Group #18080144 — subgroups

Subgroups — #18080144

Order 4864.

400 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 111 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	#14572737	C₂	1	1	yes	maximal, characteristic
2	#14562373	C₂	1	1	yes	maximal, characteristic
3	#14562320	C₂	1	2	yes	maximal
4	#14561525	C₂	1	2	yes	maximal
5	C₁₉×#3139	C₂	1	1	yes	maximal, characteristic
6	#11926675	—	2	2	no	—
7	Q₈×C₁₉⋊C₈	—	2	2	no	—
8	#11926605	—	2	2	no	—
9	#11926597	C₂²	1	2	yes	—
10	#11926568	C₂²	1	2	yes	—
11	#11926290	—	2	2	no	—
12	#11926290	—	2	2	no	—
13	#11926290	—	2	2	no	—
14	C₁₉×#533	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₁₉×#491	C₄	1	4	yes	—
17	C₁₉×#487	—	2	2	no	—
18	C₁₉×#419	—	2	2	no	—
19	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×C₁₉	—	2	1	no	—
21	C₂×M₁₆×C₁₉	—	2	1	no	—
22	C₁₉×C₄⋊Q₈	—	2	2	no	—
23	C₁₉×C₄⋊Q₈	—	2	1	no	—
24	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
25	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
26	C₁₉×#125	C₂×C₄	1	2	yes	—
27	C₁₉×C₂²⋊Q₈	—	2	2	no	—
28	C₄×Q₈×C₁₉	—	2	2	no	—
29	C₁₉×#117	D₄	1	2	yes	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	C₂×#64520	—	2	2	no	—
33	C₁₉×#103	—	2	8	no	—
34	C₁₉×#97	C₂×C₄	1	2	yes	—
35	C₄×C₈×C₁₉	—	2	1	no	—
36	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
41	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
42	#10597260	—	2	2	no	—
43	C₄×C₁₉⋊C₈	—	2	2	no	—
44	C₄×C₁₉⋊C₈	—	2	2	no	—
45	C₂×Q₈×C₁₉	—	2	2	no	—
46	C₂×Q₈×C₁₉	—	2	2	no	—
47	C₂×Q₈×C₁₉	—	4	4	no	—
48	C₂×Q₈×C₁₉	—	4	1	no	—
49	C₂²×C₄×C₁₉	—	4	1	no	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	#41	1	2	yes	—
52	M₁₆×C₁₉	—	4	2	no	—
53	C₂×C₈×C₁₉	—	2	2	no	—
54	C₄⋊C₄×C₁₉	—	2	4	no	—
55	C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₄⋊C₄×C₁₉	—	2	4	no	—
57	C₄⋊C₄×C₁₉	—	4	2	no	—
58	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
59	C₂²⋊C₄×C₁₉	—	2	2	no	—
60	C₄²×C₁₉	—	2	2	no	—
61	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₄²×C₁₉	C₂×D₄	1	2	yes	—
63	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
64	#64520	—	8	2	no	—
65	C₂×C₁₉⋊C₈	—	2	2	no	—
66	C₂×C₁₉⋊C₈	—	2	2	no	—
67	C₂×C₁₉⋊C₈	—	4	2	no	—
68	#9436	—	19	1	no	maximal, Sylow
69	C₂³×C₁₉	#123	1	1	yes	characteristic
70	Q₈×C₁₉	—	4	4	no	—
71	Q₈×C₁₉	—	4	2	no	—
72	Q₈×C₁₉	—	4	2	no	—
73	Q₈×C₁₉	—	8	2	no	—
74	C₂×C₄×C₁₉	—	2	2	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	—	2	4	no	—
78	C₂×C₄×C₁₉	—	4	2	no	—
79	C₂×C₄×C₁₉	—	8	2	no	—
80	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
82	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#121	1	2	yes	—
84	C₈×C₁₉	—	4	2	no	—
85	C₁₉⋊C₈	—	4	2	no	—
86	C₁₉⋊C₈	—	4	2	no	—
87	C₁₉⋊C₈	—	8	2	no	—
88	#3139	D₁₉	1	1	yes	characteristic
89	#2986	—	19	1	no	—
90	#1561	—	19	1	no	—
91	#1549	—	19	2	no	—
92	#1299	—	19	2	no	—
93	C₂²×C₁₉	—	2	1	no	—
94	C₂²×C₁₉	—	2	2	no	—
95	C₂²×C₁₉	#386	1	1	yes	characteristic
96	C₄×C₁₉	—	2	1	no	—
97	C₄×C₁₉	—	2	2	no	—
98	C₄×C₁₉	—	4	4	no	—
99	C₄×C₁₉	—	8	2	no	—
100	C₄×C₁₉	#454	1	2	yes	—
101	C₄×C₁₉	#471	1	2	yes	—
102	C₄×C₁₉	#473	1	2	yes	—
103	#533	C₂×D₁₉	1	1	yes	characteristic
104	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
105	#491	Dic₁₉	1	4	yes	—
106	#487	—	2	2	no	—
107	#446	—	38	2	no	—
108	C₈×Q₈	—	38	2	no	—
109	#433	—	38	2	no	—
110	#431	—	19	2	no	—
111	#423	—	19	2	no	—
112	#419	—	2	2	no	—
113	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
114	#332	—	38	2	no	—
115	#332	—	38	2	no	—
116	#332	—	38	2	no	—
117	C₂×C₁₉	—	4	1	no	—
118	C₂×C₁₉	#1888	1	1	yes	characteristic
119	C₂×C₁₉	#1908	1	2	yes	—
120	C₂²×Q₈	—	2	1	no	—
121	C₂×M₁₆	—	2	1	no	—
122	C₂×M₁₆	—	38	2	no	—
123	C₄⋊Q₈	—	2	2	no	—
124	C₄⋊Q₈	—	2	1	no	—
125	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
126	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
127	#125	C₂×Dic₁₉	1	2	yes	—
128	C₂²⋊Q₈	—	2	2	no	—
129	C₄×Q₈	—	2	2	no	—
130	#117	C₂²⋊D₁₉	1	2	yes	—
131	C₂×C₄⋊C₄	—	2	2	no	—
132	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
133	C₄⋊C₈	—	19	2	no	—
134	C₄⋊C₈	—	19	2	no	—
135	C₄⋊C₈	—	38	4	no	—
136	C₄⋊C₈	—	38	2	no	—
137	C₄⋊C₈	—	38	2	no	—
138	#103	—	2	8	no	—
139	C₂²⋊C₈	—	38	2	no	—
140	#97	—	38	2	no	—
141	#97	C₂×Dic₁₉	1	2	yes	—
142	C₄×C₈	—	2	1	no	—
143	C₄×C₈	—	38	2	no	—
144	C₄×C₈	—	38	2	no	—
145	C₁₉	#9436	1	1	yes	characteristic, complemented, Sylow
146	C₂×Q₈	—	2	2	no	—
147	C₂×Q₈	—	2	2	no	—
148	C₂×Q₈	—	4	4	no	—
149	C₂×Q₈	—	4	1	no	—
150	C₂²×C₄	—	4	1	no	—
151	C₂²×C₄	#64543	1	2	yes	—
152	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
153	M₁₆	—	4	2	no	—
154	M₁₆	—	152	2	no	—
155	C₂×C₈	—	2	2	no	—
156	C₂×C₈	—	38	2	no	—
157	C₂×C₈	—	38	2	no	—
158	C₂×C₈	—	76	2	no	—
159	C₄⋊C₄	—	2	4	no	—
160	C₄⋊C₄	—	2	2	no	—
161	C₄⋊C₄	—	2	4	no	—
162	C₄⋊C₄	—	4	2	no	—
163	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
164	C₂²⋊C₄	—	2	2	no	—
165	C₄²	—	2	2	no	—
166	C₄²	D₄×D₁₉	1	2	yes	—
167	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
168	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
169	C₂³	#10597381	1	1	yes	characteristic
170	Q₈	—	4	4	no	—
171	Q₈	—	4	2	no	—
172	Q₈	—	4	2	no	—
173	Q₈	—	8	2	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	4	2	no	—
179	C₂×C₄	—	8	2	no	—
180	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
181	C₂×C₄	#10597383	1	1	yes	characteristic
182	C₂×C₄	#10597385	1	2	yes	—
183	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
184	C₈	—	4	2	no	—
185	C₈	—	76	2	no	—
186	C₈	—	76	2	no	—
187	C₈	—	152	2	no	—
188	C₂²	—	2	2	no	—
189	C₂²	—	2	1	no	—
190	C₂²	#11926424	1	1	yes	characteristic
191	C₄	—	2	2	no	—
192	C₄	—	2	1	no	—
193	C₄	—	4	4	no	—
194	C₄	—	8	2	no	—
195	C₄	#11926716	1	2	yes	—
196	C₄	#11926809	1	2	yes	—
197	C₄	#11926817	1	2	yes	—
198	C₂	—	4	1	no	—
199	C₂	#14564039	1	1	yes	characteristic
200	C₂	#14564152	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14572737

C₂

yes

maximal, characteristic

#14562373

C₂

yes

maximal, characteristic

#14562320

C₂

yes

maximal

#14561525

C₂

yes

maximal

C₁₉×#3139

C₂

yes

maximal, characteristic

#11926675

—

Q₈×C₁₉⋊C₈

—

#11926605

—

#11926597

C₂²

yes

—

#11926568

C₂²

yes

—

#11926290

—

#11926290

—

#11926290

—

C₁₉×#533

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#491

C₄

yes

—

C₁₉×#487

—

C₁₉×#419

—

C₄×M₁₆×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#125

C₂×C₄

yes

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₁₉×#103

—

C₁₉×#97

C₂×C₄

yes

—

C₄×C₈×C₁₉

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×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

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×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

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#3139

D₁₉

yes

—

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#386

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

100

C₄×C₁₉

#454

yes

—

101

C₄×C₁₉

#471

yes

—

102

C₄×C₁₉

#473

yes

—

103

#533

C₂×D₁₉

yes

characteristic

104

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

105

#491

Dic₁₉

yes

—

106

#487

—

107

#446

—

108

C₈×Q₈

—

109

#433

—

110

#431

—

111

#423

—

112

#419

—

113

C₄×M₁₆

C₂×D₁₉

yes

characteristic

114

#332

—

115

#332

—

116

#332

—

117

C₂×C₁₉

—

118

C₂×C₁₉

#1888

yes

characteristic

119

C₂×C₁₉

#1908

yes

—

120

C₂²×Q₈

—

121

C₂×M₁₆

—

122

C₂×M₁₆

—

123

C₄⋊Q₈

—

124

C₄⋊Q₈

—

125

C₄⋊Q₈

C₂×Dic₁₉

yes

—

126

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

127

#125

C₂×Dic₁₉

yes

—

128

C₂²⋊Q₈

—

129

C₄×Q₈

—

130

#117

C₂²⋊D₁₉

yes

—

131

C₂×C₄⋊C₄

—

132

C₂×C₄²

C₂²×D₁₉

yes

characteristic

133

C₄⋊C₈

—

134

C₄⋊C₈

—

135

C₄⋊C₈

—

136

C₄⋊C₈

—

137

C₄⋊C₈

—

138

#103

—

139

C₂²⋊C₈

—

140

#97

—

141

#97

C₂×Dic₁₉

yes

—

142

C₄×C₈

—

143

C₄×C₈

—

144

C₄×C₈

—

145

C₁₉

#9436

yes

characteristic, complemented, Sylow

146

C₂×Q₈

—

147

C₂×Q₈

—

148

C₂×Q₈

—

149

C₂×Q₈

—

150

C₂²×C₄

—

151

C₂²×C₄

#64543

yes

—

152

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

153

M₁₆

—

154

M₁₆

—

152

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₄⋊C₄

—

160

C₄⋊C₄

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

164

C₂²⋊C₄

—

165

C₄²

—

166

C₄²

D₄×D₁₉

yes

—

167

C₄²

C₂²×Dic₁₉

yes

characteristic

168

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

169

C₂³

#10597381

yes

characteristic

170

Q₈

—

171

Q₈

—

172

Q₈

—

173

Q₈

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

D₄×Dic₁₉

yes

—

181

C₂×C₄

#10597383

yes

characteristic

182

C₂×C₄

#10597385

yes

—

183

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

184

C₈

—

185

C₈

—

186

C₈

—

187

C₈

—

152

—

188

C₂²

—

189

C₂²

—

190

C₂²

#11926424

yes

characteristic

191

C₄

—

192

C₄

—

193

C₄

—

194

C₄

—

195

C₄

#11926716

yes

—

196

C₄

#11926809

yes

—

197

C₄

#11926817

yes

—

198

C₂

—

199

C₂

#14564039

yes

characteristic

200

C₂

#14564152

yes

—

	subgroup	G/H
center	C₂²	#11926424
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3139	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂³×C₁₉	#123
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3139	D₁₉
hypocenter	C₁₉	#9436
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3139

subgroup

G/H

center

C₂²

#11926424

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3139

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3139

N	H ≅ G/N	type
145. C₁₉	#9436	semidirect

H ≅ G/N

type

145. C₁₉

#9436

semidirect

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

subgroup	index
#14572737	2
#14562373	2
#14562320	2
#14561525	2
C₁₉×#3139	2
#9436	19

subgroup

index

C₁₉×#3139

Subgroups — #18080144

Conjugacy classes of subgroups

Complements

Maximal subgroups