Group #14564056 — subgroups

Subgroups — #14564056

Order 2432.

380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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	C₂³×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597370	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597267	C₂	1	2	yes	maximal, complemented
4	#11926306	C₂	1	2	yes	maximal, complemented
5	C₁₉×#380	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
10	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
11	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	#10597370	—	2	2	no	—
13	#10597370	C₄	1	4	yes	complemented
14	C₂×Dic₁₉⋊C₄	—	2	1	no	—
15	C₂²×C₁₉⋊C₈	—	2	2	no	—
16	C₂²×C₁₉⋊C₈	—	2	4	no	—
17	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
18	C₁₉×#95	—	2	1	no	—
19	#10597267	—	2	4	no	—
20	C₂⁴×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	—	2	2	no	—
22	C₂²×C₄×C₁₉	—	2	2	no	—
23	C₂²×C₄×C₁₉	—	2	2	no	—
24	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
25	C₂²×C₄×C₁₉	D₄	1	2	yes	—
26	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×Dic₁₉	—	2	1	no	—
29	C₂²×Dic₁₉	—	2	1	no	—
30	C₂×Dic₃₈	—	2	2	no	—
31	C₂×Dic₃₈	—	2	2	no	—
32	C₂×Dic₃₈	—	2	1	no	—
33	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
34	C₄⋊C₄×C₁₉	—	2	2	no	—
35	C₄⋊C₄×C₁₉	—	2	2	no	—
36	C₂²⋊C₄×C₁₉	—	4	2	no	—
37	C₂²⋊Dic₁₉	—	2	4	no	—
38	C₄⋊Dic₁₉	—	2	1	no	—
39	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
40	Dic₁₉⋊C₄	—	2	4	no	—
41	C₂×C₁₉⋊C₈	—	2	8	no	—
42	C₂×C₁₉⋊C₈	—	2	2	no	—
43	C₂×C₁₉⋊C₈	—	2	2	no	—
44	C₂×C₁₉⋊C₈	D₄	1	4	yes	—
45	C₂³×C₁₉	—	2	2	no	—
46	C₂³×C₁₉	—	2	2	no	—
47	C₂³×C₁₉	C₂²⋊C₄	1	2	yes	—
48	C₂³×C₁₉	SD₁₆	1	2	yes	—
49	C₂³×C₁₉	Q₁₆	1	2	yes	—
50	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	4	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	—	4	2	no	—
56	C₂×C₄×C₁₉	—	4	2	no	—
57	C₂×C₄×C₁₉	—	4	2	no	—
58	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
59	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
62	C₂×C₄×C₁₉	#41	1	2	yes	—
63	C₂×Dic₁₉	—	2	2	no	—
64	C₂×Dic₁₉	—	2	2	no	—
65	C₂×Dic₁₉	—	4	2	no	—
66	C₂×Dic₁₉	—	4	2	no	—
67	Dic₃₈	—	2	4	no	—
68	Dic₃₈	—	4	1	no	—
69	Dic₃₈	—	4	1	no	—
70	C₁₉⋊C₈	—	2	4	no	—
71	#1892	—	19	1	no	maximal, Sylow
72	C₂²×C₁₉	—	2	2	no	—
73	C₂²×C₁₉	—	2	2	no	—
74	C₂²×C₁₉	—	2	4	no	—
75	C₂²×C₁₉	—	2	4	no	—
76	C₂²×C₁₉	#103	1	4	yes	complemented
77	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₁₉	#121	1	2	yes	—
79	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
80	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
81	C₂²×C₁₉	#135	1	2	yes	—
82	C₄×C₁₉	—	2	2	no	—
83	C₄×C₁₉	—	8	2	no	—
84	C₄×C₁₉	C₄×D₄	1	2	yes	—
85	C₄×C₁₉	#120	1	1	yes	characteristic
86	C₄×C₁₉	#123	1	1	yes	characteristic
87	Dic₁₉	—	4	2	no	—
88	Dic₁₉	—	4	2	no	—
89	C₂³×C₈	—	19	1	no	—
90	C₂×C₂²⋊Q₈	—	19	1	no	—
91	C₂×#103	—	19	2	no	—
92	#380	D₁₉	1	1	yes	characteristic
93	#340	—	19	2	no	—
94	C₂×C₁₉	—	2	4	no	—
95	C₂×C₁₉	#386	1	1	yes	characteristic
96	C₂×C₁₉	C₂×#103	1	1	yes	characteristic
97	C₂×C₁₉	#416	1	1	yes	characteristic
98	C₂×C₁₉	#465	1	2	yes	—
99	C₂×C₁₉	#467	1	2	yes	—
100	C₂²×Q₈	—	19	1	no	—
101	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
102	C₂²×C₈	—	19	2	no	—
103	C₂²×C₈	—	38	4	no	—
104	C₂²×C₈	—	38	2	no	—
105	C₂²⋊Q₈	—	19	4	no	—
106	C₂²⋊Q₈	—	38	2	no	—
107	C₂×C₄⋊C₄	—	19	1	no	—
108	C₂×C₄⋊C₄	—	38	1	no	—
109	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
110	C₂×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₂²⋊C₄	—	38	1	no	—
112	#103	—	38	4	no	—
113	#95	—	2	1	no	—
114	C₁₉	#1892	1	1	yes	characteristic, complemented, Sylow
115	C₂⁴	C₂²⋊D₁₉	1	1	yes	characteristic
116	C₂×Q₈	—	19	2	no	—
117	C₂×Q₈	—	38	1	no	—
118	C₂×Q₈	—	38	2	no	—
119	C₂×Q₈	—	38	2	no	—
120	C₂²×C₄	—	2	2	no	—
121	C₂²×C₄	—	2	2	no	—
122	C₂²×C₄	—	2	2	no	—
123	C₂²×C₄	—	38	1	no	—
124	C₂²×C₄	—	38	1	no	—
125	C₂²×C₄	C₄×D₁₉	1	2	yes	—
126	C₂²×C₄	D₇₆	1	2	yes	—
127	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
128	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
129	C₂×C₈	—	19	4	no	—
130	C₂×C₈	—	38	8	no	—
131	C₂×C₈	—	38	2	no	—
132	C₂×C₈	—	38	2	no	—
133	C₄⋊C₄	—	2	2	no	—
134	C₄⋊C₄	—	2	2	no	—
135	C₄⋊C₄	—	19	2	no	—
136	C₄⋊C₄	—	38	4	no	—
137	C₄⋊C₄	—	38	1	no	—
138	C₂²⋊C₄	—	4	2	no	—
139	C₂²⋊C₄	—	38	4	no	—
140	C₂³	—	2	2	no	—
141	C₂³	—	2	2	no	—
142	C₂³	(C₂×D₁₉)⋊C₄	1	2	yes	—
143	C₂³	#64526	1	2	yes	—
144	C₂³	#64528	1	2	yes	—
145	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
146	Q₈	—	38	4	no	—
147	Q₈	—	76	1	no	—
148	Q₈	—	76	1	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	2	4	no	—
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	4	2	no	—
154	C₂×C₄	—	4	2	no	—
155	C₂×C₄	—	4	2	no	—
156	C₂×C₄	—	38	2	no	—
157	C₂×C₄	—	38	2	no	—
158	C₂×C₄	—	76	2	no	—
159	C₂×C₄	—	76	2	no	—
160	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
161	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
162	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
163	C₂×C₄	D₄×D₁₉	1	2	yes	—
164	C₂×C₄	#64543	1	2	yes	—
165	C₈	—	38	4	no	—
166	C₂²	—	2	2	no	—
167	C₂²	—	2	2	no	—
168	C₂²	—	2	4	no	—
169	C₂²	—	2	4	no	—
170	C₂²	#10597267	1	4	yes	complemented
171	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
172	C₂²	C₂×#64526	1	1	yes	characteristic
173	C₂²	#10597385	1	2	yes	—
174	C₂²	C₂×#64528	1	1	yes	characteristic
175	C₂²	#10597396	1	2	yes	—
176	C₄	—	2	2	no	—
177	C₄	—	8	2	no	—
178	C₄	—	76	2	no	—
179	C₄	—	76	2	no	—
180	C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
181	C₄	#10597328	1	1	yes	characteristic
182	C₄	#10597332	1	1	yes	characteristic
183	C₂	—	2	4	no	—
184	C₂	#11926421	1	1	yes	characteristic
185	C₂	C₂×#10597267	1	1	yes	characteristic
186	C₂	#11926538	1	1	yes	characteristic
187	C₂	#11926771	1	2	yes	—
188	C₂	#11926783	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×C₁₉⋊C₈

C₂

yes

maximal, characteristic

C₂×#10597370

C₂

yes

maximal, characteristic

C₂×#10597267

C₂

yes

maximal, complemented

#11926306

C₂

yes

maximal, complemented

C₁₉×#380

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

#10597370

—

#10597370

C₄

yes

complemented

C₂×Dic₁₉⋊C₄

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₁₉×#95

—

#10597267

—

C₂⁴×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂×C₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₄

yes

—

C₂³×C₁₉

SD₁₆

yes

—

C₂³×C₁₉

Q₁₆

yes

—

C₂³×C₁₉

C₂×D₄

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

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₁₉⋊C₈

—

#1892

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#103

yes

complemented

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

#121

yes

—

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₂²×C₁₉

C₂×Q₁₆

yes

characteristic

C₂²×C₁₉

#135

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₂³×C₈

—

C₂×C₂²⋊Q₈

—

C₂×#103

—

#380

D₁₉

yes

characteristic

#340

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#467

yes

—

100

C₂²×Q₈

—

101

C₂³×C₄

C₂×D₁₉

yes

characteristic

102

C₂²×C₈

—

103

C₂²×C₈

—

104

C₂²×C₈

—

105

C₂²⋊Q₈

—

106

C₂²⋊Q₈

—

107

C₂×C₄⋊C₄

—

108

C₂×C₄⋊C₄

—

109

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

110

C₂×C₂²⋊C₄

—

111

C₂×C₂²⋊C₄

—

112

#103

—

113

#95

—

114

C₁₉

#1892

yes

characteristic, complemented, Sylow

115

C₂⁴

C₂²⋊D₁₉

yes

characteristic

116

C₂×Q₈

—

117

C₂×Q₈

—

118

C₂×Q₈

—

119

C₂×Q₈

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

C₄×D₁₉

yes

—

126

C₂²×C₄

D₇₆

yes

—

127

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

128

C₂²×C₄

C₂²×D₁₉

yes

characteristic

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₄⋊C₄

—

134

C₄⋊C₄

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₂²⋊C₄

—

139

C₂²⋊C₄

—

140

C₂³

—

141

C₂³

—

142

C₂³

(C₂×D₁₉)⋊C₄

yes

—

143

C₂³

#64526

yes

—

144

C₂³

#64528

yes

—

145

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

146

Q₈

—

147

Q₈

—

148

Q₈

—

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

(C₂×D₁₉)⋊C₄

yes

—

161

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

162

C₂×C₄

C₂×D₇₆

yes

characteristic

163

C₂×C₄

D₄×D₁₉

yes

—

164

C₂×C₄

#64543

yes

—

165

C₈

—

166

C₂²

—

167

C₂²

—

168

C₂²

—

169

C₂²

—

170

C₂²

#10597267

yes

complemented

171

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

172

C₂²

C₂×#64526

yes

characteristic

173

C₂²

#10597385

yes

—

174

C₂²

C₂×#64528

yes

characteristic

175

C₂²

#10597396

yes

—

176

C₄

—

177

C₄

—

178

C₄

—

179

C₄

—

180

C₄

(C₂²⋊D₁₉)⋊C₄

yes

—

181

C₄

#10597328

yes

characteristic

182

C₄

#10597332

yes

characteristic

183

C₂

—

184

C₂

#11926421

yes

characteristic

185

C₂

C₂×#10597267

yes

characteristic

186

C₂

#11926538

yes

characteristic

187

C₂

#11926771

yes

—

188

C₂

#11926783

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#380	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂⁴×C₁₉	D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#380	D₁₉
hypocenter	C₁₉	#1892
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ #380

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#380

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂⁴×C₁₉

D₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ #380

N	H ≅ G/N	type
3. C₂×#10597267	C₂	semidirect
4. #11926306	C₂	semidirect
13. #10597370	C₄	semidirect
76. C₂²×C₁₉	#103	semidirect
114. C₁₉	#1892	semidirect
170. C₂²	#10597267	semidirect

H ≅ G/N

type

3. C₂×#10597267

C₂

semidirect

4. #11926306

C₂

semidirect

13. #10597370

C₄

semidirect

76. C₂²×C₁₉

#103

semidirect

114. C₁₉

#1892

semidirect

170. C₂²

#10597267

semidirect

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

subgroup	index
C₂³×C₁₉⋊C₈	2
C₂×#10597370	2
C₂×#10597267	2
#11926306	2
C₁₉×#380	2
#1892	19

subgroup

index

C₂³×C₁₉⋊C₈

C₁₉×#380

Subgroups — #14564056

Conjugacy classes of subgroups

Complements

Maximal subgroups