Group #18076186 — subgroups

Subgroups — #18076186

Order 4864.

310 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 123 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	#14563323	C₂	1	1	yes	maximal, characteristic
2	#14562381	C₂	1	2	yes	maximal
3	#14561480	C₂	1	1	yes	maximal, characteristic
4	#14561463	C₂	1	2	yes	maximal
5	C₁₉×#1281	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	C₂×#10597272	C₄	1	1	yes	characteristic
8	C₂×#10597272	C₄	1	1	yes	characteristic
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₈×Dic₁₉	C₄	1	1	yes	characteristic
11	C₂×C₈×Dic₁₉	C₄	1	1	yes	characteristic
12	#11926390	C₂²	1	1	yes	characteristic
13	#11926296	—	2	2	no	—
14	#11926294	—	2	2	no	—
15	C₁₉×#431	C₂²	1	2	yes	—
16	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
21	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₁₉×C₄⋊C₈	—	2	2	no	—
25	C₁₉×C₂²⋊C₈	—	2	2	no	—
26	C₁₉×#97	—	2	2	no	—
27	C₄×C₈×C₁₉	—	2	2	no	—
28	C₁₉⋊#95	—	2	2	no	—
29	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
30	#10597272	—	2	2	no	—
31	#10597272	C₈	1	4	yes	complemented
32	C₈×Dic₁₉	—	2	2	no	—
33	C₈×Dic₁₉	—	2	2	no	—
34	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
35	C₄×C₁₉⋊C₈	—	2	2	no	—
36	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
37	C₄×C₁₉⋊C₈	Q₈	1	2	yes	—
38	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	#41	1	2	yes	—
40	C₂²×Dic₁₉	—	2	1	no	—
41	C₂²×Dic₁₉	—	2	1	no	—
42	C₂×C₈×C₁₉	—	2	1	no	—
43	C₂×C₈×C₁₉	—	2	1	no	—
44	C₂×C₈×C₁₉	—	2	1	no	—
45	C₂×C₈×C₁₉	—	2	1	no	—
46	C₂×C₈×C₁₉	—	4	2	no	—
47	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
48	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
49	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
51	C₄²×C₁₉	#41	1	2	yes	—
52	C₄×Dic₁₉	—	2	1	no	—
53	C₄×Dic₁₉	—	2	1	no	—
54	C₄×Dic₁₉	C₂×C₈	1	2	yes	—
55	C₄×Dic₁₉	M₁₆	1	2	yes	—
56	C₂×C₁₉⋊C₈	—	2	1	no	—
57	C₂×C₁₉⋊C₈	—	2	1	no	—
58	C₂×C₁₉⋊C₈	—	4	2	no	—
59	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
60	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
61	C₂×C₁₉⋊C₈	C₂×C₈	1	2	yes	—
62	C₂×C₁₉⋊C₈	M₁₆	1	2	yes	—
63	#8781	—	19	1	no	maximal, Sylow
64	C₂³×C₁₉	#117	1	1	yes	characteristic
65	C₂×C₄×C₁₉	—	4	2	no	—
66	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
68	C₂×C₄×C₁₉	#124	1	2	yes	—
69	C₂×C₄×C₁₉	#125	1	2	yes	—
70	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
71	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
72	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
74	C₂×Dic₁₉	—	2	2	no	—
75	C₂×Dic₁₉	—	2	2	no	—
76	C₂×Dic₁₉	—	4	2	no	—
77	C₂×Dic₁₉	—	4	2	no	—
78	C₈×C₁₉	—	2	2	no	—
79	C₈×C₁₉	—	2	2	no	—
80	C₈×C₁₉	—	8	2	no	—
81	C₁₉⋊C₈	—	2	2	no	—
82	C₁₉⋊C₈	—	8	2	no	—
83	C₁₉⋊C₈	C₄⋊C₈	1	4	yes	—
84	#1726	—	19	1	no	—
85	#1564	—	19	2	no	—
86	#1281	—	19	1	no	—
87	#1281	D₁₉	1	1	yes	characteristic
88	#1274	—	19	2	no	—
89	C₂²×C₁₉	—	2	2	no	—
90	C₂²×C₁₉	#382	1	1	yes	characteristic
91	C₂²×C₁₉	#431	1	1	yes	characteristic
92	C₂²×C₁₉	#432	1	1	yes	characteristic
93	C₄×C₁₉	—	2	2	no	—
94	C₄×C₁₉	—	2	2	no	—
95	C₄×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
96	C₄×C₁₉	#423	1	1	yes	characteristic
97	C₄×C₁₉	#431	1	1	yes	characteristic
98	C₄×C₁₉	#432	1	1	yes	characteristic
99	Dic₁₉	—	4	2	no	—
100	Dic₁₉	—	4	2	no	—
101	#431	—	19	2	no	—
102	#431	C₂×D₁₉	1	2	yes	—
103	C₂×#97	—	19	1	no	—
104	C₂×#97	—	19	1	no	—
105	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
106	C₂×C₄×C₈	—	19	1	no	—
107	C₂×C₄×C₈	—	19	1	no	—
108	C₂×C₄×C₈	—	19	1	no	—
109	#376	—	19	1	no	—
110	#335	—	38	2	no	—
111	#334	—	38	2	no	—
112	C₂×C₁₉	—	2	1	no	—
113	C₂×C₁₉	—	2	1	no	—
114	C₂×C₁₉	#1831	1	1	yes	characteristic
115	C₂×C₁₉	#1833	1	2	yes	—
116	C₂²×C₈	—	19	1	no	—
117	C₂²×C₈	—	19	1	no	—
118	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
119	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
120	C₂×C₄²	—	19	1	no	—
121	C₂×C₄²	—	19	1	no	—
122	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
123	C₄⋊C₈	—	2	2	no	—
124	C₄⋊C₈	—	38	2	no	—
125	C₂²⋊C₈	—	2	2	no	—
126	C₂²⋊C₈	—	38	2	no	—
127	#97	—	2	2	no	—
128	#97	—	19	4	no	—
129	#97	—	38	2	no	—
130	C₄×C₈	—	2	2	no	—
131	C₄×C₈	—	19	2	no	—
132	C₄×C₈	—	19	2	no	—
133	C₄×C₈	—	38	2	no	—
134	C₄×C₈	—	38	2	no	—
135	C₄×C₈	—	38	2	no	—
136	#95	—	38	2	no	—
137	C₁₉	#8781	1	1	yes	characteristic, complemented, Sylow
138	C₂²×C₄	—	38	1	no	—
139	C₂²×C₄	—	38	1	no	—
140	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
141	C₂²×C₄	#64541	1	2	yes	—
142	C₂×C₈	—	2	1	no	—
143	C₂×C₈	—	2	1	no	—
144	C₂×C₈	—	2	1	no	—
145	C₂×C₈	—	2	1	no	—
146	C₂×C₈	—	4	2	no	—
147	C₂×C₈	—	19	2	no	—
148	C₂×C₈	—	19	2	no	—
149	C₂×C₈	—	19	2	no	—
150	C₂×C₈	—	19	2	no	—
151	C₂×C₈	—	38	1	no	—
152	C₂×C₈	—	38	1	no	—
153	C₂×C₈	—	76	2	no	—
154	C₂×C₈	C₈×D₁₉	1	2	yes	—
155	C₂×C₈	#64515	1	2	yes	—
156	C₄²	—	19	2	no	—
157	C₄²	—	19	2	no	—
158	C₄²	—	38	1	no	—
159	C₄²	—	38	1	no	—
160	C₄²	D₄×D₁₉	1	1	yes	characteristic
161	C₄²	#64543	1	2	yes	—
162	C₄²	Q₈×D₁₉	1	1	yes	characteristic
163	C₂³	#10597318	1	1	yes	characteristic
164	C₂×C₄	—	4	2	no	—
165	C₂×C₄	—	38	2	no	—
166	C₂×C₄	—	38	2	no	—
167	C₂×C₄	—	76	2	no	—
168	C₂×C₄	—	76	2	no	—
169	C₂×C₄	#10597323	1	1	yes	characteristic
170	C₂×C₄	#10597331	1	2	yes	—
171	C₂×C₄	#10597335	1	2	yes	—
172	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
173	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
174	C₂×C₄	C₂×#64515	1	1	yes	characteristic
175	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
176	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
177	C₈	—	2	2	no	—
178	C₈	—	2	2	no	—
179	C₈	—	8	2	no	—
180	C₈	—	19	4	no	—
181	C₈	—	38	2	no	—
182	C₈	—	152	2	no	—
183	C₂²	—	2	2	no	—
184	C₂²	#11926408	1	1	yes	characteristic
185	C₂²	#11926595	1	1	yes	characteristic
186	C₂²	#11926599	1	1	yes	characteristic
187	C₄	—	2	2	no	—
188	C₄	—	2	2	no	—
189	C₄	—	76	2	no	—
190	C₄	—	76	2	no	—
191	C₄	C₄⋊C₈×D₁₉	1	1	yes	characteristic
192	C₄	#11926566	1	1	yes	characteristic
193	C₄	#11926594	1	1	yes	characteristic
194	C₄	#11926598	1	1	yes	characteristic
195	C₂	—	2	1	no	—
196	C₂	—	2	1	no	—
197	C₂	#14563750	1	1	yes	characteristic
198	C₂	#14563756	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563323

C₂

yes

maximal, characteristic

#14562381

C₂

yes

maximal

#14561480

C₂

yes

maximal, characteristic

#14561463

C₂

yes

maximal

C₁₉×#1281

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

C₂×#10597272

C₄

yes

characteristic

C₂×#10597272

C₄

yes

characteristic

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×C₈×Dic₁₉

C₄

yes

characteristic

C₂×C₈×Dic₁₉

C₄

yes

characteristic

#11926390

C₂²

yes

characteristic

#11926296

—

#11926294

—

C₁₉×#431

C₂²

yes

—

C₂×C₁₉×#97

C₂²

yes

characteristic

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

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

#10597272

—

#10597272

C₈

yes

complemented

C₈×Dic₁₉

—

C₈×Dic₁₉

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₄×C₁₉⋊C₈

Q₈

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₈

yes

—

C₂×C₈×C₁₉

M₁₆

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

C₂×C₈

yes

—

C₄×Dic₁₉

M₁₆

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₂×C₈

yes

—

C₂×C₁₉⋊C₈

M₁₆

yes

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#125

yes

—

C₂×C₄×C₁₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

C₄⋊C₈

yes

—

—

—

—

D₁₉

yes

characteristic

#1274

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₄⋊C₈

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

100

Dic₁₉

—

101

#431

—

102

#431

C₂×D₁₉

yes

—

103

C₂×#97

—

104

C₂×#97

—

105

C₂×#97

C₂×D₁₉

yes

characteristic

106

C₂×C₄×C₈

—

107

C₂×C₄×C₈

—

108

C₂×C₄×C₈

—

109

#376

—

110

#335

—

111

#334

—

112

C₂×C₁₉

—

113

C₂×C₁₉

—

114

C₂×C₁₉

#1831

yes

characteristic

115

C₂×C₁₉

#1833

yes

—

116

C₂²×C₈

—

117

C₂²×C₈

—

118

C₂²×C₈

C₄×D₁₉

yes

characteristic

119

C₂²×C₈

C₄×D₁₉

yes

characteristic

120

C₂×C₄²

—

121

C₂×C₄²

—

122

C₂×C₄²

C₂²×D₁₉

yes

characteristic

123

C₄⋊C₈

—

124

C₄⋊C₈

—

125

C₂²⋊C₈

—

126

C₂²⋊C₈

—

127

#97

—

128

#97

—

129

#97

—

130

C₄×C₈

—

131

C₄×C₈

—

132

C₄×C₈

—

133

C₄×C₈

—

134

C₄×C₈

—

135

C₄×C₈

—

136

#95

—

137

C₁₉

#8781

yes

characteristic, complemented, Sylow

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

141

C₂²×C₄

#64541

yes

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

C₈×D₁₉

yes

—

155

C₂×C₈

#64515

yes

—

156

C₄²

—

157

C₄²

—

158

C₄²

—

159

C₄²

—

160

C₄²

D₄×D₁₉

yes

characteristic

161

C₄²

#64543

yes

—

162

C₄²

Q₈×D₁₉

yes

characteristic

163

C₂³

#10597318

yes

characteristic

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

#10597323

yes

characteristic

170

C₂×C₄

#10597331

yes

—

171

C₂×C₄

#10597335

yes

—

172

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

173

C₂×C₄

C₂×C₈×D₁₉

yes

characteristic

174

C₂×C₄

C₂×#64515

yes

characteristic

175

C₂×C₄

M₁₆×D₁₉

yes

characteristic

176

C₂×C₄

M₁₆×D₁₉

yes

characteristic

177

C₈

—

178

C₈

—

179

C₈

—

180

C₈

—

181

C₈

—

182

C₈

—

152

—

183

C₂²

—

184

C₂²

#11926408

yes

characteristic

185

C₂²

#11926595

yes

characteristic

186

C₂²

#11926599

yes

characteristic

187

C₄

—

188

C₄

—

189

C₄

—

190

C₄

—

191

C₄

C₄⋊C₈×D₁₉

yes

characteristic

192

C₄

#11926566

yes

characteristic

193

C₄

#11926594

yes

characteristic

194

C₄

#11926598

yes

characteristic

195

C₂

—

196

C₂

—

197

C₂

#14563750

yes

characteristic

198

C₂

#14563756

yes

—

	subgroup	G/H
center	C₂×C₄	#10597323
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1281	C₂
socle	C₂²×C₁₉	#382
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1281	D₁₉
hypocenter	C₁₉	#8781
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1281

subgroup

G/H

center

C₂×C₄

#10597323

commutator

C₂×C₄×C₁₉

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1281

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1281

N	H ≅ G/N	type
31. #10597272	C₈	semidirect
137. C₁₉	#8781	semidirect

H ≅ G/N

type

31. #10597272

C₈

semidirect

137. C₁₉

#8781

semidirect

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

subgroup	index
#14563323	2
#14562381	2
#14561480	2
#14561463	2
C₁₉×#1281	2
#8781	19

subgroup

index

C₁₉×#1281

Subgroups — #18076186

Conjugacy classes of subgroups

Complements

Maximal subgroups