Group #18069339 — subgroups

Subgroups — #18069339

Order 4864.

200 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 71 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	#14561719	C₂	1	1	yes	maximal, characteristic
2	#14561719	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1940	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597269	—	2	1	no	—
5	C₂×#10597269	—	2	1	no	—
6	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
7	C₂×C₁₉×C₄⋊C₈	C₄	1	1	yes	characteristic
8	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
9	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
10	C₁₉×#336	—	2	1	no	—
11	C₂²×C₈×C₁₉	—	2	1	no	—
12	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
14	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
15	C₂×C₄²×C₁₉	—	2	1	no	—
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₁₉×C₄⋊C₈	—	4	1	no	—
18	C₁₉×C₄⋊C₈	—	4	1	no	—
19	C₁₉×C₄⋊C₈	—	4	1	no	—
20	C₁₉×#97	—	4	1	no	—
21	C₁₉×#95	C₈	1	1	yes	characteristic
22	C₁₉×#95	C₈	1	1	yes	characteristic
23	#10597269	—	2	2	no	—
24	#10597269	—	2	2	no	—
25	#10597269	—	4	1	no	—
26	#10597269	—	4	1	no	—
27	C₂×C₁₉⋊C₁₆	—	4	1	no	—
28	C₂×C₁₉⋊C₁₆	—	4	1	no	—
29	C₂²×C₄×C₁₉	—	2	1	no	—
30	C₂²×C₄×C₁₉	—	2	1	no	—
31	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
34	C₂×C₈×C₁₉	—	2	1	no	—
35	C₂×C₈×C₁₉	—	2	1	no	—
36	C₂×C₈×C₁₉	—	2	1	no	—
37	C₂×C₈×C₁₉	—	2	1	no	—
38	C₂×C₈×C₁₉	—	4	1	no	—
39	C₂×C₈×C₁₉	—	4	1	no	—
40	C₂×C₈×C₁₉	—	4	1	no	—
41	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
42	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
43	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
44	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
45	C₄⋊C₄×C₁₉	—	4	2	no	—
46	C₄²×C₁₉	—	2	1	no	—
47	C₄²×C₁₉	—	2	1	no	—
48	C₄²×C₁₉	—	4	1	no	—
49	C₄²×C₁₉	—	4	1	no	—
50	C₁₉⋊C₁₆	—	4	2	no	—
51	C₁₉⋊C₁₆	—	4	2	no	—
52	#7124	—	19	1	no	maximal, Sylow
53	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
57	C₂×C₄×C₁₉	—	4	1	no	—
58	C₂×C₄×C₁₉	—	4	1	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	—	4	1	no	—
63	C₂×C₄×C₁₉	—	4	1	no	—
64	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
68	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
69	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
70	C₈×C₁₉	—	2	1	no	—
71	C₈×C₁₉	—	2	1	no	—
72	C₈×C₁₉	—	2	1	no	—
73	C₈×C₁₉	—	2	1	no	—
74	C₈×C₁₉	—	8	1	no	—
75	#1940	D₁₉	1	1	yes	characteristic
76	#1377	—	19	1	no	—
77	#1377	—	19	1	no	—
78	C₂²×C₁₉	—	2	1	no	—
79	C₂²×C₁₉	—	2	1	no	—
80	C₂²×C₁₉	#324	1	1	yes	characteristic
81	C₂²×C₁₉	D₄⋊C₈	1	1	yes	characteristic
82	C₂²×C₁₉	Q₈⋊C₈	1	1	yes	characteristic
83	C₄×C₁₉	—	4	2	no	—
84	C₄×C₁₉	—	4	1	no	—
85	C₄×C₁₉	—	4	1	no	—
86	C₄×C₁₉	—	8	1	no	—
87	C₄×C₁₉	#327	1	1	yes	characteristic
88	C₄×C₁₉	#328	1	1	yes	characteristic
89	C₄×C₁₉	#330	1	1	yes	characteristic
90	C₄×C₁₉	#332	1	1	yes	characteristic
91	C₂×M₃₂	—	38	1	no	—
92	C₂×M₃₂	—	38	1	no	—
93	C₂×C₄⋊C₈	—	2	1	no	—
94	C₂×C₄⋊C₈	Dic₁₉	1	1	yes	characteristic
95	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
96	C₄×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
97	#336	—	2	1	no	—
98	C₂×C₁₉	—	2	1	no	—
99	C₂×C₁₉	—	2	1	no	—
100	C₂×C₁₉	#1271	1	1	yes	characteristic
101	C₂×C₁₉	#1327	1	1	yes	characteristic
102	C₂×C₁₉	#1328	1	1	yes	characteristic
103	C₂²×C₈	—	2	1	no	—
104	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
105	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
106	C₂×C₄⋊C₄	—	2	1	no	—
107	C₂×C₄²	—	2	1	no	—
108	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
109	M₃₂	—	38	2	no	—
110	M₃₂	—	38	2	no	—
111	M₃₂	—	76	1	no	—
112	M₃₂	—	76	1	no	—
113	C₂×C₁₆	—	76	1	no	—
114	C₂×C₁₆	—	76	1	no	—
115	C₄⋊C₈	—	4	1	no	—
116	C₄⋊C₈	—	4	1	no	—
117	C₄⋊C₈	—	4	1	no	—
118	#97	—	4	1	no	—
119	#95	C₁₉⋊C₈	1	1	yes	characteristic
120	#95	C₁₉⋊C₈	1	1	yes	characteristic
121	C₁₉	#7124	1	1	yes	characteristic, complemented, Sylow
122	C₂²×C₄	—	2	1	no	—
123	C₂²×C₄	—	2	1	no	—
124	C₂²×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
125	C₂²×C₄	#64520	1	1	yes	characteristic
126	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
127	C₂×C₈	—	2	1	no	—
128	C₂×C₈	—	2	1	no	—
129	C₂×C₈	—	2	1	no	—
130	C₂×C₈	—	2	1	no	—
131	C₂×C₈	—	4	1	no	—
132	C₂×C₈	—	4	1	no	—
133	C₂×C₈	—	4	1	no	—
134	C₂×C₈	#64525	1	1	yes	characteristic
135	C₂×C₈	#64526	1	1	yes	characteristic
136	C₂×C₈	#64527	1	1	yes	characteristic
137	C₂×C₈	#64528	1	1	yes	characteristic
138	C₄⋊C₄	—	4	2	no	—
139	C₄²	—	2	1	no	—
140	C₄²	—	2	1	no	—
141	C₄²	—	4	1	no	—
142	C₄²	—	4	1	no	—
143	C₁₆	—	76	2	no	—
144	C₁₆	—	76	2	no	—
145	C₂³	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	2	1	no	—
148	C₂×C₄	—	2	1	no	—
149	C₂×C₄	—	4	1	no	—
150	C₂×C₄	—	4	1	no	—
151	C₂×C₄	—	4	1	no	—
152	C₂×C₄	—	4	1	no	—
153	C₂×C₄	—	4	1	no	—
154	C₂×C₄	—	4	1	no	—
155	C₂×C₄	—	4	1	no	—
156	C₂×C₄	#10597289	1	1	yes	characteristic
157	C₂×C₄	#10597291	1	1	yes	characteristic
158	C₂×C₄	#10597292	1	1	yes	characteristic
159	C₂×C₄	#10597293	1	1	yes	characteristic
160	C₂×C₄	#10597294	1	1	yes	characteristic
161	C₂×C₄	#10597294	1	1	yes	characteristic
162	C₈	—	2	1	no	—
163	C₈	—	2	1	no	—
164	C₈	—	2	1	no	—
165	C₈	—	2	1	no	—
166	C₈	—	8	1	no	—
167	C₂²	—	2	1	no	—
168	C₂²	—	2	1	no	—
169	C₂²	#11926270	1	1	yes	characteristic
170	C₂²	D₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
171	C₂²	Q₈⋊(C₁₉⋊C₈)	1	1	yes	characteristic
172	C₄	—	4	2	no	—
173	C₄	—	4	1	no	—
174	C₄	—	4	1	no	—
175	C₄	—	8	1	no	—
176	C₄	#11926278	1	1	yes	characteristic
177	C₄	#11926281	1	1	yes	characteristic
178	C₄	#11926286	1	1	yes	characteristic
179	C₄	#11926290	1	1	yes	characteristic
180	C₂	—	2	1	no	—
181	C₂	—	2	1	no	—
182	C₂	#14561458	1	1	yes	characteristic
183	C₂	#14561586	1	1	yes	characteristic
184	C₂	#14561588	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561719

C₂

yes

maximal, characteristic

#14561719

C₂

yes

maximal, characteristic

C₁₉×#1940

C₂

yes

maximal, characteristic

C₂×#10597269

—

C₂×#10597269

—

C₂×C₁₉×C₄⋊C₈

—

C₂×C₁₉×C₄⋊C₈

C₄

yes

characteristic

C₂×C₁₉×#97

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₁₉

C₄

yes

characteristic

C₁₉×#336

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#97

—

C₁₉×#95

C₈

yes

characteristic

C₁₉×#95

C₈

yes

—

—

—

—

C₂×C₁₉⋊C₁₆

—

C₂×C₁₉⋊C₁₆

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₂×C₈×C₁₉

Q₁₆

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₁₉⋊C₁₆

—

C₁₉⋊C₁₆

—

#7124

—

maximal, Sylow

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#1940

D₁₉

yes

characteristic

#1377

—

#1377

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#324

yes

characteristic

C₂²×C₁₉

D₄⋊C₈

yes

characteristic

C₂²×C₁₉

Q₈⋊C₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×M₃₂

—

C₂×M₃₂

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

Dic₁₉

yes

characteristic

C₂×#97

C₂×D₁₉

yes

characteristic

C₄×C₄⋊C₄

Dic₁₉

yes

characteristic

#336

—

C₂×C₁₉

—

C₂×C₁₉

—

100

C₂×C₁₉

#1271

yes

characteristic

101

C₂×C₁₉

#1327

yes

characteristic

102

C₂×C₁₉

#1328

yes

characteristic

103

C₂²×C₈

—

104

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

105

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

106

C₂×C₄⋊C₄

—

107

C₂×C₄²

—

108

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

109

M₃₂

—

110

M₃₂

—

111

M₃₂

—

112

M₃₂

—

113

C₂×C₁₆

—

114

C₂×C₁₆

—

115

C₄⋊C₈

—

116

C₄⋊C₈

—

117

C₄⋊C₈

—

118

#97

—

119

#95

C₁₉⋊C₈

yes

characteristic

120

#95

C₁₉⋊C₈

yes

characteristic

121

C₁₉

#7124

yes

characteristic, complemented, Sylow

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

C₂×C₁₉⋊C₈

yes

characteristic

125

C₂²×C₄

#64520

yes

characteristic

126

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

#64525

yes

characteristic

135

C₂×C₈

#64526

yes

characteristic

136

C₂×C₈

#64527

yes

characteristic

137

C₂×C₈

#64528

yes

characteristic

138

C₄⋊C₄

—

139

C₄²

—

140

C₄²

—

141

C₄²

—

142

C₄²

—

143

C₁₆

—

144

C₁₆

—

145

C₂³

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

146

C₂×C₄

—

147

C₂×C₄

—

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

#10597289

yes

characteristic

157

C₂×C₄

#10597291

yes

characteristic

158

C₂×C₄

#10597292

yes

characteristic

159

C₂×C₄

#10597293

yes

characteristic

160

C₂×C₄

#10597294

yes

characteristic

161

C₂×C₄

#10597294

yes

characteristic

162

C₈

—

163

C₈

—

164

C₈

—

165

C₈

—

166

C₈

—

167

C₂²

—

168

C₂²

—

169

C₂²

#11926270

yes

characteristic

170

C₂²

D₄⋊(C₁₉⋊C₈)

yes

characteristic

171

C₂²

Q₈⋊(C₁₉⋊C₈)

yes

characteristic

172

C₄

—

173

C₄

—

174

C₄

—

175

C₄

—

176

C₄

#11926278

yes

characteristic

177

C₄

#11926281

yes

characteristic

178

C₄

#11926286

yes

characteristic

179

C₄

#11926290

yes

characteristic

180

C₂

—

181

C₂

—

182

C₂

#14561458

yes

characteristic

183

C₂

#14561586

yes

characteristic

184

C₂

#14561588

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597291
commutator	C₂²×C₄×C₁₉	C₂×C₈
Frattini	C₂×#97	C₂×D₁₉
Fitting	C₁₉×#1940	C₂
socle	C₂²×C₁₉	#324
prime radical	C₂³×C₁₉	C₂²⋊C₈
cosocle	C₂×C₁₉×#97	C₂²
hypercenter	#1940	D₁₉
hypocenter	C₁₉	#7124
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#97 ◁ #1940

subgroup

G/H

center

C₂×C₄

#10597291

commutator

C₂²×C₄×C₁₉

C₂×C₈

Frattini

C₂×#97

C₂×D₁₉

Fitting

C₁₉×#1940

C₂

socle

C₂²×C₁₉

#324

prime radical

C₂³×C₁₉

C₂²⋊C₈

cosocle

C₂×C₁₉×#97

C₂²

D₁₉

C₁₉

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

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#97 ◁ #1940

N	H ≅ G/N	type
121. C₁₉	#7124	semidirect

H ≅ G/N

type

121. C₁₉

#7124

semidirect

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

subgroup	index
#14561719	2
C₁₉×#1940	2
#7124	19

subgroup

index

#14561719

C₁₉×#1940

#7124

Subgroups — #18069339

Conjugacy classes of subgroups

Complements

Maximal subgroups