Group #18086639 — subgroups

Subgroups — #18086639

Order 4864.

344 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 77 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	#14574980	C₂	1	1	yes	maximal, characteristic
2	#14563754	C₂	1	1	yes	maximal, characteristic
3	#14562336	C₂	1	2	yes	maximal
4	#14562148	C₂	1	2	yes	maximal
5	C₁₉×#1290	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	2	yes	—
7	#11926840	—	2	2	no	—
8	#11926785	—	2	2	no	—
9	#11926755	—	2	2	no	—
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	#11926390	C₂²	1	1	yes	characteristic
12	#11926298	—	2	2	no	—
13	#11926291	—	2	2	no	—
14	#11926289	—	2	2	no	—
15	#11926282	—	2	4	no	—
16	C₁₉×#432	C₂²	1	2	yes	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂²×C₈×C₁₉	D₄	1	2	yes	—
19	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
20	#10597372	—	2	2	no	—
21	#10597370	—	2	2	no	—
22	#10597370	—	2	2	no	—
23	C₂×C₄×Dic₁₉	—	2	1	no	—
24	C₂²×C₁₉⋊C₈	—	2	1	no	—
25	C₂×Dic₇₆	—	2	2	no	—
26	#10597316	—	2	2	no	—
27	#10597315	D₄	1	2	yes	—
28	#10597315	D₄	1	2	yes	—
29	C₄×Dic₃₈	—	2	2	no	—
30	C₄×Dic₃₈	—	2	2	no	—
31	C₁₉×C₄⋊C₈	—	2	2	no	—
32	C₁₉×C₄⋊C₈	—	2	2	no	—
33	C₁₉×C₂²⋊C₈	—	2	2	no	—
34	C₁₉×#97	—	2	2	no	—
35	C₁₉⋊#95	—	2	1	no	—
36	C₁₉⋊#95	D₄	1	2	yes	—
37	#10597275	—	2	2	no	—
38	#10597273	—	2	4	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
43	C₂²×Dic₁₉	—	2	2	no	—
44	C₂×Dic₃₈	—	2	2	no	—
45	C₂×Dic₃₈	—	2	2	no	—
46	C₂×C₈×C₁₉	—	2	2	no	—
47	C₂×C₈×C₁₉	—	4	2	no	—
48	C₂×C₈×C₁₉	—	4	2	no	—
49	C₄²×C₁₉	C₂×D₄	1	2	yes	—
50	C₄²×C₁₉	#41	1	2	yes	—
51	C₂²⋊Dic₁₉	—	4	2	no	—
52	C₄⋊Dic₁₉	—	2	2	no	—
53	C₄⋊Dic₁₉	—	2	2	no	—
54	C₄⋊Dic₁₉	—	2	2	no	—
55	C₄⋊Dic₁₉	—	2	2	no	—
56	Dic₁₉⋊C₄	—	4	2	no	—
57	Dic₁₉⋊C₄	—	4	2	no	—
58	C₄×Dic₁₉	—	4	1	no	—
59	C₄×Dic₁₉	—	4	1	no	—
60	C₄×Dic₁₉	—	4	2	no	—
61	C₂×C₁₉⋊C₈	—	4	2	no	—
62	C₂×C₁₉⋊C₈	—	4	1	no	—
63	Dic₇₆	—	8	2	no	—
64	#10517	—	19	1	no	maximal, Sylow
65	C₂³×C₁₉	#121	1	1	yes	characteristic
66	C₂×C₄×C₁₉	—	2	2	no	—
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	1	no	—
69	C₂×C₄×C₁₉	—	4	1	no	—
70	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
71	C₂×C₄×C₁₉	#121	1	2	yes	—
72	C₂×C₄×C₁₉	#123	1	2	yes	—
73	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
74	C₂×Dic₁₉	—	4	2	no	—
75	C₂×Dic₁₉	—	4	2	no	—
76	C₂×Dic₁₉	—	4	2	no	—
77	C₂×Dic₁₉	—	4	2	no	—
78	C₂×Dic₁₉	—	4	2	no	—
79	Dic₃₈	—	4	2	no	—
80	Dic₃₈	—	4	2	no	—
81	Dic₃₈	—	8	2	no	—
82	C₈×C₁₉	—	4	2	no	—
83	C₈×C₁₉	—	8	2	no	—
84	C₁₉⋊C₈	—	8	1	no	—
85	#3249	—	19	1	no	—
86	#1832	—	19	1	no	—
87	#1552	—	19	2	no	—
88	#1506	—	19	2	no	—
89	#1290	D₁₉	1	1	yes	characteristic
90	C₂²×C₁₉	—	2	1	no	—
91	C₂²×C₁₉	—	2	1	no	—
92	C₂²×C₁₉	#394	1	1	yes	characteristic
93	C₂²×C₁₉	#473	1	2	yes	—
94	C₄×C₁₉	—	2	2	no	—
95	C₄×C₁₉	—	2	1	no	—
96	C₄×C₁₉	—	2	2	no	—
97	C₄×C₁₉	#454	1	1	yes	characteristic
98	C₄×C₁₉	#455	1	1	yes	characteristic
99	Dic₁₉	—	8	2	no	—
100	Dic₁₉	—	8	2	no	—
101	Dic₁₉	—	8	2	no	—
102	#533	—	19	2	no	—
103	#477	—	38	2	no	—
104	#467	—	38	2	no	—
105	#462	—	38	2	no	—
106	#432	C₂×D₁₉	1	2	yes	—
107	C₂×C₄⋊C₈	—	19	1	no	—
108	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
109	#376	—	19	1	no	—
110	#336	—	38	2	no	—
111	#332	—	38	2	no	—
112	#332	—	38	2	no	—
113	#328	—	38	4	no	—
114	C₂×C₁₉	—	2	2	no	—
115	C₂×C₁₉	#2040	1	1	yes	characteristic
116	C₂×C₁₉	#2047	1	1	yes	characteristic
117	C₂×C₁₉	#2053	1	1	yes	characteristic
118	C₂×Q₁₆	—	38	2	no	—
119	C₂²×C₈	—	38	1	no	—
120	C₂²×C₈	D₇₆	1	2	yes	—
121	C₄⋊Q₈	—	19	2	no	—
122	C₄⋊Q₈	—	19	2	no	—
123	#125	—	38	2	no	—
124	C₂²⋊Q₈	—	38	2	no	—
125	C₂²⋊Q₈	—	38	2	no	—
126	C₄×Q₈	—	38	2	no	—
127	C₄×Q₈	—	38	2	no	—
128	#117	—	38	2	no	—
129	C₂×C₄²	—	38	1	no	—
130	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
131	#107	—	38	2	no	—
132	C₄⋊C₈	—	2	2	no	—
133	C₄⋊C₈	—	2	2	no	—
134	C₄⋊C₈	—	38	2	no	—
135	#103	—	38	4	no	—
136	C₂²⋊C₈	—	2	2	no	—
137	#97	—	2	2	no	—
138	#95	—	19	2	no	—
139	#95	—	38	1	no	—
140	C₁₉	#10517	1	1	yes	characteristic, complemented, Sylow
141	C₂×Q₈	—	38	2	no	—
142	C₂×Q₈	—	38	2	no	—
143	C₂²×C₄	—	38	2	no	—
144	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
145	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
146	C₂²×C₄	#64545	1	1	yes	characteristic
147	Q₁₆	—	152	2	no	—
148	C₂×C₈	—	2	2	no	—
149	C₂×C₈	—	4	2	no	—
150	C₂×C₈	—	4	2	no	—
151	C₂×C₈	—	76	2	no	—
152	C₂×C₈	—	76	1	no	—
153	C₄⋊C₄	—	38	2	no	—
154	C₄⋊C₄	—	38	2	no	—
155	C₄⋊C₄	—	38	2	no	—
156	C₄⋊C₄	—	38	2	no	—
157	C₄⋊C₄	—	76	2	no	—
158	C₄⋊C₄	—	76	2	no	—
159	C₂²⋊C₄	—	76	2	no	—
160	C₄²	—	76	1	no	—
161	C₄²	—	76	1	no	—
162	C₄²	—	76	2	no	—
163	C₄²	#64541	1	2	yes	—
164	C₄²	D₄×D₁₉	1	2	yes	—
165	C₂³	#10597341	1	1	yes	characteristic
166	Q₈	—	76	2	no	—
167	Q₈	—	76	2	no	—
168	Q₈	—	152	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	1	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	4	1	no	—
173	C₂×C₄	—	76	2	no	—
174	C₂×C₄	—	76	2	no	—
175	C₂×C₄	—	76	2	no	—
176	C₂×C₄	—	76	2	no	—
177	C₂×C₄	—	76	2	no	—
178	C₂×C₄	#10597321	1	1	yes	characteristic
179	C₂×C₄	#10597328	1	1	yes	characteristic
180	C₂×C₄	#10597330	1	2	yes	—
181	C₂×C₄	#10597340	1	2	yes	—
182	C₈	—	4	2	no	—
183	C₈	—	8	2	no	—
184	C₈	—	152	1	no	—
185	C₂²	—	2	1	no	—
186	C₂²	—	2	1	no	—
187	C₂²	#11926462	1	1	yes	characteristic
188	C₂²	#11926820	1	2	yes	—
189	C₄	—	2	1	no	—
190	C₄	—	2	2	no	—
191	C₄	—	2	2	no	—
192	C₄	—	152	2	no	—
193	C₄	—	152	2	no	—
194	C₄	—	152	2	no	—
195	C₄	#11926719	1	1	yes	characteristic
196	C₄	#11926724	1	1	yes	characteristic
197	C₂	—	2	2	no	—
198	C₂	#14564865	1	1	yes	characteristic
199	C₂	#14564904	1	1	yes	characteristic
200	C₂	#14564942	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574980

C₂

yes

maximal, characteristic

#14563754

C₂

yes

maximal, characteristic

#14562336

C₂

yes

maximal

#14562148

C₂

yes

maximal

C₁₉×#1290

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

—

#11926840

—

#11926785

—

#11926755

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

#11926390

C₂²

yes

—

—

—

—

C₁₉×#432

C₂²

yes

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₂×Dic₇₆

—

#10597316

—

#10597315

D₄

yes

—

#10597315

D₄

yes

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₁₉⋊#95

—

C₁₉⋊#95

D₄

yes

—

#10597275

—

#10597273

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

—

—

—

—

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#394

yes

characteristic

C₂²×C₁₉

#473

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

100

Dic₁₉

—

101

Dic₁₉

—

102

#533

—

103

#477

—

104

#467

—

105

#462

—

106

#432

C₂×D₁₉

yes

—

107

C₂×C₄⋊C₈

—

108

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

109

#376

—

110

#336

—

111

#332

—

112

#332

—

113

#328

—

114

C₂×C₁₉

—

115

C₂×C₁₉

#2040

yes

characteristic

116

C₂×C₁₉

#2047

yes

characteristic

117

C₂×C₁₉

#2053

yes

characteristic

118

C₂×Q₁₆

—

119

C₂²×C₈

—

120

C₂²×C₈

D₇₆

yes

—

121

C₄⋊Q₈

—

122

C₄⋊Q₈

—

123

#125

—

124

C₂²⋊Q₈

—

125

C₂²⋊Q₈

—

126

C₄×Q₈

—

127

C₄×Q₈

—

128

#117

—

129

C₂×C₄²

—

130

C₂×C₄²

C₂²×D₁₉

yes

characteristic

131

#107

—

132

C₄⋊C₈

—

133

C₄⋊C₈

—

134

C₄⋊C₈

—

135

#103

—

136

C₂²⋊C₈

—

137

#97

—

138

#95

—

139

#95

—

140

C₁₉

#10517

yes

characteristic, complemented, Sylow

141

C₂×Q₈

—

142

C₂×Q₈

—

143

C₂²×C₄

—

144

C₂²×C₄

C₂×D₇₆

yes

characteristic

145

C₂²×C₄

D₄×D₁₉

yes

characteristic

146

C₂²×C₄

#64545

yes

characteristic

147

Q₁₆

—

152

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₂²⋊C₄

—

160

C₄²

—

161

C₄²

—

162

C₄²

—

163

C₄²

#64541

yes

—

164

C₄²

D₄×D₁₉

yes

—

165

C₂³

#10597341

yes

characteristic

166

Q₈

—

167

Q₈

—

168

Q₈

—

152

—

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

#10597321

yes

characteristic

179

C₂×C₄

#10597328

yes

characteristic

180

C₂×C₄

#10597330

yes

—

181

C₂×C₄

#10597340

yes

—

182

C₈

—

183

C₈

—

184

C₈

—

152

—

185

C₂²

—

186

C₂²

—

187

C₂²

#11926462

yes

characteristic

188

C₂²

#11926820

yes

—

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

—

152

—

193

C₄

—

152

—

194

C₄

—

152

—

195

C₄

#11926719

yes

characteristic

196

C₄

#11926724

yes

characteristic

197

C₂

—

198

C₂

#14564865

yes

characteristic

199

C₂

#14564904

yes

characteristic

200

C₂

#14564942

yes

characteristic

	subgroup	G/H
center	C₂²	#11926462
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1290	C₂
socle	C₂²×C₁₉	#394
prime radical	C₂³×C₁₉	#121
hypercenter	#1290	D₁₉
hypocenter	C₁₉	#10517
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1290

subgroup

G/H

center

C₂²

#11926462

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1290

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1290

N	H ≅ G/N	type
140. C₁₉	#10517	semidirect

H ≅ G/N

type

140. C₁₉

#10517

semidirect

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

subgroup	index
#14574980	2
#14563754	2
#14562336	2
#14562148	2
C₁₉×#1290	2
#10517	19

subgroup

index

C₁₉×#1290

Subgroups — #18086639

Conjugacy classes of subgroups

Complements

Maximal subgroups