Group #18082376 — subgroups

Subgroups — #18082376

Order 4864.

710 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 710 conjugacy classes of subgroups — too many to draw. Only its 191 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	C₂×#11926921	C₂	1	1	yes	maximal, characteristic
2	#14564440	C₂	1	4	yes	maximal, complemented
3	C₂×#11926265	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1844	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₁₅₂	—	2	2	no	—
6	C₂×#10597320	C₂²	1	2	yes	—
7	#11926921	—	2	2	no	—
8	#11926921	C₄	1	4	yes	complemented
9	C₂×#10597266	—	2	8	no	—
10	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
11	#11926265	—	2	2	no	—
12	C₂×C₁₉×#106	—	2	2	no	—
13	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#384	C₂²	1	2	yes	—
15	C₂²×D₇₆	—	2	4	no	—
16	C₂²×D₇₆	—	2	2	no	—
17	C₂²×C₈×C₁₉	D₄	1	2	yes	—
18	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
19	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
22	C₂×D₁₅₂	—	2	8	no	—
23	C₂×D₁₅₂	—	4	4	no	—
24	C₂×D₁₅₂	—	4	4	no	—
25	#10597320	—	2	2	no	—
26	#10597320	—	2	4	no	—
27	#10597320	C₂×C₄	1	4	yes	—
28	C₁₉×#106	—	4	4	no	—
29	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
30	C₄×C₈×C₁₉	D₄	1	2	yes	—
31	#10597266	—	4	16	no	—
32	C₄×C₁₉⋊C₈	—	2	2	no	—
33	C₄×C₁₉⋊C₈	—	2	2	no	—
34	C₂³×D₁₉	—	4	2	no	—
35	C₂²×C₄×C₁₉	—	4	2	no	—
36	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
37	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂×D₇₆	—	2	4	no	—
39	C₂×D₇₆	—	2	8	no	—
40	C₂×D₇₆	—	4	4	no	—
41	C₂×D₇₆	—	4	4	no	—
42	C₂×D₇₆	—	4	8	no	—
43	C₂×D₇₆	—	4	8	no	—
44	C₂×D₇₆	—	4	4	no	—
45	C₂×D₇₆	—	4	2	no	—
46	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
47	C₂×C₈×C₁₉	D₈	1	4	yes	—
48	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
49	C₄⋊C₄×C₁₉	—	4	4	no	—
50	C₄⋊C₄×C₁₉	—	4	8	no	—
51	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₄²×C₁₉	#41	1	2	yes	—
54	C₂×C₁₉⋊C₈	—	2	4	no	—
55	C₂×C₁₉⋊C₈	—	2	8	no	—
56	D₁₅₂	—	4	16	no	—
57	#9837	—	19	1	no	maximal, Sylow
58	C₂³×C₁₉	#127	1	1	yes	characteristic
59	C₂²×D₁₉	—	4	4	no	—
60	C₂²×D₁₉	—	8	2	no	—
61	C₂²×D₁₉	—	8	2	no	—
62	C₂²×D₁₉	—	8	4	no	—
63	C₂²×D₁₉	—	8	4	no	—
64	C₂×C₄×C₁₉	—	8	2	no	—
65	C₂×C₄×C₁₉	—	8	4	no	—
66	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
68	C₂×C₄×C₁₉	#121	1	2	yes	—
69	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
70	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
71	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
72	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	8	yes	—
73	D₇₆	—	4	8	no	—
74	D₇₆	—	4	16	no	—
75	D₇₆	—	8	8	no	—
76	D₇₆	—	8	4	no	—
77	C₈×C₁₉	#102	1	8	yes	complemented
78	C₁₉⋊C₈	—	4	4	no	—
79	C₂×#493	—	19	1	no	—
80	#1957	—	19	4	no	—
81	#1844	D₁₉	1	1	yes	characteristic, complemented
82	C₂×#322	—	19	1	no	—
83	C₂²×C₁₉	#390	1	1	yes	characteristic
84	C₂²×C₁₉	#492	1	1	yes	characteristic
85	C₂²×C₁₉	#493	1	1	yes	characteristic
86	C₂²×C₁₉	#496	1	4	yes	—
87	C₂×D₁₉	—	8	4	no	—
88	C₂×D₁₉	—	8	8	no	—
89	C₂×D₁₉	—	16	2	no	—
90	C₂×D₁₉	—	16	2	no	—
91	C₂×D₁₉	—	16	4	no	—
92	C₄×C₁₉	—	16	2	no	—
93	C₄×C₁₉	C₂×#102	1	2	yes	—
94	C₄×C₁₉	#442	1	4	yes	—
95	C₄×C₁₉	#469	1	4	yes	—
96	C₄×C₁₉	#486	1	2	yes	—
97	C₂²×D₈	—	38	2	no	—
98	C₂×#127	—	19	2	no	—
99	#493	—	19	4	no	—
100	#493	—	38	2	no	—
101	C₂×#106	—	2	2	no	—
102	C₂×#102	—	38	8	no	—
103	C₂×C₄×C₈	—	19	2	no	—
104	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
105	#384	C₂×D₁₉	1	2	yes	—
106	#322	—	38	2	no	—
107	C₂×C₁₉	#1715	1	2	yes	—
108	C₂×C₁₉	#1721	1	2	yes	—
109	C₂×C₁₉	#1957	1	1	yes	characteristic
110	C₂×C₁₉	#1972	1	2	yes	—
111	D₁₉	—	16	4	no	—
112	C₂²×D₄	—	38	4	no	—
113	C₂²×D₄	—	38	2	no	—
114	C₂×D₈	—	38	8	no	—
115	C₂×D₈	—	76	4	no	—
116	C₂×D₈	—	76	4	no	—
117	C₂²×C₈	—	19	4	no	—
118	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
119	#127	—	19	4	no	—
120	#127	—	38	2	no	—
121	#127	—	38	4	no	—
122	C₂×C₄⋊C₄	—	2	4	no	—
123	C₂×C₄⋊C₄	—	2	2	no	—
124	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
125	#106	—	4	4	no	—
126	#102	—	76	16	no	—
127	C₄×C₈	—	38	2	no	—
128	C₄×C₈	—	38	2	no	—
129	C₄×C₈	C₄×D₁₉	1	2	yes	—
130	C₄×C₈	D₇₆	1	2	yes	—
131	C₁₉	#9837	1	1	yes	characteristic, complemented, Sylow
132	C₂⁴	—	76	2	no	—
133	C₂×D₄	—	38	8	no	—
134	C₂×D₄	—	38	4	no	—
135	C₂×D₄	—	76	4	no	—
136	C₂×D₄	—	76	4	no	—
137	C₂×D₄	—	76	2	no	—
138	C₂×D₄	—	76	4	no	—
139	C₂×D₄	—	76	8	no	—
140	C₂×D₄	—	76	8	no	—
141	C₂²×C₄	—	4	2	no	—
142	C₂²×C₄	D₄×D₁₉	1	2	yes	—
143	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
144	D₈	—	76	16	no	—
145	C₂×C₈	—	38	4	no	—
146	C₂×C₈	—	38	8	no	—
147	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
148	C₂×C₈	#64525	1	4	yes	—
149	C₂×C₈	#64527	1	4	yes	—
150	C₄⋊C₄	—	4	4	no	—
151	C₄⋊C₄	—	4	8	no	—
152	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
153	C₄²	C₂×D₇₆	1	1	yes	characteristic
154	C₄²	#64545	1	2	yes	—
155	C₂³	—	76	4	no	—
156	C₂³	—	152	2	no	—
157	C₂³	—	152	2	no	—
158	C₂³	—	152	4	no	—
159	C₂³	—	152	4	no	—
160	C₂³	#10597386	1	1	yes	characteristic
161	D₄	—	76	8	no	—
162	D₄	—	76	16	no	—
163	D₄	—	152	8	no	—
164	D₄	—	152	4	no	—
165	C₂×C₄	—	8	2	no	—
166	C₂×C₄	—	8	4	no	—
167	C₂×C₄	#10597339	1	2	yes	—
168	C₂×C₄	#10597341	1	2	yes	—
169	C₂×C₄	#10597360	1	8	yes	—
170	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
171	C₂×C₄	C₂×#64525	1	2	yes	—
172	C₂×C₄	C₂×#64527	1	2	yes	—
173	C₂×C₄	#10597393	1	1	yes	characteristic
174	C₈	—	76	4	no	—
175	C₈	#10597266	1	8	yes	complemented
176	C₂²	—	304	2	no	—
177	C₂²	—	304	2	no	—
178	C₂²	—	304	4	no	—
179	C₂²	—	152	4	no	—
180	C₂²	—	152	8	no	—
181	C₂²	#11926445	1	1	yes	characteristic
182	C₂²	#11926918	1	1	yes	characteristic
183	C₂²	#11926920	1	1	yes	characteristic
184	C₂²	#11926930	1	4	yes	—
185	C₄	—	16	2	no	—
186	C₄	C₂×#10597266	1	2	yes	—
187	C₄	#11926655	1	4	yes	—
188	C₄	#11926798	1	4	yes	—
189	C₄	#11926892	1	2	yes	—
190	C₂	—	304	4	no	—
191	C₂	#14563264	1	2	yes	—
192	C₂	#14563299	1	2	yes	—
193	C₂	#14564440	1	1	yes	characteristic
194	C₂	#14564509	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926921

C₂

yes

maximal, characteristic

#14564440

C₂

yes

maximal, complemented

C₂×#11926265

C₂

yes

maximal, characteristic, complemented

C₁₉×#1844

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₅₂

—

C₂×#10597320

C₂²

yes

—

#11926921

—

#11926921

C₄

yes

complemented

C₂×#10597266

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926265

—

C₂×C₁₉×#106

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#384

C₂²

yes

—

C₂²×D₇₆

—

C₂²×D₇₆

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

D₄

yes

—

C₂×D₁₅₂

—

C₂×D₁₅₂

—

C₂×D₁₅₂

—

#10597320

—

#10597320

—

#10597320

C₂×C₄

yes

—

C₁₉×#106

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

#10597266

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

D₈

yes

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

D₁₅₂

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

#102

yes

complemented

C₁₉⋊C₈

—

C₂×#493

—

#1957

—

#1844

D₁₉

yes

characteristic, complemented

C₂×#322

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×#102

yes

—

C₄×C₁₉

#442

yes

—

C₄×C₁₉

#469

yes

—

C₄×C₁₉

#486

yes

—

C₂²×D₈

—

C₂×#127

—

#493

—

100

#493

—

101

C₂×#106

—

102

C₂×#102

—

103

C₂×C₄×C₈

—

104

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

105

#384

C₂×D₁₉

yes

—

106

#322

—

107

C₂×C₁₉

#1715

yes

—

108

C₂×C₁₉

#1721

yes

—

109

C₂×C₁₉

#1957

yes

characteristic

110

C₂×C₁₉

#1972

yes

—

111

D₁₉

—

112

C₂²×D₄

—

113

C₂²×D₄

—

114

C₂×D₈

—

115

C₂×D₈

—

116

C₂×D₈

—

117

C₂²×C₈

—

118

C₂²×C₈

C₂²⋊D₁₉

yes

—

119

#127

—

120

#127

—

121

#127

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

—

124

C₂×C₄²

C₂²×D₁₉

yes

characteristic

125

#106

—

126

#102

—

127

C₄×C₈

—

128

C₄×C₈

—

129

C₄×C₈

C₄×D₁₉

yes

—

130

C₄×C₈

D₇₆

yes

—

131

C₁₉

#9837

yes

characteristic, complemented, Sylow

132

C₂⁴

—

133

C₂×D₄

—

134

C₂×D₄

—

135

C₂×D₄

—

136

C₂×D₄

—

137

C₂×D₄

—

138

C₂×D₄

—

139

C₂×D₄

—

140

C₂×D₄

—

141

C₂²×C₄

—

142

C₂²×C₄

D₄×D₁₉

yes

—

143

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

144

D₈

—

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

148

C₂×C₈

#64525

yes

—

149

C₂×C₈

#64527

yes

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄²

C₂×C₄×D₁₉

yes

characteristic

153

C₄²

C₂×D₇₆

yes

characteristic

154

C₄²

#64545

yes

—

155

C₂³

—

156

C₂³

—

152

—

157

C₂³

—

152

—

158

C₂³

—

152

—

159

C₂³

—

152

—

160

C₂³

#10597386

yes

characteristic

161

D₄

—

162

D₄

—

163

D₄

—

152

—

164

D₄

—

152

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

#10597339

yes

—

168

C₂×C₄

#10597341

yes

—

169

C₂×C₄

#10597360

yes

—

170

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

171

C₂×C₄

C₂×#64525

yes

—

172

C₂×C₄

C₂×#64527

yes

—

173

C₂×C₄

#10597393

yes

characteristic

174

C₈

—

175

C₈

#10597266

yes

complemented

176

C₂²

—

304

—

177

C₂²

—

304

—

178

C₂²

—

304

—

179

C₂²

—

152

—

180

C₂²

—

152

—

181

C₂²

#11926445

yes

characteristic

182

C₂²

#11926918

yes

characteristic

183

C₂²

#11926920

yes

characteristic

184

C₂²

#11926930

yes

—

185

C₄

—

186

C₄

C₂×#10597266

yes

—

187

C₄

#11926655

yes

—

188

C₄

#11926798

yes

—

189

C₄

#11926892

yes

—

190

C₂

—

304

—

191

C₂

#14563264

yes

—

192

C₂

#14563299

yes

—

193

C₂

#14564440

yes

characteristic

194

C₂

#14564509

yes

—

	subgroup	G/H
center	C₂³	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1844	C₂
socle	C₂³×C₁₉	#127
prime radical	C₂×#11926921	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1844	D₁₉
hypocenter	C₁₉	#9837
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1844

subgroup

G/H

center

C₂³

#10597386

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1844

C₂

C₂³×C₁₉

C₂

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1844

N	H ≅ G/N	type
2. #14564440	C₂	semidirect
3. C₂×#11926265	C₂	semidirect
4. C₁₉×#1844	C₂	semidirect
8. #11926921	C₄	semidirect
77. C₈×C₁₉	#102	semidirect
81. #1844	D₁₉	semidirect
131. C₁₉	#9837	semidirect
175. C₈	#10597266	semidirect

H ≅ G/N

type

2. #14564440

C₂

semidirect

3. C₂×#11926265

C₂

semidirect

4. C₁₉×#1844

C₂

semidirect

8. #11926921

C₄

semidirect

77. C₈×C₁₉

#102

semidirect

81. #1844

D₁₉

semidirect

131. C₁₉

#9837

semidirect

175. C₈

#10597266

semidirect

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

subgroup	index
C₂×#11926921	2
#14564440	2
C₂×#11926265	2
C₁₉×#1844	2
#9837	19

subgroup

index

C₁₉×#1844

Subgroups — #18082376

Conjugacy classes of subgroups

Complements

Maximal subgroups