Group #18085642 — subgroups

Subgroups — #18085642

Order 4864.

400 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 99 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	#14562199	C₂	1	2	yes	maximal
3	#14561495	C₂	1	2	yes	maximal
4	#14561468	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1994	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597316	—	2	1	no	—
7	#11926597	C₂²	1	2	yes	—
8	#11926442	—	2	4	no	—
9	#11926414	—	2	1	no	—
10	#11926410	C₂²	1	2	yes	—
11	#11926281	—	2	4	no	—
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₁₉×#423	C₂²	1	1	yes	characteristic
14	C₄³×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#339	—	2	1	no	—
16	C₁₉×#339	—	2	1	no	—
17	C₂×M₁₆×C₁₉	—	2	1	no	—
18	C₁₉×C₄⋊Q₈	Q₈	1	2	yes	—
19	C₁₉×#125	—	2	1	no	—
20	C₁₉×C₂²⋊Q₈	—	2	2	no	—
21	C₄×Q₈×C₁₉	—	2	2	no	—
22	C₁₉×#117	—	2	1	no	—
23	C₂×C₄²×C₁₉	—	2	2	no	—
24	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₉	—	2	4	no	—
28	C₂×C₄⋊Dic₁₉	—	2	2	no	—
29	C₂×Dic₁₉⋊C₄	—	2	4	no	—
30	#10597316	—	4	2	no	—
31	#10597316	—	4	2	no	—
32	C₁₉×C₄⋊C₈	—	2	2	no	—
33	C₁₉⋊#95	—	2	2	no	—
34	C₁₉⋊#95	D₄	1	4	yes	—
35	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
36	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
37	C₄×C₁₉⋊C₈	—	2	2	no	—
38	C₂×Q₈×C₁₉	—	2	2	no	—
39	C₂²×C₄×C₁₉	—	2	1	no	—
40	C₂²×C₄×C₁₉	—	2	1	no	—
41	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
42	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂²×Dic₁₉	—	2	4	no	—
44	M₁₆×C₁₉	—	4	1	no	—
45	M₁₆×C₁₉	—	4	1	no	—
46	C₂×C₈×C₁₉	—	4	1	no	—
47	C₄⋊C₄×C₁₉	—	2	2	no	—
48	C₄⋊C₄×C₁₉	—	2	2	no	—
49	C₄⋊C₄×C₁₉	—	4	2	no	—
50	C₂²⋊C₄×C₁₉	—	4	1	no	—
51	C₄²×C₁₉	—	2	1	no	—
52	C₄²×C₁₉	—	2	1	no	—
53	C₄²×C₁₉	—	4	4	no	—
54	C₄²×C₁₉	—	4	1	no	—
55	C₄²×C₁₉	SD₁₆	1	2	yes	—
56	C₄²×C₁₉	Q₁₆	1	2	yes	—
57	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
58	C₄²×C₁₉	#41	1	1	yes	characteristic
59	C₄²×C₁₉	#41	1	2	yes	—
60	C₄⋊Dic₁₉	—	4	8	no	—
61	C₄⋊Dic₁₉	—	4	2	no	—
62	C₄⋊Dic₁₉	—	4	2	no	—
63	Dic₁₉⋊C₄	—	4	8	no	—
64	C₂×C₁₉⋊C₈	—	4	2	no	—
65	#10365	—	19	1	no	maximal, Sylow
66	C₂³×C₁₉	#120	1	1	yes	characteristic
67	Q₈×C₁₉	—	8	2	no	—
68	C₂×C₄×C₁₉	—	2	4	no	—
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	—	4	2	no	—
72	C₂×C₄×C₁₉	—	4	2	no	—
73	C₂×C₄×C₁₉	—	4	2	no	—
74	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
75	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
76	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
77	C₂×C₄×C₁₉	#124	1	2	yes	—
78	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
79	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
80	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
81	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
82	C₂×Dic₁₉	—	4	8	no	—
83	C₂×Dic₁₉	—	4	4	no	—
84	C₈×C₁₉	—	8	1	no	—
85	C₁₉⋊C₈	—	8	2	no	—
86	#2859	—	19	1	no	—
87	#1994	D₁₉	1	1	yes	characteristic
88	#1518	—	19	2	no	—
89	#1286	—	19	2	no	—
90	#1276	—	19	1	no	—
91	C₂²×C₁₉	—	2	2	no	—
92	C₂²×C₁₉	#393	1	1	yes	characteristic
93	C₂²×C₁₉	#450	1	1	yes	characteristic
94	C₂²×C₁₉	#451	1	1	yes	characteristic
95	C₄×C₁₉	—	2	4	no	—
96	C₄×C₁₉	—	2	2	no	—
97	C₄×C₁₉	—	2	2	no	—
98	C₄×C₁₉	—	4	2	no	—
99	C₄×C₁₉	—	8	2	no	—
100	C₄×C₁₉	#475	1	1	yes	characteristic
101	C₄×C₁₉	#477	1	1	yes	characteristic
102	C₄×C₁₉	#487	1	1	yes	characteristic
103	C₄×C₁₉	#489	1	1	yes	characteristic
104	Dic₁₉	—	8	4	no	—
105	#533	C₂×D₁₉	1	1	yes	characteristic
106	C₂×#125	—	38	1	no	—
107	#431	—	19	2	no	—
108	#423	C₂×D₁₉	1	1	yes	characteristic
109	#389	—	38	4	no	—
110	#384	—	38	1	no	—
111	#382	—	19	2	no	—
112	C₄³	C₂×D₁₉	1	1	yes	characteristic
113	#339	—	2	1	no	—
114	#339	—	2	1	no	—
115	#328	—	38	4	no	—
116	C₂×C₁₉	—	2	1	no	—
117	C₂×C₁₉	—	2	1	no	—
118	C₂×C₁₉	#2024	1	1	yes	characteristic
119	C₂×C₁₉	#2031	1	2	yes	—
120	C₂×M₁₆	—	2	1	no	—
121	C₄⋊Q₈	Dic₃₈	1	2	yes	—
122	#125	—	2	1	no	—
123	#125	—	76	2	no	—
124	#125	—	76	2	no	—
125	C₂²⋊Q₈	—	2	2	no	—
126	C₄×Q₈	—	2	2	no	—
127	#117	—	2	1	no	—
128	C₂×C₄⋊C₄	—	38	4	no	—
129	C₂×C₄⋊C₄	—	38	4	no	—
130	C₂×C₄⋊C₄	—	38	2	no	—
131	C₂×C₄²	—	2	2	no	—
132	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
133	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
134	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
135	C₄⋊C₈	—	2	2	no	—
136	C₄⋊C₈	—	38	2	no	—
137	C₂²⋊C₈	—	38	2	no	—
138	C₄×C₈	—	38	2	no	—
139	#95	—	19	4	no	—
140	#95	—	38	2	no	—
141	C₁₉	#10365	1	1	yes	characteristic, complemented, Sylow
142	C₂×Q₈	—	2	2	no	—
143	C₂²×C₄	—	2	1	no	—
144	C₂²×C₄	—	2	1	no	—
145	C₂²×C₄	—	38	4	no	—
146	C₂²×C₄	D₄×D₁₉	1	2	yes	—
147	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
148	M₁₆	—	4	1	no	—
149	M₁₆	—	4	1	no	—
150	C₂×C₈	—	4	1	no	—
151	C₂×C₈	—	76	2	no	—
152	C₄⋊C₄	—	2	2	no	—
153	C₄⋊C₄	—	2	2	no	—
154	C₄⋊C₄	—	4	2	no	—
155	C₄⋊C₄	—	76	8	no	—
156	C₄⋊C₄	—	76	8	no	—
157	C₄⋊C₄	—	76	2	no	—
158	C₄⋊C₄	—	76	2	no	—
159	C₂²⋊C₄	—	4	1	no	—
160	C₄²	—	2	1	no	—
161	C₄²	—	2	1	no	—
162	C₄²	—	4	4	no	—
163	C₄²	—	4	1	no	—
164	C₄²	#64527	1	2	yes	—
165	C₄²	#64528	1	2	yes	—
166	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
167	C₄²	#64541	1	1	yes	characteristic
168	C₄²	#64543	1	2	yes	—
169	C₂³	#10597383	1	1	yes	characteristic
170	Q₈	—	8	2	no	—
171	C₂×C₄	—	2	4	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	4	2	no	—
175	C₂×C₄	—	4	2	no	—
176	C₂×C₄	—	4	2	no	—
177	C₂×C₄	—	76	8	no	—
178	C₂×C₄	—	76	4	no	—
179	C₂×C₄	#10597324	1	2	yes	—
180	C₂×C₄	#10597331	1	2	yes	—
181	C₂×C₄	#10597370	1	1	yes	characteristic
182	C₂×C₄	#10597382	1	1	yes	characteristic
183	C₂×C₄	C₂×#64527	1	1	yes	characteristic
184	C₂×C₄	C₂×#64528	1	1	yes	characteristic
185	C₂×C₄	#10597395	1	1	yes	characteristic
186	C₂×C₄	#10597397	1	1	yes	characteristic
187	C₈	—	8	1	no	—
188	C₈	—	152	2	no	—
189	C₂²	—	2	2	no	—
190	C₂²	#11926456	1	1	yes	characteristic
191	C₂²	#11926694	1	1	yes	characteristic
192	C₂²	#11926699	1	1	yes	characteristic
193	C₄	—	2	4	no	—
194	C₄	—	2	2	no	—
195	C₄	—	2	2	no	—
196	C₄	—	4	2	no	—
197	C₄	—	8	2	no	—
198	C₄	—	152	4	no	—
199	C₄	#11926829	1	1	yes	characteristic
200	C₄	#11926839	1	1	yes	characteristic
201	C₄	#11926894	1	1	yes	characteristic
202	C₄	#11926903	1	1	yes	characteristic
203	C₂	—	2	1	no	—
204	C₂	—	2	1	no	—
205	C₂	#14564776	1	1	yes	characteristic
206	C₂	#14564807	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14571998

C₂

yes

maximal, characteristic

#14562199

C₂

yes

maximal

#14561495

C₂

yes

maximal

#14561468

C₂

yes

maximal, characteristic

C₁₉×#1994

C₂

yes

maximal, characteristic

C₂×#10597316

—

#11926597

C₂²

yes

—

#11926442

—

#11926414

—

#11926410

C₂²

yes

—

#11926281

—

C₁₉×#533

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#339

—

C₁₉×#339

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

Q₈

yes

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×Dic₁₉⋊C₄

—

#10597316

—

#10597316

—

C₁₉×C₄⋊C₈

—

C₁₉⋊#95

—

C₁₉⋊#95

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

Q₁₆

yes

—

C₄²×C₁₉

C₂×Q₈

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₁₆

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2859

—

#1994

D₁₉

yes

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

100

C₄×C₁₉

#475

yes

characteristic

101

C₄×C₁₉

#477

yes

characteristic

102

C₄×C₁₉

#487

yes

characteristic

103

C₄×C₁₉

#489

yes

characteristic

104

Dic₁₉

—

105

#533

C₂×D₁₉

yes

characteristic

106

C₂×#125

—

107

#431

—

108

#423

C₂×D₁₉

yes

characteristic

109

#389

—

110

#384

—

111

#382

—

112

C₄³

C₂×D₁₉

yes

characteristic

113

#339

—

114

#339

—

115

#328

—

116

C₂×C₁₉

—

117

C₂×C₁₉

—

118

C₂×C₁₉

#2024

yes

characteristic

119

C₂×C₁₉

#2031

yes

—

120

C₂×M₁₆

—

121

C₄⋊Q₈

Dic₃₈

yes

—

122

#125

—

123

#125

—

124

#125

—

125

C₂²⋊Q₈

—

126

C₄×Q₈

—

127

#117

—

128

C₂×C₄⋊C₄

—

129

C₂×C₄⋊C₄

—

130

C₂×C₄⋊C₄

—

131

C₂×C₄²

—

132

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

133

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

134

C₂×C₄²

C₂²×D₁₉

yes

characteristic

135

C₄⋊C₈

—

136

C₄⋊C₈

—

137

C₂²⋊C₈

—

138

C₄×C₈

—

139

#95

—

140

#95

—

141

C₁₉

#10365

yes

characteristic, complemented, Sylow

142

C₂×Q₈

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

D₄×D₁₉

yes

—

147

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

148

M₁₆

—

149

M₁₆

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₄⋊C₄

—

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

—

164

C₄²

#64527

yes

—

165

C₄²

#64528

yes

—

166

C₄²

C₂×Dic₃₈

yes

characteristic

167

C₄²

#64541

yes

characteristic

168

C₄²

#64543

yes

—

169

C₂³

#10597383

yes

characteristic

170

Q₈

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

#10597324

yes

—

180

C₂×C₄

#10597331

yes

—

181

C₂×C₄

#10597370

yes

characteristic

182

C₂×C₄

#10597382

yes

characteristic

183

C₂×C₄

C₂×#64527

yes

characteristic

184

C₂×C₄

C₂×#64528

yes

characteristic

185

C₂×C₄

#10597395

yes

characteristic

186

C₂×C₄

#10597397

yes

characteristic

187

C₈

—

188

C₈

—

152

—

189

C₂²

—

190

C₂²

#11926456

yes

characteristic

191

C₂²

#11926694

yes

characteristic

192

C₂²

#11926699

yes

characteristic

193

C₄

—

194

C₄

—

195

C₄

—

196

C₄

—

197

C₄

—

198

C₄

—

152

—

199

C₄

#11926829

yes

characteristic

200

C₄

#11926839

yes

characteristic

201

C₄

#11926894

yes

characteristic

202

C₄

#11926903

yes

characteristic

203

C₂

—

204

C₂

—

205

C₂

#14564776

yes

characteristic

206

C₂

#14564807

yes

—

	subgroup	G/H
center	C₂²	#11926456
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1994	C₂
socle	C₂²×C₁₉	#393
prime radical	C₂³×C₁₉	#120
hypercenter	#1994	D₁₉
hypocenter	C₁₉	#10365
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1994

subgroup

G/H

center

C₂²

#11926456

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1994

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1994

N	H ≅ G/N	type
141. C₁₉	#10365	semidirect

H ≅ G/N

type

141. C₁₉

#10365

semidirect

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

subgroup	index
#14571998	2
#14562199	2
#14561495	2
#14561468	2
C₁₉×#1994	2
#10365	19

subgroup

index

C₁₉×#1994

Subgroups — #18085642

Conjugacy classes of subgroups

Complements

Maximal subgroups