Group #18069074 — subgroups

Subgroups — #18069074

Order 4864.

306 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 107 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	C₄×#10597260	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1839	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597260	—	2	1	no	—
5	C₂×#10597260	—	2	1	no	—
6	C₂×C₄×C₁₉⋊C₈	C₄	1	2	yes	—
7	#11926299	—	2	1	no	—
8	#11926299	—	2	1	no	—
9	#11926299	C₄	1	2	yes	—
10	C₄³×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#336	—	2	1	no	—
12	C₁₉×#336	—	2	1	no	—
13	C₁₉×#336	C₄	1	2	yes	—
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	#10597260	—	2	4	no	—
25	#10597260	—	2	4	no	—
26	C₄×C₁₉⋊C₈	—	2	2	no	—
27	C₄×C₁₉⋊C₈	C₈	1	4	yes	complemented
28	C₂²×C₄×C₁₉	C₄²	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	C₂²⋊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	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₉	—	4	2	no	—
36	C₂×C₈×C₁₉	—	4	2	no	—
37	C₂×C₈×C₁₉	—	4	2	no	—
38	C₄²×C₁₉	—	2	2	no	—
39	C₄²×C₁₉	—	2	2	no	—
40	C₄²×C₁₉	—	4	1	no	—
41	C₄²×C₁₉	—	4	1	no	—
42	C₄²×C₁₉	—	4	1	no	—
43	C₄²×C₁₉	—	4	1	no	—
44	C₄²×C₁₉	C₂×C₈	1	2	yes	—
45	C₄²×C₁₉	M₁₆	1	2	yes	—
46	C₂×C₁₉⋊C₈	—	2	4	no	—
47	C₂×C₁₉⋊C₈	—	2	4	no	—
48	C₂×C₁₉⋊C₈	—	2	4	no	—
49	C₂×C₁₉⋊C₈	—	4	2	no	—
50	C₂×C₁₉⋊C₈	—	4	2	no	—
51	C₂×C₁₉⋊C₈	—	4	2	no	—
52	#7019	—	19	1	no	maximal, Sylow
53	C₂³×C₁₉	#95	1	1	yes	characteristic
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	C₄×C₈	1	1	yes	characteristic
71	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
72	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
73	C₂×C₄×C₁₉	#104	1	2	yes	—
74	C₂×C₄×C₁₉	#104	1	2	yes	—
75	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
76	C₈×C₁₉	—	8	2	no	—
77	C₁₉⋊C₈	—	2	8	no	—
78	C₁₉⋊C₈	—	8	2	no	—
79	#1839	—	19	1	no	—
80	#1839	D₁₉	1	1	yes	characteristic
81	C₄×#97	—	19	1	no	—
82	C₂²×C₁₉	#336	1	1	yes	characteristic
83	C₂²×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
84	C₂²×C₁₉	#338	1	1	yes	characteristic
85	C₂²×C₁₉	#339	1	1	yes	characteristic
86	C₂²×C₁₉	#339	1	1	yes	characteristic
87	C₂²×C₁₉	#344	1	1	yes	characteristic
88	C₂²×C₁₉	#344	1	1	yes	characteristic
89	C₄×C₁₉	—	2	1	no	—
90	C₄×C₁₉	—	2	1	no	—
91	C₄×C₁₉	—	2	2	no	—
92	C₄×C₁₉	—	2	2	no	—
93	C₄×C₁₉	—	2	2	no	—
94	C₄×C₁₉	—	2	2	no	—
95	C₄×C₁₉	—	4	1	no	—
96	C₄×C₁₉	—	4	1	no	—
97	C₂×#97	—	38	1	no	—
98	C₂×#97	—	38	1	no	—
99	C₂×C₄×C₈	—	19	2	no	—
100	C₄³	C₂×D₁₉	1	1	yes	characteristic
101	#336	—	2	1	no	—
102	#336	—	2	1	no	—
103	#336	—	19	2	no	—
104	#336	—	38	1	no	—
105	#336	—	38	1	no	—
106	#336	Dic₁₉	1	2	yes	—
107	C₂×C₁₉	#1275	1	1	yes	characteristic
108	C₂×C₁₉	#1276	1	1	yes	characteristic
109	C₂×C₁₉	#1281	1	1	yes	characteristic
110	C₂×C₁₉	#1288	1	1	yes	characteristic
111	C₂×C₁₉	#1288	1	1	yes	characteristic
112	C₂×C₁₉	#1291	1	1	yes	characteristic
113	C₂×C₁₉	#1291	1	1	yes	characteristic
114	C₂²×C₈	—	2	2	no	—
115	C₂²×C₈	—	38	2	no	—
116	C₂²×C₈	—	38	2	no	—
117	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
118	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
119	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
120	C₂×C₄²	D₇₆	1	1	yes	characteristic
121	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
122	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
123	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
124	#97	—	38	4	no	—
125	#97	—	38	4	no	—
126	C₄×C₈	—	19	4	no	—
127	C₄×C₈	—	38	2	no	—
128	C₁₉	#7019	1	1	yes	characteristic, complemented, Sylow
129	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
130	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
131	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
132	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
133	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
134	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
135	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
136	C₂×C₈	—	4	2	no	—
137	C₂×C₈	—	4	2	no	—
138	C₂×C₈	—	4	2	no	—
139	C₂×C₈	—	38	4	no	—
140	C₂×C₈	—	38	4	no	—
141	C₂×C₈	—	38	4	no	—
142	C₂×C₈	—	76	2	no	—
143	C₂×C₈	—	76	2	no	—
144	C₂×C₈	—	76	2	no	—
145	C₄²	—	2	2	no	—
146	C₄²	—	2	2	no	—
147	C₄²	—	4	1	no	—
148	C₄²	—	4	1	no	—
149	C₄²	—	4	1	no	—
150	C₄²	—	4	1	no	—
151	C₄²	C₈×D₁₉	1	2	yes	—
152	C₄²	#64515	1	2	yes	—
153	C₂³	C₁₉⋊#95	1	1	yes	characteristic
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	—	2	1	no	—
170	C₂×C₄	C₈×Dic₁₉	1	1	yes	characteristic
171	C₂×C₄	Dic₁₉⋊C₈	1	2	yes	—
172	C₂×C₄	#10597272	1	1	yes	characteristic
173	C₂×C₄	(C₂×D₁₉)⋊C₈	1	2	yes	—
174	C₂×C₄	#10597282	1	2	yes	—
175	C₂×C₄	#10597294	1	2	yes	—
176	C₈	—	8	2	no	—
177	C₈	—	38	8	no	—
178	C₈	—	152	2	no	—
179	C₂²	#11926298	1	1	yes	characteristic
180	C₂²	#11926300	1	1	yes	characteristic
181	C₂²	C₁₉⋊#338	1	1	yes	characteristic
182	C₂²	#11926303	1	1	yes	characteristic
183	C₂²	#11926305	1	1	yes	characteristic
184	C₂²	#11926314	1	1	yes	characteristic
185	C₂²	#11926316	1	1	yes	characteristic
186	C₄	—	2	2	no	—
187	C₄	—	2	2	no	—
188	C₄	—	2	1	no	—
189	C₄	—	2	1	no	—
190	C₄	—	2	2	no	—
191	C₄	—	2	2	no	—
192	C₄	—	4	1	no	—
193	C₄	—	4	1	no	—
194	C₂	#14561465	1	1	yes	characteristic
195	C₂	#14561467	1	1	yes	characteristic
196	C₂	#14561479	1	1	yes	characteristic
197	C₂	#14561499	1	1	yes	characteristic
198	C₂	#14561501	1	1	yes	characteristic
199	C₂	#14561506	1	1	yes	characteristic
200	C₂	#14561508	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563778

C₂

yes

maximal, characteristic

C₄×#10597260

C₂

yes

maximal, characteristic

C₁₉×#1839

C₂

yes

maximal, characteristic

C₂×#10597260

—

C₂×#10597260

—

C₂×C₄×C₁₉⋊C₈

C₄

yes

—

#11926299

—

#11926299

—

#11926299

C₄

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₁₉×#336

—

C₁₉×#336

C₄

yes

—

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

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

C₈

yes

complemented

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

C₂×C₈

yes

—

C₄²×C₁₉

M₁₆

yes

—

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

C₄×C₈

yes

characteristic

C₂×C₄×C₁₉

#97

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₈

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₂×C₄×C₁₉

C₄⋊C₈

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1839

—

#1839

D₁₉

yes

characteristic

C₄×#97

—

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×#97

—

C₂×#97

—

C₂×C₄×C₈

—

100

C₄³

C₂×D₁₉

yes

characteristic

101

#336

—

102

#336

—

103

#336

—

104

#336

—

105

#336

—

106

#336

Dic₁₉

yes

—

107

C₂×C₁₉

#1275

yes

characteristic

108

C₂×C₁₉

#1276

yes

characteristic

109

C₂×C₁₉

#1281

yes

characteristic

110

C₂×C₁₉

#1288

yes

characteristic

111

C₂×C₁₉

#1288

yes

characteristic

112

C₂×C₁₉

#1291

yes

characteristic

113

C₂×C₁₉

#1291

yes

characteristic

114

C₂²×C₈

—

115

C₂²×C₈

—

116

C₂²×C₈

—

117

C₂×C₄²

Dic₃₈

yes

characteristic

118

C₂×C₄²

C₄×D₁₉

yes

characteristic

119

C₂×C₄²

C₄×D₁₉

yes

characteristic

120

C₂×C₄²

D₇₆

yes

characteristic

121

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

122

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

123

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

124

#97

—

125

#97

—

126

C₄×C₈

—

127

C₄×C₈

—

128

C₁₉

#7019

yes

characteristic, complemented, Sylow

129

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

130

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

131

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

132

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

133

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

134

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

135

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₄²

—

146

C₄²

—

147

C₄²

—

148

C₄²

—

149

C₄²

—

150

C₄²

—

151

C₄²

C₈×D₁₉

yes

—

152

C₄²

#64515

yes

—

153

C₂³

C₁₉⋊#95

yes

characteristic

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

—

170

C₂×C₄

C₈×Dic₁₉

yes

characteristic

171

C₂×C₄

Dic₁₉⋊C₈

yes

—

172

C₂×C₄

#10597272

yes

characteristic

173

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

—

174

C₂×C₄

#10597282

yes

—

175

C₂×C₄

#10597294

yes

—

176

C₈

—

177

C₈

—

178

C₈

—

152

—

179

C₂²

#11926298

yes

characteristic

180

C₂²

#11926300

yes

characteristic

181

C₂²

C₁₉⋊#338

yes

characteristic

182

C₂²

#11926303

yes

characteristic

183

C₂²

#11926305

yes

characteristic

184

C₂²

#11926314

yes

characteristic

185

C₂²

#11926316

yes

characteristic

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

—

193

C₄

—

194

C₂

#14561465

yes

characteristic

195

C₂

#14561467

yes

characteristic

196

C₂

#14561479

yes

characteristic

197

C₂

#14561499

yes

characteristic

198

C₂

#14561501

yes

characteristic

199

C₂

#14561506

yes

characteristic

200

C₂

#14561508

yes

characteristic

	subgroup	G/H
center	C₂³	C₁₉⋊#95
commutator	C₂×C₄×C₁₉	C₄×C₈
Frattini	C₄³	C₂×D₁₉
Fitting	C₁₉×#1839	C₂
socle, prime radical	C₂³×C₁₉	#95
cosocle	C₄³×C₁₉	C₂²
hypercenter	#1839	D₁₉
hypocenter	C₁₉	#7019
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1839

subgroup

G/H

center

C₂³

C₁₉⋊#95

commutator

C₂×C₄×C₁₉

C₄×C₈

Frattini

C₄³

C₂×D₁₉

Fitting

C₁₉×#1839

C₂

socle, prime radical

C₂³×C₁₉

#95

cosocle

C₄³×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1839

N	H ≅ G/N	type
27. C₄×C₁₉⋊C₈	C₈	semidirect
128. C₁₉	#7019	semidirect

H ≅ G/N

type

27. C₄×C₁₉⋊C₈

C₈

semidirect

128. C₁₉

#7019

semidirect

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

subgroup	index
#14563778	2
C₄×#10597260	2
C₁₉×#1839	2
#7019	19

subgroup

index

#14563778

C₄×#10597260

C₁₉×#1839

#7019

Subgroups — #18069074

Conjugacy classes of subgroups

Complements

Maximal subgroups