Group #18082689 — subgroups

Subgroups — #18082689

Order 4864.

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

normal subgroups only

This group has 438 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	#14563488	C₂	1	1	yes	maximal, characteristic
3	#14561519	C₂	1	4	yes	maximal
4	C₁₉×#1842	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597316	—	2	1	no	—
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×#10597260	—	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	—	2	2	no	—
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
15	C₄³×C₁₉	C₂²	1	1	yes	characteristic
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×C₄⋊C₈	—	4	4	no	—
31	C₁₉⋊#95	—	2	4	no	—
32	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
33	C₄⋊(C₁₉⋊C₈)	Q₈	1	4	yes	—
34	#10597260	—	4	2	no	—
35	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
36	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
37	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂²×Dic₁₉	—	2	4	no	—
41	C₂×C₈×C₁₉	—	4	2	no	—
42	C₂×C₈×C₁₉	—	4	4	no	—
43	C₄²×C₁₉	—	2	2	no	—
44	C₄²×C₁₉	—	2	2	no	—
45	C₄²×C₁₉	—	2	2	no	—
46	C₄²×C₁₉	—	4	2	no	—
47	C₄²×C₁₉	D₈	1	2	yes	—
48	C₄²×C₁₉	SD₁₆	1	2	yes	—
49	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
50	C₄²×C₁₉	#41	1	2	yes	—
51	C₄⋊Dic₁₉	—	4	2	no	—
52	C₄⋊Dic₁₉	—	4	2	no	—
53	C₄⋊Dic₁₉	—	4	2	no	—
54	C₄⋊Dic₁₉	—	4	2	no	—
55	C₄⋊Dic₁₉	—	4	4	no	—
56	Dic₁₉⋊C₄	—	4	8	no	—
57	C₂×C₁₉⋊C₈	—	2	4	no	—
58	C₂×C₁₉⋊C₈	—	4	2	no	—
59	C₂×C₁₉⋊C₈	—	4	2	no	—
60	#9904	—	19	1	no	maximal, Sylow
61	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	—	2	2	no	—
66	C₂×C₄×C₁₉	—	2	2	no	—
67	C₂×C₄×C₁₉	—	2	2	no	—
68	C₂×C₄×C₁₉	#102	1	4	yes	—
69	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
70	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
71	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
72	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
75	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
76	C₂×C₄×C₁₉	#137	1	2	yes	—
77	C₂×C₄×C₁₉	#137	1	2	yes	—
78	C₂×Dic₁₉	—	4	4	no	—
79	C₂×Dic₁₉	—	4	4	no	—
80	C₂×Dic₁₉	—	4	4	no	—
81	C₈×C₁₉	—	8	2	no	—
82	C₁₉⋊C₈	—	4	4	no	—
83	#2859	—	19	1	no	—
84	#1842	D₁₉	1	1	yes	characteristic
85	#1767	—	19	1	no	—
86	#1296	—	19	4	no	—
87	C₂²×C₁₉	#391	1	1	yes	characteristic
88	C₂²×C₁₉	#413	1	2	yes	—
89	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
90	C₂²×C₁₉	#417	1	2	yes	—
91	C₂²×C₁₉	#419	1	1	yes	characteristic
92	C₄×C₁₉	—	2	4	no	—
93	C₄×C₁₉	—	2	2	no	—
94	C₄×C₁₉	—	4	2	no	—
95	C₄×C₁₉	#474	1	2	yes	—
96	C₄×C₁₉	#475	1	2	yes	—
97	C₄×C₁₉	#490	1	1	yes	characteristic
98	C₄×C₁₉	#491	1	1	yes	characteristic
99	C₄×C₁₉	#501	1	2	yes	—
100	Dic₁₉	—	8	4	no	—
101	C₂×#125	—	38	1	no	—
102	C₂×C₄⋊C₈	—	2	2	no	—
103	C₂×C₄⋊C₈	—	19	2	no	—
104	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
105	C₂×#97	—	38	1	no	—
106	#389	—	19	4	no	—
107	#389	—	38	2	no	—
108	#384	—	19	2	no	—
109	#382	—	38	1	no	—
110	C₄³	C₂×D₁₉	1	1	yes	characteristic
111	#336	—	38	1	no	—
112	C₂×C₁₉	#1547	1	2	yes	—
113	C₂×C₁₉	#1559	1	2	yes	—
114	C₂×C₁₉	#1988	1	1	yes	characteristic
115	C₂×C₁₉	#1992	1	1	yes	characteristic
116	C₂×C₁₉	#1998	1	1	yes	characteristic
117	C₂²×C₈	—	2	2	no	—
118	C₂²×C₈	—	38	2	no	—
119	#125	—	76	2	no	—
120	#125	—	76	2	no	—
121	C₂×C₄⋊C₄	—	19	4	no	—
122	C₂×C₄⋊C₄	—	38	4	no	—
123	C₂×C₄⋊C₄	—	38	2	no	—
124	C₂×C₄⋊C₄	—	38	2	no	—
125	C₂×C₄²	C₄×D₁₉	1	2	yes	—
126	C₂×C₄²	D₇₆	1	1	yes	characteristic
127	C₂×C₄²	D₇₆	1	1	yes	characteristic
128	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
129	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
130	C₄⋊C₈	—	2	4	no	—
131	C₄⋊C₈	—	4	4	no	—
132	C₄⋊C₈	—	19	4	no	—
133	C₄⋊C₈	—	38	2	no	—
134	#97	—	76	2	no	—
135	#95	—	38	4	no	—
136	C₁₉	#9904	1	1	yes	characteristic, complemented, Sylow
137	C₂²×C₄	—	38	4	no	—
138	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
139	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
140	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
141	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
142	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
143	C₂×C₈	—	4	4	no	—
144	C₂×C₈	—	4	2	no	—
145	C₂×C₈	—	38	4	no	—
146	C₂×C₈	—	76	2	no	—
147	C₂×C₈	—	76	2	no	—
148	C₄⋊C₄	—	76	4	no	—
149	C₄⋊C₄	—	76	2	no	—
150	C₄⋊C₄	—	76	2	no	—
151	C₄⋊C₄	—	76	8	no	—
152	C₄⋊C₄	—	76	2	no	—
153	C₄⋊C₄	—	76	2	no	—
154	C₄²	—	2	2	no	—
155	C₄²	—	2	2	no	—
156	C₄²	—	2	2	no	—
157	C₄²	—	4	2	no	—
158	C₄²	#64516	1	2	yes	—
159	C₄²	D₁₅₂	1	2	yes	—
160	C₄²	#64543	1	2	yes	—
161	C₄²	Q₈×D₁₉	1	2	yes	—
162	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	76	4	no	—
170	C₂×C₄	—	76	4	no	—
171	C₂×C₄	—	76	4	no	—
172	C₂×C₄	#10597278	1	4	yes	—
173	C₂×C₄	#10597333	1	2	yes	—
174	C₂×C₄	#10597343	1	2	yes	—
175	C₂×C₄	C₂×#64516	1	1	yes	characteristic
176	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
177	C₂×C₄	#10597355	1	2	yes	—
178	C₂×C₄	#10597378	1	2	yes	—
179	C₂×C₄	#10597382	1	1	yes	characteristic
180	C₂×C₄	#10597388	1	2	yes	—
181	C₂×C₄	#10597390	1	1	yes	characteristic
182	C₈	—	8	2	no	—
183	C₈	—	76	4	no	—
184	C₂²	#11926449	1	1	yes	characteristic
185	C₂²	#11926526	1	2	yes	—
186	C₂²	C₂×#10597278	1	1	yes	characteristic
187	C₂²	#11926543	1	2	yes	—
188	C₂²	#11926554	1	1	yes	characteristic
189	C₄	—	2	4	no	—
190	C₄	—	2	2	no	—
191	C₄	—	4	2	no	—
192	C₄	—	152	4	no	—
193	C₄	#11926825	1	2	yes	—
194	C₄	#11926830	1	2	yes	—
195	C₄	#11926908	1	1	yes	characteristic
196	C₄	#11926912	1	1	yes	characteristic
197	C₄	#11926950	1	2	yes	—
198	C₂	#14562310	1	2	yes	—
199	C₂	#14562363	1	2	yes	—
200	C₂	#14564586	1	1	yes	characteristic
201	C₂	#14564603	1	1	yes	characteristic
202	C₂	#14564627	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14571998

C₂

yes

maximal, characteristic

#14563488

C₂

yes

maximal, characteristic

#14561519

C₂

yes

maximal

C₁₉×#1842

C₂

yes

maximal, characteristic

C₂×#10597316

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×#10597260

—

#11926442

—

#11926442

C₄

yes

—

#11926414

C₂²

yes

—

#11926410

—

#11926299

—

C₂×C₁₉×C₄⋊C₈

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

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×C₄⋊C₈

—

C₁₉⋊#95

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

Q₈

yes

—

#10597260

—

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

—

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

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9904

—

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

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2859

—

#1842

D₁₉

yes

characteristic

#1767

—

#1296

—

C₂²×C₁₉

#391

yes

characteristic

C₂²×C₁₉

#413

yes

—

C₂²×C₁₉

C₂×#102

yes

characteristic

C₂²×C₁₉

#417

yes

—

C₂²×C₁₉

#419

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#474

yes

—

C₄×C₁₉

#475

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

100

Dic₁₉

—

101

C₂×#125

—

102

C₂×C₄⋊C₈

—

103

C₂×C₄⋊C₈

—

104

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

105

C₂×#97

—

106

#389

—

107

#389

—

108

#384

—

109

#382

—

110

C₄³

C₂×D₁₉

yes

characteristic

111

#336

—

112

C₂×C₁₉

#1547

yes

—

113

C₂×C₁₉

#1559

yes

—

114

C₂×C₁₉

#1988

yes

characteristic

115

C₂×C₁₉

#1992

yes

characteristic

116

C₂×C₁₉

#1998

yes

characteristic

117

C₂²×C₈

—

118

C₂²×C₈

—

119

#125

—

120

#125

—

121

C₂×C₄⋊C₄

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

—

124

C₂×C₄⋊C₄

—

125

C₂×C₄²

C₄×D₁₉

yes

—

126

C₂×C₄²

D₇₆

yes

characteristic

127

C₂×C₄²

D₇₆

yes

characteristic

128

C₂×C₄²

C₂²⋊D₁₉

yes

—

129

C₂×C₄²

C₂²×D₁₉

yes

characteristic

130

C₄⋊C₈

—

131

C₄⋊C₈

—

132

C₄⋊C₈

—

133

C₄⋊C₈

—

134

#97

—

135

#95

—

136

C₁₉

#9904

yes

characteristic, complemented, Sylow

137

C₂²×C₄

—

138

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

139

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

140

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

141

C₂²×C₄

C₂×D₇₆

yes

characteristic

142

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄⋊C₄

—

154

C₄²

—

155

C₄²

—

156

C₄²

—

157

C₄²

—

158

C₄²

#64516

yes

—

159

C₄²

D₁₅₂

yes

—

160

C₄²

#64543

yes

—

161

C₄²

Q₈×D₁₉

yes

—

162

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

#10597278

yes

—

173

C₂×C₄

#10597333

yes

—

174

C₂×C₄

#10597343

yes

—

175

C₂×C₄

C₂×#64516

yes

characteristic

176

C₂×C₄

C₂×D₁₅₂

yes

characteristic

177

C₂×C₄

#10597355

yes

—

178

C₂×C₄

#10597378

yes

—

179

C₂×C₄

#10597382

yes

characteristic

180

C₂×C₄

#10597388

yes

—

181

C₂×C₄

#10597390

yes

characteristic

182

C₈

—

183

C₈

—

184

C₂²

#11926449

yes

characteristic

185

C₂²

#11926526

yes

—

186

C₂²

C₂×#10597278

yes

characteristic

187

C₂²

#11926543

yes

—

188

C₂²

#11926554

yes

characteristic

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

—

152

—

193

C₄

#11926825

yes

—

194

C₄

#11926830

yes

—

195

C₄

#11926908

yes

characteristic

196

C₄

#11926912

yes

characteristic

197

C₄

#11926950

yes

—

198

C₂

#14562310

yes

—

199

C₂

#14562363

yes

—

200

C₂

#14564586

yes

characteristic

201

C₂

#14564603

yes

characteristic

202

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×#1842	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1842	D₁₉
hypocenter	C₁₉	#9904
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1842

subgroup

G/H

center

C₂³

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1842

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 ◁ #1842

N	H ≅ G/N	type
136. C₁₉	#9904	semidirect

H ≅ G/N

type

136. C₁₉

#9904

semidirect

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

subgroup	index
#14571998	2
#14563488	2
#14561519	2
C₁₉×#1842	2
#9904	19

subgroup

index

C₁₉×#1842

Subgroups — #18082689

Conjugacy classes of subgroups

Complements

Maximal subgroups