Group #18077504 — subgroups

Subgroups — #18077504

Order 4864.

398 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 103 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	#14572741	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562300	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562104	C₂	1	2	yes	maximal
4	#14561534	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3135	C₂	1	1	yes	maximal, characteristic
6	#11926675	—	2	4	no	—
7	#11926605	—	2	2	no	—
8	#11926601	C₂²	1	2	yes	—
9	#11926597	C₂²	1	2	yes	—
10	#11926290	—	2	2	no	—
11	D₄⋊(C₁₉⋊C₈)	—	2	4	no	—
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₁₉×#532	C₂²	1	1	yes	characteristic
14	C₁₉×#491	C₄	1	2	yes	—
15	C₁₉×#490	C₄	1	2	yes	—
16	C₁₉×#489	—	2	2	no	—
17	C₁₉×#416	—	2	2	no	—
18	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
19	C₂×#41×C₁₉	—	2	1	no	—
20	C₂²×C₈×C₁₉	—	2	1	no	—
21	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
22	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
23	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
24	C₁₉×#125	C₂×C₄	1	2	yes	—
25	C₁₉×#124	—	2	1	no	—
26	C₁₉×C₂²⋊Q₈	—	2	2	no	—
27	C₁₉×#121	—	2	2	no	—
28	C₄×Q₈×C₁₉	—	2	2	no	—
29	C₄×D₄×C₁₉	—	2	2	no	—
30	C₁₉×#117	D₄	1	2	yes	—
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	C₁₉×#103	—	2	4	no	—
33	C₁₉×#102	—	2	4	no	—
34	C₁₉×#97	—	2	1	no	—
35	C₁₉×#97	C₂×C₄	1	2	yes	—
36	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
37	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
41	#10597260	—	2	2	no	—
42	#10597260	—	2	2	no	—
43	C₄×C₁₉⋊C₈	—	2	2	no	—
44	C₄×C₁₉⋊C₈	—	2	2	no	—
45	#41×C₁₉	—	4	4	no	—
46	C₂×Q₈×C₁₉	—	2	2	no	—
47	C₂×Q₈×C₁₉	—	2	1	no	—
48	C₂×D₄×C₁₉	—	2	1	no	—
49	C₂×D₄×C₁₉	—	2	2	no	—
50	C₂×D₄×C₁₉	—	4	1	no	—
51	C₂²×C₄×C₁₉	—	4	1	no	—
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	#41	1	2	yes	—
54	C₂×C₈×C₁₉	—	2	2	no	—
55	C₂×C₈×C₁₉	—	4	2	no	—
56	C₄⋊C₄×C₁₉	—	2	4	no	—
57	C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
60	C₂²⋊C₄×C₁₉	—	2	2	no	—
61	C₂²⋊C₄×C₁₉	—	4	2	no	—
62	C₄²×C₁₉	—	2	2	no	—
63	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₄²×C₁₉	C₂×D₄	1	2	yes	—
65	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂×C₁₉⋊C₈	—	2	4	no	—
67	C₂×C₁₉⋊C₈	—	4	2	no	—
68	#9008	—	19	1	no	maximal, Sylow
69	C₂³×C₁₉	—	4	1	no	—
70	C₂³×C₁₉	#123	1	1	yes	characteristic
71	Q₈×C₁₉	—	4	2	no	—
72	Q₈×C₁₉	—	8	2	no	—
73	D₄×C₁₉	—	4	4	no	—
74	D₄×C₁₉	—	4	2	no	—
75	D₄×C₁₉	—	8	2	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	—	2	4	no	—
78	C₂×C₄×C₁₉	—	4	2	no	—
79	C₂×C₄×C₁₉	—	4	1	no	—
80	C₂×C₄×C₁₉	—	8	2	no	—
81	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
83	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#121	1	2	yes	—
85	C₈×C₁₉	—	4	2	no	—
86	C₁₉⋊C₈	—	4	4	no	—
87	C₁₉⋊C₈	—	8	2	no	—
88	#3135	D₁₉	1	1	yes	characteristic
89	#2987	—	19	1	no	—
90	#1544	—	19	1	no	—
91	#1496	—	19	2	no	—
92	#1302	—	19	2	no	—
93	C₂²×C₁₉	—	2	2	no	—
94	C₂²×C₁₉	—	2	1	no	—
95	C₂²×C₁₉	—	8	2	no	—
96	C₂²×C₁₉	—	8	1	no	—
97	C₂²×C₁₉	#386	1	1	yes	characteristic
98	C₄×C₁₉	—	2	2	no	—
99	C₄×C₁₉	—	2	2	no	—
100	C₄×C₁₉	—	2	1	no	—
101	C₄×C₁₉	—	4	4	no	—
102	C₄×C₁₉	—	8	1	no	—
103	C₄×C₁₉	#454	1	2	yes	—
104	#533	C₂×D₁₉	1	1	yes	characteristic
105	#532	C₂×D₁₉	1	1	yes	characteristic
106	#491	Dic₁₉	1	2	yes	—
107	#490	Dic₁₉	1	2	yes	—
108	#489	—	2	2	no	—
109	#446	—	38	4	no	—
110	#433	—	38	2	no	—
111	#432	—	19	2	no	—
112	#431	—	19	2	no	—
113	#416	—	2	2	no	—
114	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
115	#332	—	38	2	no	—
116	D₄⋊C₈	—	38	4	no	—
117	C₂×C₁₉	—	4	1	no	—
118	C₂×C₁₉	—	16	1	no	—
119	C₂×C₁₉	#1881	1	2	yes	—
120	C₂×C₁₉	#1888	1	1	yes	characteristic
121	C₂×#41	—	2	1	no	—
122	C₂²×C₈	—	2	1	no	—
123	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
124	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
125	#127	C₂×Dic₁₉	1	1	yes	characteristic
126	#125	C₂×Dic₁₉	1	2	yes	—
127	#124	—	2	1	no	—
128	C₂²⋊Q₈	—	2	2	no	—
129	#121	—	2	2	no	—
130	C₄×Q₈	—	2	2	no	—
131	C₄×D₄	—	2	2	no	—
132	#117	C₂²⋊D₁₉	1	2	yes	—
133	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
134	C₄⋊C₈	—	19	4	no	—
135	C₄⋊C₈	—	38	4	no	—
136	C₄⋊C₈	—	38	2	no	—
137	#103	—	2	4	no	—
138	#102	—	2	4	no	—
139	C₂²⋊C₈	—	38	2	no	—
140	C₂²⋊C₈	—	38	2	no	—
141	#97	—	2	1	no	—
142	#97	—	38	2	no	—
143	#97	—	38	2	no	—
144	#97	C₂×Dic₁₉	1	2	yes	—
145	C₄×C₈	—	38	2	no	—
146	C₄×C₈	—	38	2	no	—
147	C₁₉	#9008	1	1	yes	characteristic, complemented, Sylow
148	#41	—	4	4	no	—
149	C₂×Q₈	—	2	2	no	—
150	C₂×Q₈	—	2	1	no	—
151	C₂×D₄	—	2	2	no	—
152	C₂×D₄	—	2	1	no	—
153	C₂×D₄	—	4	1	no	—
154	C₂²×C₄	—	4	1	no	—
155	C₂²×C₄	#64543	1	2	yes	—
156	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
157	C₂×C₈	—	2	2	no	—
158	C₂×C₈	—	4	2	no	—
159	C₂×C₈	—	38	4	no	—
160	C₂×C₈	—	76	2	no	—
161	C₄⋊C₄	—	2	4	no	—
162	C₄⋊C₄	—	2	2	no	—
163	C₄⋊C₄	—	2	2	no	—
164	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
165	C₂²⋊C₄	—	2	2	no	—
166	C₂²⋊C₄	—	4	2	no	—
167	C₄²	—	2	2	no	—
168	C₄²	D₄×D₁₉	1	2	yes	—
169	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
170	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
171	C₂³	—	4	1	no	—
172	C₂³	#10597381	1	1	yes	characteristic
173	Q₈	—	4	2	no	—
174	Q₈	—	8	2	no	—
175	D₄	—	4	2	no	—
176	D₄	—	4	4	no	—
177	D₄	—	8	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	4	2	no	—
181	C₂×C₄	—	4	1	no	—
182	C₂×C₄	—	8	2	no	—
183	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
184	C₂×C₄	#10597383	1	1	yes	characteristic
185	C₂×C₄	#10597385	1	2	yes	—
186	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
187	C₈	—	4	2	no	—
188	C₈	—	76	4	no	—
189	C₈	—	152	2	no	—
190	C₂²	—	2	2	no	—
191	C₂²	—	2	1	no	—
192	C₂²	—	8	2	no	—
193	C₂²	—	8	1	no	—
194	C₂²	#11926424	1	1	yes	characteristic
195	C₄	—	2	2	no	—
196	C₄	—	2	2	no	—
197	C₄	—	2	1	no	—
198	C₄	—	4	4	no	—
199	C₄	—	8	1	no	—
200	C₄	#11926716	1	2	yes	—
201	C₂	—	4	1	no	—
202	C₂	—	16	1	no	—
203	C₂	#14563999	1	2	yes	—
204	C₂	#14564039	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572741

C₂

yes

maximal, characteristic, complemented

#14562300

C₂

yes

maximal, characteristic, complemented

#14562104

C₂

yes

maximal

#14561534

C₂

yes

maximal, complemented

C₁₉×#3135

C₂

yes

maximal, characteristic

#11926675

—

#11926605

—

#11926601

C₂²

yes

—

#11926597

C₂²

yes

—

#11926290

—

D₄⋊(C₁₉⋊C₈)

—

C₁₉×#533

C₂²

yes

characteristic

C₁₉×#532

C₂²

yes

characteristic

C₁₉×#491

C₄

yes

—

C₁₉×#490

C₄

yes

—

C₁₉×#489

—

C₁₉×#416

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂×#41×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

characteristic

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#127

C₂×C₄

yes

characteristic

C₁₉×#125

C₂×C₄

yes

—

C₁₉×#124

—

C₁₉×C₂²⋊Q₈

—

C₁₉×#121

—

C₄×Q₈×C₁₉

—

C₄×D₄×C₁₉

—

C₁₉×#117

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#103

—

C₁₉×#102

—

C₁₉×#97

—

C₁₉×#97

C₂×C₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9008

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#123

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#3135

D₁₉

yes

—

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#386

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

100

C₄×C₁₉

—

101

C₄×C₁₉

—

102

C₄×C₁₉

—

103

C₄×C₁₉

#454

yes

—

104

#533

C₂×D₁₉

yes

characteristic

105

#532

C₂×D₁₉

yes

characteristic

106

#491

Dic₁₉

yes

—

107

#490

Dic₁₉

yes

—

108

#489

—

109

#446

—

110

#433

—

111

#432

—

112

#431

—

113

#416

—

114

C₂×#97

C₂×D₁₉

yes

characteristic

115

#332

—

116

D₄⋊C₈

—

117

C₂×C₁₉

—

118

C₂×C₁₉

—

119

C₂×C₁₉

#1881

yes

—

120

C₂×C₁₉

#1888

yes

characteristic

121

C₂×#41

—

122

C₂²×C₈

—

123

C₄⋊Q₈

C₂×Dic₁₉

yes

characteristic

124

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

125

#127

C₂×Dic₁₉

yes

characteristic

126

#125

C₂×Dic₁₉

yes

—

127

#124

—

128

C₂²⋊Q₈

—

129

#121

—

130

C₄×Q₈

—

131

C₄×D₄

—

132

#117

C₂²⋊D₁₉

yes

—

133

C₂×C₄²

C₂²×D₁₉

yes

characteristic

134

C₄⋊C₈

—

135

C₄⋊C₈

—

136

C₄⋊C₈

—

137

#103

—

138

#102

—

139

C₂²⋊C₈

—

140

C₂²⋊C₈

—

141

#97

—

142

#97

—

143

#97

—

144

#97

C₂×Dic₁₉

yes

—

145

C₄×C₈

—

146

C₄×C₈

—

147

C₁₉

#9008

yes

characteristic, complemented, Sylow

148

#41

—

149

C₂×Q₈

—

150

C₂×Q₈

—

151

C₂×D₄

—

152

C₂×D₄

—

153

C₂×D₄

—

154

C₂²×C₄

—

155

C₂²×C₄

#64543

yes

—

156

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

165

C₂²⋊C₄

—

166

C₂²⋊C₄

—

167

C₄²

—

168

C₄²

D₄×D₁₉

yes

—

169

C₄²

C₂²×Dic₁₉

yes

characteristic

170

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

171

C₂³

—

172

C₂³

#10597381

yes

characteristic

173

Q₈

—

174

Q₈

—

175

D₄

—

176

D₄

—

177

D₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

D₄×Dic₁₉

yes

—

184

C₂×C₄

#10597383

yes

characteristic

185

C₂×C₄

#10597385

yes

—

186

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

187

C₈

—

188

C₈

—

189

C₈

—

152

—

190

C₂²

—

191

C₂²

—

192

C₂²

—

193

C₂²

—

194

C₂²

#11926424

yes

characteristic

195

C₄

—

196

C₄

—

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

#11926716

yes

—

201

C₂

—

202

C₂

—

203

C₂

#14563999

yes

—

204

C₂

#14564039

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597383
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3135	C₂
socle	C₂²×C₁₉	#386
prime radical	C₁₉×#532	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3135	D₁₉
hypocenter	C₁₉	#9008
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3135

subgroup

G/H

center

C₂×C₄

#10597383

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3135

C₂

socle

C₂²×C₁₉

#386

prime radical

C₁₉×#532

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3135

N	H ≅ G/N	type
1. #14572741	C₂	semidirect
2. #14562300	C₂	semidirect
4. #14561534	C₂	semidirect
147. C₁₉	#9008	semidirect

H ≅ G/N

type

1. #14572741

C₂

semidirect

2. #14562300

C₂

semidirect

4. #14561534

C₂

semidirect

147. C₁₉

#9008

semidirect

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

subgroup	index
#14572741	2
#14562300	2
#14562104	2
#14561534	2
C₁₉×#3135	2
#9008	19

subgroup

index

C₁₉×#3135

Subgroups — #18077504

Conjugacy classes of subgroups

Complements

Maximal subgroups