Group #14564025 — subgroups

Subgroups — #14564025

Order 2432.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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×#10597390	C₂	1	1	yes	maximal, characteristic
2	#11927021	C₂	1	1	yes	maximal, characteristic
3	#11926553	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597281	C₂	1	1	yes	maximal, characteristic
5	#11926305	C₂	1	1	yes	maximal, characteristic
6	#11926303	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#419	C₂	1	1	yes	maximal, characteristic
8	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
10	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#117	C₂²	1	1	yes	characteristic
12	#10597390	—	2	2	no	—
13	#10597390	C₄	1	4	yes	complemented
14	#10597372	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₉⋊C₄	—	2	2	no	—
16	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
17	C₂×#64520	C₂²	1	1	yes	characteristic
18	#10597333	—	2	2	no	—
19	#10597323	—	2	2	no	—
20	C₄×Dic₃₈	—	2	2	no	—
21	C₁₉×#103	—	2	2	no	—
22	#10597292	—	2	2	no	—
23	#10597281	—	2	2	no	—
24	C₂×Q₈×C₁₉	—	2	1	no	—
25	C₂×Q₈×C₁₉	—	2	1	no	—
26	C₂×Q₈×C₁₉	—	2	1	no	—
27	C₂×Q₈×C₁₉	—	2	1	no	—
28	C₂×Q₈×C₁₉	—	2	1	no	—
29	C₂×Q₈×C₁₉	C₂×C₄	1	2	yes	—
30	C₂²×C₄×C₁₉	—	2	1	no	—
31	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×Dic₁₉	—	2	1	no	—
33	C₂²×Dic₁₉	D₄	1	2	yes	—
34	C₂×Dic₃₈	—	2	1	no	—
35	C₂×Dic₃₈	—	2	1	no	—
36	C₂×Dic₃₈	—	2	1	no	—
37	C₂×Dic₃₈	—	2	1	no	—
38	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
39	C₂×Dic₃₈	D₄	1	2	yes	—
40	M₁₆×C₁₉	—	2	1	no	—
41	M₁₆×C₁₉	—	2	1	no	—
42	C₂×C₈×C₁₉	—	2	1	no	—
43	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
44	C₂²⋊C₄×C₁₉	—	2	1	no	—
45	C₄²×C₁₉	—	2	1	no	—
46	C₂²⋊Dic₁₉	—	2	1	no	—
47	C₄⋊Dic₁₉	D₄	1	2	yes	—
48	Dic₁₉⋊C₄	—	2	4	no	—
49	Dic₁₉⋊C₄	—	2	8	no	—
50	C₄×Dic₁₉	—	2	4	no	—
51	C₄×Dic₁₉	—	2	1	no	—
52	C₄×Dic₁₉	—	2	1	no	—
53	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
54	#64520	—	2	1	no	—
55	#64520	—	2	1	no	—
56	C₂×C₁₉⋊C₈	—	2	1	no	—
57	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
58	Q₈×C₁₉	—	2	2	no	—
59	Q₈×C₁₉	—	2	2	no	—
60	Q₈×C₁₉	—	4	1	no	—
61	Q₈×C₁₉	—	4	1	no	—
62	C₂×C₄×C₁₉	—	2	2	no	—
63	C₂×C₄×C₁₉	—	2	2	no	—
64	C₂×C₄×C₁₉	—	4	1	no	—
65	C₂×C₄×C₁₉	—	4	1	no	—
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	1	yes	characteristic
69	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
71	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
72	C₂×Dic₁₉	—	2	4	no	—
73	C₂×Dic₁₉	—	2	2	no	—
74	C₂×Dic₁₉	—	2	2	no	—
75	C₂×Dic₁₉	—	2	2	no	—
76	C₂×Dic₁₉	—	2	2	no	—
77	C₂×Dic₁₉	C₂²⋊C₄	1	4	yes	—
78	Dic₃₈	—	2	2	no	—
79	Dic₃₈	—	2	2	no	—
80	Dic₃₈	—	2	2	no	—
81	Dic₃₈	—	2	2	no	—
82	C₈×C₁₉	—	4	1	no	—
83	C₁₉⋊C₈	—	4	1	no	—
84	#1886	—	19	1	no	maximal, Sylow
85	C₂²×C₁₉	—	2	2	no	—
86	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₁₉	#120	1	1	yes	characteristic
88	C₂²×C₁₉	#123	1	1	yes	characteristic
89	C₄×C₁₉	—	4	2	no	—
90	C₄×C₁₉	—	4	2	no	—
91	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
92	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
93	C₄×C₁₉	#121	1	1	yes	characteristic
94	C₄×C₁₉	#121	1	1	yes	characteristic
95	Dic₁₉	—	2	4	no	—
96	Dic₁₉	—	2	4	no	—
97	Dic₁₉	—	4	2	no	—
98	C₂×C₄⋊Q₈	—	19	1	no	—
99	#519	—	19	1	no	—
100	#419	—	19	1	no	—
101	#419	D₁₉	1	1	yes	characteristic
102	C₂×#101	—	19	1	no	—
103	#339	—	19	1	no	—
104	#339	—	19	1	no	—
105	C₂×C₁₉	—	2	1	no	—
106	C₂×C₁₉	—	2	1	no	—
107	C₂×C₁₉	#386	1	1	yes	characteristic
108	C₂×C₁₉	#456	1	2	yes	—
109	C₂²×Q₈	—	19	1	no	—
110	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
111	C₂×M₁₆	—	19	1	no	—
112	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
113	C₄⋊Q₈	—	19	4	no	—
114	C₄⋊Q₈	—	38	2	no	—
115	C₄×Q₈	—	38	2	no	—
116	C₄×Q₈	—	38	2	no	—
117	#117	—	19	1	no	—
118	#117	—	38	2	no	—
119	#117	C₂×D₁₉	1	1	yes	characteristic
120	C₂×C₄⋊C₄	—	38	2	no	—
121	C₂×C₄²	—	19	1	no	—
122	#103	—	2	2	no	—
123	#103	—	38	2	no	—
124	#101	—	38	2	no	—
125	C₁₉	#1886	1	1	yes	characteristic, complemented, Sylow
126	C₂×Q₈	—	2	1	no	—
127	C₂×Q₈	—	2	1	no	—
128	C₂×Q₈	—	2	1	no	—
129	C₂×Q₈	—	2	1	no	—
130	C₂×Q₈	—	2	1	no	—
131	C₂×Q₈	—	19	2	no	—
132	C₂×Q₈	—	19	2	no	—
133	C₂×Q₈	—	38	1	no	—
134	C₂×Q₈	—	38	1	no	—
135	C₂×Q₈	—	38	1	no	—
136	C₂×Q₈	—	38	1	no	—
137	C₂×Q₈	C₄×D₁₉	1	2	yes	—
138	C₂²×C₄	—	2	1	no	—
139	C₂²×C₄	—	19	2	no	—
140	C₂²×C₄	—	38	1	no	—
141	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
142	M₁₆	—	2	1	no	—
143	M₁₆	—	2	1	no	—
144	M₁₆	—	38	1	no	—
145	M₁₆	—	38	1	no	—
146	C₂×C₈	—	2	1	no	—
147	C₂×C₈	—	38	1	no	—
148	C₄⋊C₄	—	19	2	no	—
149	C₄⋊C₄	—	38	8	no	—
150	C₄⋊C₄	—	38	4	no	—
151	C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
152	C₂²⋊C₄	—	2	1	no	—
153	C₂²⋊C₄	—	38	1	no	—
154	C₄²	—	2	1	no	—
155	C₄²	—	19	2	no	—
156	C₄²	—	38	4	no	—
157	C₄²	—	38	1	no	—
158	C₄²	—	38	1	no	—
159	C₂³	D₄×D₁₉	1	1	yes	characteristic
160	Q₈	—	2	2	no	—
161	Q₈	—	2	2	no	—
162	Q₈	—	4	1	no	—
163	Q₈	—	4	1	no	—
164	Q₈	—	38	2	no	—
165	Q₈	—	38	2	no	—
166	Q₈	—	38	2	no	—
167	Q₈	—	38	2	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	4	1	no	—
171	C₂×C₄	—	4	1	no	—
172	C₂×C₄	—	19	4	no	—
173	C₂×C₄	—	38	4	no	—
174	C₂×C₄	—	38	2	no	—
175	C₂×C₄	—	38	2	no	—
176	C₂×C₄	—	38	2	no	—
177	C₂×C₄	—	38	2	no	—
178	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
179	C₂×C₄	#64541	1	1	yes	characteristic
180	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
181	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
182	C₂×C₄	#64543	1	1	yes	characteristic
183	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
184	C₈	—	4	1	no	—
185	C₈	—	76	1	no	—
186	C₂²	—	2	2	no	—
187	C₂²	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
188	C₂²	#10597329	1	1	yes	characteristic
189	C₂²	#10597383	1	1	yes	characteristic
190	C₄	—	4	2	no	—
191	C₄	—	4	2	no	—
192	C₄	—	38	4	no	—
193	C₄	—	38	4	no	—
194	C₄	—	76	2	no	—
195	C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
196	C₄	#10597330	1	1	yes	characteristic
197	C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
198	C₄	#10597384	1	1	yes	characteristic
199	C₂	—	2	1	no	—
200	C₂	—	2	1	no	—
201	C₂	#11926420	1	1	yes	characteristic
202	C₂	#11926725	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597390

C₂

yes

maximal, characteristic

#11927021

C₂

yes

maximal, characteristic

#11926553

C₂

yes

maximal, characteristic

C₂×#10597281

C₂

yes

maximal, characteristic

#11926305

C₂

yes

maximal, characteristic

#11926303

C₂

yes

maximal, characteristic

C₁₉×#419

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

#10597390

—

#10597390

C₄

yes

complemented

#10597372

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

#10597333

—

#10597323

—

C₄×Dic₃₈

—

C₁₉×#103

—

#10597292

—

#10597281

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂×C₄

yes

—

C₂×Dic₃₈

D₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

C₂×C₄

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂²⋊C₄

yes

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1886

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

—

#519

—

100

#419

—

101

#419

D₁₉

yes

characteristic

102

C₂×#101

—

103

#339

—

104

#339

—

105

C₂×C₁₉

—

106

C₂×C₁₉

—

107

C₂×C₁₉

#386

yes

characteristic

108

C₂×C₁₉

#456

yes

—

109

C₂²×Q₈

—

110

C₂²×Q₈

C₂×D₁₉

yes

characteristic

111

C₂×M₁₆

—

112

C₂×M₁₆

C₂×D₁₉

yes

characteristic

113

C₄⋊Q₈

—

114

C₄⋊Q₈

—

115

C₄×Q₈

—

116

C₄×Q₈

—

117

#117

—

118

#117

—

119

#117

C₂×D₁₉

yes

characteristic

120

C₂×C₄⋊C₄

—

121

C₂×C₄²

—

122

#103

—

123

#103

—

124

#101

—

125

C₁₉

#1886

yes

characteristic, complemented, Sylow

126

C₂×Q₈

—

127

C₂×Q₈

—

128

C₂×Q₈

—

129

C₂×Q₈

—

130

C₂×Q₈

—

131

C₂×Q₈

—

132

C₂×Q₈

—

133

C₂×Q₈

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂×Q₈

—

137

C₂×Q₈

C₄×D₁₉

yes

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

C₂²×D₁₉

yes

characteristic

142

M₁₆

—

143

M₁₆

—

144

M₁₆

—

145

M₁₆

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₄⋊C₄

C₂²⋊D₁₉

yes

—

152

C₂²⋊C₄

—

153

C₂²⋊C₄

—

154

C₄²

—

155

C₄²

—

156

C₄²

—

157

C₄²

—

158

C₄²

—

159

C₂³

D₄×D₁₉

yes

characteristic

160

Q₈

—

161

Q₈

—

162

Q₈

—

163

Q₈

—

164

Q₈

—

165

Q₈

—

166

Q₈

—

167

Q₈

—

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

C₂×C₄×D₁₉

yes

characteristic

179

C₂×C₄

#64541

yes

characteristic

180

C₂×C₄

D₄×D₁₉

yes

characteristic

181

C₂×C₄

D₄×D₁₉

yes

characteristic

182

C₂×C₄

#64543

yes

characteristic

183

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

184

C₈

—

185

C₈

—

186

C₂²

—

187

C₂²

C₂²⋊C₄×D₁₉

yes

characteristic

188

C₂²

#10597329

yes

characteristic

189

C₂²

#10597383

yes

characteristic

190

C₄

—

191

C₄

—

192

C₄

—

193

C₄

—

194

C₄

—

195

C₄

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

196

C₄

#10597330

yes

characteristic

197

C₄

C₄×C₂²⋊D₁₉

yes

characteristic

198

C₄

#10597384

yes

characteristic

199

C₂

—

200

C₂

—

201

C₂

#11926420

yes

characteristic

202

C₂

#11926725

yes

—

	subgroup	G/H
center	C₂²	#10597383
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#419	C₂
socle	C₂²×C₁₉	#120
prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#419	D₁₉
hypocenter	C₁₉	#1886
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #419

subgroup

G/H

center

C₂²

#10597383

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#419

C₂

socle

C₂²×C₁₉

#120

prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #419

N	H ≅ G/N	type
13. #10597390	C₄	semidirect
125. C₁₉	#1886	semidirect

H ≅ G/N

type

13. #10597390

C₄

semidirect

125. C₁₉

#1886

semidirect

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

subgroup	index
C₂×#10597390	2
#11927021	2
#11926553	2
C₂×#10597281	2
#11926305	2
#11926303	2
C₁₉×#419	2
#1886	19

subgroup

index

C₁₉×#419

Subgroups — #14564025

Conjugacy classes of subgroups

Complements

Maximal subgroups