Group #18081936 — subgroups

Subgroups — #18081936

Order 4864.

478 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 119 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	#14563766	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562195	C₂	1	4	yes	maximal, complemented
3	#14561927	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3147	C₂	1	1	yes	maximal, characteristic
5	#11926597	C₂²	1	2	yes	—
6	#11926410	C₂²	1	2	yes	—
7	#11926307	—	2	2	no	—
8	#11926278	—	2	8	no	—
9	#11926266	—	2	2	no	—
10	C₂×C₁₉×#135	—	2	2	no	—
11	C₁₉×#532	C₂²	1	2	yes	—
12	C₁₉×#495	—	2	2	no	—
13	C₁₉×#494	C₄	1	1	yes	characteristic, complemented
14	C₁₉×#493	C₄	1	1	yes	characteristic, complemented
15	C₁₉×#492	C₄	1	2	yes	complemented
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×#41×C₁₉	—	2	2	no	—
18	C₁₉×#135	—	4	8	no	—
19	C₂×Q₁₆×C₁₉	—	2	2	no	—
20	C₂×SD₁₆×C₁₉	—	2	4	no	—
21	C₂×D₈×C₁₉	—	2	2	no	—
22	C₂²×C₈×C₁₉	D₄	1	2	yes	—
23	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
24	C₁₉×#127	C₂×C₄	1	2	yes	—
25	C₁₉×#124	—	2	2	no	—
26	C₁₉×#121	—	2	4	no	—
27	C₄×D₄×C₁₉	—	2	4	no	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₄⋊Dic₁₉	—	2	2	no	—
30	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₄×C₈×C₁₉	D₄	1	2	yes	—
33	C₁₉⋊#95	—	2	4	no	—
34	C₂²⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
35	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
36	C₄×C₁₉⋊C₈	—	2	2	no	—
37	#41×C₁₉	—	4	8	no	—
38	C₂×Q₈×C₁₉	—	2	2	no	—
39	C₂×D₄×C₁₉	—	2	2	no	—
40	C₂×D₄×C₁₉	—	2	4	no	—
41	C₂×D₄×C₁₉	—	4	2	no	—
42	C₂²×C₄×C₁₉	—	4	2	no	—
43	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
44	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂²×Dic₁₉	—	4	2	no	—
46	Q₁₆×C₁₉	—	4	4	no	—
47	SD₁₆×C₁₉	—	4	8	no	—
48	D₈×C₁₉	—	4	4	no	—
49	C₂×C₈×C₁₉	—	2	4	no	—
50	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
51	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
52	C₄⋊C₄×C₁₉	—	2	4	no	—
53	C₂²⋊C₄×C₁₉	—	4	4	no	—
54	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
55	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₄²×C₁₉	#41	1	2	yes	—
57	C₄⋊Dic₁₉	—	4	4	no	—
58	C₂×C₁₉⋊C₈	—	2	4	no	—
59	#9760	—	19	1	no	maximal, Sylow
60	C₂³×C₁₉	—	4	2	no	—
61	C₂³×C₁₉	#127	1	1	yes	characteristic
62	Q₈×C₁₉	—	4	4	no	—
63	D₄×C₁₉	—	4	4	no	—
64	D₄×C₁₉	—	8	4	no	—
65	D₄×C₁₉	—	8	4	no	—
66	C₂×C₄×C₁₉	—	4	2	no	—
67	C₂×C₄×C₁₉	—	4	2	no	—
68	C₂×C₄×C₁₉	—	8	4	no	—
69	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
71	C₂×C₄×C₁₉	#121	1	2	yes	—
72	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
73	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
74	C₂×Dic₁₉	—	8	4	no	—
75	C₂×Dic₁₉	—	8	2	no	—
76	C₈×C₁₉	—	2	2	no	—
77	C₈×C₁₉	—	2	2	no	—
78	C₁₉⋊C₈	—	4	4	no	—
79	#3147	D₁₉	1	1	yes	characteristic
80	#1835	—	19	1	no	—
81	#1517	—	19	4	no	—
82	#1452	—	19	1	no	—
83	C₂²×C₁₉	—	2	2	no	—
84	C₂²×C₁₉	—	8	2	no	—
85	C₂²×C₁₉	—	8	4	no	—
86	C₂²×C₁₉	#390	1	1	yes	characteristic
87	C₂²×C₁₉	#496	1	2	yes	—
88	C₄×C₁₉	—	2	2	no	—
89	C₄×C₁₉	—	2	2	no	—
90	C₄×C₁₉	—	8	2	no	—
91	C₄×C₁₉	#418	1	2	yes	—
92	C₄×C₁₉	#490	1	2	yes	—
93	Dic₁₉	—	16	2	no	—
94	C₂×#135	—	2	2	no	—
95	#532	C₂×D₁₉	1	2	yes	—
96	#495	—	2	2	no	—
97	#494	Dic₁₉	1	1	yes	characteristic, complemented
98	#493	Dic₁₉	1	1	yes	characteristic, complemented
99	#492	Dic₁₉	1	2	yes	complemented
100	#431	—	19	2	no	—
101	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
102	#382	—	19	2	no	—
103	#340	—	38	2	no	—
104	#327	—	38	8	no	—
105	#322	—	38	2	no	—
106	C₂×C₁₉	—	2	2	no	—
107	C₂×C₁₉	—	16	2	no	—
108	C₂×C₁₉	#1961	1	1	yes	characteristic
109	C₂×C₁₉	#1976	1	2	yes	—
110	C₂×#41	—	2	2	no	—
111	#135	—	4	8	no	—
112	C₂×Q₁₆	—	2	2	no	—
113	C₂×SD₁₆	—	2	4	no	—
114	C₂×D₈	—	2	2	no	—
115	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
116	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
117	#127	C₂×Dic₁₉	1	2	yes	—
118	#124	—	2	2	no	—
119	#121	—	2	4	no	—
120	C₄×D₄	—	2	4	no	—
121	C₂×C₄⋊C₄	—	38	2	no	—
122	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
123	C₄⋊C₈	—	38	2	no	—
124	C₂²⋊C₈	—	19	4	no	—
125	C₄×C₈	—	38	2	no	—
126	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
127	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
128	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
129	#95	—	38	4	no	—
130	C₁₉	#9760	1	1	yes	characteristic, complemented, Sylow
131	#41	—	4	8	no	—
132	C₂×Q₈	—	2	2	no	—
133	C₂×D₄	—	2	4	no	—
134	C₂×D₄	—	2	2	no	—
135	C₂×D₄	—	4	2	no	—
136	C₂²×C₄	—	4	2	no	—
137	C₂²×C₄	—	76	2	no	—
138	C₂²×C₄	D₄×D₁₉	1	2	yes	—
139	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
140	Q₁₆	—	4	4	no	—
141	SD₁₆	—	4	8	no	—
142	D₈	—	4	4	no	—
143	C₂×C₈	—	2	4	no	—
144	C₂×C₈	—	38	4	no	—
145	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
146	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
147	C₄⋊C₄	—	2	4	no	—
148	C₄⋊C₄	—	76	4	no	—
149	C₂²⋊C₄	—	4	4	no	—
150	C₄²	#64543	1	2	yes	—
151	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
152	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
153	C₂³	—	4	2	no	—
154	C₂³	#10597386	1	1	yes	characteristic
155	Q₈	—	4	4	no	—
156	D₄	—	4	4	no	—
157	D₄	—	8	4	no	—
158	D₄	—	8	4	no	—
159	C₂×C₄	—	4	2	no	—
160	C₂×C₄	—	4	2	no	—
161	C₂×C₄	—	8	4	no	—
162	C₂×C₄	—	152	4	no	—
163	C₂×C₄	—	152	2	no	—
164	C₂×C₄	#10597378	1	4	yes	—
165	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
166	C₂×C₄	#10597382	1	1	yes	characteristic
167	C₂×C₄	#10597384	1	2	yes	—
168	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
169	C₈	—	2	2	no	—
170	C₈	—	2	2	no	—
171	C₈	—	76	4	no	—
172	C₂²	—	2	2	no	—
173	C₂²	—	8	2	no	—
174	C₂²	—	8	4	no	—
175	C₂²	#11926447	1	1	yes	characteristic
176	C₂²	#11926931	1	2	yes	—
177	C₄	—	2	2	no	—
178	C₄	—	2	2	no	—
179	C₄	—	8	2	no	—
180	C₄	—	304	2	no	—
181	C₄	#11926549	1	2	yes	—
182	C₄	#11926908	1	2	yes	—
183	C₂	—	2	2	no	—
184	C₂	—	16	2	no	—
185	C₂	#14564460	1	1	yes	characteristic
186	C₂	#14564534	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563766

C₂

yes

maximal, characteristic, complemented

#14562195

C₂

yes

maximal, complemented

#14561927

C₂

yes

maximal, characteristic, complemented

C₁₉×#3147

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

#11926410

C₂²

yes

—

#11926307

—

#11926278

—

#11926266

—

C₂×C₁₉×#135

—

C₁₉×#532

C₂²

yes

—

C₁₉×#495

—

C₁₉×#494

C₄

yes

characteristic, complemented

C₁₉×#493

C₄

yes

characteristic, complemented

C₁₉×#492

C₄

yes

complemented

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×#41×C₁₉

—

C₁₉×#135

—

C₂×Q₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×#127

C₂×C₄

yes

—

C₁₉×#124

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

#9760

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#127

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

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

AGL(1,ℤ/8)

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#3147

D₁₉

yes

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#390

yes

characteristic

C₂²×C₁₉

#496

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#418

yes

—

C₄×C₁₉

#490

yes

—

Dic₁₉

—

C₂×#135

—

#532

C₂×D₁₉

yes

—

#495

—

#494

Dic₁₉

yes

characteristic, complemented

#493

Dic₁₉

yes

characteristic, complemented

#492

Dic₁₉

yes

complemented

100

#431

—

101

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

102

#382

—

103

#340

—

104

#327

—

105

#322

—

106

C₂×C₁₉

—

107

C₂×C₁₉

—

108

C₂×C₁₉

#1961

yes

characteristic

109

C₂×C₁₉

#1976

yes

—

110

C₂×#41

—

111

#135

—

112

C₂×Q₁₆

—

113

C₂×SD₁₆

—

114

C₂×D₈

—

115

C₂²×C₈

C₂²⋊D₁₉

yes

—

116

C₄⋊Q₈

C₂×Dic₁₉

yes

—

117

#127

C₂×Dic₁₉

yes

—

118

#124

—

119

#121

—

120

C₄×D₄

—

121

C₂×C₄⋊C₄

—

122

C₂×C₄²

C₂²×D₁₉

yes

characteristic

123

C₄⋊C₈

—

124

C₂²⋊C₈

—

125

C₄×C₈

—

126

C₄×C₈

C₂×Dic₁₉

yes

characteristic

127

C₄×C₈

C₂×Dic₁₉

yes

characteristic

128

C₄×C₈

C₂²⋊D₁₉

yes

—

129

#95

—

130

C₁₉

#9760

yes

characteristic, complemented, Sylow

131

#41

—

132

C₂×Q₈

—

133

C₂×D₄

—

134

C₂×D₄

—

135

C₂×D₄

—

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

D₄×D₁₉

yes

—

139

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

140

Q₁₆

—

141

SD₁₆

—

142

D₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

C₂²⋊Dic₁₉

yes

—

146

C₂×C₈

C₂²⋊Dic₁₉

yes

—

147

C₄⋊C₄

—

148

C₄⋊C₄

—

149

C₂²⋊C₄

—

150

C₄²

#64543

yes

—

151

C₄²

C₂²×Dic₁₉

yes

characteristic

152

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

153

C₂³

—

154

C₂³

#10597386

yes

characteristic

155

Q₈

—

156

D₄

—

157

D₄

—

158

D₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

152

—

163

C₂×C₄

—

152

—

164

C₂×C₄

#10597378

yes

—

165

C₂×C₄

D₄×Dic₁₉

yes

—

166

C₂×C₄

#10597382

yes

characteristic

167

C₂×C₄

#10597384

yes

—

168

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

169

C₈

—

170

C₈

—

171

C₈

—

172

C₂²

—

173

C₂²

—

174

C₂²

—

175

C₂²

#11926447

yes

characteristic

176

C₂²

#11926931

yes

—

177

C₄

—

178

C₄

—

179

C₄

—

180

C₄

—

304

—

181

C₄

#11926549

yes

—

182

C₄

#11926908

yes

—

183

C₂

—

184

C₂

—

185

C₂

#14564460

yes

characteristic

186

C₂

#14564534

yes

—

	subgroup	G/H
center	C₂²	#11926447
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3147	C₂
socle	C₂²×C₁₉	#390
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3147	D₁₉
hypocenter	C₁₉	#9760
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3147

subgroup

G/H

center

C₂²

#11926447

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting, prime radical

C₁₉×#3147

C₂

socle

C₂²×C₁₉

#390

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3147

N	H ≅ G/N	type
1. #14563766	C₂	semidirect
2. #14562195	C₂	semidirect
3. #14561927	C₂	semidirect
13. C₁₉×#494	C₄	semidirect
14. C₁₉×#493	C₄	semidirect
15. C₁₉×#492	C₄	semidirect
97. #494	Dic₁₉	semidirect
98. #493	Dic₁₉	semidirect
99. #492	Dic₁₉	semidirect
130. C₁₉	#9760	semidirect

H ≅ G/N

type

1. #14563766

C₂

semidirect

2. #14562195

C₂

semidirect

3. #14561927

C₂

semidirect

13. C₁₉×#494

C₄

semidirect

14. C₁₉×#493

C₄

semidirect

15. C₁₉×#492

C₄

semidirect

97. #494

Dic₁₉

semidirect

98. #493

Dic₁₉

semidirect

99. #492

Dic₁₉

semidirect

130. C₁₉

#9760

semidirect

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

subgroup	index
#14563766	2
#14562195	2
#14561927	2
C₁₉×#3147	2
#9760	19

subgroup

index

C₁₉×#3147

Subgroups — #18081936

Conjugacy classes of subgroups

Complements

Maximal subgroups