Group #18076062 — subgroups

Subgroups — #18076062

Order 4864.

566 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 99 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	#14566221	C₂	1	1	yes	maximal, characteristic
2	#14563559	C₂	1	1	yes	maximal, characteristic
3	#14561544	C₂	1	4	yes	maximal
4	C₁₉×#1784	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597372	C₄	1	2	yes	—
6	C₂×#10597293	—	2	2	no	—
7	#11926508	C₂²	1	2	yes	—
8	#11926451	—	2	2	no	—
9	#11926451	—	2	2	no	—
10	#11926407	C₄	1	2	yes	—
11	#11926407	C₂²	1	2	yes	—
12	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#101	—	2	2	no	—
14	C₁₉×#407	C₂²	1	2	yes	—
15	C₂²×Q₈×C₁₉	—	2	4	no	—
16	C₂²×Q₈×C₁₉	—	4	4	no	—
17	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
18	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
19	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×M₁₆×C₁₉	—	2	2	no	—
23	C₂×C₂²⋊Dic₁₉	C₂×C₄	1	4	yes	—
24	#10597372	—	4	4	no	—
25	C₂×C₄⋊Dic₁₉	—	2	2	no	—
26	C₂×C₄×Dic₁₉	—	2	2	no	—
27	C₂×#64520	—	2	2	no	—
28	C₁₉×#101	—	4	4	no	—
29	C₁₉×C₂²⋊C₈	—	2	4	no	—
30	#10597293	—	4	4	no	—
31	C₁₉⋊#95	—	2	4	no	—
32	C₁₉⋊#95	—	2	2	no	—
33	C₁₉⋊#95	—	2	2	no	—
34	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
35	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×Q₈×C₁₉	—	2	4	no	—
37	C₂×Q₈×C₁₉	—	2	4	no	—
38	C₂×Q₈×C₁₉	—	2	4	no	—
39	C₂×Q₈×C₁₉	—	2	4	no	—
40	C₂×Q₈×C₁₉	—	4	2	no	—
41	C₂×Q₈×C₁₉	—	4	2	no	—
42	C₂×Q₈×C₁₉	—	4	16	no	—
43	C₂²×C₄×C₁₉	—	2	2	no	—
44	C₂²×C₄×C₁₉	—	2	4	no	—
45	C₂²×C₄×C₁₉	—	2	2	no	—
46	C₂²×C₄×C₁₉	—	4	2	no	—
47	C₂²×C₄×C₁₉	—	4	2	no	—
48	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	#41	1	4	yes	—
53	C₂²×Dic₁₉	—	2	4	no	—
54	M₁₆×C₁₉	—	4	4	no	—
55	C₂×C₈×C₁₉	—	4	2	no	—
56	C₂²⋊Dic₁₉	—	4	4	no	—
57	C₄⋊Dic₁₉	—	4	4	no	—
58	C₄×Dic₁₉	—	4	4	no	—
59	#64520	—	4	4	no	—
60	C₂×C₁₉⋊C₈	—	4	2	no	—
61	#8754	—	19	1	no	maximal, Sylow
62	C₂³×C₁₉	—	2	2	no	—
63	C₂³×C₁₉	—	4	2	no	—
64	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₂³×C₁₉	#117	1	2	yes	—
66	Q₈×C₁₉	—	4	8	no	—
67	Q₈×C₁₉	—	4	8	no	—
68	C₂×C₄×C₁₉	—	2	8	no	—
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	—	2	2	no	—
74	C₂×C₄×C₁₉	—	2	2	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	4	4	no	—
77	C₂×C₄×C₁₉	—	4	4	no	—
78	C₂×C₄×C₁₉	#99	1	4	yes	—
79	C₂×C₄×C₁₉	#123	1	2	yes	—
80	C₂×C₄×C₁₉	#123	1	2	yes	—
81	C₂×Dic₁₉	—	4	8	no	—
82	C₂×Dic₁₉	—	4	4	no	—
83	C₈×C₁₉	—	8	2	no	—
84	C₁₉⋊C₈	—	8	2	no	—
85	#2310	—	19	1	no	—
86	#1784	—	19	1	no	—
87	#1784	D₁₉	1	1	yes	characteristic
88	#1306	—	19	4	no	—
89	C₂²×C₁₉	—	2	2	no	—
90	C₂²×C₁₉	—	2	2	no	—
91	C₂²×C₁₉	—	2	4	no	—
92	C₂²×C₁₉	—	4	4	no	—
93	C₂²×C₁₉	#381	1	1	yes	characteristic
94	C₂²×C₁₉	C₂×#99	1	2	yes	—
95	C₄×C₁₉	—	2	2	no	—
96	C₄×C₁₉	—	2	2	no	—
97	C₄×C₁₉	—	2	4	no	—
98	C₄×C₁₉	—	4	2	no	—
99	Dic₁₉	—	8	4	no	—
100	C₂³×Q₈	C₂×D₁₉	1	1	yes	characteristic
101	C₂×#117	—	19	2	no	—
102	C₂×#101	—	2	2	no	—
103	C₂×#101	—	38	2	no	—
104	#407	—	19	2	no	—
105	#407	C₂×D₁₉	1	2	yes	—
106	#391	—	38	2	no	—
107	#391	—	38	2	no	—
108	#381	—	19	2	no	—
109	#381	—	19	2	no	—
110	C₂×C₁₉	—	2	2	no	—
111	C₂×C₁₉	—	4	2	no	—
112	C₂×C₁₉	#1819	1	1	yes	characteristic
113	C₂×C₁₉	#1830	1	2	yes	—
114	C₂²×Q₈	—	2	4	no	—
115	C₂²×Q₈	—	4	4	no	—
116	C₂²×Q₈	D₇₆	1	2	yes	—
117	C₂²×Q₈	C₂²⋊D₁₉	1	2	yes	—
118	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
119	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
120	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
121	C₂×M₁₆	—	2	2	no	—
122	C₂×M₁₆	—	38	2	no	—
123	#117	—	76	4	no	—
124	C₂×C₄⋊C₄	—	38	2	no	—
125	C₂×C₂²⋊C₄	—	19	4	no	—
126	C₂×C₄²	—	38	2	no	—
127	#101	—	4	4	no	—
128	#101	—	76	4	no	—
129	C₂²⋊C₈	—	2	4	no	—
130	C₂²⋊C₈	—	38	4	no	—
131	#95	—	38	4	no	—
132	#95	—	38	2	no	—
133	#95	—	38	2	no	—
134	C₁₉	#8754	1	1	yes	characteristic, complemented, Sylow
135	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
136	C₂×Q₈	—	2	4	no	—
137	C₂×Q₈	—	2	4	no	—
138	C₂×Q₈	—	2	4	no	—
139	C₂×Q₈	—	2	4	no	—
140	C₂×Q₈	—	4	2	no	—
141	C₂×Q₈	—	4	2	no	—
142	C₂×Q₈	—	4	16	no	—
143	C₂²×C₄	—	2	2	no	—
144	C₂²×C₄	—	2	4	no	—
145	C₂²×C₄	—	2	2	no	—
146	C₂²×C₄	—	4	2	no	—
147	C₂²×C₄	—	4	2	no	—
148	C₂²×C₄	—	38	4	no	—
149	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
150	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
151	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
152	C₂²×C₄	#64543	1	4	yes	—
153	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
154	M₁₆	—	4	4	no	—
155	M₁₆	—	76	4	no	—
156	C₂×C₈	—	4	2	no	—
157	C₂×C₈	—	76	2	no	—
158	C₄⋊C₄	—	76	4	no	—
159	C₂²⋊C₄	—	76	4	no	—
160	C₄²	—	76	4	no	—
161	C₂³	—	2	2	no	—
162	C₂³	—	4	2	no	—
163	C₂³	#10597323	1	2	yes	—
164	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
165	Q₈	—	4	8	no	—
166	Q₈	—	4	8	no	—
167	C₂×C₄	—	2	8	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	4	4	no	—
176	C₂×C₄	—	4	4	no	—
177	C₂×C₄	—	76	8	no	—
178	C₂×C₄	—	76	4	no	—
179	C₂×C₄	#10597263	1	4	yes	—
180	C₂×C₄	#10597332	1	2	yes	—
181	C₂×C₄	#10597381	1	2	yes	—
182	C₈	—	8	2	no	—
183	C₈	—	152	2	no	—
184	C₂²	—	2	2	no	—
185	C₂²	—	2	2	no	—
186	C₂²	—	2	4	no	—
187	C₂²	—	4	4	no	—
188	C₂²	#11926405	1	1	yes	characteristic
189	C₂²	C₂×#10597263	1	2	yes	—
190	C₄	—	2	2	no	—
191	C₄	—	2	2	no	—
192	C₄	—	2	4	no	—
193	C₄	—	4	2	no	—
194	C₄	—	152	4	no	—
195	C₂	—	2	2	no	—
196	C₂	—	4	2	no	—
197	C₂	#14563707	1	1	yes	characteristic
198	C₂	#14563747	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14566221

C₂

yes

maximal, characteristic

#14563559

C₂

yes

maximal, characteristic

#14561544

C₂

yes

maximal

C₁₉×#1784

C₂

yes

maximal, characteristic

C₂×#10597372

C₄

yes

—

C₂×#10597293

—

#11926508

C₂²

yes

—

#11926451

—

#11926451

—

#11926407

C₄

yes

—

#11926407

C₂²

yes

—

C₂³×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#101

—

C₁₉×#407

C₂²

yes

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

D₄

yes

—

C₂²×Q₈×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×C₂²⋊Dic₁₉

C₂×C₄

yes

—

#10597372

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂×#64520

—

C₁₉×#101

—

C₁₉×C₂²⋊C₈

—

#10597293

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

#8754

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

#117

yes

—

Q₈×C₁₉

—

Q₈×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

#99

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2310

—

#1784

—

#1784

D₁₉

yes

characteristic

#1306

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#381

yes

characteristic

C₂²×C₁₉

C₂×#99

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

100

C₂³×Q₈

C₂×D₁₉

yes

characteristic

101

C₂×#117

—

102

C₂×#101

—

103

C₂×#101

—

104

#407

—

105

#407

C₂×D₁₉

yes

—

106

#391

—

107

#391

—

108

#381

—

109

#381

—

110

C₂×C₁₉

—

111

C₂×C₁₉

—

112

C₂×C₁₉

#1819

yes

characteristic

113

C₂×C₁₉

#1830

yes

—

114

C₂²×Q₈

—

115

C₂²×Q₈

—

116

C₂²×Q₈

D₇₆

yes

—

117

C₂²×Q₈

C₂²⋊D₁₉

yes

—

118

C₂³×C₄

C₄×D₁₉

yes

characteristic

119

C₂³×C₄

C₄×D₁₉

yes

characteristic

120

C₂³×C₄

C₂²×D₁₉

yes

characteristic

121

C₂×M₁₆

—

122

C₂×M₁₆

—

123

#117

—

124

C₂×C₄⋊C₄

—

125

C₂×C₂²⋊C₄

—

126

C₂×C₄²

—

127

#101

—

128

#101

—

129

C₂²⋊C₈

—

130

C₂²⋊C₈

—

131

#95

—

132

#95

—

133

#95

—

134

C₁₉

#8754

yes

characteristic, complemented, Sylow

135

C₂⁴

C₂×C₄×D₁₉

yes

characteristic

136

C₂×Q₈

—

137

C₂×Q₈

—

138

C₂×Q₈

—

139

C₂×Q₈

—

140

C₂×Q₈

—

141

C₂×Q₈

—

142

C₂×Q₈

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

150

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

151

C₂²×C₄

C₂×D₇₆

yes

characteristic

152

C₂²×C₄

#64543

yes

—

153

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

154

M₁₆

—

155

M₁₆

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₄⋊C₄

—

159

C₂²⋊C₄

—

160

C₄²

—

161

C₂³

—

162

C₂³

—

163

C₂³

#10597323

yes

—

164

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

165

Q₈

—

166

Q₈

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

#10597263

yes

—

180

C₂×C₄

#10597332

yes

—

181

C₂×C₄

#10597381

yes

—

182

C₈

—

183

C₈

—

152

—

184

C₂²

—

185

C₂²

—

186

C₂²

—

187

C₂²

—

188

C₂²

#11926405

yes

characteristic

189

C₂²

C₂×#10597263

yes

—

190

C₄

—

191

C₄

—

192

C₄

—

193

C₄

—

194

C₄

—

152

—

195

C₂

—

196

C₂

—

197

C₂

#14563707

yes

characteristic

198

C₂

#14563747

yes

—

	subgroup	G/H
center	C₂²	#11926405
commutator, prime radical	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1784	C₂
socle	C₂²×C₁₉	#381
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1784	D₁₉
hypocenter	C₁₉	#8754
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #1784

subgroup

G/H

center

C₂²

#11926405

commutator, prime radical

C₂⁴×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting

C₁₉×#1784

C₂

socle

C₂²×C₁₉

#381

cosocle

C₂³×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂⁴×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #1784

N	H ≅ G/N	type
134. C₁₉	#8754	semidirect

H ≅ G/N

type

134. C₁₉

#8754

semidirect

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

subgroup	index
#14566221	2
#14563559	2
#14561544	2
C₁₉×#1784	2
#8754	19

subgroup

index

C₁₉×#1784

Subgroups — #18076062

Conjugacy classes of subgroups

Complements

Maximal subgroups