Group #18077488 — subgroups

Subgroups — #18077488

Order 4864.

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

normal subgroups only

This group has 416 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	#14573980	C₂	1	1	yes	maximal, characteristic
2	#14562297	C₂	1	1	yes	maximal, characteristic
3	#14562107	C₂	1	2	yes	maximal, complemented
4	#14561533	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2980	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	1	yes	characteristic
7	#11926912	—	2	1	no	—
8	#11926908	—	2	1	no	—
9	#11926903	C₄	1	4	yes	—
10	#11926597	C₂²	1	2	yes	—
11	#11926540	—	2	2	no	—
12	C₂×#10597260	C₂²	1	1	yes	characteristic
13	#11926293	—	2	1	no	—
14	#11926288	—	2	1	no	—
15	#11926274	—	2	4	no	—
16	C₁₉×#532	C₂²	1	1	yes	characteristic
17	C₁₉×#435	—	2	4	no	—
18	C₁₉×#432	C₂²	1	2	yes	—
19	C₁₉×#408	—	2	2	no	—
20	C₂×#41×C₁₉	D₄	1	2	yes	—
21	C₂×M₁₆×C₁₉	—	2	2	no	—
22	C₂²×C₈×C₁₉	—	2	2	no	—
23	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
24	C₁₉×#127	D₄	1	1	yes	characteristic
25	C₁₉×#124	C₂×C₄	1	2	yes	—
26	C₁₉×#121	—	2	2	no	—
27	C₄×D₄×C₁₉	—	2	2	no	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	#10597372	—	2	1	no	—
30	#10597370	—	2	2	no	—
31	C₂²×C₁₉⋊C₈	—	2	1	no	—
32	#10597316	—	2	1	no	—
33	#10597315	C₂×C₄	1	2	yes	—
34	C₄×Dic₃₈	—	2	2	no	—
35	C₁₉×C₄⋊C₈	D₄	1	4	yes	—
36	C₁₉×C₂²⋊C₈	—	2	4	no	—
37	C₁₉×C₂²⋊C₈	—	2	2	no	—
38	C₁₉×#97	—	2	2	no	—
39	#10597292	—	2	4	no	—
40	#10597289	—	2	4	no	—
41	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
43	#10597260	—	2	1	no	—
44	#10597260	C₂×C₄	1	2	yes	—
45	C₄×C₁₉⋊C₈	—	2	2	no	—
46	#41×C₁₉	—	4	2	no	—
47	#41×C₁₉	—	4	2	no	—
48	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
49	C₂×D₄×C₁₉	—	2	2	no	—
50	C₂×D₄×C₁₉	—	2	2	no	—
51	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	#41	1	2	yes	—
55	C₂×Dic₃₈	—	2	2	no	—
56	M₁₆×C₁₉	—	8	2	no	—
57	C₂×C₈×C₁₉	—	2	4	no	—
58	C₂×C₈×C₁₉	—	8	2	no	—
59	C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂²⋊C₄×C₁₉	—	2	4	no	—
61	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₄²×C₁₉	C₂×D₄	1	2	yes	—
64	C₂²⋊Dic₁₉	—	4	1	no	—
65	C₄⋊Dic₁₉	—	2	2	no	—
66	C₄⋊Dic₁₉	—	2	2	no	—
67	Dic₁₉⋊C₄	—	4	2	no	—
68	C₄×Dic₁₉	—	4	1	no	—
69	C₂×C₁₉⋊C₈	—	2	2	no	—
70	C₂×C₁₉⋊C₈	—	4	2	no	—
71	C₂×C₁₉⋊C₈	—	4	2	no	—
72	#9005	—	19	1	no	maximal, Sylow
73	C₂³×C₁₉	—	2	2	no	—
74	C₂³×C₁₉	#123	1	1	yes	characteristic
75	Q₈×C₁₉	—	4	2	no	—
76	D₄×C₁₉	—	4	2	no	—
77	D₄×C₁₉	—	8	2	no	—
78	D₄×C₁₉	—	8	2	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	—	4	2	no	—
84	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
86	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#121	1	2	yes	—
88	C₂×Dic₁₉	—	4	2	no	—
89	Dic₃₈	—	4	4	no	—
90	C₈×C₁₉	—	4	4	no	—
91	C₁₉⋊C₈	—	4	2	no	—
92	C₁₉⋊C₈	—	8	2	no	—
93	#3135	—	19	1	no	—
94	#2980	D₁₉	1	1	yes	characteristic
95	#1543	—	19	1	no	—
96	#1497	—	19	2	no	—
97	#1302	—	19	2	no	—
98	C₂²×C₁₉	—	2	2	no	—
99	C₂²×C₁₉	—	2	1	no	—
100	C₂²×C₁₉	—	4	4	no	—
101	C₂²×C₁₉	—	4	2	no	—
102	C₂²×C₁₉	#386	1	1	yes	characteristic
103	C₄×C₁₉	—	2	2	no	—
104	C₄×C₁₉	—	2	2	no	—
105	C₄×C₁₉	—	2	1	no	—
106	C₄×C₁₉	—	4	2	no	—
107	C₄×C₁₉	#455	1	2	yes	—
108	Dic₁₉	—	8	2	no	—
109	#533	—	19	1	no	—
110	#532	C₂×D₁₉	1	1	yes	characteristic
111	#491	—	38	1	no	—
112	#490	—	38	1	no	—
113	#489	—	19	4	no	—
114	#435	—	2	4	no	—
115	#432	C₂×D₁₉	1	2	yes	—
116	#431	—	19	2	no	—
117	#416	—	38	2	no	—
118	#408	—	2	2	no	—
119	C₂×#97	—	19	1	no	—
120	#333	—	38	1	no	—
121	#331	—	38	1	no	—
122	Q₈⋊C₈	—	38	4	no	—
123	C₂×C₁₉	—	4	1	no	—
124	C₂×C₁₉	—	8	2	no	—
125	C₂×C₁₉	#1881	1	2	yes	—
126	C₂×C₁₉	#1885	1	1	yes	characteristic
127	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
128	C₂×M₁₆	—	2	2	no	—
129	C₂²×C₈	—	2	2	no	—
130	C₂²×C₈	—	38	1	no	—
131	C₄⋊Q₈	—	19	2	no	—
132	C₄⋊Q₈	D₇₆	1	1	yes	characteristic
133	#127	D₇₆	1	1	yes	characteristic
134	#125	—	38	1	no	—
135	#124	C₄×D₁₉	1	2	yes	—
136	C₂²⋊Q₈	—	38	2	no	—
137	#121	—	2	2	no	—
138	C₄×Q₈	—	38	2	no	—
139	C₄×D₄	—	2	2	no	—
140	#117	—	38	1	no	—
141	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
142	C₄⋊C₈	—	38	2	no	—
143	C₄⋊C₈	C₂²⋊D₁₉	1	4	yes	—
144	#103	—	38	4	no	—
145	#102	—	38	4	no	—
146	C₂²⋊C₈	—	2	4	no	—
147	C₂²⋊C₈	—	2	2	no	—
148	C₂²⋊C₈	—	38	2	no	—
149	#97	—	2	2	no	—
150	#97	—	19	2	no	—
151	#97	—	38	1	no	—
152	C₄×C₈	—	38	2	no	—
153	C₁₉	#9005	1	1	yes	characteristic, complemented, Sylow
154	#41	—	4	2	no	—
155	#41	—	4	2	no	—
156	C₂×Q₈	—	38	2	no	—
157	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
158	C₂×D₄	—	2	2	no	—
159	C₂×D₄	—	2	2	no	—
160	C₂×D₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
161	C₂²×C₄	—	2	2	no	—
162	C₂²×C₄	#64541	1	2	yes	—
163	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
164	M₁₆	—	8	2	no	—
165	C₂×C₈	—	2	4	no	—
166	C₂×C₈	—	8	2	no	—
167	C₂×C₈	—	38	2	no	—
168	C₂×C₈	—	76	2	no	—
169	C₂×C₈	—	76	2	no	—
170	C₄⋊C₄	—	2	2	no	—
171	C₄⋊C₄	—	38	2	no	—
172	C₄⋊C₄	—	38	2	no	—
173	C₄⋊C₄	—	76	2	no	—
174	C₂²⋊C₄	—	2	4	no	—
175	C₂²⋊C₄	—	76	1	no	—
176	C₄²	—	76	1	no	—
177	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
178	C₄²	C₂×D₇₆	1	1	yes	characteristic
179	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
180	C₂³	—	2	2	no	—
181	C₂³	#10597375	1	1	yes	characteristic
182	Q₈	—	4	2	no	—
183	Q₈	—	76	4	no	—
184	D₄	—	4	2	no	—
185	D₄	—	8	2	no	—
186	D₄	—	8	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	4	2	no	—
190	C₂×C₄	—	4	2	no	—
191	C₂×C₄	—	4	2	no	—
192	C₂×C₄	—	76	2	no	—
193	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
194	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
195	C₂×C₄	#10597376	1	2	yes	—
196	C₂×C₄	#10597399	1	1	yes	characteristic
197	C₈	—	4	4	no	—
198	C₈	—	76	2	no	—
199	C₈	—	152	2	no	—
200	C₂²	—	2	2	no	—
201	C₂²	—	2	1	no	—
202	C₂²	—	4	4	no	—
203	C₂²	—	4	2	no	—
204	C₂²	#11926423	1	1	yes	characteristic
205	C₄	—	2	2	no	—
206	C₄	—	2	2	no	—
207	C₄	—	2	1	no	—
208	C₄	—	4	2	no	—
209	C₄	—	152	2	no	—
210	C₄	#11926722	1	2	yes	—
211	C₂	—	4	1	no	—
212	C₂	—	8	2	no	—
213	C₂	#14563997	1	2	yes	—
214	C₂	#14564023	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14573980

C₂

yes

maximal, characteristic

#14562297

C₂

yes

maximal, characteristic

#14562107

C₂

yes

maximal, complemented

#14561533

C₂

yes

maximal, complemented

C₁₉×#2980

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

—

—

C₄

yes

—

#11926597

C₂²

yes

—

#11926540

—

C₂×#10597260

C₂²

yes

—

—

—

C₁₉×#532

C₂²

yes

characteristic

C₁₉×#435

—

C₁₉×#432

C₂²

yes

—

C₁₉×#408

—

C₂×#41×C₁₉

D₄

yes

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

D₄

yes

characteristic

C₁₉×#127

D₄

yes

characteristic

C₁₉×#124

C₂×C₄

yes

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597372

—

#10597370

—

C₂²×C₁₉⋊C₈

—

#10597316

—

#10597315

C₂×C₄

yes

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

#10597292

—

#10597289

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9005

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#123

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×Dic₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#3135

—

#2980

D₁₉

yes

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

#386

yes

characteristic

103

C₄×C₁₉

—

104

C₄×C₁₉

—

105

C₄×C₁₉

—

106

C₄×C₁₉

—

107

C₄×C₁₉

#455

yes

—

108

Dic₁₉

—

109

#533

—

110

#532

C₂×D₁₉

yes

characteristic

111

#491

—

112

#490

—

113

#489

—

114

#435

—

115

#432

C₂×D₁₉

yes

—

116

#431

—

117

#416

—

118

#408

—

119

C₂×#97

—

120

#333

—

121

#331

—

122

Q₈⋊C₈

—

123

C₂×C₁₉

—

124

C₂×C₁₉

—

125

C₂×C₁₉

#1881

yes

—

126

C₂×C₁₉

#1885

yes

characteristic

127

C₂×#41

C₂²⋊D₁₉

yes

—

128

C₂×M₁₆

—

129

C₂²×C₈

—

130

C₂²×C₈

—

131

C₄⋊Q₈

—

132

C₄⋊Q₈

D₇₆

yes

characteristic

133

#127

D₇₆

yes

characteristic

134

#125

—

135

#124

C₄×D₁₉

yes

—

136

C₂²⋊Q₈

—

137

#121

—

138

C₄×Q₈

—

139

C₄×D₄

—

140

#117

—

141

C₂×C₄²

C₂²×D₁₉

yes

characteristic

142

C₄⋊C₈

—

143

C₄⋊C₈

C₂²⋊D₁₉

yes

—

144

#103

—

145

#102

—

146

C₂²⋊C₈

—

147

C₂²⋊C₈

—

148

C₂²⋊C₈

—

149

#97

—

150

#97

—

151

#97

—

152

C₄×C₈

—

153

C₁₉

#9005

yes

characteristic, complemented, Sylow

154

#41

—

155

#41

—

156

C₂×Q₈

—

157

C₂×Q₈

(C₂×D₁₉)⋊C₄

yes

—

158

C₂×D₄

—

159

C₂×D₄

—

160

C₂×D₄

(C₂×D₁₉)⋊C₄

yes

—

161

C₂²×C₄

—

162

C₂²×C₄

#64541

yes

—

163

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

164

M₁₆

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₂²⋊C₄

—

175

C₂²⋊C₄

—

176

C₄²

—

177

C₄²

C₂×C₄×D₁₉

yes

characteristic

178

C₄²

C₂×D₇₆

yes

characteristic

179

C₄²

C₂×C₂²⋊D₁₉

yes

—

180

C₂³

—

181

C₂³

#10597375

yes

characteristic

182

Q₈

—

183

Q₈

—

184

D₄

—

185

D₄

—

186

D₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

194

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

195

C₂×C₄

#10597376

yes

—

196

C₂×C₄

#10597399

yes

characteristic

197

C₈

—

198

C₈

—

199

C₈

—

152

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

204

C₂²

#11926423

yes

characteristic

205

C₄

—

206

C₄

—

207

C₄

—

208

C₄

—

209

C₄

—

152

—

210

C₄

#11926722

yes

—

211

C₂

—

212

C₂

—

213

C₂

#14563997

yes

—

214

C₂

#14564023

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2980	C₂
socle	C₂²×C₁₉	#386
prime radical	C₁₉×#532	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2980	D₁₉
hypocenter	C₁₉	#9005
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2980

subgroup

G/H

center

C₂×C₄

#10597399

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2980

C₂

socle

C₂²×C₁₉

#386

prime radical

C₁₉×#532

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2980

N	H ≅ G/N	type
3. #14562107	C₂	semidirect
4. #14561533	C₂	semidirect
153. C₁₉	#9005	semidirect

H ≅ G/N

type

3. #14562107

C₂

semidirect

4. #14561533

C₂

semidirect

153. C₁₉

#9005

semidirect

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

subgroup	index
#14573980	2
#14562297	2
#14562107	2
#14561533	2
C₁₉×#2980	2
#9005	19

subgroup

index

C₁₉×#2980

Subgroups — #18077488

Conjugacy classes of subgroups

Complements

Maximal subgroups