Group #18082667 — subgroups

Subgroups — #18082667

Order 4864.

430 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 159 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	#14571998	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#14561519	C₂	1	4	yes	maximal
4	C₁₉×#1831	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597316	—	2	1	no	—
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
8	#11926442	—	2	2	no	—
9	#11926442	C₄	1	4	yes	—
10	#11926414	C₂²	1	2	yes	—
11	#11926410	—	2	1	no	—
12	#11926299	—	2	1	no	—
13	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
14	C₄³×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#336	—	2	2	no	—
16	C₂²×C₈×C₁₉	—	2	2	no	—
17	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	D₄	1	2	yes	—
20	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₉	—	2	2	no	—
23	C₂×C₄⋊Dic₁₉	—	2	2	no	—
24	C₂×C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
25	C₂×Dic₁₉⋊C₄	—	2	4	no	—
26	C₂²×C₁₉⋊C₈	—	2	2	no	—
27	#10597316	—	4	2	no	—
28	#10597316	—	4	2	no	—
29	C₁₉×C₄⋊C₈	—	2	4	no	—
30	C₁₉⋊#95	—	2	4	no	—
31	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
32	C₄⋊(C₁₉⋊C₈)	Q₈	1	4	yes	—
33	C₄×C₁₉⋊C₈	—	4	2	no	—
34	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
35	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
36	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂²×Dic₁₉	—	2	4	no	—
40	C₂×C₈×C₁₉	—	4	2	no	—
41	C₂×C₈×C₁₉	—	4	4	no	—
42	C₄²×C₁₉	—	2	4	no	—
43	C₄²×C₁₉	—	2	2	no	—
44	C₄²×C₁₉	—	4	2	no	—
45	C₄²×C₁₉	D₈	1	2	yes	—
46	C₄²×C₁₉	SD₁₆	1	2	yes	—
47	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
48	C₄²×C₁₉	#41	1	2	yes	—
49	C₄⋊Dic₁₉	—	4	2	no	—
50	C₄⋊Dic₁₉	—	4	2	no	—
51	C₄⋊Dic₁₉	—	4	4	no	—
52	C₄⋊Dic₁₉	—	4	4	no	—
53	Dic₁₉⋊C₄	—	4	8	no	—
54	C₂×C₁₉⋊C₈	—	2	4	no	—
55	C₂×C₁₉⋊C₈	—	4	2	no	—
56	C₂×C₁₉⋊C₈	—	4	2	no	—
57	#9899	—	19	1	no	maximal, Sylow
58	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	—	2	2	no	—
63	C₂×C₄×C₁₉	—	2	2	no	—
64	C₂×C₄×C₁₉	—	2	2	no	—
65	C₂×C₄×C₁₉	#102	1	4	yes	—
66	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
67	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
68	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
70	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
71	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
72	C₂×C₄×C₁₉	#135	1	4	yes	—
73	C₂×C₄×C₁₉	#137	1	2	yes	—
74	C₂×Dic₁₉	—	4	4	no	—
75	C₂×Dic₁₉	—	4	4	no	—
76	C₂×Dic₁₉	—	4	4	no	—
77	C₈×C₁₉	—	8	2	no	—
78	C₁₉⋊C₈	—	4	4	no	—
79	#2859	—	19	1	no	—
80	#1831	D₁₉	1	1	yes	characteristic
81	C₄×C₄⋊C₈	—	19	1	no	—
82	#1296	—	19	4	no	—
83	C₂²×C₁₉	#391	1	1	yes	characteristic
84	C₂²×C₁₉	#413	1	2	yes	—
85	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
86	C₂²×C₁₉	#416	1	2	yes	—
87	C₂²×C₁₉	#419	1	1	yes	characteristic
88	C₄×C₁₉	—	2	4	no	—
89	C₄×C₁₉	—	2	2	no	—
90	C₄×C₁₉	—	4	2	no	—
91	C₄×C₁₉	#474	1	2	yes	—
92	C₄×C₁₉	#475	1	2	yes	—
93	C₄×C₁₉	#488	1	2	yes	—
94	C₄×C₁₉	#499	1	2	yes	—
95	Dic₁₉	—	8	4	no	—
96	C₂×#125	—	38	1	no	—
97	C₂×C₄⋊C₈	—	19	2	no	—
98	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
99	C₂×C₄×C₈	—	38	1	no	—
100	#389	—	19	4	no	—
101	#389	—	38	2	no	—
102	#384	—	19	2	no	—
103	#382	—	38	1	no	—
104	C₄³	C₂×D₁₉	1	1	yes	characteristic
105	#336	—	2	2	no	—
106	#336	—	38	1	no	—
107	C₂×C₁₉	#1540	1	2	yes	—
108	C₂×C₁₉	#1554	1	2	yes	—
109	C₂×C₁₉	#1988	1	1	yes	characteristic
110	C₂×C₁₉	#1991	1	1	yes	characteristic
111	C₂×C₁₉	#1998	1	1	yes	characteristic
112	C₂²×C₈	—	2	2	no	—
113	C₂²×C₈	—	38	2	no	—
114	#125	—	76	2	no	—
115	#125	—	76	2	no	—
116	C₂×C₄⋊C₄	—	19	4	no	—
117	C₂×C₄⋊C₄	—	38	4	no	—
118	C₂×C₄⋊C₄	—	38	2	no	—
119	C₂×C₄⋊C₄	—	38	2	no	—
120	C₂×C₄²	C₄×D₁₉	1	2	yes	—
121	C₂×C₄²	D₇₆	1	1	yes	characteristic
122	C₂×C₄²	D₇₆	1	1	yes	characteristic
123	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
124	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
125	C₄⋊C₈	—	2	4	no	—
126	C₄⋊C₈	—	19	4	no	—
127	C₄⋊C₈	—	38	2	no	—
128	C₄×C₈	—	76	2	no	—
129	#95	—	38	4	no	—
130	C₁₉	#9899	1	1	yes	characteristic, complemented, Sylow
131	C₂²×C₄	—	38	4	no	—
132	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
133	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
134	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
135	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
136	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
137	C₂×C₈	—	4	2	no	—
138	C₂×C₈	—	4	4	no	—
139	C₂×C₈	—	38	4	no	—
140	C₂×C₈	—	76	2	no	—
141	C₂×C₈	—	76	2	no	—
142	C₄⋊C₄	—	76	4	no	—
143	C₄⋊C₄	—	76	4	no	—
144	C₄⋊C₄	—	76	8	no	—
145	C₄⋊C₄	—	76	2	no	—
146	C₄⋊C₄	—	76	2	no	—
147	C₄²	—	2	4	no	—
148	C₄²	—	2	2	no	—
149	C₄²	—	4	2	no	—
150	C₄²	#64516	1	2	yes	—
151	C₄²	D₁₅₂	1	2	yes	—
152	C₄²	#64543	1	2	yes	—
153	C₄²	Q₈×D₁₉	1	2	yes	—
154	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	76	4	no	—
162	C₂×C₄	—	76	4	no	—
163	C₂×C₄	—	76	4	no	—
164	C₂×C₄	#10597278	1	4	yes	—
165	C₂×C₄	#10597333	1	2	yes	—
166	C₂×C₄	#10597343	1	2	yes	—
167	C₂×C₄	C₂×#64516	1	1	yes	characteristic
168	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
169	C₂×C₄	#10597355	1	2	yes	—
170	C₂×C₄	#10597382	1	1	yes	characteristic
171	C₂×C₄	#10597390	1	1	yes	characteristic
172	C₂×C₄	#10597396	1	4	yes	—
173	C₈	—	8	2	no	—
174	C₈	—	76	4	no	—
175	C₂²	#11926449	1	1	yes	characteristic
176	C₂²	#11926526	1	2	yes	—
177	C₂²	C₂×#10597278	1	1	yes	characteristic
178	C₂²	#11926538	1	2	yes	—
179	C₂²	#11926554	1	1	yes	characteristic
180	C₄	—	2	2	no	—
181	C₄	—	2	4	no	—
182	C₄	—	4	2	no	—
183	C₄	—	152	4	no	—
184	C₄	#11926825	1	2	yes	—
185	C₄	#11926830	1	2	yes	—
186	C₄	#11926898	1	2	yes	—
187	C₄	#11926943	1	2	yes	—
188	C₂	#14562282	1	2	yes	—
189	C₂	#14562346	1	2	yes	—
190	C₂	#14564586	1	1	yes	characteristic
191	C₂	#14564599	1	1	yes	characteristic
192	C₂	#14564627	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14571998

C₂

yes

maximal, characteristic

C₄×C₄⋊(C₁₉⋊C₈)

C₂

yes

maximal, characteristic

#14561519

C₂

yes

maximal

C₁₉×#1831

C₂

yes

maximal, characteristic

C₂×#10597316

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

—

#11926442

—

#11926442

C₄

yes

—

#11926414

C₂²

yes

—

#11926410

—

#11926299

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×Dic₁₉⋊C₄

—

C₂²×C₁₉⋊C₈

—

#10597316

—

#10597316

—

C₁₉×C₄⋊C₈

—

C₁₉⋊#95

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

Q₈

yes

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₈

yes

—

C₄²×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

C₂×Q₈

yes

—

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9899

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#102

yes

—

C₂×C₄×C₁₉

C₄×Q₈

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2859

—

#1831

D₁₉

yes

characteristic

C₄×C₄⋊C₈

—

#1296

—

C₂²×C₁₉

#391

yes

characteristic

C₂²×C₁₉

#413

yes

—

C₂²×C₁₉

C₂×#102

yes

characteristic

C₂²×C₁₉

#416

yes

—

C₂²×C₁₉

#419

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#474

yes

—

C₄×C₁₉

#475

yes

—

C₄×C₁₉

#488

yes

—

C₄×C₁₉

#499

yes

—

Dic₁₉

—

C₂×#125

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

C₂×C₄×C₈

—

100

#389

—

101

#389

—

102

#384

—

103

#382

—

104

C₄³

C₂×D₁₉

yes

characteristic

105

#336

—

106

#336

—

107

C₂×C₁₉

#1540

yes

—

108

C₂×C₁₉

#1554

yes

—

109

C₂×C₁₉

#1988

yes

characteristic

110

C₂×C₁₉

#1991

yes

characteristic

111

C₂×C₁₉

#1998

yes

characteristic

112

C₂²×C₈

—

113

C₂²×C₈

—

114

#125

—

115

#125

—

116

C₂×C₄⋊C₄

—

117

C₂×C₄⋊C₄

—

118

C₂×C₄⋊C₄

—

119

C₂×C₄⋊C₄

—

120

C₂×C₄²

C₄×D₁₉

yes

—

121

C₂×C₄²

D₇₆

yes

characteristic

122

C₂×C₄²

D₇₆

yes

characteristic

123

C₂×C₄²

C₂²⋊D₁₉

yes

—

124

C₂×C₄²

C₂²×D₁₉

yes

characteristic

125

C₄⋊C₈

—

126

C₄⋊C₈

—

127

C₄⋊C₈

—

128

C₄×C₈

—

129

#95

—

130

C₁₉

#9899

yes

characteristic, complemented, Sylow

131

C₂²×C₄

—

132

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

133

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

134

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

135

C₂²×C₄

C₂×D₇₆

yes

characteristic

136

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

147

C₄²

—

148

C₄²

—

149

C₄²

—

150

C₄²

#64516

yes

—

151

C₄²

D₁₅₂

yes

—

152

C₄²

#64543

yes

—

153

C₄²

Q₈×D₁₉

yes

—

154

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

#10597278

yes

—

165

C₂×C₄

#10597333

yes

—

166

C₂×C₄

#10597343

yes

—

167

C₂×C₄

C₂×#64516

yes

characteristic

168

C₂×C₄

C₂×D₁₅₂

yes

characteristic

169

C₂×C₄

#10597355

yes

—

170

C₂×C₄

#10597382

yes

characteristic

171

C₂×C₄

#10597390

yes

characteristic

172

C₂×C₄

#10597396

yes

—

173

C₈

—

174

C₈

—

175

C₂²

#11926449

yes

characteristic

176

C₂²

#11926526

yes

—

177

C₂²

C₂×#10597278

yes

characteristic

178

C₂²

#11926538

yes

—

179

C₂²

#11926554

yes

characteristic

180

C₄

—

181

C₄

—

182

C₄

—

183

C₄

—

152

—

184

C₄

#11926825

yes

—

185

C₄

#11926830

yes

—

186

C₄

#11926898

yes

—

187

C₄

#11926943

yes

—

188

C₂

#14562282

yes

—

189

C₂

#14562346

yes

—

190

C₂

#14564586

yes

characteristic

191

C₂

#14564599

yes

characteristic

192

C₂

#14564627

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1831	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1831	D₁₉
hypocenter	C₁₉	#9899
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

subgroup

G/H

center

C₂³

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1831

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

N	H ≅ G/N	type
130. C₁₉	#9899	semidirect

H ≅ G/N

type

130. C₁₉

#9899

semidirect

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

subgroup	index
#14571998	2
C₄×C₄⋊(C₁₉⋊C₈)	2
#14561519	2
C₁₉×#1831	2
#9899	19

subgroup

index

#14571998

C₄×C₄⋊(C₁₉⋊C₈)

#14561519

C₁₉×#1831

#9899

Subgroups — #18082667

Conjugacy classes of subgroups

Complements

Maximal subgroups