Group #18077855 — subgroups

Subgroups — #18077855

Order 4864.

404 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 107 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	#14574145	C₂	1	1	yes	maximal, characteristic
2	#14562230	C₂	1	1	yes	maximal, characteristic
3	#14562055	C₂	1	2	yes	maximal
4	#14561471	C₂	1	2	yes	maximal
5	C₁₉×#2986	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	1	yes	characteristic
7	#11926947	C₄	1	2	yes	—
8	#11926943	—	2	2	no	—
9	#11926940	C₄	1	2	yes	—
10	#11926580	—	2	2	no	—
11	C₄×#64520	C₂²	1	2	yes	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#11926286	—	2	2	no	—
14	#11926274	—	2	2	no	—
15	#11926274	—	2	2	no	—
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₁₉×#446	—	2	2	no	—
18	C₈×Q₈×C₁₉	—	2	2	no	—
19	C₁₉×#433	—	2	2	no	—
20	C₁₉×#431	C₂²	1	2	yes	—
21	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
22	C₁₉×#125	D₄	1	2	yes	—
23	C₁₉×C₂²⋊Q₈	—	2	2	no	—
24	C₄×Q₈×C₁₉	—	2	2	no	—
25	C₁₉×#117	D₄	1	2	yes	—
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	#10597372	—	2	1	no	—
28	#10597370	—	2	2	no	—
29	C₂×#64520	—	2	2	no	—
30	C₂²×C₁₉⋊C₈	—	2	1	no	—
31	#10597316	—	2	1	no	—
32	#10597315	C₂×C₄	1	2	yes	—
33	C₄×Dic₃₈	—	2	2	no	—
34	C₁₉×C₄⋊C₈	—	2	4	no	—
35	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
36	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
37	C₁₉×C₂²⋊C₈	—	2	2	no	—
38	C₁₉×#97	—	2	2	no	—
39	C₄×C₈×C₁₉	—	2	2	no	—
40	C₄×C₈×C₁₉	—	2	2	no	—
41	#10597265	—	2	4	no	—
42	#10597264	—	2	4	no	—
43	#10597260	—	2	2	no	—
44	C₄×C₁₉⋊C₈	—	2	1	no	—
45	C₄×C₁₉⋊C₈	—	2	2	no	—
46	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
47	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
48	C₂×Q₈×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	#41	1	2	yes	—
51	C₂×Dic₃₈	—	2	2	no	—
52	C₂×C₈×C₁₉	—	2	2	no	—
53	C₂×C₈×C₁₉	—	2	2	no	—
54	C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₄⋊C₄×C₁₉	—	2	4	no	—
56	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
57	C₂²⋊C₄×C₁₉	—	2	2	no	—
58	C₄²×C₁₉	—	2	2	no	—
59	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
60	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₄²×C₁₉	C₂×D₄	1	2	yes	—
62	C₂²⋊Dic₁₉	—	4	1	no	—
63	C₄⋊Dic₁₉	—	2	2	no	—
64	C₄⋊Dic₁₉	—	2	2	no	—
65	Dic₁₉⋊C₄	—	4	2	no	—
66	C₄×Dic₁₉	—	4	1	no	—
67	#64520	—	2	4	no	—
68	#64520	—	4	2	no	—
69	C₂×C₁₉⋊C₈	—	2	4	no	—
70	C₂×C₁₉⋊C₈	—	2	1	no	—
71	C₂×C₁₉⋊C₈	—	2	1	no	—
72	C₂×C₁₉⋊C₈	—	4	2	no	—
73	#9068	—	19	1	no	maximal, Sylow
74	C₂³×C₁₉	#123	1	1	yes	characteristic
75	Q₈×C₁₉	—	4	2	no	—
76	Q₈×C₁₉	—	4	2	no	—
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	4	no	—
81	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
83	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#121	1	2	yes	—
85	C₂×Dic₁₉	—	4	2	no	—
86	Dic₃₈	—	4	2	no	—
87	Dic₃₈	—	4	2	no	—
88	C₈×C₁₉	—	4	2	no	—
89	C₈×C₁₉	—	4	2	no	—
90	C₁₉⋊C₈	—	2	2	no	—
91	C₁₉⋊C₈	—	2	2	no	—
92	C₁₉⋊C₈	—	4	4	no	—
93	#3160	—	19	1	no	—
94	#2986	D₁₉	1	1	yes	characteristic
95	#1526	—	19	1	no	—
96	#1485	—	19	2	no	—
97	#1278	—	19	2	no	—
98	C₂²×C₁₉	—	2	2	no	—
99	C₂²×C₁₉	—	2	1	no	—
100	C₂²×C₁₉	#386	1	1	yes	characteristic
101	C₄×C₁₉	—	2	2	no	—
102	C₄×C₁₉	—	2	1	no	—
103	C₄×C₁₉	—	4	4	no	—
104	C₄×C₁₉	#443	1	2	yes	—
105	C₄×C₁₉	#444	1	2	yes	—
106	C₄×C₁₉	#456	1	2	yes	—
107	Dic₁₉	—	8	2	no	—
108	#533	—	19	1	no	—
109	#533	C₂×D₁₉	1	1	yes	characteristic
110	#500	—	19	2	no	—
111	#499	—	38	2	no	—
112	#498	—	19	2	no	—
113	#446	—	2	2	no	—
114	C₈×Q₈	—	2	2	no	—
115	#433	—	2	2	no	—
116	#431	C₂×D₁₉	1	2	yes	—
117	#427	—	38	2	no	—
118	C₄×M₁₆	—	19	2	no	—
119	C₂×C₄×C₈	—	19	1	no	—
120	#330	—	38	2	no	—
121	Q₈⋊C₈	—	38	2	no	—
122	Q₈⋊C₈	—	38	2	no	—
123	C₂×C₁₉	—	4	1	no	—
124	C₂×C₁₉	#1876	1	2	yes	—
125	C₂×C₁₉	#1886	1	1	yes	characteristic
126	C₂×M₁₆	—	38	2	no	—
127	C₂²×C₈	—	38	1	no	—
128	C₄⋊Q₈	—	19	2	no	—
129	C₄⋊Q₈	C₄×D₁₉	1	2	yes	—
130	#125	—	38	1	no	—
131	#125	D₇₆	1	2	yes	—
132	C₂²⋊Q₈	—	2	2	no	—
133	C₂²⋊Q₈	—	38	2	no	—
134	C₄×Q₈	—	2	2	no	—
135	C₄×Q₈	—	38	2	no	—
136	#117	—	38	1	no	—
137	#117	C₂²⋊D₁₉	1	2	yes	—
138	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
139	#107	—	38	4	no	—
140	#106	—	38	4	no	—
141	C₄⋊C₈	—	2	4	no	—
142	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
143	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
144	C₂²⋊C₈	—	2	2	no	—
145	#97	—	2	2	no	—
146	#97	—	38	2	no	—
147	C₄×C₈	—	2	2	no	—
148	C₄×C₈	—	2	2	no	—
149	C₄×C₈	—	19	1	no	—
150	C₄×C₈	—	19	1	no	—
151	C₄×C₈	—	38	1	no	—
152	C₄×C₈	—	38	2	no	—
153	C₁₉	#9068	1	1	yes	characteristic, complemented, Sylow
154	C₂×Q₈	—	2	2	no	—
155	C₂×Q₈	—	38	2	no	—
156	C₂²×C₄	#64541	1	2	yes	—
157	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
158	M₁₆	—	38	4	no	—
159	M₁₆	—	76	2	no	—
160	C₂×C₈	—	2	2	no	—
161	C₂×C₈	—	2	2	no	—
162	C₂×C₈	—	38	4	no	—
163	C₂×C₈	—	38	1	no	—
164	C₂×C₈	—	38	1	no	—
165	C₂×C₈	—	76	2	no	—
166	C₄⋊C₄	—	2	4	no	—
167	C₄⋊C₄	—	2	2	no	—
168	C₄⋊C₄	—	38	2	no	—
169	C₄⋊C₄	—	38	2	no	—
170	C₄⋊C₄	—	76	2	no	—
171	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
172	C₂²⋊C₄	—	2	2	no	—
173	C₂²⋊C₄	—	76	1	no	—
174	C₄²	—	2	2	no	—
175	C₄²	—	76	1	no	—
176	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
177	C₄²	C₂×D₇₆	1	1	yes	characteristic
178	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
179	C₂³	#10597375	1	1	yes	characteristic
180	Q₈	—	4	2	no	—
181	Q₈	—	4	2	no	—
182	Q₈	—	76	2	no	—
183	Q₈	—	76	2	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	4	no	—
188	C₂×C₄	—	76	2	no	—
189	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
190	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
191	C₂×C₄	#10597376	1	2	yes	—
192	C₂×C₄	#10597399	1	1	yes	characteristic
193	C₈	—	4	2	no	—
194	C₈	—	4	2	no	—
195	C₈	—	38	2	no	—
196	C₈	—	38	2	no	—
197	C₈	—	76	4	no	—
198	C₂²	—	2	2	no	—
199	C₂²	—	2	1	no	—
200	C₂²	#11926423	1	1	yes	characteristic
201	C₄	—	2	2	no	—
202	C₄	—	2	1	no	—
203	C₄	—	4	4	no	—
204	C₄	—	152	2	no	—
205	C₄	#11926659	1	2	yes	—
206	C₄	#11926664	1	2	yes	—
207	C₄	#11926727	1	2	yes	—
208	C₂	—	4	1	no	—
209	C₂	#14563962	1	2	yes	—
210	C₂	#14564028	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574145

C₂

yes

maximal, characteristic

#14562230

C₂

yes

maximal, characteristic

#14562055

C₂

yes

maximal

#14561471

C₂

yes

maximal

C₁₉×#2986

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

characteristic

#11926947

C₄

yes

—

#11926943

—

#11926940

C₄

yes

—

#11926580

—

C₄×#64520

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

C₁₉×#533

C₂²

yes

characteristic

C₁₉×#446

—

C₈×Q₈×C₁₉

—

C₁₉×#433

—

C₁₉×#431

C₂²

yes

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×#125

D₄

yes

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂²×C₁₉⋊C₈

—

#10597316

—

#10597315

C₂×C₄

yes

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

#10597265

—

#10597264

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₄×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×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

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×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

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#3160

—

#2986

D₁₉

yes

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

—

100

C₂²×C₁₉

#386

yes

characteristic

101

C₄×C₁₉

—

102

C₄×C₁₉

—

103

C₄×C₁₉

—

104

C₄×C₁₉

#443

yes

—

105

C₄×C₁₉

#444

yes

—

106

C₄×C₁₉

#456

yes

—

107

Dic₁₉

—

108

#533

—

109

#533

C₂×D₁₉

yes

characteristic

110

#500

—

111

#499

—

112

#498

—

113

#446

—

114

C₈×Q₈

—

115

#433

—

116

#431

C₂×D₁₉

yes

—

117

#427

—

118

C₄×M₁₆

—

119

C₂×C₄×C₈

—

120

#330

—

121

Q₈⋊C₈

—

122

Q₈⋊C₈

—

123

C₂×C₁₉

—

124

C₂×C₁₉

#1876

yes

—

125

C₂×C₁₉

#1886

yes

characteristic

126

C₂×M₁₆

—

127

C₂²×C₈

—

128

C₄⋊Q₈

—

129

C₄⋊Q₈

C₄×D₁₉

yes

—

130

#125

—

131

#125

D₇₆

yes

—

132

C₂²⋊Q₈

—

133

C₂²⋊Q₈

—

134

C₄×Q₈

—

135

C₄×Q₈

—

136

#117

—

137

#117

C₂²⋊D₁₉

yes

—

138

C₂×C₄²

C₂²×D₁₉

yes

characteristic

139

#107

—

140

#106

—

141

C₄⋊C₈

—

142

C₄⋊C₈

C₂²⋊D₁₉

yes

—

143

C₄⋊C₈

C₂²⋊D₁₉

yes

—

144

C₂²⋊C₈

—

145

#97

—

146

#97

—

147

C₄×C₈

—

148

C₄×C₈

—

149

C₄×C₈

—

150

C₄×C₈

—

151

C₄×C₈

—

152

C₄×C₈

—

153

C₁₉

#9068

yes

characteristic, complemented, Sylow

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂²×C₄

#64541

yes

—

157

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

158

M₁₆

—

159

M₁₆

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

(C₂×D₁₉)⋊C₄

yes

—

172

C₂²⋊C₄

—

173

C₂²⋊C₄

—

174

C₄²

—

175

C₄²

—

176

C₄²

C₂×C₄×D₁₉

yes

characteristic

177

C₄²

C₂×D₇₆

yes

characteristic

178

C₄²

C₂×C₂²⋊D₁₉

yes

—

179

C₂³

#10597375

yes

characteristic

180

Q₈

—

181

Q₈

—

182

Q₈

—

183

Q₈

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

190

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

191

C₂×C₄

#10597376

yes

—

192

C₂×C₄

#10597399

yes

characteristic

193

C₈

—

194

C₈

—

195

C₈

—

196

C₈

—

197

C₈

—

198

C₂²

—

199

C₂²

—

200

C₂²

#11926423

yes

characteristic

201

C₄

—

202

C₄

—

203

C₄

—

204

C₄

—

152

—

205

C₄

#11926659

yes

—

206

C₄

#11926664

yes

—

207

C₄

#11926727

yes

—

208

C₂

—

209

C₂

#14563962

yes

—

210

C₂

#14564028

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2986	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂³×C₁₉	#123
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2986	D₁₉
hypocenter	C₁₉	#9068
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2986

subgroup

G/H

center

C₂×C₄

#10597399

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2986

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2986

N	H ≅ G/N	type
153. C₁₉	#9068	semidirect

H ≅ G/N

type

153. C₁₉

#9068

semidirect

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

subgroup	index
#14574145	2
#14562230	2
#14562055	2
#14561471	2
C₁₉×#2986	2
#9068	19

subgroup

index

C₁₉×#2986

Subgroups — #18077855

Conjugacy classes of subgroups

Complements

Maximal subgroups