Group #18076192 — subgroups

Subgroups — #18076192

Order 4864.

262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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	#14563386	C₂	1	1	yes	maximal, characteristic
2	#14562383	C₂	1	1	yes	maximal, characteristic
3	#14561479	C₂	1	2	yes	maximal
4	#14561463	C₂	1	2	yes	maximal
5	C₁₉×#1564	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	C₂×#10597260	C₂²	1	1	yes	characteristic
8	#11926390	C₂²	1	1	yes	characteristic
9	#11926298	C₄	1	2	yes	—
10	#11926298	C₄	1	2	yes	—
11	#11926297	—	2	1	no	—
12	#11926295	—	2	1	no	—
13	C₁₉×#431	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#335	—	2	1	no	—
16	C₁₉×#334	—	2	1	no	—
17	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
20	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
21	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
22	C₁₉×C₄⋊C₈	—	2	2	no	—
23	C₁₉×C₂²⋊C₈	—	2	2	no	—
24	C₄×C₈×C₁₉	—	2	2	no	—
25	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
28	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
29	C₁₉⋊#95	—	2	1	no	—
30	C₁₉⋊#95	—	2	1	no	—
31	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
32	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
33	#10597260	—	2	1	no	—
34	#10597260	—	2	1	no	—
35	C₄×C₁₉⋊C₈	—	2	2	no	—
36	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
39	C₂²×Dic₁₉	—	2	2	no	—
40	C₂×C₈×C₁₉	—	2	2	no	—
41	C₂×C₈×C₁₉	—	2	2	no	—
42	C₂×C₈×C₁₉	—	4	2	no	—
43	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
47	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
49	C₄²×C₁₉	#41	1	1	yes	characteristic
50	C₄²×C₁₉	#41	1	1	yes	characteristic
51	C₄×Dic₁₉	—	2	2	no	—
52	C₄×Dic₁₉	—	2	2	no	—
53	C₂×C₁₉⋊C₈	—	2	2	no	—
54	C₂×C₁₉⋊C₈	—	2	2	no	—
55	C₂×C₁₉⋊C₈	—	2	2	no	—
56	C₂×C₁₉⋊C₈	—	4	2	no	—
57	#8782	—	19	1	no	maximal, Sylow
58	C₂³×C₁₉	#117	1	1	yes	characteristic
59	C₂×C₄×C₁₉	—	4	1	no	—
60	C₂×C₄×C₁₉	—	4	1	no	—
61	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#131	1	2	yes	—
68	C₂×C₄×C₁₉	#131	1	2	yes	—
69	C₂×Dic₁₉	—	4	2	no	—
70	C₂×Dic₁₉	—	4	2	no	—
71	C₂×Dic₁₉	—	4	2	no	—
72	C₈×C₁₉	—	2	1	no	—
73	C₈×C₁₉	—	2	1	no	—
74	C₈×C₁₉	—	2	1	no	—
75	C₈×C₁₉	—	2	1	no	—
76	C₈×C₁₉	—	8	2	no	—
77	C₁₉⋊C₈	—	4	2	no	—
78	C₁₉⋊C₈	—	8	2	no	—
79	#1746	—	19	1	no	—
80	#1564	—	19	1	no	—
81	#1564	D₁₉	1	1	yes	characteristic
82	#1281	—	19	2	no	—
83	#1274	—	19	2	no	—
84	C₂²×C₁₉	—	2	1	no	—
85	C₂²×C₁₉	—	2	1	no	—
86	C₂²×C₁₉	#382	1	1	yes	characteristic
87	C₂²×C₁₉	#433	1	2	yes	—
88	C₄×C₁₉	—	2	1	no	—
89	C₄×C₁₉	—	2	1	no	—
90	C₄×C₁₉	—	2	1	no	—
91	C₄×C₁₉	—	2	1	no	—
92	C₄×C₁₉	#424	1	1	yes	characteristic
93	C₄×C₁₉	#424	1	1	yes	characteristic
94	C₄×C₁₉	#433	1	2	yes	—
95	Dic₁₉	—	8	2	no	—
96	#431	—	19	2	no	—
97	#431	C₂×D₁₉	1	2	yes	—
98	C₂×#97	—	19	1	no	—
99	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
100	#376	—	19	1	no	—
101	#336	—	19	2	no	—
102	#336	—	19	2	no	—
103	#335	—	2	1	no	—
104	#335	—	38	1	no	—
105	#334	—	2	1	no	—
106	#334	—	38	1	no	—
107	C₂×C₁₉	—	2	2	no	—
108	C₂×C₁₉	#1832	1	1	yes	characteristic
109	C₂×C₁₉	#1833	1	1	yes	characteristic
110	C₂×C₁₉	#1833	1	1	yes	characteristic
111	C₂²×C₈	—	19	2	no	—
112	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
113	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
114	C₂×C₄²	—	19	2	no	—
115	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
116	C₄⋊C₈	—	2	2	no	—
117	C₄⋊C₈	—	38	2	no	—
118	C₂²⋊C₈	—	2	2	no	—
119	C₂²⋊C₈	—	38	2	no	—
120	#97	—	38	1	no	—
121	#97	—	38	1	no	—
122	C₄×C₈	—	2	2	no	—
123	C₄×C₈	—	38	2	no	—
124	C₄×C₈	Dic₃₈	1	1	yes	characteristic
125	C₄×C₈	Dic₃₈	1	1	yes	characteristic
126	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
127	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
128	#95	—	38	1	no	—
129	#95	—	38	1	no	—
130	C₁₉	#8782	1	1	yes	characteristic, complemented, Sylow
131	C₂²×C₄	—	38	2	no	—
132	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
133	C₂²×C₄	#64543	1	1	yes	characteristic
134	C₂²×C₄	#64545	1	1	yes	characteristic
135	C₂×C₈	—	2	2	no	—
136	C₂×C₈	—	2	2	no	—
137	C₂×C₈	—	4	2	no	—
138	C₂×C₈	—	38	2	no	—
139	C₂×C₈	—	38	2	no	—
140	C₂×C₈	—	38	2	no	—
141	C₂×C₈	—	76	2	no	—
142	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
143	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
144	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
145	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
146	C₄²	—	38	2	no	—
147	C₄²	—	38	2	no	—
148	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
149	C₄²	#64543	1	1	yes	characteristic
150	C₄²	#64545	1	1	yes	characteristic
151	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
152	C₂³	#10597338	1	1	yes	characteristic
153	C₂×C₄	—	4	1	no	—
154	C₂×C₄	—	4	1	no	—
155	C₂×C₄	—	76	2	no	—
156	C₂×C₄	—	76	2	no	—
157	C₂×C₄	—	76	2	no	—
158	C₂×C₄	#10597336	1	1	yes	characteristic
159	C₂×C₄	#10597336	1	1	yes	characteristic
160	C₂×C₄	#10597338	1	1	yes	characteristic
161	C₂×C₄	#10597347	1	2	yes	—
162	C₂×C₄	#10597353	1	2	yes	—
163	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
164	C₂×C₄	#10597382	1	1	yes	characteristic
165	C₂×C₄	#10597393	1	1	yes	characteristic
166	C₈	—	2	1	no	—
167	C₈	—	2	1	no	—
168	C₈	—	2	1	no	—
169	C₈	—	2	1	no	—
170	C₈	—	8	2	no	—
171	C₈	—	76	2	no	—
172	C₈	—	152	2	no	—
173	C₂²	—	2	1	no	—
174	C₂²	—	2	1	no	—
175	C₂²	#11926409	1	1	yes	characteristic
176	C₂²	#11926604	1	2	yes	—
177	C₄	—	2	1	no	—
178	C₄	—	2	1	no	—
179	C₄	—	2	1	no	—
180	C₄	—	2	1	no	—
181	C₄	—	152	2	no	—
182	C₄	#11926570	1	1	yes	characteristic
183	C₄	#11926572	1	1	yes	characteristic
184	C₄	#11926604	1	2	yes	—
185	C₂	—	2	2	no	—
186	C₂	#14563754	1	1	yes	characteristic
187	C₂	#14563758	1	1	yes	characteristic
188	C₂	#14563760	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563386

C₂

yes

maximal, characteristic

#14562383

C₂

yes

maximal, characteristic

#14561479

C₂

yes

maximal

#14561463

C₂

yes

maximal

C₁₉×#1564

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

C₂×#10597260

C₂²

yes

characteristic

#11926390

C₂²

yes

characteristic

#11926298

C₄

yes

—

#11926298

C₄

yes

—

#11926297

—

#11926295

—

C₁₉×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₁₉×#334

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

Q₈

yes

characteristic

C₄×C₈×C₁₉

Q₈

yes

characteristic

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1746

—

#1564

—

#1564

D₁₉

yes

characteristic

#1281

—

#1274

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#382

yes

characteristic

C₂²×C₁₉

#433

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

Dic₁₉

—

#431

—

#431

C₂×D₁₉

yes

—

C₂×#97

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

100

#376

—

101

#336

—

102

#336

—

103

#335

—

104

#335

—

105

#334

—

106

#334

—

107

C₂×C₁₉

—

108

C₂×C₁₉

#1832

yes

characteristic

109

C₂×C₁₉

#1833

yes

characteristic

110

C₂×C₁₉

#1833

yes

characteristic

111

C₂²×C₈

—

112

C₂²×C₈

C₄×D₁₉

yes

characteristic

113

C₂²×C₈

C₄×D₁₉

yes

characteristic

114

C₂×C₄²

—

115

C₂×C₄²

C₂²×D₁₉

yes

characteristic

116

C₄⋊C₈

—

117

C₄⋊C₈

—

118

C₂²⋊C₈

—

119

C₂²⋊C₈

—

120

#97

—

121

#97

—

122

C₄×C₈

—

123

C₄×C₈

—

124

C₄×C₈

Dic₃₈

yes

characteristic

125

C₄×C₈

Dic₃₈

yes

characteristic

126

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

127

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

128

#95

—

129

#95

—

130

C₁₉

#8782

yes

characteristic, complemented, Sylow

131

C₂²×C₄

—

132

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

133

C₂²×C₄

#64543

yes

characteristic

134

C₂²×C₄

#64545

yes

characteristic

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

143

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

144

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

145

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

146

C₄²

—

147

C₄²

—

148

C₄²

C₂×Dic₃₈

yes

characteristic

149

C₄²

#64543

yes

characteristic

150

C₄²

#64545

yes

characteristic

151

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

152

C₂³

#10597338

yes

characteristic

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

#10597336

yes

characteristic

159

C₂×C₄

#10597336

yes

characteristic

160

C₂×C₄

#10597338

yes

characteristic

161

C₂×C₄

#10597347

yes

—

162

C₂×C₄

#10597353

yes

—

163

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

164

C₂×C₄

#10597382

yes

characteristic

165

C₂×C₄

#10597393

yes

characteristic

166

C₈

—

167

C₈

—

168

C₈

—

169

C₈

—

170

C₈

—

171

C₈

—

172

C₈

—

152

—

173

C₂²

—

174

C₂²

—

175

C₂²

#11926409

yes

characteristic

176

C₂²

#11926604

yes

—

177

C₄

—

178

C₄

—

179

C₄

—

180

C₄

—

181

C₄

—

152

—

182

C₄

#11926570

yes

characteristic

183

C₄

#11926572

yes

characteristic

184

C₄

#11926604

yes

—

185

C₂

—

186

C₂

#14563754

yes

characteristic

187

C₂

#14563758

yes

characteristic

188

C₂

#14563760

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597338
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1564	C₂
socle	C₂²×C₁₉	#382
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1564	D₁₉
hypocenter	C₁₉	#8782
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

subgroup

G/H

center

C₂×C₄

#10597338

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1564

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

N	H ≅ G/N	type
130. C₁₉	#8782	semidirect

H ≅ G/N

type

130. C₁₉

#8782

semidirect

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

subgroup	index
#14563386	2
#14562383	2
#14561479	2
#14561463	2
C₁₉×#1564	2
#8782	19

subgroup

index

C₁₉×#1564

Subgroups — #18076192

Conjugacy classes of subgroups

Complements

Maximal subgroups