Group #18070040 — subgroups

Subgroups — #18070040

Order 4864.

254 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 39 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	#14561758	C₂	1	1	yes	maximal, characteristic, complemented
2	#14561573	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2018	C₂	1	1	yes	maximal, characteristic
4	#11926528	—	2	1	no	—
5	#11926326	—	2	1	no	—
6	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
7	C₂²×D₈×C₁₉	C₄	1	1	yes	characteristic
8	C₂×C₁₉×#100	—	2	1	no	—
9	C₁₉×#408	C₂²	1	1	yes	characteristic
10	C₁₉×#341	C₄	1	1	yes	characteristic
11	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
12	C₂²×D₄×C₁₉	—	2	1	no	—
13	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
14	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
15	C₂×SD₁₆×C₁₉	—	4	1	no	—
16	C₂×D₈×C₁₉	—	4	1	no	—
17	C₂×D₈×C₁₉	—	4	1	no	—
18	C₂×D₈×C₁₉	—	4	2	no	—
19	C₂×M₁₆×C₁₉	—	2	1	no	—
20	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂×#64520	—	4	1	no	—
23	C₁₉×#100	—	4	2	no	—
24	C₁₉×C₂²⋊C₈	—	4	1	no	—
25	#10597293	—	4	1	no	—
26	#10597290	—	2	2	no	—
27	#10597269	—	4	1	no	—
28	C₂⁴×C₁₉	—	4	1	no	—
29	#41×C₁₉	—	4	1	no	—
30	#41×C₁₉	—	4	1	no	—
31	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
32	C₂×D₄×C₁₉	—	2	2	no	—
33	C₂×D₄×C₁₉	—	2	1	no	—
34	C₂×D₄×C₁₉	—	4	1	no	—
35	C₂×D₄×C₁₉	—	4	1	no	—
36	C₂×D₄×C₁₉	—	4	1	no	—
37	C₂×D₄×C₁₉	—	4	1	no	—
38	C₂×D₄×C₁₉	—	4	1	no	—
39	C₂×D₄×C₁₉	SD₁₆	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	—	2	1	no	—
41	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
42	SD₁₆×C₁₉	—	4	4	no	—
43	D₈×C₁₉	—	4	2	no	—
44	D₈×C₁₉	—	4	2	no	—
45	D₈×C₁₉	—	4	4	no	—
46	M₁₆×C₁₉	—	2	2	no	—
47	M₁₆×C₁₉	—	4	1	no	—
48	M₁₆×C₁₉	—	4	1	no	—
49	C₂×C₈×C₁₉	—	2	1	no	—
50	C₂×C₈×C₁₉	—	2	1	no	—
51	C₂×C₈×C₁₉	—	4	1	no	—
52	C₂×C₈×C₁₉	—	4	1	no	—
53	#64520	—	4	2	no	—
54	#64520	—	8	1	no	—
55	C₂×C₁₉⋊C₈	—	8	1	no	—
56	C₁₉⋊C₁₆	—	8	1	no	—
57	#7400	—	19	1	no	maximal, Sylow
58	C₂³×C₁₉	—	2	1	no	—
59	C₂³×C₁₉	—	4	2	no	—
60	C₂³×C₁₉	—	8	1	no	—
61	C₂³×C₁₉	—	8	1	no	—
62	C₂³×C₁₉	—	16	2	no	—
63	C₂³×C₁₉	#104	1	1	yes	characteristic
64	Q₈×C₁₉	—	4	1	no	—
65	D₄×C₁₉	—	4	1	no	—
66	D₄×C₁₉	—	4	2	no	—
67	D₄×C₁₉	—	4	2	no	—
68	D₄×C₁₉	—	8	1	no	—
69	D₄×C₁₉	—	8	1	no	—
70	D₄×C₁₉	—	8	1	no	—
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	—	2	1	no	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	4	1	no	—
75	C₂×C₄×C₁₉	—	4	1	no	—
76	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
77	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
78	C₈×C₁₉	—	4	2	no	—
79	C₈×C₁₉	—	4	1	no	—
80	C₈×C₁₉	—	4	1	no	—
81	C₁₉⋊C₈	—	8	2	no	—
82	#2018	D₁₉	1	1	yes	characteristic
83	#1392	—	19	1	no	—
84	#1321	—	19	1	no	—
85	C₂²×C₁₉	—	2	1	no	—
86	C₂²×C₁₉	—	4	1	no	—
87	C₂²×C₁₉	—	4	1	no	—
88	C₂²×C₁₉	—	8	1	no	—
89	C₂²×C₁₉	—	8	2	no	—
90	C₂²×C₁₉	—	16	2	no	—
91	C₂²×C₁₉	—	16	2	no	—
92	C₂²×C₁₉	—	16	2	no	—
93	C₂²×C₁₉	#327	1	1	yes	characteristic
94	C₄×C₁₉	—	2	1	no	—
95	C₄×C₁₉	—	4	1	no	—
96	C₄×C₁₉	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
97	C₄×C₁₉	#353	1	1	yes	characteristic
98	C₂×AGL(1,ℤ/8)	—	2	1	no	—
99	C₂²×D₈	Dic₁₉	1	1	yes	characteristic
100	#413	—	38	1	no	—
101	C₂×#100	—	2	1	no	—
102	#408	C₂×D₁₉	1	1	yes	characteristic
103	#349	—	38	1	no	—
104	#341	Dic₁₉	1	1	yes	characteristic
105	C₂×C₁₉	—	2	1	no	—
106	C₂×C₁₉	—	4	1	no	—
107	C₂×C₁₉	—	8	1	no	—
108	C₂×C₁₉	—	16	2	no	—
109	C₂×C₁₉	#1343	1	1	yes	characteristic
110	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
111	C₂²×D₄	—	2	1	no	—
112	AGL(1,ℤ/8)	—	4	2	no	—
113	AGL(1,ℤ/8)	—	4	2	no	—
114	C₂×SD₁₆	—	4	1	no	—
115	C₂×D₈	—	4	1	no	—
116	C₂×D₈	—	4	1	no	—
117	C₂×D₈	—	4	2	no	—
118	C₂×M₁₆	—	2	1	no	—
119	C₂×M₁₆	—	76	1	no	—
120	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
121	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
122	M₃₂	—	76	1	no	—
123	#101	—	76	1	no	—
124	#100	—	4	2	no	—
125	#100	—	38	2	no	—
126	C₂²⋊C₈	—	4	1	no	—
127	C₁₉	#7400	1	1	yes	characteristic, complemented, Sylow
128	C₂⁴	—	4	1	no	—
129	#41	—	4	1	no	—
130	#41	—	4	1	no	—
131	C₂×Q₈	#64525	1	1	yes	characteristic
132	C₂×D₄	—	2	2	no	—
133	C₂×D₄	—	2	1	no	—
134	C₂×D₄	—	4	1	no	—
135	C₂×D₄	—	4	1	no	—
136	C₂×D₄	—	4	1	no	—
137	C₂×D₄	—	4	1	no	—
138	C₂×D₄	—	4	1	no	—
139	C₂×D₄	#64526	1	1	yes	characteristic
140	C₂²×C₄	—	2	1	no	—
141	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
142	SD₁₆	—	4	4	no	—
143	D₈	—	4	2	no	—
144	D₈	—	4	2	no	—
145	D₈	—	4	4	no	—
146	M₁₆	—	2	2	no	—
147	M₁₆	—	4	1	no	—
148	M₁₆	—	4	1	no	—
149	M₁₆	—	76	2	no	—
150	M₁₆	—	152	1	no	—
151	C₂×C₈	—	2	1	no	—
152	C₂×C₈	—	2	1	no	—
153	C₂×C₈	—	4	1	no	—
154	C₂×C₈	—	4	1	no	—
155	C₂×C₈	—	152	1	no	—
156	C₁₆	—	152	1	no	—
157	C₂³	—	2	1	no	—
158	C₂³	—	4	2	no	—
159	C₂³	—	8	1	no	—
160	C₂³	—	8	1	no	—
161	C₂³	—	16	2	no	—
162	C₂³	#10597294	1	1	yes	characteristic
163	Q₈	—	4	1	no	—
164	D₄	—	4	1	no	—
165	D₄	—	4	2	no	—
166	D₄	—	4	2	no	—
167	D₄	—	8	1	no	—
168	D₄	—	8	1	no	—
169	D₄	—	8	1	no	—
170	C₂×C₄	—	2	1	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	2	1	no	—
173	C₂×C₄	—	4	1	no	—
174	C₂×C₄	—	4	1	no	—
175	C₂×C₄	#10597289	1	1	yes	characteristic
176	C₂×C₄	#10597291	1	1	yes	characteristic
177	C₈	—	4	2	no	—
178	C₈	—	4	1	no	—
179	C₈	—	4	1	no	—
180	C₈	—	152	2	no	—
181	C₂²	—	2	1	no	—
182	C₂²	—	4	1	no	—
183	C₂²	—	4	1	no	—
184	C₂²	—	8	1	no	—
185	C₂²	—	8	2	no	—
186	C₂²	—	16	2	no	—
187	C₂²	—	16	2	no	—
188	C₂²	—	16	2	no	—
189	C₂²	#11926278	1	1	yes	characteristic
190	C₄	—	2	1	no	—
191	C₄	—	4	1	no	—
192	C₄	#11926331	1	1	yes	characteristic
193	C₄	#11926337	1	1	yes	characteristic
194	C₂	—	2	1	no	—
195	C₂	—	4	1	no	—
196	C₂	—	8	1	no	—
197	C₂	—	16	2	no	—
198	C₂	#14561632	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561758

C₂

yes

maximal, characteristic, complemented

#14561573

C₂

yes

maximal, characteristic, complemented

C₁₉×#2018

C₂

yes

maximal, characteristic

#11926528

—

#11926326

—

C₂×C₁₉×AGL(1,ℤ/8)

—

C₂²×D₈×C₁₉

C₄

yes

characteristic

C₂×C₁₉×#100

—

C₁₉×#408

C₂²

yes

characteristic

C₁₉×#341

C₄

yes

characteristic

C₂×#41×C₁₉

D₄

yes

characteristic

C₂²×D₄×C₁₉

—

C₁₉×AGL(1,ℤ/8)

—

C₁₉×AGL(1,ℤ/8)

—

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×#64520

—

C₁₉×#100

—

C₁₉×C₂²⋊C₈

—

#10597293

—

#10597290

—

#10597269

—

C₂⁴×C₁₉

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

D₈

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

SD₁₆

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

SD₁₆×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₁₉⋊C₁₆

—

#7400

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#104

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2018

D₁₉

yes

characteristic

#1392

—

#1321

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#327

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

AΣL(1,𝔽₁₆)

yes

C₄×C₁₉

yes

—

C₂²×D₈

Dic₁₉

yes

characteristic

100

#413

—

101

C₂×#100

—

102

#408

C₂×D₁₉

yes

characteristic

103

#349

—

104

#341

Dic₁₉

yes

characteristic

105

C₂×C₁₉

—

106

C₂×C₁₉

—

107

C₂×C₁₉

—

108

C₂×C₁₉

—

109

C₂×C₁₉

#1343

yes

characteristic

110

C₂×#41

C₂²⋊D₁₉

yes

characteristic

111

C₂²×D₄

—

112

AGL(1,ℤ/8)

—

113

AGL(1,ℤ/8)

—

114

C₂×SD₁₆

—

115

C₂×D₈

—

116

C₂×D₈

—

117

C₂×D₈

—

118

C₂×M₁₆

—

119

C₂×M₁₆

—

120

C₂×M₁₆

C₂²⋊D₁₉

yes

characteristic

121

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

122

M₃₂

—

123

#101

—

124

#100

—

125

#100

—

126

C₂²⋊C₈

—

127

C₁₉

#7400

yes

characteristic, complemented, Sylow

128

C₂⁴

—

129

#41

—

130

#41

—

131

C₂×Q₈

#64525

yes

characteristic

132

C₂×D₄

—

133

C₂×D₄

—

134

C₂×D₄

—

135

C₂×D₄

—

136

C₂×D₄

—

137

C₂×D₄

—

138

C₂×D₄

—

139

C₂×D₄

#64526

yes

characteristic

140

C₂²×C₄

—

141

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

142

SD₁₆

—

143

D₈

—

144

D₈

—

145

D₈

—

146

M₁₆

—

147

M₁₆

—

148

M₁₆

—

149

M₁₆

—

150

M₁₆

—

152

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

—

152

—

156

C₁₆

—

152

—

157

C₂³

—

158

C₂³

—

159

C₂³

—

160

C₂³

—

161

C₂³

—

162

C₂³

#10597294

yes

characteristic

163

Q₈

—

164

D₄

—

165

D₄

—

166

D₄

—

167

D₄

—

168

D₄

—

169

D₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

#10597289

yes

characteristic

176

C₂×C₄

#10597291

yes

characteristic

177

C₈

—

178

C₈

—

179

C₈

—

180

C₈

—

152

—

181

C₂²

—

182

C₂²

—

183

C₂²

—

184

C₂²

—

185

C₂²

—

186

C₂²

—

187

C₂²

—

188

C₂²

—

189

C₂²

#11926278

yes

characteristic

190

C₄

—

191

C₄

—

192

C₄

#11926331

yes

characteristic

193

C₄

#11926337

yes

characteristic

194

C₂

—

195

C₂

—

196

C₂

—

197

C₂

—

198

C₂

#14561632

yes

characteristic

	subgroup	G/H
center	C₂	#14561632
commutator	C₂²×C₈×C₁₉	C₂×C₄
Frattini	#408	C₂×D₁₉
Fitting, prime radical	C₁₉×#2018	C₂
socle	C₂×C₁₉	#1343
cosocle	C₁₉×#408	C₂²
hypercenter	#2018	D₁₉
hypocenter	C₁₉	#7400
LCS	G ▷ C₂²×C₈×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #408 ◁ #2018

subgroup

G/H

center

C₂

#14561632

commutator

C₂²×C₈×C₁₉

C₂×C₄

Frattini

#408

C₂×D₁₉

Fitting, prime radical

C₁₉×#2018

C₂

socle

C₂×C₁₉

#1343

cosocle

C₁₉×#408

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₈×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #408 ◁ #2018

N	H ≅ G/N	type
1. #14561758	C₂	semidirect
2. #14561573	C₂	semidirect
127. C₁₉	#7400	semidirect

H ≅ G/N

type

1. #14561758

C₂

semidirect

2. #14561573

C₂

semidirect

127. C₁₉

#7400

semidirect

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

subgroup	index
#14561758	2
#14561573	2
C₁₉×#2018	2
#7400	19

subgroup

index

#14561758

#14561573

C₁₉×#2018

#7400

Subgroups — #18070040

Conjugacy classes of subgroups

Complements

Maximal subgroups