Group #18069167 — subgroups

Subgroups — #18069167

Order 4864.

194 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 47 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	#14563704	C₂	1	1	yes	maximal, characteristic
2	#14561559	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1314	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597372	C₄	1	1	yes	characteristic
5	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	1	yes	characteristic
6	C₂²⋊(C₁₉⋊C₁₆)	—	2	1	no	—
7	#11926298	—	2	1	no	—
8	#11926298	—	2	1	no	—
9	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
10	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
11	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
14	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
15	#10597372	—	4	1	no	—
16	#10597372	—	4	1	no	—
17	C₂×C₄⋊Dic₁₉	C₈	1	1	yes	characteristic
18	C₂×C₄⋊Dic₁₉	C₈	1	1	yes	characteristic
19	C₂×C₄×Dic₁₉	—	2	1	no	—
20	C₂²×C₁₉⋊C₈	—	2	1	no	—
21	C₂×C₁₆×C₁₉	—	4	1	no	—
22	C₁₉×C₂²⋊C₈	—	4	1	no	—
23	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
24	C₂×C₁₉⋊C₁₆	—	4	1	no	—
25	C₂⁴×C₁₉	M₁₆	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	—	2	1	no	—
27	C₂²×C₄×C₁₉	—	2	1	no	—
28	C₂²×C₄×C₁₉	—	4	1	no	—
29	C₂²×C₄×C₁₉	—	4	1	no	—
30	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
32	C₂²×Dic₁₉	—	2	1	no	—
33	C₂²×Dic₁₉	—	2	1	no	—
34	C₂×C₈×C₁₉	—	2	1	no	—
35	C₂×C₈×C₁₉	—	2	1	no	—
36	C₂×C₈×C₁₉	—	4	1	no	—
37	C₂×C₈×C₁₉	—	4	1	no	—
38	C₂²⋊Dic₁₉	—	4	2	no	—
39	C₄⋊Dic₁₉	—	4	1	no	—
40	C₄⋊Dic₁₉	—	4	1	no	—
41	C₄×Dic₁₉	—	4	1	no	—
42	C₄×Dic₁₉	—	4	1	no	—
43	C₂×C₁₉⋊C₈	—	4	1	no	—
44	C₂×C₁₉⋊C₈	—	4	1	no	—
45	C₂×C₁₉⋊C₈	—	4	1	no	—
46	C₁₆×C₁₉	—	8	1	no	—
47	C₁₉⋊C₁₆	—	8	1	no	—
48	#7059	—	19	1	no	maximal, Sylow
49	C₂³×C₁₉	—	2	1	no	—
50	C₂³×C₁₉	—	2	1	no	—
51	C₂³×C₁₉	—	2	1	no	—
52	C₂³×C₁₉	—	4	1	no	—
53	C₂³×C₁₉	—	4	1	no	—
54	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
57	C₂×C₄×C₁₉	—	2	1	no	—
58	C₂×C₄×C₁₉	—	4	2	no	—
59	C₂×C₄×C₁₉	—	4	1	no	—
60	C₂×C₄×C₁₉	—	4	1	no	—
61	C₂×C₄×C₁₉	—	4	1	no	—
62	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
64	C₂×Dic₁₉	—	4	2	no	—
65	C₂×Dic₁₉	—	4	1	no	—
66	C₂×Dic₁₉	—	4	1	no	—
67	C₂×Dic₁₉	—	4	1	no	—
68	C₂×Dic₁₉	—	4	1	no	—
69	C₈×C₁₉	—	4	1	no	—
70	C₈×C₁₉	—	4	1	no	—
71	C₁₉⋊C₈	—	8	1	no	—
72	#1818	—	19	1	no	—
73	#1314	—	19	1	no	—
74	#1314	D₁₉	1	1	yes	characteristic
75	C₂²×C₁₉	—	2	1	no	—
76	C₂²×C₁₉	—	2	1	no	—
77	C₂²×C₁₉	—	4	1	no	—
78	C₂²×C₁₉	—	4	1	no	—
79	C₂²×C₁₉	—	4	1	no	—
80	C₂²×C₁₉	—	8	1	no	—
81	C₂²×C₁₉	—	8	1	no	—
82	C₂²×C₁₉	#323	1	1	yes	characteristic
83	C₂²×C₁₉	#350	1	1	yes	characteristic
84	C₂²×C₁₉	#350	1	1	yes	characteristic
85	C₄×C₁₉	—	2	1	no	—
86	C₄×C₁₉	—	4	1	no	—
87	C₄×C₁₉	#352	1	1	yes	characteristic
88	C₄×C₁₉	#352	1	1	yes	characteristic
89	Dic₁₉	—	8	1	no	—
90	Dic₁₉	—	8	1	no	—
91	C₂×#117	—	19	1	no	—
92	C₂×C₂²⋊C₈	—	19	1	no	—
93	C₂×C₂²⋊C₈	C₂×D₁₉	1	1	yes	characteristic
94	C₂²⋊C₁₆	—	2	1	no	—
95	C₂²⋊C₁₆	—	38	1	no	—
96	#336	—	38	1	no	—
97	#336	—	38	1	no	—
98	C₂×C₁₉	—	2	1	no	—
99	C₂×C₁₉	—	2	1	no	—
100	C₂×C₁₉	—	8	1	no	—
101	C₂×C₁₉	#1315	1	1	yes	characteristic
102	C₂×C₁₉	#1317	1	1	yes	characteristic
103	C₂×C₁₉	#1321	1	1	yes	characteristic
104	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
105	C₂²×C₈	—	38	1	no	—
106	C₂²×C₈	D₇₆	1	1	yes	characteristic
107	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
108	#117	—	76	1	no	—
109	#117	—	76	1	no	—
110	C₂×C₄⋊C₄	—	19	1	no	—
111	C₂×C₄⋊C₄	—	19	1	no	—
112	C₂×C₂²⋊C₄	—	38	1	no	—
113	C₂×C₄²	—	38	1	no	—
114	C₂×C₁₆	—	4	1	no	—
115	C₂×C₁₆	—	76	1	no	—
116	C₂²⋊C₈	—	4	1	no	—
117	C₂²⋊C₈	—	76	1	no	—
118	C₁₉	#7059	1	1	yes	characteristic, complemented, Sylow
119	C₂⁴	#64515	1	1	yes	characteristic
120	C₂²×C₄	—	2	1	no	—
121	C₂²×C₄	—	2	1	no	—
122	C₂²×C₄	—	4	1	no	—
123	C₂²×C₄	—	4	1	no	—
124	C₂²×C₄	—	38	1	no	—
125	C₂²×C₄	—	38	1	no	—
126	C₂²×C₄	C₈×D₁₉	1	1	yes	characteristic
127	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
128	C₂×C₈	—	2	1	no	—
129	C₂×C₈	—	2	1	no	—
130	C₂×C₈	—	4	1	no	—
131	C₂×C₈	—	4	1	no	—
132	C₂×C₈	—	76	1	no	—
133	C₂×C₈	—	76	1	no	—
134	C₂×C₈	—	76	1	no	—
135	C₄⋊C₄	—	76	1	no	—
136	C₄⋊C₄	—	76	1	no	—
137	C₂²⋊C₄	—	76	2	no	—
138	C₄²	—	76	1	no	—
139	C₄²	—	76	1	no	—
140	C₁₆	—	8	1	no	—
141	C₁₆	—	152	1	no	—
142	C₂³	—	2	1	no	—
143	C₂³	—	2	1	no	—
144	C₂³	—	2	1	no	—
145	C₂³	—	4	1	no	—
146	C₂³	—	4	1	no	—
147	C₂³	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
148	C₂×C₄	—	2	1	no	—
149	C₂×C₄	—	2	1	no	—
150	C₂×C₄	—	2	1	no	—
151	C₂×C₄	—	4	2	no	—
152	C₂×C₄	—	4	1	no	—
153	C₂×C₄	—	4	1	no	—
154	C₂×C₄	—	4	1	no	—
155	C₂×C₄	—	76	2	no	—
156	C₂×C₄	—	76	1	no	—
157	C₂×C₄	—	76	1	no	—
158	C₂×C₄	—	76	1	no	—
159	C₂×C₄	—	76	1	no	—
160	C₂×C₄	#10597263	1	1	yes	characteristic
161	C₂×C₄	#10597280	1	1	yes	characteristic
162	C₈	—	4	1	no	—
163	C₈	—	4	1	no	—
164	C₈	—	152	1	no	—
165	C₂²	—	2	1	no	—
166	C₂²	—	2	1	no	—
167	C₂²	—	4	1	no	—
168	C₂²	—	4	1	no	—
169	C₂²	—	4	1	no	—
170	C₂²	—	8	1	no	—
171	C₂²	—	8	1	no	—
172	C₂²	#11926267	1	1	yes	characteristic
173	C₂²	#11926327	1	1	yes	characteristic
174	C₂²	#11926329	1	1	yes	characteristic
175	C₄	—	2	1	no	—
176	C₄	—	4	1	no	—
177	C₄	—	152	1	no	—
178	C₄	—	152	1	no	—
179	C₄	#11926333	1	1	yes	characteristic
180	C₄	#11926335	1	1	yes	characteristic
181	C₂	—	2	1	no	—
182	C₂	—	2	1	no	—
183	C₂	—	8	1	no	—
184	C₂	#14561560	1	1	yes	characteristic
185	C₂	#14561564	1	1	yes	characteristic
186	C₂	#14561572	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563704

C₂

yes

maximal, characteristic

#14561559

C₂

yes

maximal, characteristic

C₁₉×#1314

C₂

yes

maximal, characteristic

C₂×#10597372

C₄

yes

characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

C₄

yes

characteristic

C₂²⋊(C₁₉⋊C₁₆)

—

#11926298

—

#11926298

—

C₂×C₁₉×C₂²⋊C₈

C₂²

yes

characteristic

C₁₉×C₂²⋊C₁₆

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

#10597372

—

#10597372

—

C₂×C₄⋊Dic₁₉

C₈

yes

characteristic

C₂×C₄⋊Dic₁₉

C₈

yes

characteristic

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₂×C₁₆×C₁₉

—

C₁₉×C₂²⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₂×C₁₉⋊C₁₆

—

C₂⁴×C₁₉

M₁₆

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

#7059

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1818

—

#1314

—

#1314

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₂×#117

—

C₂×C₂²⋊C₈

—

C₂×C₂²⋊C₈

C₂×D₁₉

yes

characteristic

C₂²⋊C₁₆

—

C₂²⋊C₁₆

—

#336

—

#336

—

C₂×C₁₉

—

C₂×C₁₉

—

100

C₂×C₁₉

—

101

C₂×C₁₉

#1315

yes

characteristic

102

C₂×C₁₉

#1317

yes

characteristic

103

C₂×C₁₉

#1321

yes

characteristic

104

C₂³×C₄

C₄×D₁₉

yes

characteristic

105

C₂²×C₈

—

106

C₂²×C₈

D₇₆

yes

characteristic

107

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

108

#117

—

109

#117

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄⋊C₄

—

112

C₂×C₂²⋊C₄

—

113

C₂×C₄²

—

114

C₂×C₁₆

—

115

C₂×C₁₆

—

116

C₂²⋊C₈

—

117

C₂²⋊C₈

—

118

C₁₉

#7059

yes

characteristic, complemented, Sylow

119

C₂⁴

#64515

yes

characteristic

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

C₈×D₁₉

yes

characteristic

127

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₂²⋊C₄

—

138

C₄²

—

139

C₄²

—

140

C₁₆

—

141

C₁₆

—

152

—

142

C₂³

—

143

C₂³

—

144

C₂³

—

145

C₂³

—

146

C₂³

—

147

C₂³

(C₂×D₁₉)⋊C₈

yes

characteristic

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

#10597263

yes

characteristic

161

C₂×C₄

#10597280

yes

characteristic

162

C₈

—

163

C₈

—

164

C₈

—

152

—

165

C₂²

—

166

C₂²

—

167

C₂²

—

168

C₂²

—

169

C₂²

—

170

C₂²

—

171

C₂²

—

172

C₂²

#11926267

yes

characteristic

173

C₂²

#11926327

yes

characteristic

174

C₂²

#11926329

yes

characteristic

175

C₄

—

176

C₄

—

177

C₄

—

152

—

178

C₄

—

152

—

179

C₄

#11926333

yes

characteristic

180

C₄

#11926335

yes

characteristic

181

C₂

—

182

C₂

—

183

C₂

—

184

C₂

#14561560

yes

characteristic

185

C₂

#14561564

yes

characteristic

186

C₂

#14561572

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597263
commutator	C₂²×C₄×C₁₉	C₂×C₈
Frattini	C₂×C₂²⋊C₈	C₂×D₁₉
Fitting	C₁₉×#1314	C₂
socle	C₂²×C₁₉	#323
prime radical	C₂⁴×C₁₉	M₁₆
cosocle	C₂×C₁₉×C₂²⋊C₈	C₂²
hypercenter	#1314	D₁₉
hypocenter	C₁₉	#7059
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈ ◁ #1314

subgroup

G/H

center

C₂×C₄

#10597263

commutator

C₂²×C₄×C₁₉

C₂×C₈

Frattini

C₂×C₂²⋊C₈

C₂×D₁₉

Fitting

C₁₉×#1314

C₂

socle

C₂²×C₁₉

#323

prime radical

C₂⁴×C₁₉

M₁₆

cosocle

C₂×C₁₉×C₂²⋊C₈

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈ ◁ #1314

N	H ≅ G/N	type
118. C₁₉	#7059	semidirect

H ≅ G/N

type

118. C₁₉

#7059

semidirect

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

subgroup	index
#14563704	2
#14561559	2
C₁₉×#1314	2
#7059	19

subgroup

index

#14563704

#14561559

C₁₉×#1314

#7059

Subgroups — #18069167

Conjugacy classes of subgroups

Complements

Maximal subgroups