Group #18087655 — subgroups

Subgroups — #18087655

Order 4864.

442 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 165 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	#14563792	C₂	1	1	yes	maximal, characteristic
4	#14563792	C₂	1	2	yes	maximal
5	C₁₉×#1273	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	C₂×#10597274	—	2	2	no	—
8	C₂×#10597274	—	2	4	no	—
9	C₂×#10597273	—	2	2	no	—
10	#11926414	C₂²	1	1	yes	characteristic
11	#11926414	C₂²	1	2	yes	—
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	2	yes	—
17	C₂²×C₈×C₁₉	D₄	1	4	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	#10597274	—	4	4	no	—
32	#10597274	—	4	8	no	—
33	#10597273	—	4	4	no	—
34	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
36	C₂²×Dic₁₉	—	4	1	no	—
37	C₂²×Dic₁₉	—	4	1	no	—
38	C₂²×Dic₁₉	—	4	2	no	—
39	C₂×Dic₃₈	—	2	2	no	—
40	C₂×Dic₃₈	—	4	2	no	—
41	C₂×Dic₃₈	—	4	2	no	—
42	C₂×Dic₃₈	—	4	1	no	—
43	C₂×C₈×C₁₉	—	2	2	no	—
44	C₂×C₈×C₁₉	—	2	4	no	—
45	C₂×C₈×C₁₉	—	2	2	no	—
46	C₂×C₈×C₁₉	—	2	4	no	—
47	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
48	C₂×C₈×C₁₉	SD₁₆	1	8	yes	—
49	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
50	C₄²×C₁₉	#41	1	2	yes	—
51	C₄²×C₁₉	#41	1	1	yes	characteristic
52	C₄⋊Dic₁₉	—	2	4	no	—
53	C₄⋊Dic₁₉	—	4	2	no	—
54	C₄⋊Dic₁₉	—	4	2	no	—
55	C₄⋊Dic₁₉	—	4	4	no	—
56	C₄⋊Dic₁₉	—	4	4	no	—
57	C₄⋊Dic₁₉	—	4	4	no	—
58	C₄⋊Dic₁₉	—	4	4	no	—
59	#10685	—	19	1	no	maximal, Sylow
60	C₂³×C₁₉	#127	1	1	yes	characteristic
61	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
62	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#123	1	2	yes	—
65	C₂×C₄×C₁₉	C₂×SD₁₆	1	4	yes	—
66	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
67	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
68	C₂×C₄×C₁₉	#137	1	4	yes	—
69	C₂×Dic₁₉	—	4	2	no	—
70	C₂×Dic₁₉	—	8	1	no	—
71	C₂×Dic₁₉	—	8	1	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	C₂×Dic₁₉	—	8	2	no	—
77	Dic₃₈	—	4	4	no	—
78	Dic₃₈	—	8	2	no	—
79	C₈×C₁₉	—	2	4	no	—
80	C₈×C₁₉	—	2	8	no	—
81	#1990	—	19	2	no	—
82	#1956	—	19	1	no	—
83	#1844	—	19	2	no	—
84	#1844	—	19	1	no	—
85	#1273	D₁₉	1	1	yes	characteristic
86	C₂²×C₁₉	#399	1	1	yes	characteristic
87	C₂²×C₁₉	#492	1	1	yes	characteristic
88	C₂²×C₁₉	#492	1	2	yes	—
89	C₂²×C₁₉	#496	1	1	yes	characteristic
90	C₂²×C₁₉	#497	1	2	yes	—
91	C₄×C₁₉	#475	1	4	yes	—
92	C₄×C₁₉	#476	1	2	yes	—
93	C₄×C₁₉	#481	1	2	yes	—
94	C₄×C₁₉	#483	1	4	yes	—
95	Dic₁₉	—	8	2	no	—
96	Dic₁₉	—	16	1	no	—
97	Dic₁₉	—	16	2	no	—
98	C₂×C₄⋊Q₈	—	19	1	no	—
99	C₂×#106	—	38	2	no	—
100	C₂×#106	—	38	4	no	—
101	C₂×#103	—	38	2	no	—
102	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
103	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
104	#384	—	19	1	no	—
105	#384	—	19	2	no	—
106	#340	—	38	4	no	—
107	C₂×C₁₉	#1705	1	1	yes	characteristic
108	C₂×C₁₉	#1714	1	2	yes	—
109	C₂×C₁₉	#1716	1	1	yes	characteristic
110	C₂×C₁₉	#2094	1	1	yes	characteristic
111	C₂×C₁₉	#2096	1	2	yes	—
112	C₂²×Q₈	—	38	1	no	—
113	C₂²×C₈	D₇₆	1	4	yes	—
114	C₂²×C₈	D₇₆	1	2	yes	—
115	C₄⋊Q₈	—	19	2	no	—
116	C₄⋊Q₈	—	38	2	no	—
117	C₄⋊Q₈	—	38	1	no	—
118	C₂×C₄⋊C₄	—	38	2	no	—
119	C₂×C₄⋊C₄	—	38	2	no	—
120	C₂×C₄⋊C₄	—	38	1	no	—
121	C₂×C₄⋊C₄	—	38	2	no	—
122	C₂×C₄⋊C₄	—	38	2	no	—
123	C₂×C₄⋊C₄	—	38	2	no	—
124	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
125	#106	—	76	4	no	—
126	#106	—	76	8	no	—
127	#103	—	76	4	no	—
128	C₄×C₈	—	2	2	no	—
129	C₄×C₈	—	2	2	no	—
130	C₄×C₈	—	2	2	no	—
131	C₁₉	#10685	1	1	yes	characteristic, complemented, Sylow
132	C₂×Q₈	—	38	2	no	—
133	C₂×Q₈	—	76	1	no	—
134	C₂×Q₈	—	76	2	no	—
135	C₂×Q₈	—	76	2	no	—
136	C₂²×C₄	—	76	1	no	—
137	C₂²×C₄	—	76	1	no	—
138	C₂²×C₄	—	76	2	no	—
139	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
140	C₂²×C₄	C₂×D₇₆	1	2	yes	—
141	C₂×C₈	—	2	2	no	—
142	C₂×C₈	—	2	4	no	—
143	C₂×C₈	—	2	2	no	—
144	C₂×C₈	—	2	4	no	—
145	C₂×C₈	#64516	1	4	yes	—
146	C₂×C₈	#64516	1	8	yes	—
147	C₄⋊C₄	—	38	4	no	—
148	C₄⋊C₄	—	76	2	no	—
149	C₄⋊C₄	—	76	2	no	—
150	C₄⋊C₄	—	76	4	no	—
151	C₄⋊C₄	—	76	4	no	—
152	C₄⋊C₄	—	76	4	no	—
153	C₄⋊C₄	—	76	4	no	—
154	C₄²	#64543	1	2	yes	—
155	C₄²	#64543	1	1	yes	characteristic
156	C₄²	Q₈×D₁₉	1	1	yes	characteristic
157	C₂³	#10597320	1	1	yes	characteristic
158	Q₈	—	76	4	no	—
159	Q₈	—	152	2	no	—
160	C₂×C₄	—	76	2	no	—
161	C₂×C₄	—	152	1	no	—
162	C₂×C₄	—	152	2	no	—
163	C₂×C₄	—	152	2	no	—
164	C₂×C₄	—	152	2	no	—
165	C₂×C₄	—	152	2	no	—
166	C₂×C₄	—	152	1	no	—
167	C₂×C₄	—	152	1	no	—
168	C₂×C₄	#10597332	1	1	yes	characteristic
169	C₂×C₄	#10597332	1	2	yes	—
170	C₂×C₄	#10597343	1	2	yes	—
171	C₂×C₄	#10597343	1	1	yes	characteristic
172	C₂×C₄	C₂×#64516	1	4	yes	—
173	C₂×C₄	C₂×#64516	1	2	yes	—
174	C₂×C₄	#10597354	1	2	yes	—
175	C₂×C₄	#10597355	1	4	yes	—
176	C₈	—	2	4	no	—
177	C₈	—	2	8	no	—
178	C₂²	#11926481	1	1	yes	characteristic
179	C₂²	#11926917	1	1	yes	characteristic
180	C₂²	#11926917	1	2	yes	—
181	C₂²	#11926933	1	1	yes	characteristic
182	C₂²	#11926938	1	2	yes	—
183	C₄	—	304	1	no	—
184	C₄	—	304	2	no	—
185	C₄	—	152	2	no	—
186	C₄	#11926830	1	4	yes	—
187	C₄	#11926835	1	2	yes	—
188	C₄	#11926863	1	2	yes	—
189	C₄	#11926875	1	4	yes	—
190	C₂	#14563222	1	1	yes	characteristic
191	C₂	#14563257	1	2	yes	—
192	C₂	#14563268	1	1	yes	characteristic
193	C₂	#14565167	1	1	yes	characteristic
194	C₂	#14565177	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564596

C₂

yes

maximal

#14564437

C₂

yes

maximal, characteristic

#14563792

C₂

yes

maximal, characteristic

#14563792

C₂

yes

maximal

C₁₉×#1273

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

—

—

—

C₂²

yes

characteristic

#11926414

C₂²

yes

—

#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

—

#10597274

—

#10597274

—

#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

SD₁₆

yes

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

—

C₂³×C₁₉

yes

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

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

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

#496

yes

characteristic

C₂²×C₁₉

#497

yes

—

C₄×C₁₉

#475

yes

—

C₄×C₁₉

#476

yes

—

C₄×C₁₉

#481

yes

—

C₄×C₁₉

#483

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

—

C₂×#106

—

100

C₂×#106

—

101

C₂×#103

—

102

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

103

C₂×C₄×C₈

C₂×D₁₉

yes

—

104

#384

—

105

#384

—

106

#340

—

107

C₂×C₁₉

#1705

yes

characteristic

108

C₂×C₁₉

#1714

yes

—

109

C₂×C₁₉

#1716

yes

characteristic

110

C₂×C₁₉

#2094

yes

characteristic

111

C₂×C₁₉

#2096

yes

—

112

C₂²×Q₈

—

113

C₂²×C₈

D₇₆

yes

—

114

C₂²×C₈

D₇₆

yes

—

115

C₄⋊Q₈

—

116

C₄⋊Q₈

—

117

C₄⋊Q₈

—

118

C₂×C₄⋊C₄

—

119

C₂×C₄⋊C₄

—

120

C₂×C₄⋊C₄

—

121

C₂×C₄⋊C₄

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

—

124

C₂×C₄²

C₂²×D₁₉

yes

characteristic

125

#106

—

126

#106

—

127

#103

—

128

C₄×C₈

—

129

C₄×C₈

—

130

C₄×C₈

—

131

C₁₉

#10685

yes

characteristic, complemented, Sylow

132

C₂×Q₈

—

133

C₂×Q₈

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

C₂×D₇₆

yes

characteristic

140

C₂²×C₄

C₂×D₇₆

yes

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

#64516

yes

—

146

C₂×C₈

#64516

yes

—

147

C₄⋊C₄

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄⋊C₄

—

154

C₄²

#64543

yes

—

155

C₄²

#64543

yes

characteristic

156

C₄²

Q₈×D₁₉

yes

characteristic

157

C₂³

#10597320

yes

characteristic

158

Q₈

—

159

Q₈

—

152

—

160

C₂×C₄

—

161

C₂×C₄

—

152

—

162

C₂×C₄

—

152

—

163

C₂×C₄

—

152

—

164

C₂×C₄

—

152

—

165

C₂×C₄

—

152

—

166

C₂×C₄

—

152

—

167

C₂×C₄

—

152

—

168

C₂×C₄

#10597332

yes

characteristic

169

C₂×C₄

#10597332

yes

—

170

C₂×C₄

#10597343

yes

—

171

C₂×C₄

#10597343

yes

characteristic

172

C₂×C₄

C₂×#64516

yes

—

173

C₂×C₄

C₂×#64516

yes

—

174

C₂×C₄

#10597354

yes

—

175

C₂×C₄

#10597355

yes

—

176

C₈

—

177

C₈

—

178

C₂²

#11926481

yes

characteristic

179

C₂²

#11926917

yes

characteristic

180

C₂²

#11926917

yes

—

181

C₂²

#11926933

yes

characteristic

182

C₂²

#11926938

yes

—

183

C₄

—

304

—

184

C₄

—

304

—

185

C₄

—

152

—

186

C₄

#11926830

yes

—

187

C₄

#11926835

yes

—

188

C₄

#11926863

yes

—

189

C₄

#11926875

yes

—

190

C₂

#14563222

yes

characteristic

191

C₂

#14563257

yes

—

192

C₂

#14563268

yes

characteristic

193

C₂

#14565167

yes

characteristic

194

C₂

#14565177

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	#10685
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
131. C₁₉	#10685	semidirect

H ≅ G/N

type

131. C₁₉

#10685

semidirect

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

subgroup	index
#14564596	2
#14564437	2
#14563792	2
C₁₉×#1273	2
#10685	19

subgroup

index

C₁₉×#1273

Subgroups — #18087655

Conjugacy classes of subgroups

Complements

Maximal subgroups