Group #18069360 — subgroups

Subgroups — #18069360

Order 4864.

216 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 67 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	#14564575	C₂	1	1	yes	maximal, characteristic
2	#14561719	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1377	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×Dic₃₈	C₄	1	1	yes	characteristic
5	C₂×#10597269	—	2	1	no	—
6	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	1	yes	characteristic
7	#11926298	—	2	1	no	—
8	#11926298	—	2	1	no	—
9	C₂×C₁₉×M₃₂	—	2	1	no	—
10	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
11	C₂²×Dic₃₈	C₈	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
14	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄⋊Dic₁₉	C₈	1	1	yes	characteristic
16	C₂×Dic₁₉⋊C₄	—	2	1	no	—
17	C₂×C₄×Dic₁₉	—	2	1	no	—
18	C₂²×C₁₉⋊C₈	—	2	1	no	—
19	C₄×Dic₃₈	—	4	1	no	—
20	C₄×Dic₃₈	—	4	1	no	—
21	C₁₉×M₃₂	—	2	2	no	—
22	C₁₉×M₃₂	—	4	1	no	—
23	C₂×C₁₆×C₁₉	—	4	1	no	—
24	C₁₉×#97	—	4	1	no	—
25	#10597269	—	2	2	no	—
26	#10597269	—	4	1	no	—
27	C₂×C₁₉⋊C₁₆	—	4	1	no	—
28	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
29	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
32	C₂²×Dic₁₉	—	2	1	no	—
33	C₂²×Dic₁₉	—	2	1	no	—
34	C₂×Dic₃₈	—	4	1	no	—
35	C₂×Dic₃₈	—	4	2	no	—
36	C₂×C₈×C₁₉	—	2	1	no	—
37	C₂×C₈×C₁₉	—	2	1	no	—
38	C₂×C₈×C₁₉	—	2	1	no	—
39	C₂×C₈×C₁₉	—	2	1	no	—
40	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
41	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
42	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
43	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
44	C₄²×C₁₉	—	2	1	no	—
45	C₄²×C₁₉	—	2	1	no	—
46	C₄⋊Dic₁₉	—	4	1	no	—
47	Dic₁₉⋊C₄	—	4	2	no	—
48	C₄×Dic₁₉	—	4	1	no	—
49	C₄×Dic₁₉	—	4	1	no	—
50	C₂×C₁₉⋊C₈	—	4	1	no	—
51	C₂×C₁₉⋊C₈	—	4	1	no	—
52	C₂×C₁₉⋊C₈	—	4	1	no	—
53	C₁₆×C₁₉	—	4	2	no	—
54	C₁₉⋊C₁₆	—	4	2	no	—
55	#7133	—	19	1	no	maximal, Sylow
56	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
57	C₂×C₄×C₁₉	—	2	1	no	—
58	C₂×C₄×C₁₉	—	2	1	no	—
59	C₂×C₄×C₁₉	—	4	1	no	—
60	C₂×C₄×C₁₉	—	4	1	no	—
61	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
62	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
67	C₂×Dic₁₉	—	2	2	no	—
68	C₂×Dic₁₉	—	4	1	no	—
69	C₂×Dic₁₉	—	4	1	no	—
70	C₂×Dic₁₉	—	4	2	no	—
71	C₂×Dic₁₉	—	4	1	no	—
72	Dic₃₈	—	4	2	no	—
73	Dic₃₈	—	4	2	no	—
74	C₈×C₁₉	—	2	1	no	—
75	C₈×C₁₉	—	2	1	no	—
76	C₈×C₁₉	—	2	1	no	—
77	C₈×C₁₉	—	2	1	no	—
78	C₁₉⋊C₈	—	8	1	no	—
79	#1985	—	19	1	no	—
80	#1377	—	19	1	no	—
81	#1377	D₁₉	1	1	yes	characteristic
82	C₂²×C₁₉	—	2	1	no	—
83	C₂²×C₁₉	—	2	1	no	—
84	C₂²×C₁₉	#323	1	1	yes	characteristic
85	C₂²×C₁₉	Q₈⋊C₈	1	1	yes	characteristic
86	C₂²×C₁₉	Q₈⋊C₈	1	1	yes	characteristic
87	C₄×C₁₉	—	4	1	no	—
88	C₄×C₁₉	—	4	1	no	—
89	C₄×C₁₉	#328	1	1	yes	characteristic
90	C₄×C₁₉	#328	1	1	yes	characteristic
91	C₄×C₁₉	#329	1	1	yes	characteristic
92	C₄×C₁₉	#333	1	1	yes	characteristic
93	Dic₁₉	—	4	2	no	—
94	Dic₁₉	—	8	1	no	—
95	C₂×C₄×Q₈	—	19	1	no	—
96	C₂×M₃₂	—	2	1	no	—
97	C₂×M₃₂	—	38	1	no	—
98	C₂×C₄⋊C₈	—	19	1	no	—
99	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
100	#336	—	38	1	no	—
101	#336	—	38	1	no	—
102	C₂×C₁₉	—	2	1	no	—
103	C₂×C₁₉	—	2	1	no	—
104	C₂×C₁₉	#1272	1	1	yes	characteristic
105	C₂×C₁₉	#1320	1	1	yes	characteristic
106	C₂×C₁₉	#1321	1	1	yes	characteristic
107	C₂²×Q₈	—	19	1	no	—
108	C₂²×C₈	—	38	1	no	—
109	C₂²×C₈	D₇₆	1	1	yes	characteristic
110	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
111	C₄×Q₈	—	76	1	no	—
112	C₄×Q₈	—	76	1	no	—
113	C₂×C₄⋊C₄	—	19	1	no	—
114	C₂×C₄⋊C₄	—	38	1	no	—
115	C₂×C₄²	—	38	1	no	—
116	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
117	M₃₂	—	2	2	no	—
118	M₃₂	—	4	1	no	—
119	M₃₂	—	38	2	no	—
120	M₃₂	—	76	1	no	—
121	C₂×C₁₆	—	4	1	no	—
122	C₂×C₁₆	—	76	1	no	—
123	C₄⋊C₈	—	76	1	no	—
124	#97	—	4	1	no	—
125	C₁₉	#7133	1	1	yes	characteristic, complemented, Sylow
126	C₂×Q₈	—	76	1	no	—
127	C₂×Q₈	—	76	2	no	—
128	C₂²×C₄	—	38	1	no	—
129	C₂²×C₄	—	38	1	no	—
130	C₂²×C₄	C₈×D₁₉	1	1	yes	characteristic
131	C₂²×C₄	#64515	1	1	yes	characteristic
132	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
133	C₂×C₈	—	2	1	no	—
134	C₂×C₈	—	2	1	no	—
135	C₂×C₈	—	2	1	no	—
136	C₂×C₈	—	2	1	no	—
137	C₂×C₈	—	76	1	no	—
138	C₂×C₈	—	76	1	no	—
139	C₂×C₈	—	76	1	no	—
140	C₂×C₈	#64516	1	1	yes	characteristic
141	C₂×C₈	Dic₇₆	1	1	yes	characteristic
142	C₂×C₈	#64526	1	1	yes	characteristic
143	C₂×C₈	#64528	1	1	yes	characteristic
144	C₄⋊C₄	—	76	1	no	—
145	C₄⋊C₄	—	76	2	no	—
146	C₄²	—	2	1	no	—
147	C₄²	—	2	1	no	—
148	C₄²	—	76	1	no	—
149	C₄²	—	76	1	no	—
150	C₁₆	—	4	2	no	—
151	C₁₆	—	76	2	no	—
152	C₂³	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
153	Q₈	—	76	2	no	—
154	Q₈	—	76	2	no	—
155	C₂×C₄	—	2	1	no	—
156	C₂×C₄	—	2	1	no	—
157	C₂×C₄	—	4	1	no	—
158	C₂×C₄	—	4	1	no	—
159	C₂×C₄	—	38	2	no	—
160	C₂×C₄	—	76	1	no	—
161	C₂×C₄	—	76	1	no	—
162	C₂×C₄	—	76	2	no	—
163	C₂×C₄	—	76	1	no	—
164	C₂×C₄	#10597262	1	1	yes	characteristic
165	C₂×C₄	#10597263	1	1	yes	characteristic
166	C₂×C₄	#10597267	1	1	yes	characteristic
167	C₂×C₄	#10597273	1	1	yes	characteristic
168	C₂×C₄	#10597280	1	1	yes	characteristic
169	C₂×C₄	#10597282	1	1	yes	characteristic
170	C₈	—	2	1	no	—
171	C₈	—	2	1	no	—
172	C₈	—	2	1	no	—
173	C₈	—	2	1	no	—
174	C₈	—	152	1	no	—
175	C₂²	—	2	1	no	—
176	C₂²	—	2	1	no	—
177	C₂²	#11926267	1	1	yes	characteristic
178	C₂²	#11926274	1	1	yes	characteristic
179	C₂²	#11926276	1	1	yes	characteristic
180	C₄	—	4	1	no	—
181	C₄	—	4	1	no	—
182	C₄	—	76	2	no	—
183	C₄	—	152	1	no	—
184	C₄	#11926280	1	1	yes	characteristic
185	C₄	#11926282	1	1	yes	characteristic
186	C₄	#11926283	1	1	yes	characteristic
187	C₄	#11926292	1	1	yes	characteristic
188	C₂	—	2	1	no	—
189	C₂	—	2	1	no	—
190	C₂	#14561460	1	1	yes	characteristic
191	C₂	#14561570	1	1	yes	characteristic
192	C₂	#14561572	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564575

C₂

yes

maximal, characteristic

#14561719

C₂

yes

maximal, characteristic

C₁₉×#1377

C₂

yes

maximal, characteristic

C₂×C₄×Dic₃₈

C₄

yes

characteristic

C₂×#10597269

—

C₂×C₄⋊(C₁₉⋊C₈)

C₄

yes

characteristic

#11926298

—

#11926298

—

C₂×C₁₉×M₃₂

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂²×Dic₃₈

C₈

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊Dic₁₉

C₈

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×M₃₂

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₁₉×#97

—

#10597269

—

#10597269

—

C₂×C₁₉⋊C₁₆

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₂×C₈×C₁₉

Q₁₆

yes

characteristic

C₂×C₈×C₁₉

Q₁₆

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

#7133

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1985

—

#1377

—

#1377

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#323

yes

characteristic

C₂²×C₁₉

Q₈⋊C₈

yes

characteristic

C₂²×C₁₉

Q₈⋊C₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₂×C₄×Q₈

—

C₂×M₃₂

—

C₂×M₃₂

—

C₂×C₄⋊C₈

—

C₂×#97

C₂×D₁₉

yes

characteristic

100

#336

—

101

#336

—

102

C₂×C₁₉

—

103

C₂×C₁₉

—

104

C₂×C₁₉

#1272

yes

characteristic

105

C₂×C₁₉

#1320

yes

characteristic

106

C₂×C₁₉

#1321

yes

characteristic

107

C₂²×Q₈

—

108

C₂²×C₈

—

109

C₂²×C₈

D₇₆

yes

characteristic

110

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

111

C₄×Q₈

—

112

C₄×Q₈

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄⋊C₄

—

115

C₂×C₄²

—

116

C₂×C₄²

C₄×D₁₉

yes

characteristic

117

M₃₂

—

118

M₃₂

—

119

M₃₂

—

120

M₃₂

—

121

C₂×C₁₆

—

122

C₂×C₁₆

—

123

C₄⋊C₈

—

124

#97

—

125

C₁₉

#7133

yes

characteristic, complemented, Sylow

126

C₂×Q₈

—

127

C₂×Q₈

—

128

C₂²×C₄

—

129

C₂²×C₄

—

130

C₂²×C₄

C₈×D₁₉

yes

characteristic

131

C₂²×C₄

#64515

yes

characteristic

132

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

#64516

yes

characteristic

141

C₂×C₈

Dic₇₆

yes

characteristic

142

C₂×C₈

#64526

yes

characteristic

143

C₂×C₈

#64528

yes

characteristic

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₄²

—

147

C₄²

—

148

C₄²

—

149

C₄²

—

150

C₁₆

—

151

C₁₆

—

152

C₂³

(C₂×D₁₉)⋊C₈

yes

characteristic

153

Q₈

—

154

Q₈

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

#10597262

yes

characteristic

165

C₂×C₄

#10597263

yes

characteristic

166

C₂×C₄

#10597267

yes

characteristic

167

C₂×C₄

#10597273

yes

characteristic

168

C₂×C₄

#10597280

yes

characteristic

169

C₂×C₄

#10597282

yes

characteristic

170

C₈

—

171

C₈

—

172

C₈

—

173

C₈

—

174

C₈

—

152

—

175

C₂²

—

176

C₂²

—

177

C₂²

#11926267

yes

characteristic

178

C₂²

#11926274

yes

characteristic

179

C₂²

#11926276

yes

characteristic

180

C₄

—

181

C₄

—

182

C₄

—

183

C₄

—

152

—

184

C₄

#11926280

yes

characteristic

185

C₄

#11926282

yes

characteristic

186

C₄

#11926283

yes

characteristic

187

C₄

#11926292

yes

characteristic

188

C₂

—

189

C₂

—

190

C₂

#14561460

yes

characteristic

191

C₂

#14561570

yes

characteristic

192

C₂

#14561572

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597263
commutator	C₂²×C₄×C₁₉	C₂×C₈
Frattini	C₂×#97	C₂×D₁₉
Fitting	C₁₉×#1377	C₂
socle	C₂²×C₁₉	#323
prime radical	C₂³×C₁₉	C₂²⋊C₈
cosocle	C₂×C₁₉×#97	C₂²
hypercenter	#1377	D₁₉
hypocenter	C₁₉	#7133
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#97 ◁ #1377

subgroup

G/H

center

C₂×C₄

#10597263

commutator

C₂²×C₄×C₁₉

C₂×C₈

Frattini

C₂×#97

C₂×D₁₉

Fitting

C₁₉×#1377

C₂

socle

C₂²×C₁₉

#323

prime radical

C₂³×C₁₉

C₂²⋊C₈

cosocle

C₂×C₁₉×#97

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#97 ◁ #1377

N	H ≅ G/N	type
125. C₁₉	#7133	semidirect

H ≅ G/N

type

125. C₁₉

#7133

semidirect

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

subgroup	index
#14564575	2
#14561719	2
C₁₉×#1377	2
#7133	19

subgroup

index

#14564575

#14561719

C₁₉×#1377

#7133

Subgroups — #18069360

Conjugacy classes of subgroups

Complements

Maximal subgroups