Group #18073236 — subgroups

Subgroups — #18073236

Order 4864.

412 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 143 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	#14572277	C₂	1	1	yes	maximal, characteristic
2	#14562015	C₂	1	2	yes	maximal
3	C₂×#11926265	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561471	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1452	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#64541	C₂²	1	1	yes	characteristic
7	#11926603	—	2	2	no	—
8	#11926595	—	2	2	no	—
9	#11926570	C₄	1	2	yes	—
10	#11926510	C₄	1	2	yes	—
11	C₄×#64520	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
13	#11926274	C₄	1	4	yes	—
14	#11926271	C₄	1	4	yes	—
15	#11926265	—	2	2	no	—
16	C₁₉×#431	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#322	—	2	2	no	—
19	C₂×#64541	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
21	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	C₄×C₂²⋊D₁₉	—	2	2	no	—
23	#10597372	C₂×C₄	1	1	yes	characteristic
24	C₂×#64520	C₂×C₄	1	2	yes	—
25	C₂²×C₁₉⋊C₈	—	2	2	no	—
26	C₄×D₇₆	C₂×C₄	1	2	yes	—
27	#10597318	—	2	1	no	—
28	C₄²×D₁₉	—	2	1	no	—
29	C₄×Dic₃₈	C₂×C₄	1	2	yes	—
30	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
31	C₁₉×C₂²⋊C₈	—	2	2	no	—
32	C₄×C₈×C₁₉	—	2	2	no	—
33	C₄×C₈×C₁₉	D₄	1	2	yes	—
34	C₄×C₈×C₁₉	D₄	1	2	yes	—
35	(C₂×D₁₉)⋊C₈	—	2	4	no	—
36	Dic₁₉⋊C₈	—	2	4	no	—
37	#10597260	—	2	1	no	—
38	C₄×C₁₉⋊C₈	—	2	1	no	—
39	C₄×C₁₉⋊C₈	—	2	2	no	—
40	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
41	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	#41	1	2	yes	—
43	C₂×C₂²⋊D₁₉	—	2	1	no	—
44	#64541	—	2	4	no	—
45	C₂×D₇₆	C₄²	1	1	yes	characteristic
46	C₂×C₄×D₁₉	—	2	1	no	—
47	C₂×C₄×D₁₉	—	2	2	no	—
48	C₂×Dic₃₈	C₄²	1	1	yes	characteristic
49	C₂×C₈×C₁₉	—	2	4	no	—
50	C₂×C₈×C₁₉	—	2	4	no	—
51	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
52	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
53	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂²⋊Dic₁₉	—	2	1	no	—
56	(C₂×D₁₉)⋊C₄	—	2	2	no	—
57	C₄⋊Dic₁₉	C₄²	1	2	yes	—
58	Dic₁₉⋊C₄	—	2	2	no	—
59	C₄×Dic₁₉	—	2	1	no	—
60	C₄×Dic₁₉	—	2	2	no	—
61	#64520	—	2	4	no	—
62	C₂×C₁₉⋊C₈	—	2	2	no	—
63	C₂×C₁₉⋊C₈	—	2	4	no	—
64	C₂×C₁₉⋊C₈	—	4	4	no	—
65	#8188	—	19	1	no	maximal, Sylow
66	C₂³×C₁₉	#117	1	1	yes	characteristic
67	C₂²×D₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	4	no	—
69	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
70	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
72	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
73	C₂×C₄×C₁₉	#131	1	4	yes	—
74	C₂²⋊D₁₉	—	4	2	no	—
75	C₂×Dic₁₉	—	2	1	no	—
76	C₂×Dic₁₉	—	2	2	no	—
77	D₇₆	—	2	2	no	—
78	C₄×D₁₉	—	4	2	no	—
79	C₄×D₁₉	—	4	4	no	—
80	Dic₃₈	—	2	2	no	—
81	C₈×C₁₉	—	2	4	no	—
82	C₈×C₁₉	—	4	4	no	—
83	C₁₉⋊C₈	—	4	4	no	—
84	C₁₉⋊C₈	—	4	2	no	—
85	#2922	—	19	1	no	—
86	#1476	—	19	2	no	—
87	#1452	D₁₉	1	1	yes	characteristic, complemented
88	C₂×#322	—	19	1	no	—
89	#1278	—	19	2	no	—
90	C₂²×C₁₉	—	2	2	no	—
91	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₁₉	#433	1	2	yes	—
93	C₂×D₁₉	—	4	1	no	—
94	C₂×D₁₉	—	4	2	no	—
95	C₄×C₁₉	—	2	2	no	—
96	C₄×C₁₉	#405	1	2	yes	—
97	C₄×C₁₉	#408	1	2	yes	—
98	C₄×C₁₉	#444	1	4	yes	—
99	Dic₁₉	—	4	1	no	—
100	Dic₁₉	—	4	2	no	—
101	C₄×#41	—	19	1	no	—
102	#433	—	38	2	no	—
103	#431	—	38	2	no	—
104	#431	C₂×D₁₉	1	2	yes	—
105	#424	—	19	2	no	—
106	#408	—	19	2	no	—
107	C₄×M₁₆	—	19	1	no	—
108	C₂×C₄×C₈	—	19	2	no	—
109	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
110	Q₈⋊C₈	—	19	4	no	—
111	D₄⋊C₈	—	19	4	no	—
112	#322	—	2	2	no	—
113	#322	—	38	2	no	—
114	C₂×C₁₉	—	2	2	no	—
115	C₂×C₁₉	#1750	1	1	yes	characteristic
116	C₂×C₁₉	#1765	1	2	yes	—
117	D₁₉	—	8	1	no	—
118	C₂×#41	—	19	1	no	—
119	C₂×M₁₆	—	19	2	no	—
120	C₂²×C₈	—	38	2	no	—
121	C₂²×C₈	C₄×D₁₉	1	2	yes	—
122	C₄×Q₈	—	19	2	no	—
123	C₄×D₄	—	19	2	no	—
124	C₄×D₄	—	38	2	no	—
125	#117	—	19	1	no	—
126	#117	—	38	1	no	—
127	C₂×C₄²	—	38	1	no	—
128	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
129	C₄⋊C₈	—	38	4	no	—
130	C₄⋊C₈	C₄×D₁₉	1	4	yes	—
131	C₂²⋊C₈	—	2	2	no	—
132	C₂²⋊C₈	—	38	4	no	—
133	#97	—	38	1	no	—
134	C₄×C₈	—	2	2	no	—
135	C₄×C₈	—	19	4	no	—
136	C₄×C₈	—	38	2	no	—
137	C₄×C₈	—	38	1	no	—
138	C₄×C₈	D₇₆	1	2	yes	—
139	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
140	C₁₉	#8188	1	1	yes	characteristic, complemented, Sylow
141	#41	—	38	4	no	—
142	C₂×Q₈	—	19	1	no	—
143	C₂×D₄	—	19	1	no	—
144	C₂×D₄	—	38	1	no	—
145	C₂²×C₄	—	38	1	no	—
146	C₂²×C₄	—	38	2	no	—
147	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
148	C₂²×C₄	#64541	1	2	yes	—
149	M₁₆	—	38	4	no	—
150	C₂×C₈	—	2	4	no	—
151	C₂×C₈	—	2	4	no	—
152	C₂×C₈	—	38	4	no	—
153	C₂×C₈	—	38	2	no	—
154	C₂×C₈	—	76	4	no	—
155	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
156	C₄⋊C₄	—	19	2	no	—
157	C₄⋊C₄	—	38	2	no	—
158	C₂²⋊C₄	—	38	1	no	—
159	C₂²⋊C₄	—	38	2	no	—
160	C₄²	—	38	1	no	—
161	C₄²	—	38	2	no	—
162	C₄²	C₂×C₄×D₁₉	1	2	yes	—
163	C₄²	C₂×D₇₆	1	1	yes	characteristic
164	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
165	C₂³	—	38	1	no	—
166	C₂³	#10597318	1	1	yes	characteristic
167	Q₈	—	38	2	no	—
168	D₄	—	38	2	no	—
169	D₄	—	76	2	no	—
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	38	2	no	—
172	C₂×C₄	—	38	1	no	—
173	C₂×C₄	—	76	4	no	—
174	C₂×C₄	—	76	2	no	—
175	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
176	C₂×C₄	C₄×D₇₆	1	2	yes	—
177	C₂×C₄	#10597353	1	4	yes	—
178	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
179	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
180	C₈	—	2	4	no	—
181	C₈	—	4	4	no	—
182	C₈	—	76	4	no	—
183	C₈	—	76	2	no	—
184	C₂²	—	2	2	no	—
185	C₂²	—	76	1	no	—
186	C₂²	—	76	2	no	—
187	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
188	C₂²	#11926606	1	2	yes	—
189	C₄	—	2	2	no	—
190	C₄	—	76	1	no	—
191	C₄	—	76	2	no	—
192	C₄	#11926501	1	2	yes	—
193	C₄	#11926512	1	2	yes	—
194	C₄	#11926664	1	4	yes	—
195	C₂	—	2	2	no	—
196	C₂	—	152	1	no	—
197	C₂	#14563404	1	1	yes	characteristic
198	C₂	#14563481	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14572277

C₂

yes

maximal, characteristic

#14562015

C₂

yes

maximal

C₂×#11926265

C₂

yes

maximal, characteristic, complemented

#14561471

C₂

yes

maximal, complemented

C₁₉×#1452

C₂

yes

maximal, characteristic, complemented

C₄×#64541

C₂²

yes

—

—

C₄

yes

—

#11926510

C₄

yes

—

C₄×#64520

C₂²

yes

characteristic

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926274

C₄

yes

—

#11926271

C₄

yes

—

#11926265

—

C₁₉×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

—

C₂×#64541

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₄×C₂²⋊D₁₉

—

#10597372

C₂×C₄

yes

characteristic

C₂×#64520

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

—

C₄×D₇₆

C₂×C₄

yes

—

#10597318

—

C₄²×D₁₉

—

C₄×Dic₃₈

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

C₂×C₄

yes

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

(C₂×D₁₉)⋊C₈

—

Dic₁₉⋊C₈

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₂²⋊D₁₉

—

#64541

—

C₂×D₇₆

C₄²

yes

characteristic

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

C₄²

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₄²×C₁₉

C₂²×C₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

C₄²

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2922

—

#1476

—

#1452

D₁₉

yes

characteristic, complemented

C₂×#322

—

#1278

—

C₂²×C₁₉

—

C₂²×C₁₉

C₄×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

#433

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#405

yes

—

C₄×C₁₉

#408

yes

—

C₄×C₁₉

#444

yes

—

Dic₁₉

—

100

Dic₁₉

—

101

C₄×#41

—

102

#433

—

103

#431

—

104

#431

C₂×D₁₉

yes

—

105

#424

—

106

#408

—

107

C₄×M₁₆

—

108

C₂×C₄×C₈

—

109

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

110

Q₈⋊C₈

—

111

D₄⋊C₈

—

112

#322

—

113

#322

—

114

C₂×C₁₉

—

115

C₂×C₁₉

#1750

yes

characteristic

116

C₂×C₁₉

#1765

yes

—

117

D₁₉

—

118

C₂×#41

—

119

C₂×M₁₆

—

120

C₂²×C₈

—

121

C₂²×C₈

C₄×D₁₉

yes

—

122

C₄×Q₈

—

123

C₄×D₄

—

124

C₄×D₄

—

125

#117

—

126

#117

—

127

C₂×C₄²

—

128

C₂×C₄²

C₂²×D₁₉

yes

characteristic

129

C₄⋊C₈

—

130

C₄⋊C₈

C₄×D₁₉

yes

—

131

C₂²⋊C₈

—

132

C₂²⋊C₈

—

133

#97

—

134

C₄×C₈

—

135

C₄×C₈

—

136

C₄×C₈

—

137

C₄×C₈

—

138

C₄×C₈

D₇₆

yes

—

139

C₄×C₈

C₂²⋊D₁₉

yes

—

140

C₁₉

#8188

yes

characteristic, complemented, Sylow

141

#41

—

142

C₂×Q₈

—

143

C₂×D₄

—

144

C₂×D₄

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

148

C₂²×C₄

#64541

yes

—

149

M₁₆

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₂²⋊C₄

—

159

C₂²⋊C₄

—

160

C₄²

—

161

C₄²

—

162

C₄²

C₂×C₄×D₁₉

yes

—

163

C₄²

C₂×D₇₆

yes

characteristic

164

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

165

C₂³

—

166

C₂³

#10597318

yes

characteristic

167

Q₈

—

168

D₄

—

169

D₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

C₄²×D₁₉

yes

characteristic

176

C₂×C₄

C₄×D₇₆

yes

—

177

C₂×C₄

#10597353

yes

—

178

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

179

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

180

C₈

—

181

C₈

—

182

C₈

—

183

C₈

—

184

C₂²

—

185

C₂²

—

186

C₂²

—

187

C₂²

C₄×(C₂×D₁₉)⋊C₄

yes

characteristic

188

C₂²

#11926606

yes

—

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

#11926501

yes

—

193

C₄

#11926512

yes

—

194

C₄

#11926664

yes

—

195

C₂

—

196

C₂

—

152

—

197

C₂

#14563404

yes

characteristic

198

C₂

#14563481

yes

—

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1452	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
prime radical	C₂×#64541	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1452	D₁₉
hypocenter	C₁₉	#8188
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ #1452

subgroup

G/H

center

C₄²

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1452

C₂

socle

C₂²×C₁₉

C₄×C₂²⋊C₄

prime radical

C₂×#64541

C₂×C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ #1452

N	H ≅ G/N	type
3. C₂×#11926265	C₂	semidirect
4. #14561471	C₂	semidirect
5. C₁₉×#1452	C₂	semidirect
87. #1452	D₁₉	semidirect
140. C₁₉	#8188	semidirect

H ≅ G/N

type

3. C₂×#11926265

C₂

semidirect

4. #14561471

C₂

semidirect

5. C₁₉×#1452

C₂

semidirect

87. #1452

D₁₉

semidirect

140. C₁₉

#8188

semidirect

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

subgroup	index
#14572277	2
#14562015	2
C₂×#11926265	2
#14561471	2
C₁₉×#1452	2
#8188	19

subgroup

index

C₁₉×#1452

Subgroups — #18073236

Conjugacy classes of subgroups

Complements

Maximal subgroups