Group #14574775 — subgroups

Subgroups — #14574775

Order 2432.

360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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	#11927099	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic
3	#11926942	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926940	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926894	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926873	C₂	1	4	yes	maximal
7	#11926827	C₂	1	4	yes	maximal, complemented
8	#11926595	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#487	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×Q₈×D₁₉	—	2	1	no	—
11	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	#10597392	C₂²	1	2	yes	—
14	Q₈×Dic₁₉	C₂²	1	2	yes	—
15	#10597390	—	2	1	no	—
16	#10597343	—	2	1	no	—
17	#10597338	—	2	1	no	—
18	C₄⋊C₄×D₁₉	—	2	1	no	—
19	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
20	#10597336	—	2	1	no	—
21	#10597334	—	2	1	no	—
22	#10597334	C₂²	1	2	yes	—
23	#10597333	—	2	1	no	—
24	C₄²×D₁₉	C₂²	1	1	yes	characteristic
25	#10597315	C₂²	1	1	yes	characteristic
26	#10597315	C₂²	1	1	yes	characteristic
27	C₁₉×#103	C₂²	1	4	yes	—
28	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
29	#10597292	C₂²	1	4	yes	—
30	(C₂×D₁₉)⋊C₈	C₂²	1	2	yes	—
31	#10597274	C₂²	1	4	yes	—
32	Dic₁₉⋊C₈	C₂²	1	2	yes	—
33	#10597265	C₂²	1	4	yes	—
34	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×Q₈×C₁₉	—	2	1	no	—
36	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
37	Q₈×D₁₉	—	4	4	no	—
38	C₂×C₄×D₁₉	—	2	2	no	—
39	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
42	C₂×Dic₃₈	—	2	1	no	—
43	C₂×Dic₃₈	—	2	1	no	—
44	C₂×Dic₃₈	—	2	2	no	—
45	C₂×C₈×C₁₉	C₂³	1	2	yes	—
46	C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
50	C₄²×C₁₉	C₂³	1	1	yes	characteristic
51	(C₂×D₁₉)⋊C₄	—	2	2	no	—
52	C₄⋊Dic₁₉	—	2	1	no	—
53	C₄⋊Dic₁₉	—	2	1	no	—
54	C₄⋊Dic₁₉	—	2	2	no	—
55	C₄⋊Dic₁₉	C₂³	1	2	yes	—
56	C₄⋊Dic₁₉	C₂³	1	2	yes	—
57	Dic₁₉⋊C₄	—	2	2	no	—
58	Dic₁₉⋊C₄	—	2	2	no	—
59	Dic₁₉⋊C₄	—	2	2	no	—
60	C₄×Dic₁₉	—	2	2	no	—
61	C₄×Dic₁₉	D₄	1	1	yes	characteristic
62	C₄×Dic₁₉	D₄	1	1	yes	characteristic
63	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
64	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
65	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
66	Q₈×C₁₉	—	2	4	no	—
67	Q₈×C₁₉	—	4	2	no	—
68	C₂×C₄×C₁₉	—	2	2	no	—
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
73	C₂×Dic₁₉	—	2	2	no	—
74	C₂×Dic₁₉	—	2	2	no	—
75	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
78	C₄×D₁₉	—	2	2	no	—
79	C₄×D₁₉	—	2	2	no	—
80	C₄×D₁₉	—	4	4	no	—
81	C₄×D₁₉	SD₁₆	1	4	yes	—
82	Dic₃₈	—	4	2	no	—
83	Dic₃₈	—	4	2	no	—
84	Dic₃₈	—	4	4	no	—
85	C₈×C₁₉	—	2	2	no	—
86	C₁₉⋊C₈	—	2	2	no	—
87	#3229	—	19	1	no	maximal, Sylow
88	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
89	C₂×D₁₉	—	2	1	no	—
90	C₂×D₁₉	—	2	1	no	—
91	C₂×D₁₉	C₂×SD₁₆	1	2	yes	—
92	C₄×C₁₉	—	4	2	no	—
93	C₄×C₁₉	—	4	2	no	—
94	C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
95	C₄×C₁₉	#137	1	2	yes	—
96	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
97	Dic₁₉	—	2	1	no	—
98	Dic₁₉	—	2	1	no	—
99	Dic₁₉	—	4	2	no	—
100	Dic₁₉	—	4	2	no	—
101	Dic₁₉	C₂×SD₁₆	1	2	yes	—
102	#533	—	19	1	no	—
103	C₂×C₄⋊Q₈	—	19	1	no	—
104	#498	—	19	1	no	—
105	#498	—	19	1	no	—
106	#487	—	19	1	no	—
107	#487	D₁₉	1	1	yes	characteristic, complemented
108	#483	—	19	4	no	—
109	#475	—	19	4	no	—
110	#431	—	19	1	no	—
111	C₂×C₁₉	#536	1	1	yes	characteristic
112	C₂×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
113	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
114	D₁₉	—	2	2	no	—
115	C₂²×Q₈	—	38	1	no	—
116	C₄⋊Q₈	—	19	2	no	—
117	C₄⋊Q₈	—	19	1	no	—
118	C₄⋊Q₈	—	19	1	no	—
119	C₄⋊Q₈	—	38	1	no	—
120	C₄⋊Q₈	—	38	1	no	—
121	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
122	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
123	#125	—	38	1	no	—
124	C₂²⋊Q₈	—	19	2	no	—
125	C₂²⋊Q₈	—	38	1	no	—
126	C₄×Q₈	—	19	2	no	—
127	C₄×Q₈	—	38	1	no	—
128	#117	—	38	1	no	—
129	C₂×C₄⋊C₄	—	19	2	no	—
130	C₂×C₄⋊C₄	—	38	1	no	—
131	C₂×C₄²	—	19	1	no	—
132	#106	—	19	4	no	—
133	#106	—	19	4	no	—
134	C₄⋊C₈	—	19	2	no	—
135	#103	—	19	4	no	—
136	#103	C₂×D₁₉	1	4	yes	—
137	C₂²⋊C₈	—	19	2	no	—
138	C₄×C₈	—	19	1	no	—
139	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
140	C₁₉	#3229	1	1	yes	characteristic, complemented, Sylow
141	C₂×Q₈	—	2	1	no	—
142	C₂×Q₈	—	38	2	no	—
143	C₂×Q₈	—	38	1	no	—
144	C₂×Q₈	—	38	1	no	—
145	C₂×Q₈	—	76	4	no	—
146	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
147	C₂²×C₄	—	19	1	no	—
148	C₂²×C₄	—	19	1	no	—
149	C₂²×C₄	—	19	1	no	—
150	C₂²×C₄	—	38	2	no	—
151	C₂×C₈	—	19	2	no	—
152	C₂×C₈	C₂²×D₁₉	1	2	yes	—
153	C₄⋊C₄	—	2	1	no	—
154	C₄⋊C₄	—	2	1	no	—
155	C₄⋊C₄	—	2	1	no	—
156	C₄⋊C₄	—	19	2	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	—	38	2	no	—
162	C₄⋊C₄	—	38	1	no	—
163	C₄⋊C₄	—	38	1	no	—
164	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
165	C₂²⋊C₄	—	38	2	no	—
166	C₄²	—	19	1	no	—
167	C₄²	—	19	1	no	—
168	C₄²	—	19	1	no	—
169	C₄²	—	38	2	no	—
170	C₄²	C₂²×D₁₉	1	1	yes	characteristic
171	C₂³	—	19	1	no	—
172	Q₈	—	2	4	no	—
173	Q₈	—	4	2	no	—
174	Q₈	—	76	4	no	—
175	Q₈	—	76	2	no	—
176	Q₈	—	76	2	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	19	1	no	—
180	C₂×C₄	—	19	4	no	—
181	C₂×C₄	—	19	1	no	—
182	C₂×C₄	—	19	1	no	—
183	C₂×C₄	—	38	2	no	—
184	C₂×C₄	—	38	2	no	—
185	C₂×C₄	—	38	2	no	—
186	C₂×C₄	—	38	2	no	—
187	C₂×C₄	—	76	4	no	—
188	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
189	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
190	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
191	C₈	—	2	2	no	—
192	C₈	—	38	2	no	—
193	C₂²	—	19	2	no	—
194	C₂²	—	38	1	no	—
195	C₂²	—	38	1	no	—
196	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
197	C₄	—	4	2	no	—
198	C₄	—	4	2	no	—
199	C₄	—	19	2	no	—
200	C₄	—	38	1	no	—
201	C₄	—	38	1	no	—
202	C₄	—	76	2	no	—
203	C₄	—	76	2	no	—
204	C₄	SD₁₆×D₁₉	1	2	yes	—
205	C₄	#10597364	1	2	yes	—
206	C₄	#10597436	1	2	yes	—
207	C₂	—	38	2	no	—
208	C₂	#11927114	1	1	yes	characteristic
209	C₂	C₂×SD₁₆×D₁₉	1	1	yes	characteristic
210	C₂	C₂×#10597364	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927099

C₂

yes

maximal, characteristic

C₄⋊Q₈×D₁₉

C₂

yes

maximal, characteristic

#11926942

C₂

yes

maximal, characteristic, complemented

#11926940

C₂

yes

maximal, characteristic, complemented

#11926894

C₂

yes

maximal, characteristic, complemented

#11926873

C₂

yes

maximal

#11926827

C₂

yes

maximal, complemented

#11926595

C₂

yes

maximal, characteristic

C₁₉×#487

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₁₉

—

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

#10597392

C₂²

yes

—

Q₈×Dic₁₉

C₂²

yes

—

#10597390

—

#10597343

—

#10597338

—

C₄⋊C₄×D₁₉

—

C₄⋊C₄×D₁₉

C₂²

yes

—

#10597336

—

#10597334

—

#10597334

C₂²

yes

—

#10597333

—

C₄²×D₁₉

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₁₉×#103

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597292

C₂²

yes

—

(C₂×D₁₉)⋊C₈

C₂²

yes

—

#10597274

C₂²

yes

—

Dic₁₉⋊C₈

C₂²

yes

—

#10597265

C₂²

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂³

yes

—

Q₈×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

C₂³

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂²×D₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

SD₁₆

yes

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#3229

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

C₂×SD₁₆

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×SD₁₆

yes

—

C₄×C₁₉

#137

yes

—

C₄×C₁₉

2₋¹⁺⁴

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

100

Dic₁₉

—

101

Dic₁₉

C₂×SD₁₆

yes

—

102

#533

—

103

C₂×C₄⋊Q₈

—

104

#498

—

105

#498

—

106

#487

—

107

#487

D₁₉

yes

characteristic, complemented

108

#483

—

109

#475

—

110

#431

—

111

C₂×C₁₉

#536

yes

characteristic

112

C₂×C₁₉

C₂²×SD₁₆

yes

characteristic

113

C₂×C₁₉

C₂×#137

yes

characteristic

114

D₁₉

—

115

C₂²×Q₈

—

116

C₄⋊Q₈

—

117

C₄⋊Q₈

—

118

C₄⋊Q₈

—

119

C₄⋊Q₈

—

120

C₄⋊Q₈

—

121

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

122

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

123

#125

—

124

C₂²⋊Q₈

—

125

C₂²⋊Q₈

—

126

C₄×Q₈

—

127

C₄×Q₈

—

128

#117

—

129

C₂×C₄⋊C₄

—

130

C₂×C₄⋊C₄

—

131

C₂×C₄²

—

132

#106

—

133

#106

—

134

C₄⋊C₈

—

135

#103

—

136

#103

C₂×D₁₉

yes

—

137

C₂²⋊C₈

—

138

C₄×C₈

—

139

C₄×C₈

C₂×D₁₉

yes

characteristic

140

C₁₉

#3229

yes

characteristic, complemented, Sylow

141

C₂×Q₈

—

142

C₂×Q₈

—

143

C₂×Q₈

—

144

C₂×Q₈

—

145

C₂×Q₈

—

146

C₂×Q₈

C₂²×D₁₉

yes

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

—

151

C₂×C₈

—

152

C₂×C₈

C₂²×D₁₉

yes

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄⋊C₄

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

C₂²×D₁₉

yes

—

165

C₂²⋊C₄

—

166

C₄²

—

167

C₄²

—

168

C₄²

—

169

C₄²

—

170

C₄²

C₂²×D₁₉

yes

characteristic

171

C₂³

—

172

Q₈

—

173

Q₈

—

174

Q₈

—

175

Q₈

—

176

Q₈

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

D₄×D₁₉

yes

characteristic

189

C₂×C₄

D₄×D₁₉

yes

characteristic

190

C₂×C₄

C₂³×D₁₉

yes

characteristic

191

C₈

—

192

C₈

—

193

C₂²

—

194

C₂²

—

195

C₂²

—

196

C₂²

C₂×D₄×D₁₉

yes

characteristic

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

—

201

C₄

—

202

C₄

—

203

C₄

—

204

C₄

SD₁₆×D₁₉

yes

—

205

C₄

#10597364

yes

—

206

C₄

#10597436

yes

—

207

C₂

—

208

C₂

#11927114

yes

characteristic

209

C₂

C₂×SD₁₆×D₁₉

yes

characteristic

210

C₂

C₂×#10597364

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#487	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂²×D₁₉	C₂×D₄
hypercenter	#487	D₁₉
hypocenter	C₁₉	#3229
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #487

subgroup

G/H

center

C₂²

C₂×D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#487

C₂

socle

C₂²×C₁₉

C₂²×D₄

prime radical

C₂²×D₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #487

N	H ≅ G/N	type
3. #11926942	C₂	semidirect
4. #11926940	C₂	semidirect
5. #11926894	C₂	semidirect
7. #11926827	C₂	semidirect
9. C₁₉×#487	C₂	semidirect
107. #487	D₁₉	semidirect
140. C₁₉	#3229	semidirect

H ≅ G/N

type

3. #11926942

C₂

semidirect

4. #11926940

C₂

semidirect

5. #11926894

C₂

semidirect

7. #11926827

C₂

semidirect

9. C₁₉×#487

C₂

semidirect

107. #487

D₁₉

semidirect

140. C₁₉

#3229

semidirect

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

subgroup	index
#11927099	2
C₄⋊Q₈×D₁₉	2
#11926942	2
#11926940	2
#11926894	2
#11926873	2
#11926827	2
#11926595	2
C₁₉×#487	2
#3229	19

subgroup

index

C₄⋊Q₈×D₁₉

C₁₉×#487

Subgroups — #14574775

Conjugacy classes of subgroups

Complements

Maximal subgroups