Group #18069890 — subgroups

Subgroups — #18069890

Order 4864.

452 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 43 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	#14561571	C₂	1	2	yes	maximal, complemented
2	C₁₉×#1783	C₂	1	1	yes	maximal, characteristic
3	#11926326	—	2	2	no	—
4	C₂³×D₄×C₁₉	C₄	1	1	yes	characteristic
5	C₂×C₁₉×#100	—	2	2	no	—
6	C₁₉×#407	C₄	1	1	yes	characteristic
7	C₁₉×#407	C₂²	1	1	yes	characteristic
8	C₂⁵×C₁₉	C₈	1	2	yes	—
9	C₂²×D₄×C₁₉	—	2	1	no	—
10	C₂²×D₄×C₁₉	—	2	1	no	—
11	C₂²×D₄×C₁₉	—	4	1	no	—
12	C₂²×D₄×C₁₉	—	4	1	no	—
13	C₂²×D₄×C₁₉	—	4	4	no	—
14	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂×M₁₆×C₁₉	—	2	1	no	—
16	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
17	C₁₉×#100	—	4	4	no	—
18	C₁₉×C₂²⋊C₈	—	4	1	no	—
19	C₁₉×C₂²⋊C₈	—	4	1	no	—
20	#10597269	—	4	2	no	—
21	C₂⁴×C₁₉	—	2	2	no	—
22	C₂⁴×C₁₉	—	4	2	no	—
23	C₂⁴×C₁₉	—	4	4	no	—
24	C₂⁴×C₁₉	—	8	4	no	—
25	C₂⁴×C₁₉	C₂×C₈	1	1	yes	characteristic
26	C₂×D₄×C₁₉	—	2	4	no	—
27	C₂×D₄×C₁₉	—	4	2	no	—
28	C₂×D₄×C₁₉	—	4	2	no	—
29	C₂×D₄×C₁₉	—	4	4	no	—
30	C₂×D₄×C₁₉	—	4	8	no	—
31	C₂×D₄×C₁₉	—	4	4	no	—
32	C₂×D₄×C₁₉	—	4	4	no	—
33	C₂×D₄×C₁₉	—	4	1	no	—
34	C₂×D₄×C₁₉	—	4	1	no	—
35	C₂²×C₄×C₁₉	—	2	1	no	—
36	C₂²×C₄×C₁₉	—	2	1	no	—
37	C₂²×C₄×C₁₉	—	4	2	no	—
38	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
40	M₁₆×C₁₉	—	4	2	no	—
41	M₁₆×C₁₉	—	4	2	no	—
42	C₂×C₈×C₁₉	—	2	2	no	—
43	C₂×C₈×C₁₉	—	4	1	no	—
44	C₁₉⋊C₁₆	—	8	2	no	—
45	#7340	—	19	1	no	maximal, Sylow
46	C₂³×C₁₉	—	2	1	no	—
47	C₂³×C₁₉	—	2	4	no	—
48	C₂³×C₁₉	—	4	1	no	—
49	C₂³×C₁₉	—	4	2	no	—
50	C₂³×C₁₉	—	4	2	no	—
51	C₂³×C₁₉	—	4	4	no	—
52	C₂³×C₁₉	—	4	4	no	—
53	C₂³×C₁₉	—	4	2	no	—
54	C₂³×C₁₉	—	8	4	no	—
55	C₂³×C₁₉	—	8	4	no	—
56	C₂³×C₁₉	—	8	8	no	—
57	C₂³×C₁₉	—	8	4	no	—
58	C₂³×C₁₉	—	8	8	no	—
59	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
60	D₄×C₁₉	—	4	4	no	—
61	D₄×C₁₉	—	4	8	no	—
62	D₄×C₁₉	—	4	4	no	—
63	C₂×C₄×C₁₉	—	2	2	no	—
64	C₂×C₄×C₁₉	—	2	1	no	—
65	C₂×C₄×C₁₉	—	4	2	no	—
66	C₂×C₄×C₁₉	—	4	2	no	—
67	C₂×C₄×C₁₉	—	4	1	no	—
68	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
69	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
70	C₈×C₁₉	—	4	2	no	—
71	C₈×C₁₉	—	8	1	no	—
72	#1783	D₁₉	1	1	yes	characteristic
73	#1320	—	19	2	no	—
74	C₂²×C₁₉	—	2	2	no	—
75	C₂²×C₁₉	—	2	1	no	—
76	C₂²×C₁₉	—	4	1	no	—
77	C₂²×C₁₉	—	4	1	no	—
78	C₂²×C₁₉	—	4	2	no	—
79	C₂²×C₁₉	—	4	2	no	—
80	C₂²×C₁₉	—	4	1	no	—
81	C₂²×C₁₉	—	4	4	no	—
82	C₂²×C₁₉	—	8	4	no	—
83	C₂²×C₁₉	—	8	4	no	—
84	C₂²×C₁₉	—	8	8	no	—
85	C₂²×C₁₉	—	8	4	no	—
86	C₂²×C₁₉	—	8	8	no	—
87	C₂²×C₁₉	#323	1	1	yes	characteristic
88	C₄×C₁₉	—	2	1	no	—
89	C₄×C₁₉	—	4	1	no	—
90	C₄×C₁₉	AΣL(1,𝔽₁₆)	1	2	yes	—
91	C₂³×D₄	Dic₁₉	1	1	yes	characteristic
92	C₂×#100	—	2	2	no	—
93	#407	Dic₁₉	1	1	yes	characteristic
94	#407	C₂×D₁₉	1	1	yes	characteristic
95	#349	—	38	2	no	—
96	C₂×C₁₉	—	2	1	no	—
97	C₂×C₁₉	—	4	2	no	—
98	C₂×C₁₉	—	4	1	no	—
99	C₂×C₁₉	—	8	4	no	—
100	C₂×C₁₉	#1316	1	1	yes	characteristic
101	C₂⁵	C₁₉⋊C₈	1	2	yes	—
102	C₂²×D₄	—	2	1	no	—
103	C₂²×D₄	—	2	1	no	—
104	C₂²×D₄	—	4	1	no	—
105	C₂²×D₄	—	4	1	no	—
106	C₂²×D₄	—	4	4	no	—
107	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
108	C₂×M₁₆	—	2	1	no	—
109	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
110	M₃₂	—	76	2	no	—
111	#100	—	4	4	no	—
112	C₂²⋊C₈	—	4	1	no	—
113	C₂²⋊C₈	—	4	1	no	—
114	C₁₉	#7340	1	1	yes	characteristic, complemented, Sylow
115	C₂⁴	—	2	2	no	—
116	C₂⁴	—	4	2	no	—
117	C₂⁴	—	4	4	no	—
118	C₂⁴	—	8	4	no	—
119	C₂⁴	C₂×C₁₉⋊C₈	1	1	yes	characteristic
120	C₂×D₄	—	2	4	no	—
121	C₂×D₄	—	4	2	no	—
122	C₂×D₄	—	4	2	no	—
123	C₂×D₄	—	4	4	no	—
124	C₂×D₄	—	4	8	no	—
125	C₂×D₄	—	4	4	no	—
126	C₂×D₄	—	4	4	no	—
127	C₂×D₄	—	4	1	no	—
128	C₂×D₄	—	4	1	no	—
129	C₂²×C₄	—	2	1	no	—
130	C₂²×C₄	—	2	1	no	—
131	C₂²×C₄	—	4	2	no	—
132	C₂²×C₄	#64520	1	1	yes	characteristic
133	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
134	M₁₆	—	4	2	no	—
135	M₁₆	—	4	2	no	—
136	C₂×C₈	—	2	2	no	—
137	C₂×C₈	—	4	1	no	—
138	C₁₆	—	152	2	no	—
139	C₂³	—	2	1	no	—
140	C₂³	—	2	4	no	—
141	C₂³	—	4	1	no	—
142	C₂³	—	4	2	no	—
143	C₂³	—	4	2	no	—
144	C₂³	—	4	4	no	—
145	C₂³	—	4	4	no	—
146	C₂³	—	4	2	no	—
147	C₂³	—	8	4	no	—
148	C₂³	—	8	4	no	—
149	C₂³	—	8	8	no	—
150	C₂³	—	8	4	no	—
151	C₂³	—	8	8	no	—
152	C₂³	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
153	D₄	—	4	4	no	—
154	D₄	—	4	8	no	—
155	D₄	—	4	4	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	1	no	—
158	C₂×C₄	—	4	2	no	—
159	C₂×C₄	—	4	2	no	—
160	C₂×C₄	—	4	1	no	—
161	C₂×C₄	#10597290	1	1	yes	characteristic
162	C₂×C₄	#10597291	1	1	yes	characteristic
163	C₈	—	4	2	no	—
164	C₈	—	8	1	no	—
165	C₂²	—	2	2	no	—
166	C₂²	—	2	1	no	—
167	C₂²	—	4	1	no	—
168	C₂²	—	4	1	no	—
169	C₂²	—	4	2	no	—
170	C₂²	—	4	2	no	—
171	C₂²	—	4	1	no	—
172	C₂²	—	4	4	no	—
173	C₂²	—	8	4	no	—
174	C₂²	—	8	4	no	—
175	C₂²	—	8	8	no	—
176	C₂²	—	8	4	no	—
177	C₂²	—	8	8	no	—
178	C₂²	#11926268	1	1	yes	characteristic
179	C₄	—	2	1	no	—
180	C₄	—	4	1	no	—
181	C₄	#11926331	1	2	yes	—
182	C₂	—	2	1	no	—
183	C₂	—	4	2	no	—
184	C₂	—	4	1	no	—
185	C₂	—	8	4	no	—
186	C₂	#14561563	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561571

C₂

yes

maximal, complemented

C₁₉×#1783

C₂

yes

maximal, characteristic

#11926326

—

C₂³×D₄×C₁₉

C₄

yes

characteristic

C₂×C₁₉×#100

—

C₁₉×#407

C₄

yes

characteristic

C₁₉×#407

C₂²

yes

characteristic

C₂⁵×C₁₉

C₈

yes

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

D₄

yes

—

C₁₉×#100

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

#10597269

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂×C₈

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₁₉⋊C₁₆

—

#7340

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₈

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

#1783

D₁₉

yes

characteristic

#1320

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#323

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

AΣL(1,𝔽₁₆)

yes

—

C₂³×D₄

Dic₁₉

yes

characteristic

C₂×#100

—

#407

Dic₁₉

yes

characteristic

#407

C₂×D₁₉

yes

characteristic

#349

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

100

C₂×C₁₉

#1316

yes

characteristic

101

C₂⁵

C₁₉⋊C₈

yes

—

102

C₂²×D₄

—

103

C₂²×D₄

—

104

C₂²×D₄

—

105

C₂²×D₄

—

106

C₂²×D₄

—

107

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

108

C₂×M₁₆

—

109

C₂×M₁₆

C₂²⋊D₁₉

yes

—

110

M₃₂

—

111

#100

—

112

C₂²⋊C₈

—

113

C₂²⋊C₈

—

114

C₁₉

#7340

yes

characteristic, complemented, Sylow

115

C₂⁴

—

116

C₂⁴

—

117

C₂⁴

—

118

C₂⁴

—

119

C₂⁴

C₂×C₁₉⋊C₈

yes

characteristic

120

C₂×D₄

—

121

C₂×D₄

—

122

C₂×D₄

—

123

C₂×D₄

—

124

C₂×D₄

—

125

C₂×D₄

—

126

C₂×D₄

—

127

C₂×D₄

—

128

C₂×D₄

—

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

#64520

yes

characteristic

133

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

134

M₁₆

—

135

M₁₆

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₁₆

—

152

—

139

C₂³

—

140

C₂³

—

141

C₂³

—

142

C₂³

—

143

C₂³

—

144

C₂³

—

145

C₂³

—

146

C₂³

—

147

C₂³

—

148

C₂³

—

149

C₂³

—

150

C₂³

—

151

C₂³

—

152

C₂³

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

153

D₄

—

154

D₄

—

155

D₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

#10597290

yes

characteristic

162

C₂×C₄

#10597291

yes

characteristic

163

C₈

—

164

C₈

—

165

C₂²

—

166

C₂²

—

167

C₂²

—

168

C₂²

—

169

C₂²

—

170

C₂²

—

171

C₂²

—

172

C₂²

—

173

C₂²

—

174

C₂²

—

175

C₂²

—

176

C₂²

—

177

C₂²

—

178

C₂²

#11926268

yes

characteristic

179

C₄

—

180

C₄

—

181

C₄

#11926331

yes

—

182

C₂

—

183

C₂

—

184

C₂

—

185

C₂

—

186

C₂

#14561563

yes

characteristic

	subgroup	G/H
center	C₂	#14561563
commutator	C₂⁴×C₁₉	C₂×C₈
Frattini	#407	C₂×D₁₉
Fitting	C₁₉×#1783	C₂
socle	C₂×C₁₉	#1316
prime radical	C₂³×D₄×C₁₉	C₄
cosocle	C₁₉×#407	C₂²
hypercenter	#1783	D₁₉
hypocenter	C₁₉	#7340
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #407 ◁ #1783

subgroup

G/H

center

C₂

#14561563

commutator

C₂⁴×C₁₉

C₂×C₈

Frattini

#407

C₂×D₁₉

Fitting

C₁₉×#1783

C₂

socle

C₂×C₁₉

#1316

prime radical

C₂³×D₄×C₁₉

C₄

cosocle

C₁₉×#407

C₂²

D₁₉

C₁₉

G ▷ C₂⁴×C₁₉ ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #407 ◁ #1783

N	H ≅ G/N	type
1. #14561571	C₂	semidirect
114. C₁₉	#7340	semidirect

H ≅ G/N

type

1. #14561571

C₂

semidirect

114. C₁₉

#7340

semidirect

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

subgroup	index
#14561571	2
C₁₉×#1783	2
#7340	19

subgroup

index

#14561571

C₁₉×#1783

#7340

Subgroups — #18069890

Conjugacy classes of subgroups

Complements

Maximal subgroups