Group #18076211 — subgroups

Subgroups — #18076211

Order 4864.

322 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 131 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	#14563751	C₂	1	2	yes	maximal
2	#14563380	C₂	1	1	yes	maximal, characteristic
3	#14561470	C₂	1	1	yes	maximal, characteristic
4	#14561469	C₂	1	2	yes	maximal
5	C₁₉×#1277	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
9	#11926298	—	2	2	no	—
10	#11926298	—	2	2	no	—
11	#11926298	C₄	1	2	yes	—
12	#11926298	C₄	1	2	yes	—
13	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	—	2	2	no	—
16	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
18	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
19	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
20	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
21	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
22	C₂²×C₁₉⋊C₈	—	2	2	no	—
23	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₁₉×C₄⋊C₈	—	2	2	no	—
26	C₁₉×C₄⋊C₈	—	2	2	no	—
27	C₄×C₈×C₁₉	—	2	2	no	—
28	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
29	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
30	C₄×C₁₉⋊C₈	—	2	2	no	—
31	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
34	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
35	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
36	C₂×C₈×C₁₉	—	2	2	no	—
37	C₂×C₈×C₁₉	—	2	2	no	—
38	C₂×C₈×C₁₉	—	2	2	no	—
39	C₂×C₈×C₁₉	—	4	2	no	—
40	C₂×C₈×C₁₉	—	4	2	no	—
41	C₂×C₈×C₁₉	—	4	2	no	—
42	C₄²×C₁₉	#41	1	2	yes	—
43	C₄²×C₁₉	#41	1	2	yes	—
44	C₄×Dic₁₉	—	2	2	no	—
45	C₄×Dic₁₉	—	2	2	no	—
46	C₄×Dic₁₉	—	2	1	no	—
47	C₄×Dic₁₉	—	2	2	no	—
48	C₄×Dic₁₉	—	2	1	no	—
49	C₄×Dic₁₉	—	4	2	no	—
50	C₂×C₁₉⋊C₈	—	2	1	no	—
51	C₂×C₁₉⋊C₈	—	2	1	no	—
52	C₂×C₁₉⋊C₈	—	2	2	no	—
53	C₂×C₁₉⋊C₈	—	2	2	no	—
54	C₂×C₁₉⋊C₈	—	4	2	no	—
55	C₂×C₁₉⋊C₈	—	4	2	no	—
56	C₂×C₁₉⋊C₈	—	4	2	no	—
57	#8788	—	19	1	no	maximal, Sylow
58	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
61	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
62	C₂×C₄×C₁₉	#124	1	2	yes	—
63	C₂×C₄×C₁₉	#125	1	2	yes	—
64	C₂×C₄×C₁₉	#131	1	2	yes	—
65	C₂×C₄×C₁₉	#131	1	2	yes	—
66	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#135	1	2	yes	—
68	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
69	C₂×Dic₁₉	—	2	2	no	—
70	C₂×Dic₁₉	—	2	2	no	—
71	C₂×Dic₁₉	—	2	2	no	—
72	C₂×Dic₁₉	—	2	2	no	—
73	C₂×Dic₁₉	—	2	2	no	—
74	C₂×Dic₁₉	—	2	2	no	—
75	C₈×C₁₉	—	4	2	no	—
76	C₈×C₁₉	—	8	2	no	—
77	C₁₉⋊C₈	—	4	1	no	—
78	C₁₉⋊C₈	—	4	1	no	—
79	C₁₉⋊C₈	—	8	2	no	—
80	#1831	—	19	2	no	—
81	#1744	—	19	1	no	—
82	#1277	—	19	2	no	—
83	#1277	—	19	1	no	—
84	#1277	D₁₉	1	1	yes	characteristic
85	C₂²×C₁₉	#382	1	1	yes	characteristic
86	C₂²×C₁₉	#424	1	2	yes	—
87	C₂²×C₁₉	#427	1	1	yes	characteristic
88	C₂²×C₁₉	#427	1	1	yes	characteristic
89	C₂²×C₁₉	#430	1	2	yes	—
90	C₄×C₁₉	—	2	2	no	—
91	C₄×C₁₉	#433	1	2	yes	—
92	C₄×C₁₉	#433	1	1	yes	characteristic
93	C₄×C₁₉	#433	1	1	yes	characteristic
94	C₄×C₁₉	#488	1	2	yes	—
95	C₄×C₁₉	#488	1	2	yes	—
96	Dic₁₉	—	4	2	no	—
97	Dic₁₉	—	4	2	no	—
98	C₂×C₄⋊C₈	—	19	2	no	—
99	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
100	C₂×C₄×C₈	—	19	1	no	—
101	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
102	C₄³	—	19	1	no	—
103	#336	—	19	2	no	—
104	#336	—	19	2	no	—
105	#336	—	38	2	no	—
106	#336	—	38	2	no	—
107	C₂×C₁₉	#1572	1	2	yes	—
108	C₂×C₁₉	#1572	1	2	yes	—
109	C₂×C₁₉	#1832	1	1	yes	characteristic
110	C₂×C₁₉	#1835	1	1	yes	characteristic
111	C₂×C₁₉	#1838	1	1	yes	characteristic
112	C₂²×C₈	—	2	2	no	—
113	C₂²×C₈	—	19	1	no	—
114	C₂²×C₈	—	19	1	no	—
115	C₂²×C₈	—	38	2	no	—
116	C₂²×C₈	C₄×D₁₉	1	2	yes	—
117	C₂×C₄²	—	19	2	no	—
118	C₂×C₄²	—	19	1	no	—
119	C₂×C₄²	—	19	1	no	—
120	C₂×C₄²	—	19	2	no	—
121	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
122	C₄⋊C₈	—	2	2	no	—
123	C₄⋊C₈	—	2	2	no	—
124	C₄⋊C₈	—	38	2	no	—
125	C₄⋊C₈	—	38	2	no	—
126	C₄×C₈	—	2	2	no	—
127	C₄×C₈	—	38	2	no	—
128	C₁₉	#8788	1	1	yes	characteristic, complemented, Sylow
129	C₂²×C₄	—	19	2	no	—
130	C₂²×C₄	—	19	2	no	—
131	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
132	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
133	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
134	C₂×C₈	—	2	2	no	—
135	C₂×C₈	—	2	2	no	—
136	C₂×C₈	—	2	2	no	—
137	C₂×C₈	—	4	2	no	—
138	C₂×C₈	—	4	2	no	—
139	C₂×C₈	—	4	2	no	—
140	C₂×C₈	—	38	1	no	—
141	C₂×C₈	—	38	1	no	—
142	C₂×C₈	—	38	2	no	—
143	C₂×C₈	—	38	2	no	—
144	C₂×C₈	—	76	2	no	—
145	C₂×C₈	—	76	2	no	—
146	C₂×C₈	—	76	2	no	—
147	C₄²	—	38	2	no	—
148	C₄²	—	38	2	no	—
149	C₄²	—	38	1	no	—
150	C₄²	—	38	2	no	—
151	C₄²	—	38	1	no	—
152	C₄²	—	76	2	no	—
153	C₄²	#64541	1	2	yes	—
154	C₄²	#64543	1	2	yes	—
155	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	38	2	no	—
158	C₂×C₄	—	38	2	no	—
159	C₂×C₄	—	38	2	no	—
160	C₂×C₄	—	38	2	no	—
161	C₂×C₄	—	38	2	no	—
162	C₂×C₄	—	38	2	no	—
163	C₂×C₄	#10597318	1	1	yes	characteristic
164	C₂×C₄	#10597323	1	1	yes	characteristic
165	C₂×C₄	#10597331	1	2	yes	—
166	C₂×C₄	#10597335	1	2	yes	—
167	C₂×C₄	#10597347	1	2	yes	—
168	C₂×C₄	#10597353	1	2	yes	—
169	C₂×C₄	#10597358	1	1	yes	characteristic
170	C₂×C₄	#10597362	1	2	yes	—
171	C₂×C₄	#10597365	1	1	yes	characteristic
172	C₈	—	4	2	no	—
173	C₈	—	8	2	no	—
174	C₈	—	76	1	no	—
175	C₈	—	76	1	no	—
176	C₈	—	152	2	no	—
177	C₂²	#11926408	1	1	yes	characteristic
178	C₂²	#11926569	1	2	yes	—
179	C₂²	#11926579	1	1	yes	characteristic
180	C₂²	#11926581	1	1	yes	characteristic
181	C₂²	#11926591	1	2	yes	—
182	C₄	—	2	2	no	—
183	C₄	—	76	2	no	—
184	C₄	—	76	2	no	—
185	C₄	#11926602	1	2	yes	—
186	C₄	#11926603	1	1	yes	characteristic
187	C₄	#11926606	1	1	yes	characteristic
188	C₄	#11926897	1	2	yes	—
189	C₄	#11926900	1	2	yes	—
190	C₂	#14562412	1	2	yes	—
191	C₂	#14562414	1	2	yes	—
192	C₂	#14563753	1	1	yes	characteristic
193	C₂	#14563764	1	1	yes	characteristic
194	C₂	#14563774	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563751

C₂

yes

maximal

#14563380

C₂

yes

maximal, characteristic

#14561470

C₂

yes

maximal, characteristic

#14561469

C₂

yes

maximal

C₁₉×#1277

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₄²×Dic₁₉

C₂²

yes

—

—

C₄

yes

—

#11926298

C₄

yes

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

—

C₂×C₄×Dic₁₉

D₄

yes

characteristic

C₂×C₄×Dic₁₉

D₄

yes

characteristic

C₂×C₄×Dic₁₉

Q₈

yes

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×Dic₁₉

C₄⋊C₄

yes

—

C₂²×Dic₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8788

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#125

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

#135

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#135

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

—

—

—

D₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

#433

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₄×C₁₉

#488

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

100

C₂×C₄×C₈

—

101

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

102

C₄³

—

103

#336

—

104

#336

—

105

#336

—

106

#336

—

107

C₂×C₁₉

#1572

yes

—

108

C₂×C₁₉

#1572

yes

—

109

C₂×C₁₉

#1832

yes

characteristic

110

C₂×C₁₉

#1835

yes

characteristic

111

C₂×C₁₉

#1838

yes

characteristic

112

C₂²×C₈

—

113

C₂²×C₈

—

114

C₂²×C₈

—

115

C₂²×C₈

—

116

C₂²×C₈

C₄×D₁₉

yes

—

117

C₂×C₄²

—

118

C₂×C₄²

—

119

C₂×C₄²

—

120

C₂×C₄²

—

121

C₂×C₄²

C₂²×D₁₉

yes

characteristic

122

C₄⋊C₈

—

123

C₄⋊C₈

—

124

C₄⋊C₈

—

125

C₄⋊C₈

—

126

C₄×C₈

—

127

C₄×C₈

—

128

C₁₉

#8788

yes

characteristic, complemented, Sylow

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

132

C₂²×C₄

D₄×D₁₉

yes

characteristic

133

C₂²×C₄

Q₈×D₁₉

yes

characteristic

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

—

147

C₄²

—

148

C₄²

—

149

C₄²

—

150

C₄²

—

151

C₄²

—

152

C₄²

—

153

C₄²

#64541

yes

—

154

C₄²

#64543

yes

—

155

C₂³

C₄⋊C₄×D₁₉

yes

characteristic

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

#10597318

yes

characteristic

164

C₂×C₄

#10597323

yes

characteristic

165

C₂×C₄

#10597331

yes

—

166

C₂×C₄

#10597335

yes

—

167

C₂×C₄

#10597347

yes

—

168

C₂×C₄

#10597353

yes

—

169

C₂×C₄

#10597358

yes

characteristic

170

C₂×C₄

#10597362

yes

—

171

C₂×C₄

#10597365

yes

characteristic

172

C₈

—

173

C₈

—

174

C₈

—

175

C₈

—

176

C₈

—

152

—

177

C₂²

#11926408

yes

characteristic

178

C₂²

#11926569

yes

—

179

C₂²

#11926579

yes

characteristic

180

C₂²

#11926581

yes

characteristic

181

C₂²

#11926591

yes

—

182

C₄

—

183

C₄

—

184

C₄

—

185

C₄

#11926602

yes

—

186

C₄

#11926603

yes

characteristic

187

C₄

#11926606

yes

characteristic

188

C₄

#11926897

yes

—

189

C₄

#11926900

yes

—

190

C₂

#14562412

yes

—

191

C₂

#14562414

yes

—

192

C₂

#14563753

yes

characteristic

193

C₂

#14563764

yes

characteristic

194

C₂

#14563774

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1277	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1277	D₁₉
hypocenter	C₁₉	#8788
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

subgroup

G/H

center

C₂²×C₄

D₄×D₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1277

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

N	H ≅ G/N	type
128. C₁₉	#8788	semidirect

H ≅ G/N

type

128. C₁₉

#8788

semidirect

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

subgroup	index
#14563751	2
#14563380	2
#14561470	2
#14561469	2
C₁₉×#1277	2
#8788	19

subgroup

index

C₁₉×#1277

Subgroups — #18076211

Conjugacy classes of subgroups

Complements

Maximal subgroups