Group #18087591 — subgroups

Subgroups — #18087591

Order 4864.

442 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 155 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	#14564597	C₂	1	2	yes	maximal
2	#14563795	C₂	1	1	yes	maximal, characteristic
3	#14563794	C₂	1	2	yes	maximal
4	C₁₉⋊#1273	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1956	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597275	—	2	2	no	—
7	C₂×#10597264	—	2	4	no	—
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
9	#11926414	C₂²	1	2	yes	—
10	#11926306	—	2	4	no	—
11	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#103	—	2	2	no	—
13	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#384	C₂²	1	1	yes	characteristic
15	C₂²×Q₈×C₁₉	—	2	1	no	—
16	C₂²×C₈×C₁₉	D₄	1	2	yes	—
17	C₁₉×C₄⋊Q₈	—	2	2	no	—
18	C₁₉×C₄⋊Q₈	—	2	1	no	—
19	C₁₉×C₄⋊Q₈	Q₈	1	2	yes	—
20	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
21	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
22	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉	—	2	2	no	—
25	C₂×C₄⋊Dic₁₉	—	2	2	no	—
26	C₂×C₄⋊Dic₁₉	—	2	2	no	—
27	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
28	C₁₉×#103	—	4	4	no	—
29	C₄×C₈×C₁₉	—	2	2	no	—
30	#10597275	—	4	4	no	—
31	#10597264	—	4	8	no	—
32	C₄×C₁₉⋊C₈	—	2	2	no	—
33	C₄×C₁₉⋊C₈	—	2	2	no	—
34	C₂×Q₈×C₁₉	—	2	2	no	—
35	C₂×Q₈×C₁₉	—	4	1	no	—
36	C₂×Q₈×C₁₉	—	4	2	no	—
37	C₂×Q₈×C₁₉	—	4	2	no	—
38	C₂²×C₄×C₁₉	—	4	1	no	—
39	C₂²×C₄×C₁₉	—	4	1	no	—
40	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×Dic₁₉	—	4	2	no	—
43	C₂×C₈×C₁₉	—	2	2	no	—
44	C₂×C₈×C₁₉	—	2	2	no	—
45	C₂×C₈×C₁₉	D₈	1	4	yes	—
46	C₄⋊C₄×C₁₉	—	2	4	no	—
47	C₄⋊C₄×C₁₉	—	4	2	no	—
48	C₄⋊C₄×C₁₉	—	4	2	no	—
49	C₄⋊C₄×C₁₉	—	4	4	no	—
50	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
51	C₄²×C₁₉	#41	1	1	yes	characteristic
52	C₄²×C₁₉	#41	1	2	yes	—
53	C₄⋊Dic₁₉	—	4	4	no	—
54	C₄⋊Dic₁₉	—	4	4	no	—
55	C₄⋊Dic₁₉	—	4	4	no	—
56	C₂×C₁₉⋊C₈	—	2	4	no	—
57	C₂×C₁₉⋊C₈	—	2	4	no	—
58	C₂×C₁₉⋊C₈	Q₁₆	1	8	yes	—
59	#10674	—	19	1	no	maximal, Sylow
60	C₂³×C₁₉	#127	1	1	yes	characteristic
61	Q₈×C₁₉	—	4	4	no	—
62	Q₈×C₁₉	—	8	2	no	—
63	C₂×C₄×C₁₉	—	4	2	no	—
64	C₂×C₄×C₁₉	—	8	1	no	—
65	C₂×C₄×C₁₉	—	8	1	no	—
66	C₂×C₄×C₁₉	—	8	1	no	—
67	C₂×C₄×C₁₉	—	8	2	no	—
68	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
69	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
70	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
71	C₂×C₄×C₁₉	#123	1	2	yes	—
72	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
73	C₂×C₄×C₁₉	C₂×Q₁₆	1	4	yes	—
74	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
75	C₂×C₄×C₁₉	#137	1	2	yes	—
76	C₂×Dic₁₉	—	8	2	no	—
77	C₂×Dic₁₉	—	8	2	no	—
78	C₂×Dic₁₉	—	8	2	no	—
79	C₈×C₁₉	—	2	4	no	—
80	C₁₉⋊C₈	—	2	8	no	—
81	#1990	—	19	2	no	—
82	#1956	D₁₉	1	1	yes	characteristic
83	#1845	—	19	1	no	—
84	#1845	—	19	2	no	—
85	#1273	—	19	1	no	—
86	C₂²×C₁₉	#399	1	1	yes	characteristic
87	C₂²×C₁₉	#493	1	1	yes	characteristic
88	C₂²×C₁₉	#494	1	2	yes	—
89	C₂²×C₁₉	#496	1	2	yes	—
90	C₂²×C₁₉	#497	1	1	yes	characteristic
91	C₄×C₁₉	—	8	2	no	—
92	C₄×C₁₉	—	16	1	no	—
93	C₄×C₁₉	#474	1	2	yes	—
94	C₄×C₁₉	#477	1	4	yes	—
95	C₄×C₁₉	#480	1	2	yes	—
96	C₄×C₁₉	#484	1	4	yes	—
97	Dic₁₉	—	16	2	no	—
98	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
99	C₂×#107	—	38	4	no	—
100	C₂×#107	—	38	2	no	—
101	C₂×#103	—	2	2	no	—
102	C₂×C₄×C₈	—	19	2	no	—
103	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
104	#384	—	19	2	no	—
105	#384	C₂×D₁₉	1	1	yes	characteristic
106	#340	—	38	4	no	—
107	C₂×C₁₉	#1713	1	1	yes	characteristic
108	C₂×C₁₉	#1721	1	1	yes	characteristic
109	C₂×C₁₉	#1723	1	2	yes	—
110	C₂×C₁₉	#2093	1	1	yes	characteristic
111	C₂×C₁₉	#2095	1	2	yes	—
112	C₂²×Q₈	—	2	1	no	—
113	C₂²×C₈	—	19	4	no	—
114	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
115	C₄⋊Q₈	—	2	1	no	—
116	C₄⋊Q₈	—	2	2	no	—
117	C₄⋊Q₈	Dic₃₈	1	2	yes	—
118	C₂×C₄⋊C₄	—	2	2	no	—
119	C₂×C₄⋊C₄	—	2	2	no	—
120	C₂×C₄⋊C₄	—	2	1	no	—
121	C₂×C₄⋊C₄	—	38	2	no	—
122	C₂×C₄⋊C₄	—	38	2	no	—
123	C₂×C₄⋊C₄	—	38	2	no	—
124	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
125	#107	—	76	8	no	—
126	#107	—	76	4	no	—
127	#103	—	4	4	no	—
128	C₄×C₈	—	2	2	no	—
129	C₄×C₈	—	38	2	no	—
130	C₄×C₈	—	38	2	no	—
131	C₁₉	#10674	1	1	yes	characteristic, complemented, Sylow
132	C₂×Q₈	—	2	2	no	—
133	C₂×Q₈	—	4	1	no	—
134	C₂×Q₈	—	4	2	no	—
135	C₂×Q₈	—	4	2	no	—
136	C₂²×C₄	—	4	1	no	—
137	C₂²×C₄	—	4	1	no	—
138	C₂²×C₄	—	76	2	no	—
139	C₂²×C₄	D₄×D₁₉	1	2	yes	—
140	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
141	C₂×C₈	—	2	2	no	—
142	C₂×C₈	—	2	2	no	—
143	C₂×C₈	—	19	8	no	—
144	C₂×C₈	—	38	4	no	—
145	C₂×C₈	—	38	4	no	—
146	C₂×C₈	#64525	1	4	yes	—
147	C₄⋊C₄	—	2	4	no	—
148	C₄⋊C₄	—	4	2	no	—
149	C₄⋊C₄	—	4	2	no	—
150	C₄⋊C₄	—	4	4	no	—
151	C₄⋊C₄	—	76	4	no	—
152	C₄⋊C₄	—	76	4	no	—
153	C₄⋊C₄	—	76	4	no	—
154	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
155	C₄²	#64541	1	1	yes	characteristic
156	C₄²	#64543	1	2	yes	—
157	C₂³	#10597386	1	1	yes	characteristic
158	Q₈	—	4	4	no	—
159	Q₈	—	8	2	no	—
160	C₂×C₄	—	4	2	no	—
161	C₂×C₄	—	8	1	no	—
162	C₂×C₄	—	8	1	no	—
163	C₂×C₄	—	8	1	no	—
164	C₂×C₄	—	8	2	no	—
165	C₂×C₄	—	152	2	no	—
166	C₂×C₄	—	152	2	no	—
167	C₂×C₄	—	152	2	no	—
168	C₂×C₄	#10597324	1	2	yes	—
169	C₂×C₄	#10597329	1	2	yes	—
170	C₂×C₄	#10597360	1	4	yes	—
171	C₂×C₄	Q₁₆×D₁₉	1	4	yes	—
172	C₂×C₄	#10597370	1	1	yes	characteristic
173	C₂×C₄	C₂×#64525	1	2	yes	—
174	C₂×C₄	#10597381	1	1	yes	characteristic
175	C₂×C₄	#10597397	1	2	yes	—
176	C₈	—	2	4	no	—
177	C₈	—	38	8	no	—
178	C₂²	#11926480	1	1	yes	characteristic
179	C₂²	#11926920	1	1	yes	characteristic
180	C₂²	#11926922	1	2	yes	—
181	C₂²	#11926930	1	2	yes	—
182	C₂²	#11926939	1	1	yes	characteristic
183	C₄	—	8	2	no	—
184	C₄	—	16	1	no	—
185	C₄	—	304	2	no	—
186	C₄	#11926824	1	2	yes	—
187	C₄	#11926837	1	4	yes	—
188	C₄	#11926855	1	2	yes	—
189	C₄	#11926878	1	4	yes	—
190	C₂	#14563251	1	1	yes	characteristic
191	C₂	#14563299	1	1	yes	characteristic
192	C₂	#14563315	1	2	yes	—
193	C₂	#14565163	1	1	yes	characteristic
194	C₂	#14565171	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564597

C₂

yes

maximal

#14563795

C₂

yes

maximal, characteristic

#14563794

C₂

yes

maximal

C₁₉⋊#1273

C₂

yes

maximal, characteristic

C₁₉×#1956

C₂

yes

maximal, characteristic

C₂×#10597275

—

C₂×#10597264

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926414

C₂²

yes

—

#11926306

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×#103

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#384

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

Q₈

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

D₄

yes

—

C₁₉×#103

—

C₄×C₈×C₁₉

—

#10597275

—

#10597264

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×Q₈

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

Q₁₆

yes

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×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×D₈

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1990

—

#1956

D₁₉

yes

—

—

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#496

yes

—

C₂²×C₁₉

#497

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#474

yes

—

C₄×C₁₉

#477

yes

—

C₄×C₁₉

#480

yes

—

C₄×C₁₉

#484

yes

—

Dic₁₉

—

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

C₂×#107

—

100

C₂×#107

—

101

C₂×#103

—

102

C₂×C₄×C₈

—

103

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

104

#384

—

105

#384

C₂×D₁₉

yes

characteristic

106

#340

—

107

C₂×C₁₉

#1713

yes

characteristic

108

C₂×C₁₉

#1721

yes

characteristic

109

C₂×C₁₉

#1723

yes

—

110

C₂×C₁₉

#2093

yes

characteristic

111

C₂×C₁₉

#2095

yes

—

112

C₂²×Q₈

—

113

C₂²×C₈

—

114

C₂²×C₈

C₂²⋊D₁₉

yes

—

115

C₄⋊Q₈

—

116

C₄⋊Q₈

—

117

C₄⋊Q₈

Dic₃₈

yes

—

118

C₂×C₄⋊C₄

—

119

C₂×C₄⋊C₄

—

120

C₂×C₄⋊C₄

—

121

C₂×C₄⋊C₄

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

—

124

C₂×C₄²

C₂²×D₁₉

yes

characteristic

125

#107

—

126

#107

—

127

#103

—

128

C₄×C₈

—

129

C₄×C₈

—

130

C₄×C₈

—

131

C₁₉

#10674

yes

characteristic, complemented, Sylow

132

C₂×Q₈

—

133

C₂×Q₈

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

D₄×D₁₉

yes

—

140

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

#64525

yes

—

147

C₄⋊C₄

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄⋊C₄

—

154

C₄²

C₂×Dic₃₈

yes

characteristic

155

C₄²

#64541

yes

characteristic

156

C₄²

#64543

yes

—

157

C₂³

#10597386

yes

characteristic

158

Q₈

—

159

Q₈

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

152

—

166

C₂×C₄

—

152

—

167

C₂×C₄

—

152

—

168

C₂×C₄

#10597324

yes

—

169

C₂×C₄

#10597329

yes

—

170

C₂×C₄

#10597360

yes

—

171

C₂×C₄

Q₁₆×D₁₉

yes

—

172

C₂×C₄

#10597370

yes

characteristic

173

C₂×C₄

C₂×#64525

yes

—

174

C₂×C₄

#10597381

yes

characteristic

175

C₂×C₄

#10597397

yes

—

176

C₈

—

177

C₈

—

178

C₂²

#11926480

yes

characteristic

179

C₂²

#11926920

yes

characteristic

180

C₂²

#11926922

yes

—

181

C₂²

#11926930

yes

—

182

C₂²

#11926939

yes

characteristic

183

C₄

—

184

C₄

—

185

C₄

—

304

—

186

C₄

#11926824

yes

—

187

C₄

#11926837

yes

—

188

C₄

#11926855

yes

—

189

C₄

#11926878

yes

—

190

C₂

#14563251

yes

characteristic

191

C₂

#14563299

yes

characteristic

192

C₂

#14563315

yes

—

193

C₂

#14565163

yes

characteristic

194

C₂

#14565171

yes

—

	subgroup	G/H
center	C₂³	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1956	C₂
socle, prime radical	C₂³×C₁₉	#127
hypercenter	#1956	D₁₉
hypocenter	C₁₉	#10674
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

subgroup

G/H

center

C₂³

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1956

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

N	H ≅ G/N	type
131. C₁₉	#10674	semidirect

H ≅ G/N

type

131. C₁₉

#10674

semidirect

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

subgroup	index
#14564597	2
#14563795	2
#14563794	2
C₁₉⋊#1273	2
C₁₉×#1956	2
#10674	19

subgroup

index

#14564597

#14563795

#14563794

C₁₉⋊#1273

C₁₉×#1956

#10674

Subgroups — #18087591

Conjugacy classes of subgroups

Complements

Maximal subgroups