Group #18076055 — subgroups

Subgroups — #18076055

Order 4864.

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

normal subgroups only

This group has 754 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	#14563556	C₂	1	2	yes	maximal
2	#14561543	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2308	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597290	—	2	4	no	—
5	#11926508	C₂²	1	4	yes	—
6	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
8	C₁₉×#386	—	2	4	no	—
9	C₁₉×#381	C₂²	1	2	yes	—
10	C₁₉×#379	C₄	1	2	yes	—
11	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂²×D₄×C₁₉	—	2	4	no	—
14	C₂²×D₄×C₁₉	—	4	4	no	—
15	C₂²×D₄×C₁₉	D₄	1	4	yes	—
16	C₂³×C₄×C₁₉	—	2	2	no	—
17	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
19	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
20	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
21	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
22	C₂×#64520	—	2	4	no	—
23	C₁₉×#95	—	2	4	no	—
24	#10597290	—	4	8	no	—
25	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
26	C₂⁴×C₁₉	—	2	4	no	—
27	C₂⁴×C₁₉	—	2	2	no	—
28	C₂⁴×C₁₉	—	2	2	no	—
29	C₂⁴×C₁₉	—	4	2	no	—
30	C₂⁴×C₁₉	—	8	2	no	—
31	C₂⁴×C₁₉	—	8	2	no	—
32	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
33	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
34	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
35	C₂×D₄×C₁₉	—	2	8	no	—
36	C₂×D₄×C₁₉	—	2	8	no	—
37	C₂×D₄×C₁₉	—	4	4	no	—
38	C₂×D₄×C₁₉	—	4	16	no	—
39	C₂²×C₄×C₁₉	—	2	4	no	—
40	C₂²×C₄×C₁₉	—	4	2	no	—
41	C₂²×C₄×C₁₉	—	4	4	no	—
42	C₂²×C₄×C₁₉	—	8	4	no	—
43	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
44	C₂²×C₄×C₁₉	#41	1	4	yes	—
45	C₂²⋊C₄×C₁₉	—	4	4	no	—
46	C₂²⋊C₄×C₁₉	—	4	4	no	—
47	C₂²⋊C₄×C₁₉	—	8	4	no	—
48	#64520	—	4	8	no	—
49	C₂×C₁₉⋊C₈	—	4	4	no	—
50	#8751	—	19	1	no	maximal, Sylow
51	C₂³×C₁₉	—	2	8	no	—
52	C₂³×C₁₉	—	2	2	no	—
53	C₂³×C₁₉	—	2	2	no	—
54	C₂³×C₁₉	—	2	2	no	—
55	C₂³×C₁₉	—	2	2	no	—
56	C₂³×C₁₉	—	2	4	no	—
57	C₂³×C₁₉	—	4	2	no	—
58	C₂³×C₁₉	—	4	4	no	—
59	C₂³×C₁₉	—	4	4	no	—
60	C₂³×C₁₉	—	4	4	no	—
61	C₂³×C₁₉	—	8	4	no	—
62	C₂³×C₁₉	—	8	4	no	—
63	C₂³×C₁₉	—	8	8	no	—
64	C₂³×C₁₉	—	8	8	no	—
65	C₂³×C₁₉	#99	1	4	yes	—
66	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₂³×C₁₉	#117	1	2	yes	—
68	D₄×C₁₉	—	4	16	no	—
69	C₂×C₄×C₁₉	—	2	4	no	—
70	C₂×C₄×C₁₉	—	4	4	no	—
71	C₂×C₄×C₁₉	—	4	8	no	—
72	C₂×C₄×C₁₉	—	4	4	no	—
73	C₂×C₄×C₁₉	—	8	8	no	—
74	C₂×C₄×C₁₉	#123	1	4	yes	—
75	C₁₉⋊C₈	—	8	4	no	—
76	#2308	D₁₉	1	1	yes	characteristic
77	#1783	—	19	2	no	—
78	#1306	—	19	4	no	—
79	C₂²×C₁₉	—	2	2	no	—
80	C₂²×C₁₉	—	2	2	no	—
81	C₂²×C₁₉	—	2	4	no	—
82	C₂²×C₁₉	—	2	4	no	—
83	C₂²×C₁₉	—	4	4	no	—
84	C₂²×C₁₉	—	4	4	no	—
85	C₂²×C₁₉	—	4	4	no	—
86	C₂²×C₁₉	—	4	4	no	—
87	C₂²×C₁₉	—	4	2	no	—
88	C₂²×C₁₉	—	4	4	no	—
89	C₂²×C₁₉	—	8	4	no	—
90	C₂²×C₁₉	—	8	8	no	—
91	C₂²×C₁₉	—	8	8	no	—
92	C₂²×C₁₉	#381	1	1	yes	characteristic
93	C₂²×C₁₉	C₂×#99	1	2	yes	—
94	C₄×C₁₉	—	2	4	no	—
95	C₄×C₁₉	—	8	4	no	—
96	C₂³×D₄	C₂×D₁₉	1	1	yes	characteristic
97	C₂²×C₂²⋊C₄	Dic₁₉	1	2	yes	—
98	C₂×#100	—	38	4	no	—
99	#407	—	19	4	no	—
100	#386	—	2	4	no	—
101	#381	C₂×D₁₉	1	2	yes	—
102	#379	Dic₁₉	1	2	yes	—
103	C₂×C₁₉	—	2	2	no	—
104	C₂×C₁₉	—	4	2	no	—
105	C₂×C₁₉	—	4	4	no	—
106	C₂×C₁₉	—	8	2	no	—
107	C₂×C₁₉	#1819	1	1	yes	characteristic
108	C₂×C₁₉	#1829	1	2	yes	—
109	C₂⁵	C₂×Dic₁₉	1	1	yes	characteristic
110	C₂⁵	C₂×Dic₁₉	1	1	yes	characteristic
111	C₂²×D₄	—	2	4	no	—
112	C₂²×D₄	—	4	4	no	—
113	C₂²×D₄	C₂²⋊D₁₉	1	4	yes	—
114	C₂³×C₄	—	2	2	no	—
115	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
116	C₂×M₁₆	—	38	4	no	—
117	C₂×C₂²⋊C₄	—	2	2	no	—
118	C₂×C₂²⋊C₄	—	2	4	no	—
119	C₂×C₂²⋊C₄	—	4	4	no	—
120	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	4	yes	—
121	#100	—	76	8	no	—
122	C₂²⋊C₈	—	38	8	no	—
123	#95	—	2	4	no	—
124	C₁₉	#8751	1	1	yes	characteristic, complemented, Sylow
125	C₂⁴	—	2	4	no	—
126	C₂⁴	—	2	2	no	—
127	C₂⁴	—	2	2	no	—
128	C₂⁴	—	4	2	no	—
129	C₂⁴	—	8	2	no	—
130	C₂⁴	—	8	2	no	—
131	C₂⁴	C₂²⋊Dic₁₉	1	2	yes	—
132	C₂⁴	C₂²⋊Dic₁₉	1	2	yes	—
133	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
134	C₂×D₄	—	2	8	no	—
135	C₂×D₄	—	2	8	no	—
136	C₂×D₄	—	4	4	no	—
137	C₂×D₄	—	4	16	no	—
138	C₂²×C₄	—	2	4	no	—
139	C₂²×C₄	—	4	2	no	—
140	C₂²×C₄	—	4	4	no	—
141	C₂²×C₄	—	8	4	no	—
142	C₂²×C₄	#64541	1	4	yes	—
143	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
144	M₁₆	—	76	8	no	—
145	C₂×C₈	—	76	4	no	—
146	C₂²⋊C₄	—	4	4	no	—
147	C₂²⋊C₄	—	4	4	no	—
148	C₂²⋊C₄	—	8	4	no	—
149	C₂³	—	2	8	no	—
150	C₂³	—	2	2	no	—
151	C₂³	—	2	2	no	—
152	C₂³	—	2	2	no	—
153	C₂³	—	2	2	no	—
154	C₂³	—	2	4	no	—
155	C₂³	—	4	2	no	—
156	C₂³	—	4	4	no	—
157	C₂³	—	4	4	no	—
158	C₂³	—	4	4	no	—
159	C₂³	—	8	4	no	—
160	C₂³	—	8	4	no	—
161	C₂³	—	8	8	no	—
162	C₂³	—	8	8	no	—
163	C₂³	#10597291	1	4	yes	—
164	C₂³	#10597372	1	2	yes	—
165	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
166	D₄	—	4	16	no	—
167	C₂×C₄	—	2	4	no	—
168	C₂×C₄	—	4	4	no	—
169	C₂×C₄	—	4	8	no	—
170	C₂×C₄	—	4	4	no	—
171	C₂×C₄	—	8	8	no	—
172	C₂×C₄	#10597375	1	4	yes	—
173	C₈	—	152	4	no	—
174	C₂²	—	2	2	no	—
175	C₂²	—	2	2	no	—
176	C₂²	—	2	4	no	—
177	C₂²	—	2	4	no	—
178	C₂²	—	4	4	no	—
179	C₂²	—	4	4	no	—
180	C₂²	—	4	4	no	—
181	C₂²	—	4	4	no	—
182	C₂²	—	4	2	no	—
183	C₂²	—	4	4	no	—
184	C₂²	—	8	4	no	—
185	C₂²	—	8	8	no	—
186	C₂²	—	8	8	no	—
187	C₂²	#11926407	1	1	yes	characteristic
188	C₂²	C₂×#10597291	1	2	yes	—
189	C₄	—	2	4	no	—
190	C₄	—	8	4	no	—
191	C₂	—	2	2	no	—
192	C₂	—	4	2	no	—
193	C₂	—	4	4	no	—
194	C₂	—	8	2	no	—
195	C₂	#14563709	1	1	yes	characteristic
196	C₂	#14563746	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563556

C₂

yes

maximal

#14561543

C₂

yes

maximal, complemented

C₁₉×#2308

C₂

yes

maximal, characteristic

C₂×#10597290

—

#11926508

C₂²

yes

—

C₂³×D₄×C₁₉

C₂²

yes

characteristic

C₂²×C₂²⋊C₄×C₁₉

C₄

yes

—

C₁₉×#386

—

C₁₉×#381

C₂²

yes

—

C₁₉×#379

C₄

yes

—

C₂⁵×C₁₉

C₂×C₄

yes

characteristic

C₂⁵×C₁₉

C₂×C₄

yes

characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×#64520

—

C₁₉×#95

—

#10597290

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

#41

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

#8751

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#99

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

#117

yes

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#123

yes

—

C₁₉⋊C₈

—

#2308

D₁₉

yes

characteristic

#1783

—

#1306

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#381

yes

characteristic

C₂²×C₁₉

C₂×#99

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂³×D₄

C₂×D₁₉

yes

characteristic

C₂²×C₂²⋊C₄

Dic₁₉

yes

—

C₂×#100

—

#407

—

100

#386

—

101

#381

C₂×D₁₉

yes

—

102

#379

Dic₁₉

yes

—

103

C₂×C₁₉

—

104

C₂×C₁₉

—

105

C₂×C₁₉

—

106

C₂×C₁₉

—

107

C₂×C₁₉

#1819

yes

characteristic

108

C₂×C₁₉

#1829

yes

—

109

C₂⁵

C₂×Dic₁₉

yes

characteristic

110

C₂⁵

C₂×Dic₁₉

yes

characteristic

111

C₂²×D₄

—

112

C₂²×D₄

—

113

C₂²×D₄

C₂²⋊D₁₉

yes

—

114

C₂³×C₄

—

115

C₂³×C₄

C₂²×D₁₉

yes

characteristic

116

C₂×M₁₆

—

117

C₂×C₂²⋊C₄

—

118

C₂×C₂²⋊C₄

—

119

C₂×C₂²⋊C₄

—

120

C₂×C₂²⋊C₄

C₂×Dic₁₉

yes

—

121

#100

—

122

C₂²⋊C₈

—

123

#95

—

124

C₁₉

#8751

yes

characteristic, complemented, Sylow

125

C₂⁴

—

126

C₂⁴

—

127

C₂⁴

—

128

C₂⁴

—

129

C₂⁴

—

130

C₂⁴

—

131

C₂⁴

C₂²⋊Dic₁₉

yes

—

132

C₂⁴

C₂²⋊Dic₁₉

yes

—

133

C₂⁴

C₂²×Dic₁₉

yes

characteristic

134

C₂×D₄

—

135

C₂×D₄

—

136

C₂×D₄

—

137

C₂×D₄

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

#64541

yes

—

143

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

144

M₁₆

—

145

C₂×C₈

—

146

C₂²⋊C₄

—

147

C₂²⋊C₄

—

148

C₂²⋊C₄

—

149

C₂³

—

150

C₂³

—

151

C₂³

—

152

C₂³

—

153

C₂³

—

154

C₂³

—

155

C₂³

—

156

C₂³

—

157

C₂³

—

158

C₂³

—

159

C₂³

—

160

C₂³

—

161

C₂³

—

162

C₂³

—

163

C₂³

#10597291

yes

—

164

C₂³

#10597372

yes

—

165

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

166

D₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

#10597375

yes

—

173

C₈

—

152

—

174

C₂²

—

175

C₂²

—

176

C₂²

—

177

C₂²

—

178

C₂²

—

179

C₂²

—

180

C₂²

—

181

C₂²

—

182

C₂²

—

183

C₂²

—

184

C₂²

—

185

C₂²

—

186

C₂²

—

187

C₂²

#11926407

yes

characteristic

188

C₂²

C₂×#10597291

yes

—

189

C₄

—

190

C₄

—

191

C₂

—

192

C₂

—

193

C₂

—

194

C₂

—

195

C₂

#14563709

yes

characteristic

196

C₂

#14563746

yes

—

	subgroup	G/H
center	C₂²	#11926407
commutator	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#2308	C₂
socle	C₂²×C₁₉	#381
prime radical	C₂³×D₄×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#2308	D₁₉
hypocenter	C₁₉	#8751
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #2308

subgroup

G/H

center

C₂²

#11926407

commutator

C₂⁴×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting

C₁₉×#2308

C₂

socle

C₂²×C₁₉

#381

prime radical

C₂³×D₄×C₁₉

C₂²

cosocle

C₂³×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂⁴×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #2308

N	H ≅ G/N	type
2. #14561543	C₂	semidirect
124. C₁₉	#8751	semidirect

H ≅ G/N

type

2. #14561543

C₂

semidirect

124. C₁₉

#8751

semidirect

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

subgroup	index
#14563556	2
#14561543	2
C₁₉×#2308	2
#8751	19

subgroup

index

#14563556

#14561543

C₁₉×#2308

#8751

Subgroups — #18076055

Conjugacy classes of subgroups

Complements

Maximal subgroups