Group #18087659 — subgroups

Subgroups — #18087659

Order 4864.

410 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 147 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	#14564597	C₂	1	2	yes	maximal
2	#14563792	C₂	1	1	yes	maximal, characteristic
3	#14563762	C₂	1	2	yes	maximal
4	C₁₉⋊#1273	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1956	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597274	—	2	2	no	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
8	#11926414	C₂²	1	2	yes	—
9	#11926306	—	2	4	no	—
10	#11926306	—	2	4	no	—
11	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#103	—	2	2	no	—
13	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#384	C₂²	1	1	yes	characteristic
15	C₂²×Q₈×C₁₉	—	2	1	no	—
16	C₂²×C₈×C₁₉	D₄	1	2	yes	—
17	C₁₉×C₄⋊Q₈	—	2	2	no	—
18	C₁₉×C₄⋊Q₈	—	2	1	no	—
19	C₁₉×C₄⋊Q₈	Q₈	1	2	yes	—
20	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
21	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
22	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉	—	2	2	no	—
25	C₂×C₄⋊Dic₁₉	—	2	2	no	—
26	C₂×C₄⋊Dic₁₉	—	2	2	no	—
27	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
28	C₁₉×#103	—	4	4	no	—
29	C₄×C₈×C₁₉	—	2	2	no	—
30	#10597274	—	4	4	no	—
31	C₄×C₁₉⋊C₈	—	2	2	no	—
32	C₄×C₁₉⋊C₈	—	2	2	no	—
33	C₂×Q₈×C₁₉	—	2	2	no	—
34	C₂×Q₈×C₁₉	—	4	1	no	—
35	C₂×Q₈×C₁₉	—	4	2	no	—
36	C₂×Q₈×C₁₉	—	4	2	no	—
37	C₂²×C₄×C₁₉	—	4	1	no	—
38	C₂²×C₄×C₁₉	—	4	1	no	—
39	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
40	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂²×Dic₁₉	—	4	2	no	—
42	C₂×C₈×C₁₉	—	2	2	no	—
43	C₂×C₈×C₁₉	—	2	2	no	—
44	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
45	C₄⋊C₄×C₁₉	—	2	4	no	—
46	C₄⋊C₄×C₁₉	—	4	2	no	—
47	C₄⋊C₄×C₁₉	—	4	2	no	—
48	C₄⋊C₄×C₁₉	—	4	4	no	—
49	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
50	C₄²×C₁₉	#41	1	1	yes	characteristic
51	C₄²×C₁₉	#41	1	2	yes	—
52	C₄⋊Dic₁₉	—	4	4	no	—
53	C₄⋊Dic₁₉	—	4	4	no	—
54	C₄⋊Dic₁₉	—	4	4	no	—
55	C₂×C₁₉⋊C₈	—	2	4	no	—
56	C₂×C₁₉⋊C₈	—	2	4	no	—
57	C₂×C₁₉⋊C₈	—	2	4	no	—
58	#10686	—	19	1	no	maximal, Sylow
59	C₂³×C₁₉	#127	1	1	yes	characteristic
60	Q₈×C₁₉	—	4	4	no	—
61	Q₈×C₁₉	—	8	2	no	—
62	C₂×C₄×C₁₉	—	4	2	no	—
63	C₂×C₄×C₁₉	—	8	1	no	—
64	C₂×C₄×C₁₉	—	8	1	no	—
65	C₂×C₄×C₁₉	—	8	1	no	—
66	C₂×C₄×C₁₉	—	8	2	no	—
67	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
68	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
69	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
70	C₂×C₄×C₁₉	#123	1	2	yes	—
71	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
72	C₂×C₄×C₁₉	#135	1	4	yes	—
73	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
74	C₂×C₄×C₁₉	#137	1	4	yes	—
75	C₂×Dic₁₉	—	8	2	no	—
76	C₂×Dic₁₉	—	8	2	no	—
77	C₂×Dic₁₉	—	8	2	no	—
78	C₈×C₁₉	—	2	4	no	—
79	C₁₉⋊C₈	—	4	4	no	—
80	#1990	—	19	2	no	—
81	#1956	D₁₉	1	1	yes	characteristic
82	#1844	—	19	1	no	—
83	#1834	—	19	2	no	—
84	#1273	—	19	1	no	—
85	C₂²×C₁₉	#399	1	1	yes	characteristic
86	C₂²×C₁₉	#492	1	1	yes	characteristic
87	C₂²×C₁₉	#495	1	2	yes	—
88	C₂²×C₁₉	#496	1	1	yes	characteristic
89	C₂²×C₁₉	#497	1	2	yes	—
90	C₄×C₁₉	—	8	2	no	—
91	C₄×C₁₉	—	16	1	no	—
92	C₄×C₁₉	#476	1	2	yes	—
93	C₄×C₁₉	#479	1	4	yes	—
94	C₄×C₁₉	#481	1	2	yes	—
95	C₄×C₁₉	#485	1	4	yes	—
96	Dic₁₉	—	16	2	no	—
97	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
98	C₂×#106	—	38	2	no	—
99	C₂×#103	—	2	2	no	—
100	C₂×C₄×C₈	—	19	2	no	—
101	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
102	#384	—	19	2	no	—
103	#384	C₂×D₁₉	1	1	yes	characteristic
104	#340	—	38	4	no	—
105	#340	—	38	4	no	—
106	C₂×C₁₉	#1708	1	1	yes	characteristic
107	C₂×C₁₉	#1716	1	1	yes	characteristic
108	C₂×C₁₉	#1719	1	2	yes	—
109	C₂×C₁₉	#2094	1	1	yes	characteristic
110	C₂×C₁₉	#2097	1	2	yes	—
111	C₂²×Q₈	—	2	1	no	—
112	C₂²×C₈	—	19	4	no	—
113	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
114	C₄⋊Q₈	—	2	1	no	—
115	C₄⋊Q₈	—	2	2	no	—
116	C₄⋊Q₈	Dic₃₈	1	2	yes	—
117	C₂×C₄⋊C₄	—	2	2	no	—
118	C₂×C₄⋊C₄	—	2	2	no	—
119	C₂×C₄⋊C₄	—	2	1	no	—
120	C₂×C₄⋊C₄	—	38	2	no	—
121	C₂×C₄⋊C₄	—	38	2	no	—
122	C₂×C₄⋊C₄	—	38	2	no	—
123	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
124	#106	—	76	4	no	—
125	#103	—	4	4	no	—
126	C₄×C₈	—	2	2	no	—
127	C₄×C₈	—	38	2	no	—
128	C₄×C₈	—	38	2	no	—
129	C₁₉	#10686	1	1	yes	characteristic, complemented, Sylow
130	C₂×Q₈	—	2	2	no	—
131	C₂×Q₈	—	4	1	no	—
132	C₂×Q₈	—	4	2	no	—
133	C₂×Q₈	—	4	2	no	—
134	C₂²×C₄	—	4	1	no	—
135	C₂²×C₄	—	4	1	no	—
136	C₂²×C₄	—	76	2	no	—
137	C₂²×C₄	D₄×D₁₉	1	2	yes	—
138	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	—	2	2	no	—
141	C₂×C₈	—	38	4	no	—
142	C₂×C₈	—	38	4	no	—
143	C₂×C₈	—	38	4	no	—
144	C₂×C₈	#64526	1	4	yes	—
145	C₄⋊C₄	—	2	4	no	—
146	C₄⋊C₄	—	4	2	no	—
147	C₄⋊C₄	—	4	2	no	—
148	C₄⋊C₄	—	4	4	no	—
149	C₄⋊C₄	—	76	4	no	—
150	C₄⋊C₄	—	76	4	no	—
151	C₄⋊C₄	—	76	4	no	—
152	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
153	C₄²	#64541	1	1	yes	characteristic
154	C₄²	#64543	1	2	yes	—
155	C₂³	#10597386	1	1	yes	characteristic
156	Q₈	—	4	4	no	—
157	Q₈	—	8	2	no	—
158	C₂×C₄	—	4	2	no	—
159	C₂×C₄	—	8	1	no	—
160	C₂×C₄	—	8	1	no	—
161	C₂×C₄	—	8	1	no	—
162	C₂×C₄	—	8	2	no	—
163	C₂×C₄	—	152	2	no	—
164	C₂×C₄	—	152	2	no	—
165	C₂×C₄	—	152	2	no	—
166	C₂×C₄	#10597324	1	2	yes	—
167	C₂×C₄	#10597329	1	2	yes	—
168	C₂×C₄	#10597362	1	4	yes	—
169	C₂×C₄	#10597364	1	4	yes	—
170	C₂×C₄	#10597370	1	1	yes	characteristic
171	C₂×C₄	C₂×#64526	1	2	yes	—
172	C₂×C₄	#10597381	1	1	yes	characteristic
173	C₂×C₄	#10597395	1	2	yes	—
174	C₈	—	2	4	no	—
175	C₈	—	76	4	no	—
176	C₂²	#11926480	1	1	yes	characteristic
177	C₂²	#11926916	1	1	yes	characteristic
178	C₂²	#11926925	1	2	yes	—
179	C₂²	#11926934	1	1	yes	characteristic
180	C₂²	#11926937	1	2	yes	—
181	C₄	—	8	2	no	—
182	C₄	—	16	1	no	—
183	C₄	—	304	2	no	—
184	C₄	#11926834	1	2	yes	—
185	C₄	#11926849	1	4	yes	—
186	C₄	#11926860	1	2	yes	—
187	C₄	#11926883	1	4	yes	—
188	C₂	#14563234	1	1	yes	characteristic
189	C₂	#14563266	1	1	yes	characteristic
190	C₂	#14563290	1	2	yes	—
191	C₂	#14565168	1	1	yes	characteristic
192	C₂	#14565185	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564597

C₂

yes

maximal

#14563792

C₂

yes

maximal, characteristic

#14563762

C₂

yes

maximal

C₁₉⋊#1273

C₂

yes

maximal, characteristic

C₁₉×#1956

C₂

yes

maximal, characteristic

C₂×#10597274

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926414

C₂²

yes

—

#11926306

—

#11926306

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×#103

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#384

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

Q₈

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

D₄

yes

—

C₁₉×#103

—

C₄×C₈×C₁₉

—

#10597274

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×Q₈

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1990

—

#1956

D₁₉

yes

—

—

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#496

yes

characteristic

C₂²×C₁₉

#497

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#476

yes

—

C₄×C₁₉

#479

yes

—

C₄×C₁₉

#481

yes

—

C₄×C₁₉

#485

yes

—

Dic₁₉

—

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

C₂×#106

—

C₂×#103

—

100

C₂×C₄×C₈

—

101

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

102

#384

—

103

#384

C₂×D₁₉

yes

characteristic

104

#340

—

105

#340

—

106

C₂×C₁₉

#1708

yes

characteristic

107

C₂×C₁₉

#1716

yes

characteristic

108

C₂×C₁₉

#1719

yes

—

109

C₂×C₁₉

#2094

yes

characteristic

110

C₂×C₁₉

#2097

yes

—

111

C₂²×Q₈

—

112

C₂²×C₈

—

113

C₂²×C₈

C₂²⋊D₁₉

yes

—

114

C₄⋊Q₈

—

115

C₄⋊Q₈

—

116

C₄⋊Q₈

Dic₃₈

yes

—

117

C₂×C₄⋊C₄

—

118

C₂×C₄⋊C₄

—

119

C₂×C₄⋊C₄

—

120

C₂×C₄⋊C₄

—

121

C₂×C₄⋊C₄

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄²

C₂²×D₁₉

yes

characteristic

124

#106

—

125

#103

—

126

C₄×C₈

—

127

C₄×C₈

—

128

C₄×C₈

—

129

C₁₉

#10686

yes

characteristic, complemented, Sylow

130

C₂×Q₈

—

131

C₂×Q₈

—

132

C₂×Q₈

—

133

C₂×Q₈

—

134

C₂²×C₄

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

D₄×D₁₉

yes

—

138

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

#64526

yes

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

147

C₄⋊C₄

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄²

C₂×Dic₃₈

yes

characteristic

153

C₄²

#64541

yes

characteristic

154

C₄²

#64543

yes

—

155

C₂³

#10597386

yes

characteristic

156

Q₈

—

157

Q₈

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

152

—

164

C₂×C₄

—

152

—

165

C₂×C₄

—

152

—

166

C₂×C₄

#10597324

yes

—

167

C₂×C₄

#10597329

yes

—

168

C₂×C₄

#10597362

yes

—

169

C₂×C₄

#10597364

yes

—

170

C₂×C₄

#10597370

yes

characteristic

171

C₂×C₄

C₂×#64526

yes

—

172

C₂×C₄

#10597381

yes

characteristic

173

C₂×C₄

#10597395

yes

—

174

C₈

—

175

C₈

—

176

C₂²

#11926480

yes

characteristic

177

C₂²

#11926916

yes

characteristic

178

C₂²

#11926925

yes

—

179

C₂²

#11926934

yes

characteristic

180

C₂²

#11926937

yes

—

181

C₄

—

182

C₄

—

183

C₄

—

304

—

184

C₄

#11926834

yes

—

185

C₄

#11926849

yes

—

186

C₄

#11926860

yes

—

187

C₄

#11926883

yes

—

188

C₂

#14563234

yes

characteristic

189

C₂

#14563266

yes

characteristic

190

C₂

#14563290

yes

—

191

C₂

#14565168

yes

characteristic

192

C₂

#14565185

yes

—

	subgroup	G/H
center	C₂³	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1956	C₂
socle, prime radical	C₂³×C₁₉	#127
hypercenter	#1956	D₁₉
hypocenter	C₁₉	#10686
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

subgroup

G/H

center

C₂³

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1956

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

N	H ≅ G/N	type
129. C₁₉	#10686	semidirect

H ≅ G/N

type

129. C₁₉

#10686

semidirect

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

subgroup	index
#14564597	2
#14563792	2
#14563762	2
C₁₉⋊#1273	2
C₁₉×#1956	2
#10686	19

subgroup

index

#14564597

#14563792

#14563762

C₁₉⋊#1273

C₁₉×#1956

#10686

Subgroups — #18087659

Conjugacy classes of subgroups

Complements

Maximal subgroups