no	—
45	C₄×Dic₁₉	—	2	1	no	—
46	C₂×C₁₉⋊C₈	—	2	1	no	—
47	C₂×C₁₉⋊C₈	—	2	1	no	—
48	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
49	C₂³×C₁₉	—	2	2	no	—
50	C₂³×C₁₉	—	4	1	no	—
51	C₂³×C₁₉	—	4	1	no	—
52	C₂³×C₁₉	—	4	2	no	—
53	C₂³×C₁₉	—	4	2	no	—
54	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
55	D₄×C₁₉	—	2	2	no	—
56	D₄×C₁₉	—	2	2	no	—
57	D₄×C₁₉	—	4	1	no	—
58	D₄×C₁₉	—	4	1	no	—
59	C₂×C₄×C₁₉	—	4	1	no	—
60	C₂×C₄×C₁₉	—	4	2	no	—
61	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
67	C₂×Dic₁₉	—	2	2	no	—
68	C₂×Dic₁₉	—	2	2	no	—
69	C₂×Dic₁₉	—	4	1	no	—
70	C₂×Dic₁₉	—	4	1	no	—
71	C₂×Dic₁₉	—	4	2	no	—
72	C₂×Dic₁₉	—	4	2	no	—
73	C₂×Dic₁₉	D₈	1	4	yes	—
74	C₈×C₁₉	—	2	2	no	—
75	C₁₉⋊C₈	—	2	2	no	—
76	#2093	—	19	1	no	maximal, Sylow
77	C₂²×C₁₉	—	4	2	no	—
78	C₂²×C₁₉	—	4	4	no	—
79	C₂²×C₁₉	—	8	2	no	—
80	C₂²×C₁₉	—	8	1	no	—
81	C₂²×C₁₉	—	8	1	no	—
82	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
83	C₂²×C₁₉	#123	1	1	yes	characteristic
84	C₂²×C₁₉	#127	1	1	yes	characteristic
85	C₂²×C₁₉	C₂×D₈	1	2	yes	—
86	C₂²×C₁₉	#137	1	2	yes	—
87	C₄×C₁₉	—	8	1	no	—
88	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
89	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
90	C₄×C₁₉	#123	1	1	yes	characteristic
91	C₄×C₁₉	#123	1	1	yes	characteristic
92	Dic₁₉	—	2	4	no	—
93	Dic₁₉	—	8	1	no	—
94	Dic₁₉	—	8	1	no	—
95	C₂×#107	—	19	1	no	—
96	C₂×#107	—	19	1	no	—
97	C₂×#102	—	19	1	no	—
98	C₂×#102	D₁₉	1	1	yes	characteristic
99	#390	—	19	1	no	—
100	#384	—	19	1	no	—
101	#336	—	19	1	no	—
102	C₂×C₁₉	—	8	2	no	—
103	C₂×C₁₉	#399	1	1	yes	characteristic
104	C₂×C₁₉	#474	1	2	yes	—
105	C₂×C₁₉	#480	1	2	yes	—
106	C₂×C₁₉	#493	1	1	yes	characteristic
107	C₂×C₁₉	#497	1	1	yes	characteristic
108	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
109	C₂²×C₈	—	19	1	no	—
110	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
111	C₂×C₄⋊C₄	—	19	1	no	—
112	C₂×C₄⋊C₄	—	19	1	no	—
113	C₂×C₄⋊C₄	—	38	2	no	—
114	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
115	C₂×C₂²⋊C₄	—	38	2	no	—
116	C₂×C₄²	—	19	1	no	—
117	#107	—	38	2	no	—
118	#107	—	38	2	no	—
119	#102	—	2	2	no	—
120	#102	—	38	2	no	—
121	C₁₉	#2093	1	1	yes	characteristic, complemented, Sylow
122	C₂⁴	—	2	1	no	—
123	C₂×D₄	—	2	1	no	—
124	C₂×D₄	—	2	1	no	—
125	C₂×D₄	—	2	1	no	—
126	C₂×D₄	—	2	1	no	—
127	C₂×D₄	—	2	1	no	—
128	C₂×D₄	Dic₃₈	1	2	yes	—
129	C₂²×C₄	—	2	1	no	—
130	C₂²×C₄	—	19	2	no	—
131	C₂²×C₄	—	38	1	no	—
132	C₂²×C₄	—	38	1	no	—
133	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
134	C₂×C₈	—	2	1	no	—
135	C₂×C₈	—	2	1	no	—
136	C₂×C₈	—	19	2	no	—
137	C₂×C₈	—	38	1	no	—
138	C₂×C₈	—	38	1	no	—
139	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
140	C₄⋊C₄	—	2	1	no	—
141	C₄⋊C₄	—	2	1	no	—
142	C₄⋊C₄	—	38	1	no	—
143	C₄⋊C₄	—	38	1	no	—
144	C₄⋊C₄	—	38	1	no	—
145	C₄⋊C₄	—	38	1	no	—
146	C₄⋊C₄	—	76	4	no	—
147	C₂²⋊C₄	—	76	4	no	—
148	C₄²	—	38	1	no	—
149	C₄²	—	38	1	no	—
150	C₂³	—	2	2	no	—
151	C₂³	—	4	1	no	—
152	C₂³	—	4	1	no	—
153	C₂³	—	4	2	no	—
154	C₂³	—	4	2	no	—
155	C₂³	D₄×D₁₉	1	1	yes	characteristic
156	D₄	—	2	2	no	—
157	D₄	—	2	2	no	—
158	D₄	—	4	1	no	—
159	D₄	—	4	1	no	—
160	C₂×C₄	—	4	1	no	—
161	C₂×C₄	—	4	2	no	—
162	C₂×C₄	—	19	4	no	—
163	C₂×C₄	—	38	2	no	—
164	C₂×C₄	—	38	2	no	—
165	C₂×C₄	—	76	1	no	—
166	C₂×C₄	—	76	1	no	—
167	C₂×C₄	—	76	2	no	—
168	C₂×C₄	—	76	2	no	—
169	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
170	C₂×C₄	#64541	1	1	yes	characteristic
171	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
172	C₂×C₄	#64543	1	1	yes	characteristic
173	C₂×C₄	#64543	1	1	yes	characteristic
174	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
175	C₈	—	2	2	no	—
176	C₈	—	38	2	no	—
177	C₂²	—	4	4	no	—
178	C₂²	—	4	2	no	—
179	C₂²	—	8	2	no	—
180	C₂²	—	8	1	no	—
181	C₂²	—	8	1	no	—
182	C₂²	#10597324	1	1	yes	characteristic
183	C₂²	#10597329	1	1	yes	characteristic
184	C₂²	D₈×D₁₉	1	2	yes	—
185	C₂²	#10597361	1	2	yes	—
186	C₂²	#10597386	1	1	yes	characteristic
187	C₄	—	8	1	no	—
188	C₄	—	38	4	no	—
189	C₄	—	152	1	no	—
190	C₄	—	152	1	no	—
191	C₄	#10597324	1	1	yes	characteristic
192	C₄	#10597329	1	1	yes	characteristic
193	C₄	#10597370	1	1	yes	characteristic
194	C₄	#10597381	1	1	yes	characteristic
195	C₂	—	8	2	no	—
196	C₂	#11926480	1	1	yes	characteristic
197	C₂	#11926822	1	2	yes	—
198	C₂	#11926856	1	2	yes	—
199	C₂	#11926919	1	1	yes	characteristic
200	C₂	#11926935	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597275

C₂

yes

maximal, characteristic, complemented

C₂×#10597264

C₂

yes

maximal, characteristic, complemented

C₂×#10597289

C₂

yes

maximal, characteristic

#11926447

C₂

yes

maximal, characteristic

#11926413

C₂

yes

maximal, characteristic, complemented

#11926298

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#102

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#102

—

#10597289

—

#10597275

—

#10597264

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

Q₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

D₈

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2093

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²⋊Q₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₂×D₈

yes

—

C₂²×C₁₉

#137

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

D₁₉

yes

characteristic

#390

—

100

#384

—

101

#336

—

102

C₂×C₁₉

—

103

C₂×C₁₉

#399

yes

characteristic

104

C₂×C₁₉

#474

yes

—

105

C₂×C₁₉

#480

yes

—

106

C₂×C₁₉

#493

yes

characteristic

107

C₂×C₁₉

#497

yes

characteristic

108

C₂²×D₄

C₂×D₁₉

yes

characteristic

109

C₂²×C₈

—

110

C₂²×C₈

C₂×D₁₉

yes

characteristic

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

115

C₂×C₂²⋊C₄

—

116

C₂×C₄²

—

117

#107

—

118

#107

—

119

#102

—

120

#102

—

121

C₁₉

#2093

yes

characteristic, complemented, Sylow

122

C₂⁴

—

123

C₂×D₄

—

124

C₂×D₄

—

125

C₂×D₄

—

126

C₂×D₄

—

127

C₂×D₄

—

128

C₂×D₄

Dic₃₈

yes

—

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

C₂²×D₁₉

yes

characteristic

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

C₂²⋊D₁₉

yes

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

147

C₂²⋊C₄

—

148

C₄²

—

149

C₄²

—

150

C₂³

—

151

C₂³

—

152

C₂³

—

153

C₂³

—

154

C₂³

—

155

C₂³

D₄×D₁₉

yes

characteristic

156

D₄

—

157

D₄

—

158

D₄

—

159

D₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

C₂×Dic₃₈

yes

characteristic

170

C₂×C₄

#64541

yes

characteristic

171

C₂×C₄

D₄×D₁₉

yes

characteristic

172

C₂×C₄

#64543

yes

characteristic

173

C₂×C₄

#64543

yes

characteristic

174

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

175

C₈

—

176

C₈

—

177

C₂²

—

178

C₂²

—

179

C₂²

—

180

C₂²

—

181

C₂²

—

182

C₂²

#10597324

yes

characteristic

183

C₂²

#10597329

yes

characteristic

184

C₂²

D₈×D₁₉

yes

—

185

C₂²

#10597361

yes

—

186

C₂²

#10597386

yes

characteristic

187

C₄

—

188

C₄

—

189

C₄

—

152

—

190

C₄

—

152

—

191

C₄

#10597324

yes

characteristic

192

C₄

#10597329

yes

characteristic

193

C₄

#10597370

yes

characteristic

194

C₄

#10597381

yes

characteristic

195

C₂

—

196

C₂

#11926480

yes

characteristic

197

C₂

#11926822

yes

—

198

C₂

#11926856

yes

—

199

C₂

#11926919

yes

characteristic

200

C₂

#11926935

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#102	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂²×D₄×C₁₉	C₂²
hypercenter	C₂×#102	D₁₉
hypocenter	C₁₉	#2093
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#102

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#102

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂²×D₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#102

N	H ≅ G/N	type
1. C₂×#10597275	C₂	semidirect
2. C₂×#10597264	C₂	semidirect
5. #11926413	C₂	semidirect
6. #11926298	C₂	semidirect
121. C₁₉	#2093	semidirect

H ≅ G/N

type

1. C₂×#10597275

C₂

semidirect

2. C₂×#10597264

C₂

semidirect

5. #11926413

C₂

semidirect

6. #11926298

C₂

semidirect

121. C₁₉

#2093

semidirect

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

subgroup	index
C₂×#10597275	2
C₂×#10597264	2
C₂×#10597289	2
#11926447	2
#11926413	2
#11926298	2
C₂×C₁₉×#102	2
#2093	19

subgroup

index

C₂×C₁₉×#102

Subgroups — #14565161

Conjugacy classes of subgroups

Complements

Maximal subgroups