Group #18086635 — subgroups

Subgroups — #18086635

Order 4864.

344 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 81 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	#14563754	C₂	1	1	yes	maximal, characteristic
2	#14562335	C₂	1	2	yes	maximal
3	#14562147	C₂	1	2	yes	maximal
4	#14561505	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#3249	C₂	1	1	yes	maximal, characteristic
6	#11926601	C₂²	1	2	yes	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
8	#11926390	C₂²	1	1	yes	characteristic
9	#11926298	—	2	2	no	—
10	#11926290	—	2	2	no	—
11	#11926290	—	2	2	no	—
12	#11926281	—	2	4	no	—
13	C₁₉×#533	C₂²	1	2	yes	—
14	C₁₉×#477	—	2	2	no	—
15	C₁₉×#467	—	2	2	no	—
16	C₁₉×#462	—	2	2	no	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×Q₁₆×C₁₉	—	2	2	no	—
19	C₂²×C₈×C₁₉	D₄	1	2	yes	—
20	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
21	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
22	C₁₉×#125	—	2	2	no	—
23	C₁₉×C₂²⋊Q₈	—	2	2	no	—
24	C₁₉×C₂²⋊Q₈	—	2	2	no	—
25	C₄×Q₈×C₁₉	—	2	2	no	—
26	C₄×Q₈×C₁₉	—	2	2	no	—
27	C₁₉×#117	—	2	2	no	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₄×Dic₁₉	—	2	1	no	—
30	C₂²×C₁₉⋊C₈	—	2	1	no	—
31	C₁₉×#107	—	2	2	no	—
32	C₁₉×C₄⋊C₈	—	2	2	no	—
33	C₁₉×#103	—	2	4	no	—
34	C₁₉⋊#95	—	2	1	no	—
35	C₁₉⋊#95	D₄	1	2	yes	—
36	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
39	#10597260	—	2	2	no	—
40	C₂×Q₈×C₁₉	—	2	2	no	—
41	C₂×Q₈×C₁₉	—	2	2	no	—
42	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
45	C₂²×Dic₁₉	—	2	2	no	—
46	Q₁₆×C₁₉	—	8	2	no	—
47	C₂×C₈×C₁₉	—	2	2	no	—
48	C₂×C₈×C₁₉	—	4	2	no	—
49	C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₄⋊C₄×C₁₉	—	2	2	no	—
52	C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₄⋊C₄×C₁₉	—	4	2	no	—
54	C₄⋊C₄×C₁₉	—	4	2	no	—
55	C₂²⋊C₄×C₁₉	—	4	2	no	—
56	C₄²×C₁₉	—	4	2	no	—
57	C₄²×C₁₉	C₂×D₄	1	2	yes	—
58	C₄²×C₁₉	#41	1	2	yes	—
59	C₄×Dic₁₉	—	4	1	no	—
60	C₄×Dic₁₉	—	4	1	no	—
61	C₂×C₁₉⋊C₈	—	4	2	no	—
62	C₂×C₁₉⋊C₈	—	4	1	no	—
63	C₂×C₁₉⋊C₈	—	4	2	no	—
64	#10517	—	19	1	no	maximal, Sylow
65	C₂³×C₁₉	#121	1	1	yes	characteristic
66	Q₈×C₁₉	—	4	2	no	—
67	Q₈×C₁₉	—	4	2	no	—
68	Q₈×C₁₉	—	8	2	no	—
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	—	4	1	no	—
73	C₂×C₄×C₁₉	—	4	2	no	—
74	C₂×C₄×C₁₉	—	4	2	no	—
75	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
76	C₂×C₄×C₁₉	#121	1	2	yes	—
77	C₂×C₄×C₁₉	#123	1	2	yes	—
78	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
79	C₂×Dic₁₉	—	4	2	no	—
80	C₂×Dic₁₉	—	4	2	no	—
81	C₂×Dic₁₉	—	4	2	no	—
82	C₈×C₁₉	—	4	2	no	—
83	C₁₉⋊C₈	—	8	2	no	—
84	C₁₉⋊C₈	—	8	1	no	—
85	#3249	D₁₉	1	1	yes	characteristic
86	#1832	—	19	1	no	—
87	#1552	—	19	2	no	—
88	#1506	—	19	2	no	—
89	#1290	—	19	1	no	—
90	C₂²×C₁₉	—	2	1	no	—
91	C₂²×C₁₉	—	2	1	no	—
92	C₂²×C₁₉	#394	1	1	yes	characteristic
93	C₂²×C₁₉	#473	1	2	yes	—
94	C₄×C₁₉	—	2	2	no	—
95	C₄×C₁₉	—	2	1	no	—
96	C₄×C₁₉	—	2	2	no	—
97	C₄×C₁₉	—	8	2	no	—
98	C₄×C₁₉	—	8	2	no	—
99	C₄×C₁₉	#454	1	1	yes	characteristic
100	C₄×C₁₉	#455	1	1	yes	characteristic
101	Dic₁₉	—	8	2	no	—
102	#533	C₂×D₁₉	1	2	yes	—
103	#477	—	2	2	no	—
104	#467	—	2	2	no	—
105	#462	—	2	2	no	—
106	#432	—	19	2	no	—
107	C₂×C₄⋊C₈	—	19	1	no	—
108	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
109	#376	—	19	1	no	—
110	#336	—	38	2	no	—
111	#332	—	38	2	no	—
112	#332	—	38	2	no	—
113	#328	—	38	4	no	—
114	C₂×C₁₉	—	2	2	no	—
115	C₂×C₁₉	#2040	1	1	yes	characteristic
116	C₂×C₁₉	#2047	1	1	yes	characteristic
117	C₂×C₁₉	#2053	1	1	yes	characteristic
118	C₂×Q₁₆	—	2	2	no	—
119	C₂²×C₈	—	38	1	no	—
120	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
121	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
122	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
123	#125	—	2	2	no	—
124	C₂²⋊Q₈	—	2	2	no	—
125	C₂²⋊Q₈	—	2	2	no	—
126	C₄×Q₈	—	2	2	no	—
127	C₄×Q₈	—	2	2	no	—
128	#117	—	2	2	no	—
129	C₂×C₄²	—	38	1	no	—
130	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
131	#107	—	2	2	no	—
132	C₄⋊C₈	—	2	2	no	—
133	C₄⋊C₈	—	38	2	no	—
134	C₄⋊C₈	—	38	2	no	—
135	#103	—	2	4	no	—
136	C₂²⋊C₈	—	38	2	no	—
137	#97	—	38	2	no	—
138	#95	—	19	2	no	—
139	#95	—	38	1	no	—
140	C₁₉	#10517	1	1	yes	characteristic, complemented, Sylow
141	C₂×Q₈	—	2	2	no	—
142	C₂×Q₈	—	2	2	no	—
143	C₂²×C₄	—	38	2	no	—
144	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
145	C₂²×C₄	#64543	1	1	yes	characteristic
146	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
147	Q₁₆	—	8	2	no	—
148	C₂×C₈	—	2	2	no	—
149	C₂×C₈	—	4	2	no	—
150	C₂×C₈	—	76	2	no	—
151	C₂×C₈	—	76	2	no	—
152	C₂×C₈	—	76	1	no	—
153	C₄⋊C₄	—	2	2	no	—
154	C₄⋊C₄	—	2	2	no	—
155	C₄⋊C₄	—	2	2	no	—
156	C₄⋊C₄	—	2	2	no	—
157	C₄⋊C₄	—	4	2	no	—
158	C₄⋊C₄	—	4	2	no	—
159	C₂²⋊C₄	—	4	2	no	—
160	C₄²	—	4	2	no	—
161	C₄²	—	76	1	no	—
162	C₄²	—	76	1	no	—
163	C₄²	#64543	1	2	yes	—
164	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
165	C₂³	#10597384	1	1	yes	characteristic
166	Q₈	—	4	2	no	—
167	Q₈	—	4	2	no	—
168	Q₈	—	8	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	1	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	4	1	no	—
173	C₂×C₄	—	4	2	no	—
174	C₂×C₄	—	4	2	no	—
175	C₂×C₄	—	76	2	no	—
176	C₂×C₄	—	76	2	no	—
177	C₂×C₄	—	76	2	no	—
178	C₂×C₄	#10597381	1	2	yes	—
179	C₂×C₄	#10597382	1	1	yes	characteristic
180	C₂×C₄	#10597385	1	2	yes	—
181	C₂×C₄	#10597399	1	1	yes	characteristic
182	C₈	—	4	2	no	—
183	C₈	—	152	2	no	—
184	C₈	—	152	1	no	—
185	C₂²	—	2	1	no	—
186	C₂²	—	2	1	no	—
187	C₂²	#11926458	1	1	yes	characteristic
188	C₂²	#11926816	1	2	yes	—
189	C₄	—	2	2	no	—
190	C₄	—	2	2	no	—
191	C₄	—	2	1	no	—
192	C₄	—	8	2	no	—
193	C₄	—	8	2	no	—
194	C₄	—	152	2	no	—
195	C₄	#11926717	1	1	yes	characteristic
196	C₄	#11926722	1	1	yes	characteristic
197	C₂	—	2	2	no	—
198	C₂	#14564861	1	1	yes	characteristic
199	C₂	#14564900	1	1	yes	characteristic
200	C₂	#14564938	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563754

C₂

yes

maximal, characteristic

#14562335

C₂

yes

maximal

#14562147

C₂

yes

maximal

#14561505

C₂

yes

maximal, characteristic

C₁₉×#3249

C₂

yes

maximal, characteristic

#11926601

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

#11926390

C₂²

yes

—

—

—

—

C₁₉×#533

C₂²

yes

—

C₁₉×#477

—

C₁₉×#467

—

C₁₉×#462

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×Q₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×#107

—

C₁₉×C₄⋊C₈

—

C₁₉×#103

—

C₁₉⋊#95

—

C₁₉⋊#95

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#3249

D₁₉

yes

—

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#394

yes

characteristic

C₂²×C₁₉

#473

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#454

yes

characteristic

100

C₄×C₁₉

#455

yes

characteristic

101

Dic₁₉

—

102

#533

C₂×D₁₉

yes

—

103

#477

—

104

#467

—

105

#462

—

106

#432

—

107

C₂×C₄⋊C₈

—

108

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

109

#376

—

110

#336

—

111

#332

—

112

#332

—

113

#328

—

114

C₂×C₁₉

—

115

C₂×C₁₉

#2040

yes

characteristic

116

C₂×C₁₉

#2047

yes

characteristic

117

C₂×C₁₉

#2053

yes

characteristic

118

C₂×Q₁₆

—

119

C₂²×C₈

—

120

C₂²×C₈

C₂²⋊D₁₉

yes

—

121

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

122

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

123

#125

—

124

C₂²⋊Q₈

—

125

C₂²⋊Q₈

—

126

C₄×Q₈

—

127

C₄×Q₈

—

128

#117

—

129

C₂×C₄²

—

130

C₂×C₄²

C₂²×D₁₉

yes

characteristic

131

#107

—

132

C₄⋊C₈

—

133

C₄⋊C₈

—

134

C₄⋊C₈

—

135

#103

—

136

C₂²⋊C₈

—

137

#97

—

138

#95

—

139

#95

—

140

C₁₉

#10517

yes

characteristic, complemented, Sylow

141

C₂×Q₈

—

142

C₂×Q₈

—

143

C₂²×C₄

—

144

C₂²×C₄

D₄×D₁₉

yes

characteristic

145

C₂²×C₄

#64543

yes

characteristic

146

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

147

Q₁₆

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₂²⋊C₄

—

160

C₄²

—

161

C₄²

—

162

C₄²

—

163

C₄²

#64543

yes

—

164

C₄²

C₂×C₂²⋊D₁₉

yes

—

165

C₂³

#10597384

yes

characteristic

166

Q₈

—

167

Q₈

—

168

Q₈

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

#10597381

yes

—

179

C₂×C₄

#10597382

yes

characteristic

180

C₂×C₄

#10597385

yes

—

181

C₂×C₄

#10597399

yes

characteristic

182

C₈

—

183

C₈

—

152

—

184

C₈

—

152

—

185

C₂²

—

186

C₂²

—

187

C₂²

#11926458

yes

characteristic

188

C₂²

#11926816

yes

—

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

—

193

C₄

—

194

C₄

—

152

—

195

C₄

#11926717

yes

characteristic

196

C₄

#11926722

yes

characteristic

197

C₂

—

198

C₂

#14564861

yes

characteristic

199

C₂

#14564900

yes

characteristic

200

C₂

#14564938

yes

characteristic

	subgroup	G/H
center	C₂²	#11926458
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3249	C₂
socle	C₂²×C₁₉	#394
prime radical	C₂³×C₁₉	#121
hypercenter	#3249	D₁₉
hypocenter	C₁₉	#10517
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3249

subgroup

G/H

center

C₂²

#11926458

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3249

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3249

N	H ≅ G/N	type
140. C₁₉	#10517	semidirect

H ≅ G/N

type

140. C₁₉

#10517

semidirect

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

subgroup	index
#14563754	2
#14562335	2
#14562147	2
#14561505	2
C₁₉×#3249	2
#10517	19

subgroup

index

C₁₉×#3249

Subgroups — #18086635

Conjugacy classes of subgroups

Complements

Maximal subgroups