Group #14575090 — subgroups

Subgroups — #14575090

Order 2432.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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	#11927161	C₂	1	2	yes	maximal, complemented
2	#11926838	C₂	1	2	yes	maximal, complemented
3	#11926822	C₂	1	2	yes	maximal, complemented
4	#11926788	C₂	1	2	yes	maximal, complemented
5	#11926785	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926765	C₂	1	2	yes	maximal, complemented
7	#11926757	C₂	1	2	yes	maximal, complemented
8	#11926570	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#466	C₂	1	1	yes	maximal, characteristic
10	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#121	C₂²	1	2	yes	—
13	#10597382	—	2	2	no	—
14	#10597382	C₂²	1	2	yes	—
15	#10597381	—	2	2	no	—
16	D₄×Dic₁₉	C₂²	1	2	yes	—
17	C₂×#64526	C₂²	1	2	yes	—
18	#10597372	C₂²	1	1	yes	characteristic
19	#10597370	C₂²	1	2	yes	—
20	C₂×#64520	C₂²	1	1	yes	characteristic
21	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
22	#10597334	C₂²	1	2	yes	—
23	#10597333	C₂²	1	2	yes	—
24	#10597325	—	2	2	no	—
25	#10597324	—	2	2	no	—
26	C₁₉×#107	C₂²	1	1	yes	characteristic
27	C₁₉×#102	C₂²	1	2	yes	—
28	#10597289	C₂²	1	2	yes	—
29	#10597275	C₂²	1	1	yes	characteristic
30	#10597273	C₂²	1	2	yes	—
31	Dic₁₉⋊C₈	C₂²	1	2	yes	—
32	Dic₁₉⋊C₈	C₂²	1	2	yes	—
33	#10597267	C₂²	1	2	yes	—
34	#10597264	C₂²	1	2	yes	—
35	C₂×D₄×C₁₉	—	2	2	no	—
36	C₂×D₄×C₁₉	C₂³	1	2	yes	—
37	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²×Dic₁₉	—	2	2	no	—
39	C₂×Dic₃₈	—	2	2	no	—
40	C₂×Dic₃₈	C₂³	1	2	yes	—
41	D₈×C₁₉	—	4	1	no	—
42	C₂×C₈×C₁₉	—	4	1	no	—
43	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
46	C₂²⋊C₄×C₁₉	—	2	2	no	—
47	C₂²⋊Dic₁₉	—	2	2	no	—
48	C₂²⋊Dic₁₉	—	2	2	no	—
49	C₂²⋊Dic₁₉	—	2	2	no	—
50	C₂²⋊Dic₁₉	—	2	2	no	—
51	C₂²⋊Dic₁₉	D₄	1	2	yes	—
52	#64526	—	4	2	no	—
53	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
54	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
55	C₄⋊Dic₁₉	C₂³	1	2	yes	—
56	Dic₁₉⋊C₄	—	2	2	no	—
57	Dic₁₉⋊C₄	—	2	2	no	—
58	Dic₁₉⋊C₄	—	2	2	no	—
59	C₄×Dic₁₉	—	2	2	no	—
60	C₄×Dic₁₉	C₂³	1	2	yes	—
61	#64520	—	4	1	no	—
62	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
63	Dic₇₆	—	4	1	no	—
64	C₂³×C₁₉	—	2	2	no	—
65	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
66	D₄×C₁₉	—	2	2	no	—
67	D₄×C₁₉	—	2	2	no	—
68	D₄×C₁₉	—	8	2	no	—
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
74	C₂×Dic₁₉	—	2	2	no	—
75	C₂×Dic₁₉	—	2	2	no	—
76	C₂×Dic₁₉	—	8	2	no	—
77	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
78	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
79	Dic₃₈	—	2	2	no	—
80	Dic₃₈	—	2	2	no	—
81	Dic₃₈	—	8	2	no	—
82	C₈×C₁₉	—	2	1	no	—
83	C₈×C₁₉	—	2	1	no	—
84	C₁₉⋊C₈	—	2	2	no	—
85	#3262	—	19	1	no	maximal, Sylow
86	C₂²×C₁₉	—	2	1	no	—
87	C₂²×C₁₉	—	2	1	no	—
88	C₂²×C₁₉	—	2	1	no	—
89	C₂²×C₁₉	—	4	2	no	—
90	C₂²×C₁₉	—	4	2	no	—
91	C₂²×C₁₉	—	4	2	no	—
92	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
93	C₄×C₁₉	—	2	1	no	—
94	C₄×C₁₉	—	4	2	no	—
95	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
96	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
97	Dic₁₉	—	2	2	no	—
98	Dic₁₉	—	2	2	no	—
99	Dic₁₉	—	4	2	no	—
100	Dic₁₉	—	4	2	no	—
101	#542	—	19	2	no	—
102	#477	—	19	2	no	—
103	#474	—	19	2	no	—
104	#468	—	19	2	no	—
105	#467	—	19	1	no	—
106	#466	D₁₉	1	1	yes	characteristic
107	#464	—	19	2	no	—
108	#463	—	19	2	no	—
109	#424	—	19	1	no	—
110	C₂×C₁₉	—	4	1	no	—
111	C₂×C₁₉	—	8	2	no	—
112	C₂×C₁₉	#537	1	1	yes	characteristic
113	C₂×C₁₉	#576	1	1	yes	characteristic
114	C₂×C₁₉	#578	1	1	yes	characteristic
115	C₂×Q₁₆	—	19	1	no	—
116	C₂×SD₁₆	—	19	2	no	—
117	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
118	C₂×M₁₆	—	19	1	no	—
119	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
120	C₄⋊Q₈	—	19	2	no	—
121	#126	—	38	2	no	—
122	#124	—	19	2	no	—
123	#124	—	38	2	no	—
124	#123	—	38	2	no	—
125	C₂²⋊Q₈	—	19	2	no	—
126	C₂²⋊Q₈	—	38	2	no	—
127	#121	C₂×D₁₉	1	2	yes	—
128	C₄×Q₈	—	19	2	no	—
129	C₄×D₄	—	19	2	no	—
130	#117	—	19	1	no	—
131	#107	—	19	1	no	—
132	#107	—	19	2	no	—
133	#107	C₂×D₁₉	1	1	yes	characteristic
134	C₄⋊C₈	—	19	2	no	—
135	C₄⋊C₈	—	19	2	no	—
136	#103	—	19	2	no	—
137	#103	—	19	2	no	—
138	#102	—	19	2	no	—
139	#102	C₂×D₁₉	1	2	yes	—
140	C₁₉	#3262	1	1	yes	characteristic, complemented, Sylow
141	C₂×Q₈	—	19	2	no	—
142	C₂×Q₈	—	38	2	no	—
143	C₂×D₄	—	2	2	no	—
144	C₂×D₄	C₂²×D₁₉	1	2	yes	—
145	C₂²×C₄	—	38	2	no	—
146	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
147	Q₁₆	—	76	1	no	—
148	SD₁₆	—	76	2	no	—
149	D₈	—	4	1	no	—
150	M₁₆	—	76	1	no	—
151	C₂×C₈	—	4	1	no	—
152	C₂×C₈	—	19	2	no	—
153	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
154	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
155	C₄⋊C₄	—	19	1	no	—
156	C₄⋊C₄	—	19	1	no	—
157	C₄⋊C₄	—	19	2	no	—
158	C₄⋊C₄	—	38	2	no	—
159	C₄⋊C₄	—	38	2	no	—
160	C₄⋊C₄	—	38	2	no	—
161	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
162	C₂²⋊C₄	—	2	2	no	—
163	C₂²⋊C₄	—	19	2	no	—
164	C₂²⋊C₄	—	38	2	no	—
165	C₂²⋊C₄	—	38	2	no	—
166	C₂²⋊C₄	—	38	2	no	—
167	C₂²⋊C₄	—	38	2	no	—
168	C₄²	—	19	2	no	—
169	C₄²	—	38	2	no	—
170	C₂³	—	2	2	no	—
171	C₂³	D₄×D₁₉	1	1	yes	characteristic
172	Q₈	—	38	2	no	—
173	Q₈	—	38	2	no	—
174	Q₈	—	152	2	no	—
175	D₄	—	2	2	no	—
176	D₄	—	2	2	no	—
177	D₄	—	8	2	no	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	2	1	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	19	2	no	—
182	C₂×C₄	—	19	2	no	—
183	C₂×C₄	—	38	2	no	—
184	C₂×C₄	—	38	2	no	—
185	C₂×C₄	—	152	2	no	—
186	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
187	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
188	C₈	—	2	1	no	—
189	C₈	—	2	1	no	—
190	C₈	—	38	2	no	—
191	C₂²	—	2	1	no	—
192	C₂²	—	2	1	no	—
193	C₂²	—	2	1	no	—
194	C₂²	—	4	2	no	—
195	C₂²	—	4	2	no	—
196	C₂²	—	4	2	no	—
197	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
198	C₄	—	2	1	no	—
199	C₄	—	4	2	no	—
200	C₄	—	38	2	no	—
201	C₄	—	38	2	no	—
202	C₄	—	76	2	no	—
203	C₄	—	76	2	no	—
204	C₄	#10597430	1	1	yes	characteristic
205	C₄	#10597436	1	1	yes	characteristic
206	C₂	—	4	1	no	—
207	C₂	—	8	2	no	—
208	C₂	#11927121	1	1	yes	characteristic
209	C₂	#11927345	1	1	yes	characteristic
210	C₂	#11927358	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927161

C₂

yes

maximal, complemented

#11926838

C₂

yes

maximal, complemented

#11926822

C₂

yes

maximal, complemented

#11926788

C₂

yes

maximal, complemented

#11926785

C₂

yes

maximal, characteristic, complemented

#11926765

C₂

yes

maximal, complemented

#11926757

C₂

yes

maximal, complemented

#11926570

C₂

yes

maximal, characteristic, complemented

C₁₉×#466

C₂

yes

maximal, characteristic

C₂×D₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#121

C₂²

yes

—

#10597382

—

#10597382

C₂²

yes

—

#10597381

—

D₄×Dic₁₉

C₂²

yes

—

C₂×#64526

C₂²

yes

—

#10597372

C₂²

yes

characteristic

#10597370

C₂²

yes

—

C₂×#64520

C₂²

yes

characteristic

C₂×Dic₇₆

C₂²

yes

characteristic

#10597334

C₂²

yes

—

#10597333

C₂²

yes

—

#10597325

—

#10597324

—

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#102

C₂²

yes

—

#10597289

C₂²

yes

—

#10597275

C₂²

yes

characteristic

#10597273

C₂²

yes

—

Dic₁₉⋊C₈

C₂²

yes

—

Dic₁₉⋊C₈

C₂²

yes

—

#10597267

C₂²

yes

—

#10597264

C₂²

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂³

yes

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

C₂³

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

D₄

yes

—

#64526

—

C₄⋊Dic₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

C₂³

yes

—

#64520

—

C₂×C₁₉⋊C₈

C₂³

yes

—

Dic₇₆

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

C₂×D₄

yes

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#3262

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

H(5,𝔽₂)

yes

characteristic

C₄×C₁₉

2₋¹⁺⁴

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

100

Dic₁₉

—

101

#542

—

102

#477

—

103

#474

—

104

#468

—

105

#467

—

106

#466

D₁₉

yes

characteristic

107

#464

—

108

#463

—

109

#424

—

110

C₂×C₁₉

—

111

C₂×C₁₉

—

112

C₂×C₁₉

#537

yes

characteristic

113

C₂×C₁₉

#576

yes

characteristic

114

C₂×C₁₉

#578

yes

characteristic

115

C₂×Q₁₆

—

116

C₂×SD₁₆

—

117

C₂×D₈

C₂×D₁₉

yes

characteristic

118

C₂×M₁₆

—

119

C₂²×C₈

C₂×D₁₉

yes

characteristic

120

C₄⋊Q₈

—

121

#126

—

122

#124

—

123

#124

—

124

#123

—

125

C₂²⋊Q₈

—

126

C₂²⋊Q₈

—

127

#121

C₂×D₁₉

yes

—

128

C₄×Q₈

—

129

C₄×D₄

—

130

#117

—

131

#107

—

132

#107

—

133

#107

C₂×D₁₉

yes

characteristic

134

C₄⋊C₈

—

135

C₄⋊C₈

—

136

#103

—

137

#103

—

138

#102

—

139

#102

C₂×D₁₉

yes

—

140

C₁₉

#3262

yes

characteristic, complemented, Sylow

141

C₂×Q₈

—

142

C₂×Q₈

—

143

C₂×D₄

—

144

C₂×D₄

C₂²×D₁₉

yes

—

145

C₂²×C₄

—

146

C₂²×C₄

C₂²×D₁₉

yes

characteristic

147

Q₁₆

—

148

SD₁₆

—

149

D₈

—

150

M₁₆

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

C₂²×D₁₉

yes

characteristic

154

C₂×C₈

C₂²×D₁₉

yes

characteristic

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄⋊C₄

—

161

C₄⋊C₄

C₂²×D₁₉

yes

—

162

C₂²⋊C₄

—

163

C₂²⋊C₄

—

164

C₂²⋊C₄

—

165

C₂²⋊C₄

—

166

C₂²⋊C₄

—

167

C₂²⋊C₄

—

168

C₄²

—

169

C₄²

—

170

C₂³

—

171

C₂³

D₄×D₁₉

yes

characteristic

172

Q₈

—

173

Q₈

—

174

Q₈

—

152

—

175

D₄

—

176

D₄

—

177

D₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

152

—

186

C₂×C₄

D₄×D₁₉

yes

characteristic

187

C₂×C₄

C₂³×D₁₉

yes

characteristic

188

C₈

—

189

C₈

—

190

C₈

—

191

C₂²

—

192

C₂²

—

193

C₂²

—

194

C₂²

—

195

C₂²

—

196

C₂²

—

197

C₂²

C₂×D₄×D₁₉

yes

characteristic

198

C₄

—

199

C₄

—

200

C₄

—

201

C₄

—

202

C₄

—

203

C₄

—

204

C₄

#10597430

yes

characteristic

205

C₄

#10597436

yes

characteristic

206

C₂

—

207

C₂

—

208

C₂

#11927121

yes

characteristic

209

C₂

#11927345

yes

characteristic

210

C₂

#11927358

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting, prime radical	C₁₉×#466	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	#466	D₁₉
hypocenter	C₁₉	#3262
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #466

subgroup

G/H

center

C₂²

C₂×D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting, prime radical

C₁₉×#466

C₂

socle

C₂²×C₁₉

C₂²×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #466

N	H ≅ G/N	type
1. #11927161	C₂	semidirect
2. #11926838	C₂	semidirect
3. #11926822	C₂	semidirect
4. #11926788	C₂	semidirect
5. #11926785	C₂	semidirect
6. #11926765	C₂	semidirect
7. #11926757	C₂	semidirect
8. #11926570	C₂	semidirect
140. C₁₉	#3262	semidirect

H ≅ G/N

type

1. #11927161

C₂

semidirect

2. #11926838

C₂

semidirect

3. #11926822

C₂

semidirect

4. #11926788

C₂

semidirect

5. #11926785

C₂

semidirect

6. #11926765

C₂

semidirect

7. #11926757

C₂

semidirect

8. #11926570

C₂

semidirect

140. C₁₉

#3262

semidirect

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

subgroup	index
#11927161	2
#11926838	2
#11926822	2
#11926788	2
#11926785	2
#11926765	2
#11926757	2
#11926570	2
C₁₉×#466	2
#3262	19

subgroup

index

C₁₉×#466

Subgroups — #14575090

Conjugacy classes of subgroups

Complements

Maximal subgroups