Group #18069137 — subgroups

Subgroups — #18069137

Order 4864.

284 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 91 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	#14563778	C₂	1	1	yes	maximal, characteristic
2	#14563384	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1767	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597260	—	2	1	no	—
5	#11926299	—	2	1	no	—
6	#11926299	—	2	1	no	—
7	#11926299	—	2	1	no	—
8	#11926299	C₄	1	2	yes	—
9	#11926299	C₄	1	2	yes	—
10	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
11	C₂×C₁₉×#97	C₄	1	2	yes	—
12	C₄³×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#336	—	2	1	no	—
14	C₂²×C₈×C₁₉	—	2	2	no	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
22	C₂²×C₁₉⋊C₈	—	2	2	no	—
23	C₂²×C₁₉⋊C₈	—	2	2	no	—
24	C₁₉×C₄⋊C₈	—	2	4	no	—
25	C₁₉×#97	—	4	2	no	—
26	#10597260	—	2	4	no	—
27	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₈×C₁₉	—	2	4	no	—
35	C₂×C₈×C₁₉	—	4	2	no	—
36	C₂×C₈×C₁₉	—	4	2	no	—
37	C₄²×C₁₉	—	2	1	no	—
38	C₄²×C₁₉	—	2	1	no	—
39	C₄²×C₁₉	—	2	2	no	—
40	C₄²×C₁₉	—	2	2	no	—
41	C₄²×C₁₉	—	2	2	no	—
42	C₄²×C₁₉	—	4	1	no	—
43	C₄²×C₁₉	—	4	1	no	—
44	C₄²×C₁₉	—	4	1	no	—
45	C₂×C₁₉⋊C₈	—	2	4	no	—
46	C₂×C₁₉⋊C₈	—	4	2	no	—
47	C₂×C₁₉⋊C₈	—	4	2	no	—
48	C₂×C₁₉⋊C₈	—	4	2	no	—
49	C₂×C₁₉⋊C₈	—	4	2	no	—
50	C₂×C₁₉⋊C₈	—	4	2	no	—
51	#7043	—	19	1	no	maximal, Sylow
52	C₂³×C₁₉	#95	1	1	yes	characteristic
53	C₂×C₄×C₁₉	—	2	1	no	—
54	C₂×C₄×C₁₉	—	2	1	no	—
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
57	C₂×C₄×C₁₉	—	2	1	no	—
58	C₂×C₄×C₁₉	—	2	1	no	—
59	C₂×C₄×C₁₉	—	2	1	no	—
60	C₂×C₄×C₁₉	—	2	1	no	—
61	C₂×C₄×C₁₉	—	2	1	no	—
62	C₂×C₄×C₁₉	—	2	1	no	—
63	C₂×C₄×C₁₉	—	2	1	no	—
64	C₂×C₄×C₁₉	—	2	1	no	—
65	C₂×C₄×C₁₉	—	2	1	no	—
66	C₂×C₄×C₁₉	—	2	1	no	—
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	1	no	—
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
71	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
72	C₂×C₄×C₁₉	#104	1	2	yes	—
73	C₂×C₄×C₁₉	#104	1	2	yes	—
74	C₂×C₄×C₁₉	#108	1	2	yes	—
75	C₈×C₁₉	—	4	4	no	—
76	C₁₉⋊C₈	—	4	4	no	—
77	C₁₉⋊C₈	—	8	2	no	—
78	#1839	—	19	1	no	—
79	#1767	D₁₉	1	1	yes	characteristic
80	#1745	—	19	1	no	—
81	C₂²×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
82	C₂²×C₁₉	#339	1	1	yes	characteristic
83	C₂²×C₁₉	#339	1	1	yes	characteristic
84	C₂²×C₁₉	#341	1	1	yes	characteristic
85	C₂²×C₁₉	#343	1	1	yes	characteristic
86	C₂²×C₁₉	#344	1	1	yes	characteristic
87	C₂²×C₁₉	#344	1	1	yes	characteristic
88	C₄×C₁₉	—	2	1	no	—
89	C₄×C₁₉	—	2	1	no	—
90	C₄×C₁₉	—	2	2	no	—
91	C₄×C₁₉	—	2	2	no	—
92	C₄×C₁₉	—	2	2	no	—
93	C₄×C₁₉	—	4	1	no	—
94	C₄×C₁₉	—	4	1	no	—
95	C₄×C₁₉	—	4	1	no	—
96	C₂×C₄⋊C₈	—	2	1	no	—
97	C₂×#97	—	38	1	no	—
98	C₂×#97	Dic₁₉	1	2	yes	—
99	C₄³	C₂×D₁₉	1	1	yes	characteristic
100	#336	—	2	1	no	—
101	#336	—	19	2	no	—
102	#336	—	19	2	no	—
103	#336	—	38	1	no	—
104	#336	—	38	1	no	—
105	#336	—	38	1	no	—
106	C₂×C₁₉	#1285	1	1	yes	characteristic
107	C₂×C₁₉	#1287	1	1	yes	characteristic
108	C₂×C₁₉	#1288	1	1	yes	characteristic
109	C₂×C₁₉	#1299	1	1	yes	characteristic
110	C₂×C₁₉	#1300	1	1	yes	characteristic
111	C₂×C₁₉	#1302	1	1	yes	characteristic
112	C₂×C₁₉	#1307	1	1	yes	characteristic
113	C₂²×C₈	—	2	2	no	—
114	C₂²×C₈	—	38	2	no	—
115	C₂²×C₈	—	38	2	no	—
116	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
117	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
118	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
119	C₂×C₄²	D₇₆	1	1	yes	characteristic
120	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
121	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
122	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
123	C₄⋊C₈	—	2	4	no	—
124	#97	—	4	2	no	—
125	#97	—	38	4	no	—
126	C₁₉	#7043	1	1	yes	characteristic, complemented, Sylow
127	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
128	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
129	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
130	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
131	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
132	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
133	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
134	C₂×C₈	—	2	4	no	—
135	C₂×C₈	—	4	2	no	—
136	C₂×C₈	—	4	2	no	—
137	C₂×C₈	—	38	4	no	—
138	C₂×C₈	—	76	2	no	—
139	C₂×C₈	—	76	2	no	—
140	C₂×C₈	—	76	2	no	—
141	C₂×C₈	—	76	2	no	—
142	C₂×C₈	—	76	2	no	—
143	C₄²	—	2	2	no	—
144	C₄²	—	2	2	no	—
145	C₄²	—	2	2	no	—
146	C₄²	—	2	1	no	—
147	C₄²	—	2	1	no	—
148	C₄²	—	4	1	no	—
149	C₄²	—	4	1	no	—
150	C₄²	—	4	1	no	—
151	C₂³	C₁₉⋊#95	1	1	yes	characteristic
152	C₂×C₄	—	2	1	no	—
153	C₂×C₄	—	2	1	no	—
154	C₂×C₄	—	2	1	no	—
155	C₂×C₄	—	2	1	no	—
156	C₂×C₄	—	2	1	no	—
157	C₂×C₄	—	2	1	no	—
158	C₂×C₄	—	2	1	no	—
159	C₂×C₄	—	2	1	no	—
160	C₂×C₄	—	2	1	no	—
161	C₂×C₄	—	2	1	no	—
162	C₂×C₄	—	2	1	no	—
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	1	no	—
166	C₂×C₄	—	2	1	no	—
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	#10597262	1	2	yes	—
170	C₂×C₄	#10597279	1	2	yes	—
171	C₂×C₄	#10597282	1	2	yes	—
172	C₂×C₄	#10597290	1	1	yes	characteristic
173	C₂×C₄	#10597293	1	1	yes	characteristic
174	C₈	—	4	4	no	—
175	C₈	—	76	4	no	—
176	C₈	—	152	2	no	—
177	C₂²	#11926300	1	1	yes	characteristic
178	C₂²	#11926304	1	1	yes	characteristic
179	C₂²	#11926305	1	1	yes	characteristic
180	C₂²	#11926308	1	1	yes	characteristic
181	C₂²	#11926313	1	1	yes	characteristic
182	C₂²	#11926316	1	1	yes	characteristic
183	C₂²	#11926316	1	1	yes	characteristic
184	C₄	—	2	1	no	—
185	C₄	—	2	1	no	—
186	C₄	—	2	2	no	—
187	C₄	—	2	2	no	—
188	C₄	—	2	2	no	—
189	C₄	—	4	1	no	—
190	C₄	—	4	1	no	—
191	C₄	—	4	1	no	—
192	C₂	#14561491	1	1	yes	characteristic
193	C₂	#14561496	1	1	yes	characteristic
194	C₂	#14561501	1	1	yes	characteristic
195	C₂	#14561524	1	1	yes	characteristic
196	C₂	#14561529	1	1	yes	characteristic
197	C₂	#14561534	1	1	yes	characteristic
198	C₂	#14561546	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563778

C₂

yes

maximal, characteristic

#14563384

C₂

yes

maximal, characteristic

C₁₉×#1767

C₂

yes

maximal, characteristic

—

—

—

—

C₄

yes

—

#11926299

C₄

yes

—

C₂×C₁₉×C₄⋊C₈

—

C₂×C₁₉×#97

C₄

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

Q₈

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#97

—

#10597260

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

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

#104

yes

—

C₂×C₄×C₁₉

#108

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1839

—

#1767

D₁₉

yes

characteristic

#1745

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂×C₄⋊C₈

—

C₂×#97

—

C₂×#97

Dic₁₉

yes

—

C₄³

C₂×D₁₉

yes

characteristic

100

#336

—

101

#336

—

102

#336

—

103

#336

—

104

#336

—

105

#336

—

106

C₂×C₁₉

#1285

yes

characteristic

107

C₂×C₁₉

#1287

yes

characteristic

108

C₂×C₁₉

#1288

yes

characteristic

109

C₂×C₁₉

#1299

yes

characteristic

110

C₂×C₁₉

#1300

yes

characteristic

111

C₂×C₁₉

#1302

yes

characteristic

112

C₂×C₁₉

#1307

yes

characteristic

113

C₂²×C₈

—

114

C₂²×C₈

—

115

C₂²×C₈

—

116

C₂×C₄²

Dic₃₈

yes

characteristic

117

C₂×C₄²

C₄×D₁₉

yes

characteristic

118

C₂×C₄²

C₄×D₁₉

yes

characteristic

119

C₂×C₄²

D₇₆

yes

characteristic

120

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

121

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

122

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

123

C₄⋊C₈

—

124

#97

—

125

#97

—

126

C₁₉

#7043

yes

characteristic, complemented, Sylow

127

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

128

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

129

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

130

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

131

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

132

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

133

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₄²

—

144

C₄²

—

145

C₄²

—

146

C₄²

—

147

C₄²

—

148

C₄²

—

149

C₄²

—

150

C₄²

—

151

C₂³

C₁₉⋊#95

yes

characteristic

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

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

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

#10597262

yes

—

170

C₂×C₄

#10597279

yes

—

171

C₂×C₄

#10597282

yes

—

172

C₂×C₄

#10597290

yes

characteristic

173

C₂×C₄

#10597293

yes

characteristic

174

C₈

—

175

C₈

—

176

C₈

—

152

—

177

C₂²

#11926300

yes

characteristic

178

C₂²

#11926304

yes

characteristic

179

C₂²

#11926305

yes

characteristic

180

C₂²

#11926308

yes

characteristic

181

C₂²

#11926313

yes

characteristic

182

C₂²

#11926316

yes

characteristic

183

C₂²

#11926316

yes

characteristic

184

C₄

—

185

C₄

—

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

—

190

C₄

—

191

C₄

—

192

C₂

#14561491

yes

characteristic

193

C₂

#14561496

yes

characteristic

194

C₂

#14561501

yes

characteristic

195

C₂

#14561524

yes

characteristic

196

C₂

#14561529

yes

characteristic

197

C₂

#14561534

yes

characteristic

198

C₂

#14561546

yes

characteristic

	subgroup	G/H
center	C₂³	C₁₉⋊#95
commutator	C₂²×C₄×C₁₉	C₄²
Frattini	C₄³	C₂×D₁₉
Fitting	C₁₉×#1767	C₂
socle, prime radical	C₂³×C₁₉	#95
cosocle	C₄³×C₁₉	C₂²
hypercenter	#1767	D₁₉
hypocenter	C₁₉	#7043
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1767

subgroup

G/H

center

C₂³

C₁₉⋊#95

commutator

C₂²×C₄×C₁₉

C₄²

Frattini

C₄³

C₂×D₁₉

Fitting

C₁₉×#1767

C₂

socle, prime radical

C₂³×C₁₉

#95

cosocle

C₄³×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1767

N	H ≅ G/N	type
126. C₁₉	#7043	semidirect

H ≅ G/N

type

126. C₁₉

#7043

semidirect

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

subgroup	index
#14563778	2
#14563384	2
C₁₉×#1767	2
#7043	19

subgroup

index

#14563778

#14563384

C₁₉×#1767

#7043

Subgroups — #18069137

Conjugacy classes of subgroups

Complements

Maximal subgroups