Group #18087313 — subgroups

Subgroups — #18087313

Order 4864.

292 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 93 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	#14564616	C₂	1	1	yes	maximal, characteristic
2	#14562293	C₂	1	2	yes	maximal
3	#14561532	C₂	1	2	yes	maximal
4	#14561464	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1843	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	1	yes	characteristic
7	#11926597	C₂²	1	2	yes	—
8	#11926568	C₂²	1	1	yes	characteristic
9	#11926304	—	2	1	no	—
10	#11926304	—	2	1	no	—
11	#11926292	—	2	2	no	—
12	#11926289	—	2	2	no	—
13	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
14	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
15	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
16	C₁₉×#376	C₂²	1	1	yes	characteristic
17	C₂²×C₈×C₁₉	—	2	2	no	—
18	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	#10597372	—	2	1	no	—
22	#10597370	—	2	2	no	—
23	C₂×#64520	—	2	1	no	—
24	#10597316	—	2	1	no	—
25	#10597315	D₄	1	2	yes	—
26	C₄×Dic₃₈	—	2	2	no	—
27	C₁₉×C₄⋊C₈	—	2	2	no	—
28	C₁₉×C₄⋊C₈	—	2	2	no	—
29	C₁₉×C₄⋊C₈	—	4	2	no	—
30	C₁₉×C₄⋊C₈	—	4	2	no	—
31	C₁₉×#95	—	2	2	no	—
32	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
33	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
34	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
35	C₄×C₁₉⋊C₈	—	2	2	no	—
36	C₂²×C₄×C₁₉	—	2	1	no	—
37	C₂²×C₄×C₁₉	—	2	1	no	—
38	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	#41	1	2	yes	—
40	C₂×Dic₃₈	—	2	2	no	—
41	C₂×C₈×C₁₉	—	4	2	no	—
42	C₂×C₈×C₁₉	—	4	2	no	—
43	C₂×C₈×C₁₉	—	4	2	no	—
44	C₄²×C₁₉	—	2	1	no	—
45	C₄²×C₁₉	—	2	1	no	—
46	C₄²×C₁₉	SD₁₆	1	2	yes	—
47	C₄²×C₁₉	Q₁₆	1	2	yes	—
48	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₄²×C₁₉	#41	1	1	yes	characteristic
50	C₄²×C₁₉	#41	1	2	yes	—
51	C₂²⋊Dic₁₉	—	4	1	no	—
52	C₄⋊Dic₁₉	—	2	2	no	—
53	C₄⋊Dic₁₉	—	2	2	no	—
54	Dic₁₉⋊C₄	—	4	2	no	—
55	C₄×Dic₁₉	—	4	1	no	—
56	#64520	—	4	1	no	—
57	#64520	—	4	1	no	—
58	C₂×C₁₉⋊C₈	—	4	2	no	—
59	C₂×C₁₉⋊C₈	—	4	1	no	—
60	#10628	—	19	1	no	maximal, Sylow
61	C₂³×C₁₉	#123	1	1	yes	characteristic
62	C₂×C₄×C₁₉	—	2	2	no	—
63	C₂×C₄×C₁₉	—	2	2	no	—
64	C₂×C₄×C₁₉	—	4	2	no	—
65	C₂×C₄×C₁₉	—	4	2	no	—
66	C₂×C₄×C₁₉	—	4	2	no	—
67	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
68	C₂×C₄×C₁₉	#123	1	2	yes	—
69	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
70	C₂×C₄×C₁₉	#126	1	2	yes	—
71	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
72	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
73	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
74	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
75	C₂×Dic₁₉	—	4	2	no	—
76	Dic₃₈	—	8	2	no	—
77	C₈×C₁₉	—	8	2	no	—
78	C₁₉⋊C₈	—	8	2	no	—
79	C₁₉⋊C₈	—	8	1	no	—
80	#1995	—	19	1	no	—
81	#1843	D₁₉	1	1	yes	characteristic
82	#1542	—	19	2	no	—
83	#1301	—	19	2	no	—
84	#1274	—	19	1	no	—
85	C₂²×C₁₉	—	2	2	no	—
86	C₂²×C₁₉	#397	1	1	yes	characteristic
87	C₂²×C₁₉	#483	1	1	yes	characteristic
88	C₂²×C₁₉	#484	1	1	yes	characteristic
89	C₄×C₁₉	—	2	2	no	—
90	C₄×C₁₉	—	2	2	no	—
91	C₄×C₁₉	—	4	2	no	—
92	C₄×C₁₉	—	4	2	no	—
93	C₄×C₁₉	#460	1	1	yes	characteristic
94	C₄×C₁₉	#462	1	1	yes	characteristic
95	C₄×C₁₉	#487	1	1	yes	characteristic
96	C₄×C₁₉	#489	1	1	yes	characteristic
97	Dic₁₉	—	8	2	no	—
98	#533	—	19	1	no	—
99	#431	—	19	2	no	—
100	#423	—	19	1	no	—
101	C₂×C₄⋊C₈	—	2	1	no	—
102	C₂×C₄⋊C₈	—	2	1	no	—
103	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
104	#376	C₂×D₁₉	1	1	yes	characteristic
105	#339	—	38	1	no	—
106	#339	—	38	1	no	—
107	#333	—	38	2	no	—
108	#332	—	38	2	no	—
109	C₂×C₁₉	—	2	1	no	—
110	C₂×C₁₉	—	2	1	no	—
111	C₂×C₁₉	#2072	1	1	yes	characteristic
112	C₂×C₁₉	#2080	1	2	yes	—
113	C₂×M₁₆	—	38	1	no	—
114	C₂²×C₈	—	2	2	no	—
115	C₄⋊Q₈	—	19	2	no	—
116	#125	—	38	1	no	—
117	C₂²⋊Q₈	—	38	2	no	—
118	C₄×Q₈	—	38	2	no	—
119	#117	—	38	1	no	—
120	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
121	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
122	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
123	C₄⋊C₈	—	2	2	no	—
124	C₄⋊C₈	—	2	2	no	—
125	C₄⋊C₈	—	4	2	no	—
126	C₄⋊C₈	—	4	2	no	—
127	C₄⋊C₈	—	38	2	no	—
128	C₄⋊C₈	—	38	2	no	—
129	C₂²⋊C₈	—	38	2	no	—
130	C₄×C₈	—	38	2	no	—
131	#95	—	2	2	no	—
132	C₁₉	#10628	1	1	yes	characteristic, complemented, Sylow
133	C₂×Q₈	—	38	2	no	—
134	C₂²×C₄	—	2	1	no	—
135	C₂²×C₄	—	2	1	no	—
136	C₂²×C₄	#64541	1	2	yes	—
137	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
138	M₁₆	—	76	1	no	—
139	M₁₆	—	76	1	no	—
140	C₂×C₈	—	4	2	no	—
141	C₂×C₈	—	4	2	no	—
142	C₂×C₈	—	4	2	no	—
143	C₂×C₈	—	76	1	no	—
144	C₂×C₈	—	76	2	no	—
145	C₄⋊C₄	—	38	2	no	—
146	C₄⋊C₄	—	38	2	no	—
147	C₄⋊C₄	—	76	2	no	—
148	C₂²⋊C₄	—	76	1	no	—
149	C₄²	—	2	1	no	—
150	C₄²	—	2	1	no	—
151	C₄²	—	76	1	no	—
152	C₄²	#64526	1	2	yes	—
153	C₄²	#64528	1	2	yes	—
154	C₄²	D₄×D₁₉	1	1	yes	characteristic
155	C₄²	#64543	1	1	yes	characteristic
156	C₄²	#64545	1	2	yes	—
157	C₂³	#10597375	1	1	yes	characteristic
158	Q₈	—	152	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	4	2	no	—
162	C₂×C₄	—	4	2	no	—
163	C₂×C₄	—	4	2	no	—
164	C₂×C₄	—	76	2	no	—
165	C₂×C₄	#10597340	1	2	yes	—
166	C₂×C₄	#10597344	1	2	yes	—
167	C₂×C₄	#10597378	1	1	yes	characteristic
168	C₂×C₄	C₂×#64526	1	1	yes	characteristic
169	C₂×C₄	#10597384	1	1	yes	characteristic
170	C₂×C₄	#10597388	1	1	yes	characteristic
171	C₂×C₄	C₂×#64528	1	1	yes	characteristic
172	C₂×C₄	#10597393	1	1	yes	characteristic
173	C₈	—	8	2	no	—
174	C₈	—	152	2	no	—
175	C₈	—	152	1	no	—
176	C₂²	—	2	2	no	—
177	C₂²	#11926470	1	1	yes	characteristic
178	C₂²	#11926874	1	1	yes	characteristic
179	C₂²	#11926879	1	1	yes	characteristic
180	C₄	—	2	2	no	—
181	C₄	—	2	2	no	—
182	C₄	—	4	2	no	—
183	C₄	—	4	2	no	—
184	C₄	—	152	2	no	—
185	C₄	#11926741	1	1	yes	characteristic
186	C₄	#11926751	1	1	yes	characteristic
187	C₄	#11926896	1	1	yes	characteristic
188	C₄	#11926906	1	1	yes	characteristic
189	C₂	—	2	1	no	—
190	C₂	—	2	1	no	—
191	C₂	#14565044	1	1	yes	characteristic
192	C₂	#14565086	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564616

C₂

yes

maximal, characteristic

#14562293

C₂

yes

maximal

#14561532

C₂

yes

maximal

#14561464

C₂

yes

maximal, characteristic

C₁₉×#1843

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

characteristic

#11926597

C₂²

yes

—

#11926568

C₂²

yes

—

—

—

—

C₂×C₁₉×C₄⋊C₈

—

C₂×C₁₉×C₄⋊C₈

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×#376

C₂²

yes

characteristic

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

—

D₄

yes

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

Q₁₆

yes

—

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#121

yes

characteristic

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

#126

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₁₆

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1995

—

#1843

D₁₉

yes

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

#533

—

#431

—

100

#423

—

101

C₂×C₄⋊C₈

—

102

C₂×C₄⋊C₈

—

103

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

104

#376

C₂×D₁₉

yes

characteristic

105

#339

—

106

#339

—

107

#333

—

108

#332

—

109

C₂×C₁₉

—

110

C₂×C₁₉

—

111

C₂×C₁₉

#2072

yes

characteristic

112

C₂×C₁₉

#2080

yes

—

113

C₂×M₁₆

—

114

C₂²×C₈

—

115

C₄⋊Q₈

—

116

#125

—

117

C₂²⋊Q₈

—

118

C₄×Q₈

—

119

#117

—

120

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

121

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

122

C₂×C₄²

C₂²×D₁₉

yes

characteristic

123

C₄⋊C₈

—

124

C₄⋊C₈

—

125

C₄⋊C₈

—

126

C₄⋊C₈

—

127

C₄⋊C₈

—

128

C₄⋊C₈

—

129

C₂²⋊C₈

—

130

C₄×C₈

—

131

#95

—

132

C₁₉

#10628

yes

characteristic, complemented, Sylow

133

C₂×Q₈

—

134

C₂²×C₄

—

135

C₂²×C₄

—

136

C₂²×C₄

#64541

yes

—

137

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

138

M₁₆

—

139

M₁₆

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

147

C₄⋊C₄

—

148

C₂²⋊C₄

—

149

C₄²

—

150

C₄²

—

151

C₄²

—

152

C₄²

#64526

yes

—

153

C₄²

#64528

yes

—

154

C₄²

D₄×D₁₉

yes

characteristic

155

C₄²

#64543

yes

characteristic

156

C₄²

#64545

yes

—

157

C₂³

#10597375

yes

characteristic

158

Q₈

—

152

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

#10597340

yes

—

166

C₂×C₄

#10597344

yes

—

167

C₂×C₄

#10597378

yes

characteristic

168

C₂×C₄

C₂×#64526

yes

characteristic

169

C₂×C₄

#10597384

yes

characteristic

170

C₂×C₄

#10597388

yes

characteristic

171

C₂×C₄

C₂×#64528

yes

characteristic

172

C₂×C₄

#10597393

yes

characteristic

173

C₈

—

174

C₈

—

152

—

175

C₈

—

152

—

176

C₂²

—

177

C₂²

#11926470

yes

characteristic

178

C₂²

#11926874

yes

characteristic

179

C₂²

#11926879

yes

characteristic

180

C₄

—

181

C₄

—

182

C₄

—

183

C₄

—

184

C₄

—

152

—

185

C₄

#11926741

yes

characteristic

186

C₄

#11926751

yes

characteristic

187

C₄

#11926896

yes

characteristic

188

C₄

#11926906

yes

characteristic

189

C₂

—

190

C₂

—

191

C₂

#14565044

yes

characteristic

192

C₂

#14565086

yes

—

	subgroup	G/H
center	C₂×C₄	#10597393
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1843	C₂
socle	C₂²×C₁₉	#397
prime radical	C₂³×C₁₉	#123
hypercenter	#1843	D₁₉
hypocenter	C₁₉	#10628
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1843

subgroup

G/H

center

C₂×C₄

#10597393

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1843

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1843

N	H ≅ G/N	type
132. C₁₉	#10628	semidirect

H ≅ G/N

type

132. C₁₉

#10628

semidirect

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

subgroup	index
#14564616	2
#14562293	2
#14561532	2
#14561464	2
C₁₉×#1843	2
#10628	19

subgroup

index

C₁₉×#1843

Subgroups — #18087313

Conjugacy classes of subgroups

Complements

Maximal subgroups