Group #18087522 — subgroups

Subgroups — #18087522

Order 4864.

372 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 99 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	#14563810	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562405	C₂	1	2	yes	maximal, complemented
3	#14562060	C₂	1	2	yes	maximal
4	#14561466	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1955	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	C₂×#10597276	—	2	2	no	—
8	#11926568	C₂²	1	2	yes	—
9	#11926294	—	2	4	no	—
10	D₄⋊(C₁₉⋊C₈)	—	2	4	no	—
11	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
14	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
15	C₂²×D₄×C₁₉	Q₈	1	1	yes	characteristic
16	C₂³×C₄×C₁₉	—	2	1	no	—
17	C₂²×C₈×C₁₉	—	2	1	no	—
18	C₂²×C₈×C₁₉	D₄	1	2	yes	—
19	C₄×D₄×C₁₉	—	2	2	no	—
20	C₄×D₄×C₁₉	—	2	2	no	—
21	C₂×C₄⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
22	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×#64520	—	2	2	no	—
25	C₁₉×C₄⋊C₈	—	2	2	no	—
26	C₁₉×C₂²⋊C₈	—	4	4	no	—
27	C₁₉×#97	—	2	2	no	—
28	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
29	#10597276	—	4	4	no	—
30	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
31	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
32	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
33	C₄×C₁₉⋊C₈	D₄	1	4	yes	—
34	C₂⁴×C₁₉	—	2	1	no	—
35	C₂×D₄×C₁₉	—	2	2	no	—
36	C₂×D₄×C₁₉	—	4	2	no	—
37	C₂²×C₄×C₁₉	—	2	1	no	—
38	C₂²×C₄×C₁₉	—	4	1	no	—
39	C₂²×C₄×C₁₉	—	4	1	no	—
40	C₂²×C₄×C₁₉	—	4	2	no	—
41	C₂²×C₄×C₁₉	—	4	2	no	—
42	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
45	C₂×C₈×C₁₉	—	2	2	no	—
46	C₂×C₈×C₁₉	—	2	2	no	—
47	C₂×C₈×C₁₉	—	4	1	no	—
48	C₂×C₈×C₁₉	—	4	2	no	—
49	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
50	C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂²⋊C₄×C₁₉	—	4	2	no	—
52	C₄²×C₁₉	C₂×D₄	1	2	yes	—
53	C₄²×C₁₉	#41	1	2	yes	—
54	#64520	—	4	4	no	—
55	C₂×C₁₉⋊C₈	—	2	4	no	—
56	C₂×C₁₉⋊C₈	—	4	2	no	—
57	#10661	—	19	1	no	maximal, Sylow
58	C₂³×C₁₉	—	2	2	no	—
59	C₂³×C₁₉	—	4	1	no	—
60	C₂³×C₁₉	—	4	2	no	—
61	C₂³×C₁₉	—	4	1	no	—
62	C₂³×C₁₉	—	4	2	no	—
63	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
64	D₄×C₁₉	—	2	4	no	—
65	D₄×C₁₉	—	4	2	no	—
66	C₂×C₄×C₁₉	—	4	1	no	—
67	C₂×C₄×C₁₉	—	4	1	no	—
68	C₂×C₄×C₁₉	—	4	1	no	—
69	C₂×C₄×C₁₉	—	4	2	no	—
70	C₂×C₄×C₁₉	—	8	2	no	—
71	C₂×C₄×C₁₉	—	8	1	no	—
72	C₂×C₄×C₁₉	—	8	1	no	—
73	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
74	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
75	C₂×C₄×C₁₉	#123	1	2	yes	—
76	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
77	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
78	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
79	C₈×C₁₉	—	2	4	no	—
80	C₈×C₁₉	—	8	1	no	—
81	C₁₉⋊C₈	—	4	4	no	—
82	C₁₉⋊C₈	—	8	2	no	—
83	#1955	D₁₉	1	1	yes	characteristic
84	#1849	—	19	1	no	—
85	#1570	—	19	2	no	—
86	#1486	—	19	2	no	—
87	#1275	—	19	1	no	—
88	C₂²×C₁₉	—	2	1	no	—
89	C₂²×C₁₉	—	2	1	no	—
90	C₂²×C₁₉	—	4	4	no	—
91	C₂²×C₁₉	—	4	2	no	—
92	C₂²×C₁₉	—	8	2	no	—
93	C₂²×C₁₉	—	8	1	no	—
94	C₂²×C₁₉	—	8	1	no	—
95	C₂²×C₁₉	#399	1	1	yes	characteristic
96	C₂²×C₁₉	#476	1	2	yes	—
97	C₄×C₁₉	—	2	2	no	—
98	C₄×C₁₉	—	2	2	no	—
99	C₄×C₁₉	—	8	1	no	—
100	C₄×C₁₉	#481	1	2	yes	—
101	C₄×C₁₉	#492	1	1	yes	characteristic
102	C₄×C₁₉	#496	1	1	yes	characteristic
103	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
104	#431	—	19	2	no	—
105	C₂×#108	—	38	2	no	—
106	#423	—	19	2	no	—
107	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
108	C₂×C₂²⋊C₈	—	2	2	no	—
109	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
110	#334	—	38	4	no	—
111	D₄⋊C₈	—	38	4	no	—
112	C₂×C₁₉	—	2	2	no	—
113	C₂×C₁₉	—	8	2	no	—
114	C₂×C₁₉	#2091	1	1	yes	characteristic
115	C₂×C₁₉	#2094	1	1	yes	characteristic
116	C₂×C₁₉	#2098	1	1	yes	characteristic
117	C₂²×D₄	Dic₃₈	1	1	yes	characteristic
118	C₂³×C₄	—	2	1	no	—
119	C₂×M₁₆	—	38	2	no	—
120	C₂²×C₈	—	2	1	no	—
121	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
122	C₄×D₄	—	2	2	no	—
123	C₄×D₄	—	2	2	no	—
124	C₂×C₄⋊C₄	Dic₃₈	1	1	yes	characteristic
125	C₂×C₂²⋊C₄	—	2	1	no	—
126	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
127	#108	—	76	4	no	—
128	C₄⋊C₈	—	2	2	no	—
129	C₄⋊C₈	—	38	2	no	—
130	C₄⋊C₈	—	38	2	no	—
131	C₄⋊C₈	—	38	2	no	—
132	C₂²⋊C₈	—	4	4	no	—
133	C₂²⋊C₈	—	38	2	no	—
134	#97	—	2	2	no	—
135	C₄×C₈	—	19	4	no	—
136	C₁₉	#10661	1	1	yes	characteristic, complemented, Sylow
137	C₂⁴	—	2	1	no	—
138	C₂×D₄	—	2	2	no	—
139	C₂×D₄	—	4	2	no	—
140	C₂²×C₄	—	2	1	no	—
141	C₂²×C₄	—	4	2	no	—
142	C₂²×C₄	—	4	1	no	—
143	C₂²×C₄	—	4	1	no	—
144	C₂²×C₄	—	4	2	no	—
145	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
146	C₂²×C₄	#64541	1	1	yes	characteristic
147	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
148	M₁₆	—	76	4	no	—
149	C₂×C₈	—	2	2	no	—
150	C₂×C₈	—	2	2	no	—
151	C₂×C₈	—	4	2	no	—
152	C₂×C₈	—	4	1	no	—
153	C₂×C₈	—	38	4	no	—
154	C₂×C₈	—	76	2	no	—
155	C₂×C₈	#64526	1	4	yes	—
156	C₄⋊C₄	—	2	2	no	—
157	C₂²⋊C₄	—	4	2	no	—
158	C₄²	D₄×D₁₉	1	2	yes	—
159	C₄²	#64543	1	2	yes	—
160	C₂³	—	2	2	no	—
161	C₂³	—	4	1	no	—
162	C₂³	—	4	2	no	—
163	C₂³	—	4	2	no	—
164	C₂³	—	4	1	no	—
165	C₂³	#10597370	1	1	yes	characteristic
166	D₄	—	2	4	no	—
167	D₄	—	4	2	no	—
168	C₂×C₄	—	4	1	no	—
169	C₂×C₄	—	4	1	no	—
170	C₂×C₄	—	4	2	no	—
171	C₂×C₄	—	4	1	no	—
172	C₂×C₄	—	8	2	no	—
173	C₂×C₄	—	8	1	no	—
174	C₂×C₄	—	8	1	no	—
175	C₂×C₄	#10597324	1	2	yes	—
176	C₂×C₄	#10597329	1	2	yes	—
177	C₂×C₄	C₂×#64526	1	2	yes	—
178	C₂×C₄	#10597381	1	1	yes	characteristic
179	C₂×C₄	#10597386	1	1	yes	characteristic
180	C₂×C₄	#10597395	1	2	yes	—
181	C₈	—	2	4	no	—
182	C₈	—	8	1	no	—
183	C₈	—	76	4	no	—
184	C₈	—	152	2	no	—
185	C₂²	—	2	1	no	—
186	C₂²	—	2	1	no	—
187	C₂²	—	4	4	no	—
188	C₂²	—	4	2	no	—
189	C₂²	—	8	2	no	—
190	C₂²	—	8	1	no	—
191	C₂²	—	8	1	no	—
192	C₂²	#11926480	1	1	yes	characteristic
193	C₂²	#11926834	1	2	yes	—
194	C₄	—	2	2	no	—
195	C₄	—	2	2	no	—
196	C₄	—	8	1	no	—
197	C₄	#11926860	1	2	yes	—
198	C₄	#11926916	1	1	yes	characteristic
199	C₄	#11926934	1	1	yes	characteristic
200	C₂	—	2	2	no	—
201	C₂	—	8	2	no	—
202	C₂	#14565151	1	1	yes	characteristic
203	C₂	#14565168	1	1	yes	characteristic
204	C₂	#14565188	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563810

C₂

yes

maximal, characteristic, complemented

#14562405

C₂

yes

maximal, complemented

#14562060

C₂

yes

maximal

#14561466

C₂

yes

maximal, characteristic, complemented

C₁₉×#1955

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

C₂×#10597276

—

#11926568

C₂²

yes

—

#11926294

—

D₄⋊(C₁₉⋊C₈)

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂²×D₄×C₁₉

Q₈

yes

characteristic

C₂³×C₄×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₂²⋊(C₁₉⋊C₈)

—

#10597276

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#10661

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊Q₈

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

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⋊Q₈

yes

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1955

D₁₉

yes

—

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#399

yes

characteristic

C₂²×C₁₉

#476

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

100

C₄×C₁₉

#481

yes

—

101

C₄×C₁₉

#492

yes

characteristic

102

C₄×C₁₉

#496

yes

characteristic

103

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

104

#431

—

105

C₂×#108

—

106

#423

—

107

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

108

C₂×C₂²⋊C₈

—

109

C₂×#97

C₂×D₁₉

yes

characteristic

110

#334

—

111

D₄⋊C₈

—

112

C₂×C₁₉

—

113

C₂×C₁₉

—

114

C₂×C₁₉

#2091

yes

characteristic

115

C₂×C₁₉

#2094

yes

characteristic

116

C₂×C₁₉

#2098

yes

characteristic

117

C₂²×D₄

Dic₃₈

yes

characteristic

118

C₂³×C₄

—

119

C₂×M₁₆

—

120

C₂²×C₈

—

121

C₂²×C₈

C₂²⋊D₁₉

yes

—

122

C₄×D₄

—

123

C₄×D₄

—

124

C₂×C₄⋊C₄

Dic₃₈

yes

characteristic

125

C₂×C₂²⋊C₄

—

126

C₂×C₄²

C₂²×D₁₉

yes

characteristic

127

#108

—

128

C₄⋊C₈

—

129

C₄⋊C₈

—

130

C₄⋊C₈

—

131

C₄⋊C₈

—

132

C₂²⋊C₈

—

133

C₂²⋊C₈

—

134

#97

—

135

C₄×C₈

—

136

C₁₉

#10661

yes

characteristic, complemented, Sylow

137

C₂⁴

—

138

C₂×D₄

—

139

C₂×D₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

146

C₂²×C₄

#64541

yes

characteristic

147

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

148

M₁₆

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

#64526

yes

—

156

C₄⋊C₄

—

157

C₂²⋊C₄

—

158

C₄²

D₄×D₁₉

yes

—

159

C₄²

#64543

yes

—

160

C₂³

—

161

C₂³

—

162

C₂³

—

163

C₂³

—

164

C₂³

—

165

C₂³

#10597370

yes

characteristic

166

D₄

—

167

D₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

#10597324

yes

—

176

C₂×C₄

#10597329

yes

—

177

C₂×C₄

C₂×#64526

yes

—

178

C₂×C₄

#10597381

yes

characteristic

179

C₂×C₄

#10597386

yes

characteristic

180

C₂×C₄

#10597395

yes

—

181

C₈

—

182

C₈

—

183

C₈

—

184

C₈

—

152

—

185

C₂²

—

186

C₂²

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

—

191

C₂²

—

192

C₂²

#11926480

yes

characteristic

193

C₂²

#11926834

yes

—

194

C₄

—

195

C₄

—

196

C₄

—

197

C₄

#11926860

yes

—

198

C₄

#11926916

yes

characteristic

199

C₄

#11926934

yes

characteristic

200

C₂

—

201

C₂

—

202

C₂

#14565151

yes

characteristic

203

C₂

#14565168

yes

characteristic

204

C₂

#14565188

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1955	C₂
socle	C₂²×C₁₉	#399
prime radical	C₂²×D₄×C₁₉	Q₈
hypercenter	#1955	D₁₉
hypocenter	C₁₉	#10661
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1955

subgroup

G/H

center

C₂×C₄

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1955

C₂

socle

C₂²×C₁₉

#399

prime radical

C₂²×D₄×C₁₉

Q₈

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1955

N	H ≅ G/N	type
1. #14563810	C₂	semidirect
2. #14562405	C₂	semidirect
4. #14561466	C₂	semidirect
136. C₁₉	#10661	semidirect

H ≅ G/N

type

1. #14563810

C₂

semidirect

2. #14562405

C₂

semidirect

4. #14561466

C₂

semidirect

136. C₁₉

#10661

semidirect

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

subgroup	index
#14563810	2
#14562405	2
#14562060	2
#14561466	2
C₁₉×#1955	2
#10661	19

subgroup

index

C₁₉×#1955

Subgroups — #18087522

Conjugacy classes of subgroups

Complements

Maximal subgroups