Group #18087604 — subgroups

Subgroups — #18087604

Order 4864.

410 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 149 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	#14564596	C₂	1	2	yes	maximal
2	#14564437	C₂	1	1	yes	maximal, characteristic
3	#14563795	C₂	1	1	yes	maximal, characteristic
4	#14563763	C₂	1	2	yes	maximal
5	C₁₉×#1273	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	C₂×#10597275	—	2	2	no	—
8	C₂×#10597273	—	2	2	no	—
9	#11926414	C₂²	1	1	yes	characteristic
10	#11926414	C₂²	1	2	yes	—
11	#11926307	—	2	4	no	—
12	#11926307	—	2	4	no	—
13	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
15	C₂²×Dic₃₈	—	2	1	no	—
16	C₂²×C₈×C₁₉	D₄	1	4	yes	—
17	C₂²×C₈×C₁₉	D₄	1	2	yes	—
18	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
19	C₂×C₄⋊Dic₁₉	—	2	2	no	—
20	C₂×C₄⋊Dic₁₉	—	2	1	no	—
21	C₂×C₄⋊Dic₁₉	—	2	2	no	—
22	C₂×C₄⋊Dic₁₉	—	2	2	no	—
23	C₂×C₄⋊Dic₁₉	—	2	2	no	—
24	C₂×C₄⋊Dic₁₉	—	2	2	no	—
25	#10597315	—	2	2	no	—
26	#10597315	—	2	1	no	—
27	#10597315	Q₈	1	2	yes	—
28	C₄×C₈×C₁₉	—	2	2	no	—
29	C₄×C₈×C₁₉	—	2	2	no	—
30	C₄×C₈×C₁₉	—	2	2	no	—
31	#10597275	—	4	4	no	—
32	#10597273	—	4	4	no	—
33	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
35	C₂²×Dic₁₉	—	4	1	no	—
36	C₂²×Dic₁₉	—	4	2	no	—
37	C₂²×Dic₁₉	—	4	1	no	—
38	C₂×Dic₃₈	—	2	2	no	—
39	C₂×Dic₃₈	—	4	2	no	—
40	C₂×Dic₃₈	—	4	2	no	—
41	C₂×Dic₃₈	—	4	1	no	—
42	C₂×C₈×C₁₉	—	2	2	no	—
43	C₂×C₈×C₁₉	—	2	2	no	—
44	C₂×C₈×C₁₉	—	2	4	no	—
45	C₂×C₈×C₁₉	—	2	4	no	—
46	C₂×C₈×C₁₉	—	2	4	no	—
47	C₂×C₈×C₁₉	D₈	1	4	yes	—
48	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
49	C₄²×C₁₉	#41	1	1	yes	characteristic
50	C₄²×C₁₉	#41	1	2	yes	—
51	C₄⋊Dic₁₉	—	2	4	no	—
52	C₄⋊Dic₁₉	—	4	2	no	—
53	C₄⋊Dic₁₉	—	4	2	no	—
54	C₄⋊Dic₁₉	—	4	4	no	—
55	C₄⋊Dic₁₉	—	4	4	no	—
56	C₄⋊Dic₁₉	—	4	4	no	—
57	C₄⋊Dic₁₉	—	4	4	no	—
58	#10676	—	19	1	no	maximal, Sylow
59	C₂³×C₁₉	#127	1	1	yes	characteristic
60	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
61	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
62	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#123	1	2	yes	—
64	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
65	C₂×C₄×C₁₉	#135	1	4	yes	—
66	C₂×C₄×C₁₉	#137	1	2	yes	—
67	C₂×C₄×C₁₉	#137	1	4	yes	—
68	C₂×Dic₁₉	—	4	2	no	—
69	C₂×Dic₁₉	—	8	1	no	—
70	C₂×Dic₁₉	—	8	1	no	—
71	C₂×Dic₁₉	—	8	2	no	—
72	C₂×Dic₁₉	—	8	1	no	—
73	C₂×Dic₁₉	—	8	2	no	—
74	C₂×Dic₁₉	—	8	2	no	—
75	C₂×Dic₁₉	—	8	2	no	—
76	Dic₃₈	—	4	4	no	—
77	Dic₃₈	—	8	2	no	—
78	C₈×C₁₉	—	2	4	no	—
79	C₈×C₁₉	—	4	4	no	—
80	#1990	—	19	2	no	—
81	#1956	—	19	1	no	—
82	#1845	—	19	1	no	—
83	#1834	—	19	2	no	—
84	#1273	D₁₉	1	1	yes	characteristic
85	C₂²×C₁₉	#399	1	1	yes	characteristic
86	C₂²×C₁₉	#493	1	1	yes	characteristic
87	C₂²×C₁₉	#495	1	2	yes	—
88	C₂²×C₁₉	#497	1	1	yes	characteristic
89	C₂²×C₁₉	#497	1	2	yes	—
90	C₄×C₁₉	#474	1	2	yes	—
91	C₄×C₁₉	#479	1	4	yes	—
92	C₄×C₁₉	#480	1	2	yes	—
93	C₄×C₁₉	#485	1	4	yes	—
94	Dic₁₉	—	8	2	no	—
95	Dic₁₉	—	16	2	no	—
96	Dic₁₉	—	16	1	no	—
97	C₂×C₄⋊Q₈	—	19	1	no	—
98	C₂×#107	—	38	2	no	—
99	C₂×#103	—	38	2	no	—
100	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
101	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
102	#384	—	19	1	no	—
103	#384	—	19	2	no	—
104	#340	—	38	4	no	—
105	#340	—	38	4	no	—
106	C₂×C₁₉	#1709	1	1	yes	characteristic
107	C₂×C₁₉	#1718	1	2	yes	—
108	C₂×C₁₉	#1722	1	1	yes	characteristic
109	C₂×C₁₉	#2093	1	1	yes	characteristic
110	C₂×C₁₉	#2097	1	2	yes	—
111	C₂²×Q₈	—	38	1	no	—
112	C₂²×C₈	D₇₆	1	4	yes	—
113	C₂²×C₈	D₇₆	1	2	yes	—
114	C₄⋊Q₈	—	19	2	no	—
115	C₄⋊Q₈	—	38	2	no	—
116	C₄⋊Q₈	—	38	1	no	—
117	C₂×C₄⋊C₄	—	38	2	no	—
118	C₂×C₄⋊C₄	—	38	2	no	—
119	C₂×C₄⋊C₄	—	38	2	no	—
120	C₂×C₄⋊C₄	—	38	2	no	—
121	C₂×C₄⋊C₄	—	38	1	no	—
122	C₂×C₄⋊C₄	—	38	2	no	—
123	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
124	#107	—	76	4	no	—
125	#103	—	76	4	no	—
126	C₄×C₈	—	2	2	no	—
127	C₄×C₈	—	2	2	no	—
128	C₄×C₈	—	2	2	no	—
129	C₁₉	#10676	1	1	yes	characteristic, complemented, Sylow
130	C₂×Q₈	—	38	2	no	—
131	C₂×Q₈	—	76	1	no	—
132	C₂×Q₈	—	76	2	no	—
133	C₂×Q₈	—	76	2	no	—
134	C₂²×C₄	—	76	1	no	—
135	C₂²×C₄	—	76	2	no	—
136	C₂²×C₄	—	76	1	no	—
137	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
138	C₂²×C₄	C₂×D₇₆	1	2	yes	—
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	—	2	2	no	—
141	C₂×C₈	—	2	4	no	—
142	C₂×C₈	—	2	4	no	—
143	C₂×C₈	—	2	4	no	—
144	C₂×C₈	D₁₅₂	1	4	yes	—
145	C₄⋊C₄	—	38	4	no	—
146	C₄⋊C₄	—	76	2	no	—
147	C₄⋊C₄	—	76	2	no	—
148	C₄⋊C₄	—	76	4	no	—
149	C₄⋊C₄	—	76	4	no	—
150	C₄⋊C₄	—	76	4	no	—
151	C₄⋊C₄	—	76	4	no	—
152	C₄²	#64543	1	2	yes	—
153	C₄²	#64543	1	1	yes	characteristic
154	C₄²	Q₈×D₁₉	1	1	yes	characteristic
155	C₂³	#10597320	1	1	yes	characteristic
156	Q₈	—	76	4	no	—
157	Q₈	—	152	2	no	—
158	C₂×C₄	—	76	2	no	—
159	C₂×C₄	—	152	2	no	—
160	C₂×C₄	—	152	1	no	—
161	C₂×C₄	—	152	2	no	—
162	C₂×C₄	—	152	2	no	—
163	C₂×C₄	—	152	2	no	—
164	C₂×C₄	—	152	1	no	—
165	C₂×C₄	—	152	1	no	—
166	C₂×C₄	#10597332	1	1	yes	characteristic
167	C₂×C₄	#10597332	1	2	yes	—
168	C₂×C₄	#10597343	1	1	yes	characteristic
169	C₂×C₄	#10597343	1	2	yes	—
170	C₂×C₄	C₂×D₁₅₂	1	2	yes	—
171	C₂×C₄	#10597350	1	4	yes	—
172	C₂×C₄	#10597355	1	2	yes	—
173	C₂×C₄	#10597355	1	4	yes	—
174	C₈	—	2	4	no	—
175	C₈	—	4	4	no	—
176	C₂²	#11926481	1	1	yes	characteristic
177	C₂²	#11926921	1	1	yes	characteristic
178	C₂²	#11926928	1	2	yes	—
179	C₂²	#11926938	1	1	yes	characteristic
180	C₂²	#11926938	1	2	yes	—
181	C₄	—	304	2	no	—
182	C₄	—	304	1	no	—
183	C₄	—	152	2	no	—
184	C₄	#11926825	1	2	yes	—
185	C₄	#11926852	1	4	yes	—
186	C₄	#11926858	1	2	yes	—
187	C₄	#11926886	1	4	yes	—
188	C₂	#14563241	1	1	yes	characteristic
189	C₂	#14563281	1	2	yes	—
190	C₂	#14563306	1	1	yes	characteristic
191	C₂	#14565162	1	1	yes	characteristic
192	C₂	#14565182	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564596

C₂

yes

maximal

#14564437

C₂

yes

maximal, characteristic

#14563795

C₂

yes

maximal, characteristic

#14563763

C₂

yes

maximal

C₁₉×#1273

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

—

—

C₂²

yes

characteristic

#11926414

C₂²

yes

—

#11926307

—

#11926307

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

#10597315

—

#10597315

—

#10597315

Q₈

yes

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

#10597275

—

#10597273

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

—

C₄²×C₁₉

C₂×Q₈

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

—

—

—

—

D₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#497

yes

characteristic

C₂²×C₁₉

#497

yes

—

C₄×C₁₉

#474

yes

—

C₄×C₁₉

#479

yes

—

C₄×C₁₉

#480

yes

—

C₄×C₁₉

#485

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

—

C₂×#107

—

C₂×#103

—

100

C₂×C₄×C₈

C₂×D₁₉

yes

—

101

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

102

#384

—

103

#384

—

104

#340

—

105

#340

—

106

C₂×C₁₉

#1709

yes

characteristic

107

C₂×C₁₉

#1718

yes

—

108

C₂×C₁₉

#1722

yes

characteristic

109

C₂×C₁₉

#2093

yes

characteristic

110

C₂×C₁₉

#2097

yes

—

111

C₂²×Q₈

—

112

C₂²×C₈

D₇₆

yes

—

113

C₂²×C₈

D₇₆

yes

—

114

C₄⋊Q₈

—

115

C₄⋊Q₈

—

116

C₄⋊Q₈

—

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

#107

—

125

#103

—

126

C₄×C₈

—

127

C₄×C₈

—

128

C₄×C₈

—

129

C₁₉

#10676

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

C₂×D₇₆

yes

characteristic

138

C₂²×C₄

C₂×D₇₆

yes

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

D₁₅₂

yes

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

147

C₄⋊C₄

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄²

#64543

yes

—

153

C₄²

#64543

yes

characteristic

154

C₄²

Q₈×D₁₉

yes

characteristic

155

C₂³

#10597320

yes

characteristic

156

Q₈

—

157

Q₈

—

152

—

158

C₂×C₄

—

159

C₂×C₄

—

152

—

160

C₂×C₄

—

152

—

161

C₂×C₄

—

152

—

162

C₂×C₄

—

152

—

163

C₂×C₄

—

152

—

164

C₂×C₄

—

152

—

165

C₂×C₄

—

152

—

166

C₂×C₄

#10597332

yes

characteristic

167

C₂×C₄

#10597332

yes

—

168

C₂×C₄

#10597343

yes

characteristic

169

C₂×C₄

#10597343

yes

—

170

C₂×C₄

C₂×D₁₅₂

yes

—

171

C₂×C₄

#10597350

yes

—

172

C₂×C₄

#10597355

yes

—

173

C₂×C₄

#10597355

yes

—

174

C₈

—

175

C₈

—

176

C₂²

#11926481

yes

characteristic

177

C₂²

#11926921

yes

characteristic

178

C₂²

#11926928

yes

—

179

C₂²

#11926938

yes

characteristic

180

C₂²

#11926938

yes

—

181

C₄

—

304

—

182

C₄

—

304

—

183

C₄

—

152

—

184

C₄

#11926825

yes

—

185

C₄

#11926852

yes

—

186

C₄

#11926858

yes

—

187

C₄

#11926886

yes

—

188

C₂

#14563241

yes

characteristic

189

C₂

#14563281

yes

—

190

C₂

#14563306

yes

characteristic

191

C₂

#14565162

yes

characteristic

192

C₂

#14565182

yes

—

	subgroup	G/H
center	C₂³	#10597320
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1273	C₂
socle, prime radical	C₂³×C₁₉	#127
hypercenter	#1273	D₁₉
hypocenter	C₁₉	#10676
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center

C₂³

#10597320

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1273

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
129. C₁₉	#10676	semidirect

H ≅ G/N

type

129. C₁₉

#10676

semidirect

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

subgroup	index
#14564596	2
#14564437	2
#14563795	2
#14563763	2
C₁₉×#1273	2
#10676	19

subgroup

index

C₁₉×#1273

Subgroups — #18087604

Conjugacy classes of subgroups

Complements

Maximal subgroups