Group #18075877 — subgroups

Subgroups — #18075877

Order 4864.

530 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 139 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	#14563703	C₂	1	2	yes	maximal
2	#14561478	C₂	1	4	yes	maximal
3	C₂×C₁₉×#382	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
5	#11926299	—	2	2	no	—
6	#11926299	—	2	2	no	—
7	C₂²×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
8	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#382	—	2	2	no	—
10	C₁₉×#382	—	2	2	no	—
11	C₂×C₁₉×#95	C₄	1	2	yes	—
12	C₂×C₁₉×#95	C₂²	1	2	yes	—
13	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
16	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
17	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
18	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
20	C₂×C₄²×C₁₉	—	2	4	no	—
21	C₂×C₄²×C₁₉	D₄	1	2	yes	—
22	C₂×C₄²×C₁₉	D₄	1	2	yes	—
23	C₂²×C₁₉⋊C₈	—	2	4	no	—
24	C₁₉×#95	—	2	4	no	—
25	C₁₉×#95	—	2	4	no	—
26	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
27	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	—	2	2	no	—
29	C₂²×C₄×C₁₉	—	2	2	no	—
30	C₂²×C₄×C₁₉	—	2	2	no	—
31	C₂²×C₄×C₁₉	—	2	2	no	—
32	C₂²×C₄×C₁₉	—	2	4	no	—
33	C₂²×C₄×C₁₉	—	2	4	no	—
34	C₂²×C₄×C₁₉	—	2	8	no	—
35	C₂²×C₄×C₁₉	—	4	2	no	—
36	C₂²×C₄×C₁₉	—	4	4	no	—
37	C₂²×C₄×C₁₉	—	4	4	no	—
38	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
39	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
42	C₂²×C₄×C₁₉	#41	1	4	yes	—
43	C₄⋊C₄×C₁₉	—	4	4	no	—
44	C₄⋊C₄×C₁₉	—	4	4	no	—
45	C₄²×C₁₉	—	2	4	no	—
46	C₄²×C₁₉	—	2	4	no	—
47	C₂×C₁₉⋊C₈	—	4	8	no	—
48	C₂×C₁₉⋊C₈	—	4	4	no	—
49	#8703	—	19	1	no	maximal, Sylow
50	C₂³×C₁₉	—	2	2	no	—
51	C₂³×C₁₉	—	2	1	no	—
52	C₂³×C₁₉	—	2	1	no	—
53	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
54	C₂³×C₁₉	#117	1	2	yes	—
55	C₂³×C₁₉	#131	1	4	yes	—
56	C₂×C₄×C₁₉	—	2	8	no	—
57	C₂×C₄×C₁₉	—	2	1	no	—
58	C₂×C₄×C₁₉	—	2	1	no	—
59	C₂×C₄×C₁₉	—	2	4	no	—
60	C₂×C₄×C₁₉	—	2	1	no	—
61	C₂×C₄×C₁₉	—	2	1	no	—
62	C₂×C₄×C₁₉	—	2	2	no	—
63	C₂×C₄×C₁₉	—	2	4	no	—
64	C₂×C₄×C₁₉	—	4	4	no	—
65	C₂×C₄×C₁₉	—	4	4	no	—
66	C₂×C₄×C₁₉	—	4	4	no	—
67	C₂×C₄×C₁₉	—	4	4	no	—
68	C₂×C₄×C₁₉	—	4	4	no	—
69	C₂×C₄×C₁₉	—	8	8	no	—
70	C₂×C₄×C₁₉	#100	1	2	yes	—
71	C₂×C₄×C₁₉	#101	1	2	yes	—
72	C₂×C₄×C₁₉	#123	1	4	yes	—
73	C₁₉⋊C₈	—	8	4	no	—
74	C₂×#382	D₁₉	1	1	yes	characteristic
75	#1817	—	19	2	no	—
76	#1280	—	19	4	no	—
77	C₂²×C₁₉	—	2	2	no	—
78	C₂²×C₁₉	—	2	2	no	—
79	C₂²×C₁₉	—	2	4	no	—
80	C₂²×C₁₉	—	2	4	no	—
81	C₂²×C₁₉	#381	1	1	yes	characteristic
82	C₂²×C₁₉	#408	1	2	yes	—
83	C₂²×C₁₉	#410	1	2	yes	—
84	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
85	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
86	C₂²×C₁₉	#433	1	4	yes	—
87	C₄×C₁₉	—	2	4	no	—
88	C₄×C₁₉	—	2	2	no	—
89	C₄×C₁₉	—	2	2	no	—
90	C₄×C₁₉	—	4	2	no	—
91	C₄×C₁₉	—	8	4	no	—
92	C₂²×C₄⋊C₄	Dic₁₉	1	2	yes	—
93	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
94	C₂×C₂²⋊C₈	—	19	4	no	—
95	#382	—	2	2	no	—
96	#382	—	2	2	no	—
97	C₂×#95	Dic₁₉	1	2	yes	—
98	C₂×#95	C₂×D₁₉	1	2	yes	—
99	#336	—	38	2	no	—
100	#336	—	38	2	no	—
101	C₂×C₁₉	—	2	4	no	—
102	C₂×C₁₉	#1469	1	2	yes	—
103	C₂×C₁₉	#1470	1	2	yes	—
104	C₂×C₁₉	#1818	1	1	yes	characteristic
105	C₂×C₁₉	#1820	1	1	yes	characteristic
106	C₂×C₁₉	#1821	1	1	yes	characteristic
107	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
108	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
109	C₂³×C₄	C₂×Dic₁₉	1	4	yes	—
110	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
111	C₂²×C₈	—	38	4	no	—
112	C₂×C₄⋊C₄	—	2	2	no	—
113	C₂×C₄⋊C₄	—	2	2	no	—
114	C₂×C₄⋊C₄	—	4	4	no	—
115	C₂×C₄²	—	2	4	no	—
116	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
117	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
118	C₂²⋊C₈	—	38	8	no	—
119	#95	—	2	4	no	—
120	#95	—	2	4	no	—
121	C₁₉	#8703	1	1	yes	characteristic, complemented, Sylow
122	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
123	C₂²×C₄	—	2	2	no	—
124	C₂²×C₄	—	2	2	no	—
125	C₂²×C₄	—	2	2	no	—
126	C₂²×C₄	—	2	4	no	—
127	C₂²×C₄	—	2	2	no	—
128	C₂²×C₄	—	2	4	no	—
129	C₂²×C₄	—	2	8	no	—
130	C₂²×C₄	—	4	2	no	—
131	C₂²×C₄	—	4	4	no	—
132	C₂²×C₄	—	4	4	no	—
133	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
134	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
135	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
136	C₂²×C₄	#64541	1	4	yes	—
137	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
138	C₂×C₈	—	76	8	no	—
139	C₂×C₈	—	76	4	no	—
140	C₄⋊C₄	—	4	4	no	—
141	C₄⋊C₄	—	4	4	no	—
142	C₄²	—	2	4	no	—
143	C₄²	—	2	4	no	—
144	C₂³	—	2	2	no	—
145	C₂³	—	2	1	no	—
146	C₂³	—	2	1	no	—
147	C₂³	#10597372	1	2	yes	—
148	C₂³	#10597394	1	4	yes	—
149	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
150	C₂×C₄	—	2	8	no	—
151	C₂×C₄	—	2	1	no	—
152	C₂×C₄	—	2	1	no	—
153	C₂×C₄	—	2	4	no	—
154	C₂×C₄	—	2	1	no	—
155	C₂×C₄	—	2	1	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	4	no	—
158	C₂×C₄	—	4	4	no	—
159	C₂×C₄	—	4	4	no	—
160	C₂×C₄	—	4	4	no	—
161	C₂×C₄	—	4	4	no	—
162	C₂×C₄	—	4	4	no	—
163	C₂×C₄	—	8	8	no	—
164	C₂×C₄	#10597290	1	2	yes	—
165	C₂×C₄	#10597293	1	2	yes	—
166	C₂×C₄	#10597375	1	4	yes	—
167	C₈	—	152	4	no	—
168	C₂²	—	2	2	no	—
169	C₂²	—	2	2	no	—
170	C₂²	—	2	4	no	—
171	C₂²	—	2	4	no	—
172	C₂²	#11926407	1	1	yes	characteristic
173	C₂²	#11926511	1	2	yes	—
174	C₂²	#11926518	1	2	yes	—
175	C₂²	C₂×#10597290	1	1	yes	characteristic
176	C₂²	C₂×#10597293	1	1	yes	characteristic
177	C₂²	#11926605	1	4	yes	—
178	C₄	—	2	4	no	—
179	C₄	—	2	2	no	—
180	C₄	—	2	2	no	—
181	C₄	—	4	2	no	—
182	C₄	—	8	4	no	—
183	C₂	—	2	4	no	—
184	C₂	#14561987	1	2	yes	—
185	C₂	#14561991	1	2	yes	—
186	C₂	#14563706	1	1	yes	characteristic
187	C₂	#14563712	1	1	yes	characteristic
188	C₂	#14563715	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563703

C₂

yes

maximal

#14561478

C₂

yes

maximal

C₂×C₁₉×#382

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926299

—

#11926299

—

C₂²×C₄⋊C₄×C₁₉

C₄

yes

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×#382

—

C₁₉×#382

—

C₂×C₁₉×#95

C₄

yes

—

C₂×C₁₉×#95

C₂²

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

#41

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8703

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

#117

yes

—

C₂³×C₁₉

#131

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#100

yes

—

C₂×C₄×C₁₉

#101

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₁₉⋊C₈

—

C₂×#382

D₁₉

yes

characteristic

#1817

—

#1280

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#381

yes

characteristic

C₂²×C₁₉

#408

yes

—

C₂²×C₁₉

#410

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂²×C₄⋊C₄

Dic₁₉

yes

—

C₂²×C₄²

C₂×D₁₉

yes

characteristic

C₂×C₂²⋊C₈

—

#382

—

#382

—

C₂×#95

Dic₁₉

yes

—

C₂×#95

C₂×D₁₉

yes

—

#336

—

100

#336

—

101

C₂×C₁₉

—

102

C₂×C₁₉

#1469

yes

—

103

C₂×C₁₉

#1470

yes

—

104

C₂×C₁₉

#1818

yes

characteristic

105

C₂×C₁₉

#1820

yes

characteristic

106

C₂×C₁₉

#1821

yes

characteristic

107

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

108

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

109

C₂³×C₄

C₂×Dic₁₉

yes

—

110

C₂³×C₄

C₂²×D₁₉

yes

characteristic

111

C₂²×C₈

—

112

C₂×C₄⋊C₄

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄⋊C₄

—

115

C₂×C₄²

—

116

C₂×C₄²

C₂²⋊D₁₉

yes

—

117

C₂×C₄²

C₂²⋊D₁₉

yes

—

118

C₂²⋊C₈

—

119

#95

—

120

#95

—

121

C₁₉

#8703

yes

characteristic, complemented, Sylow

122

C₂⁴

C₂²×Dic₁₉

yes

characteristic

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

—

127

C₂²×C₄

—

128

C₂²×C₄

—

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

134

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

135

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

136

C₂²×C₄

#64541

yes

—

137

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄²

—

143

C₄²

—

144

C₂³

—

145

C₂³

—

146

C₂³

—

147

C₂³

#10597372

yes

—

148

C₂³

#10597394

yes

—

149

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

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

#10597290

yes

—

165

C₂×C₄

#10597293

yes

—

166

C₂×C₄

#10597375

yes

—

167

C₈

—

152

—

168

C₂²

—

169

C₂²

—

170

C₂²

—

171

C₂²

—

172

C₂²

#11926407

yes

characteristic

173

C₂²

#11926511

yes

—

174

C₂²

#11926518

yes

—

175

C₂²

C₂×#10597290

yes

characteristic

176

C₂²

C₂×#10597293

yes

characteristic

177

C₂²

#11926605

yes

—

178

C₄

—

179

C₄

—

180

C₄

—

181

C₄

—

182

C₄

—

183

C₂

—

184

C₂

#14561987

yes

—

185

C₂

#14561991

yes

—

186

C₂

#14563706

yes

characteristic

187

C₂

#14563712

yes

characteristic

188

C₂

#14563715

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator, prime radical	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#382	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#382	D₁₉
hypocenter	C₁₉	#8703
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#382

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator, prime radical

C₂⁴×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#382

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂³×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#382

N	H ≅ G/N	type
121. C₁₉	#8703	semidirect

H ≅ G/N

type

121. C₁₉

#8703

semidirect

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

subgroup	index
#14563703	2
#14561478	2
C₂×C₁₉×#382	2
#8703	19

subgroup

index

#14563703

#14561478

C₂×C₁₉×#382

#8703

Subgroups — #18075877

Conjugacy classes of subgroups

Complements

Maximal subgroups