Group #14564901 — subgroups

Subgroups — #14564901

Order 2432.

256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 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	C₂²×#64528	C₂	1	1	yes	maximal, characteristic
2	#11926572	C₂	1	1	yes	maximal, characteristic
3	#11926554	C₂	1	1	yes	maximal, characteristic
4	#11926553	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597281	C₂	1	1	yes	maximal, characteristic
6	#11926308	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#101	C₂	1	1	yes	maximal, characteristic
8	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
10	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×#64528	—	2	2	no	—
13	C₂×#64528	—	2	2	no	—
14	C₂×#64528	—	2	2	no	—
15	#10597372	C₂²	1	1	yes	characteristic
16	C₂×#64520	C₂²	1	1	yes	characteristic
17	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₁₉×#101	—	2	2	no	—
19	#10597292	—	2	2	no	—
20	#10597281	—	2	2	no	—
21	#10597273	—	2	2	no	—
22	Dic₁₉⋊C₈	—	2	2	no	—
23	C₂×Q₈×C₁₉	—	2	1	no	—
24	C₂×Q₈×C₁₉	—	2	1	no	—
25	C₂×Q₈×C₁₉	—	2	1	no	—
26	C₂×Q₈×C₁₉	—	2	1	no	—
27	C₂×Q₈×C₁₉	—	2	1	no	—
28	C₂×Q₈×C₁₉	D₄	1	2	yes	—
29	C₂²×C₄×C₁₉	—	2	1	no	—
30	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×Dic₁₉	—	2	1	no	—
32	C₂×Dic₃₈	—	2	1	no	—
33	C₂×Dic₃₈	—	2	1	no	—
34	C₂×Dic₃₈	—	2	1	no	—
35	C₂×Dic₃₈	—	2	1	no	—
36	C₂×Dic₃₈	—	2	1	no	—
37	C₂×Dic₃₈	D₄	1	2	yes	—
38	M₁₆×C₁₉	—	2	1	no	—
39	M₁₆×C₁₉	—	2	1	no	—
40	M₁₆×C₁₉	—	2	1	no	—
41	M₁₆×C₁₉	—	2	1	no	—
42	C₂×C₈×C₁₉	—	2	1	no	—
43	C₂×C₈×C₁₉	—	2	1	no	—
44	C₂²⋊Dic₁₉	—	2	1	no	—
45	#64528	—	2	8	no	—
46	C₄⋊Dic₁₉	D₄	1	2	yes	—
47	C₄×Dic₁₉	—	2	1	no	—
48	#64520	—	2	1	no	—
49	#64520	—	2	1	no	—
50	C₂×C₁₉⋊C₈	—	2	1	no	—
51	C₂×C₁₉⋊C₈	—	2	1	no	—
52	C₂×C₁₉⋊C₈	—	2	1	no	—
53	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
54	C₂³×C₁₉	#41	1	1	yes	characteristic
55	Q₈×C₁₉	—	2	2	no	—
56	Q₈×C₁₉	—	2	2	no	—
57	Q₈×C₁₉	—	4	1	no	—
58	Q₈×C₁₉	—	4	1	no	—
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	4	1	no	—
61	C₂×C₄×C₁₉	—	4	1	no	—
62	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
68	C₂×Dic₁₉	—	2	2	no	—
69	C₂×Dic₁₉	—	2	2	no	—
70	C₂×Dic₁₉	—	4	1	no	—
71	C₂×Dic₁₉	—	4	1	no	—
72	Dic₃₈	—	2	2	no	—
73	Dic₃₈	—	2	2	no	—
74	Dic₃₈	—	4	1	no	—
75	Dic₃₈	—	4	1	no	—
76	C₈×C₁₉	—	4	1	no	—
77	C₈×C₁₉	—	4	1	no	—
78	C₁₉⋊C₈	—	2	2	no	—
79	C₁₉⋊C₈	—	4	1	no	—
80	#2047	—	19	1	no	maximal, Sylow
81	C₂²×C₁₉	—	2	2	no	—
82	C₂²×C₁₉	#121	1	1	yes	characteristic
83	C₂²×C₁₉	#123	1	1	yes	characteristic
84	C₂²×C₁₉	#123	1	1	yes	characteristic
85	C₄×C₁₉	—	4	2	no	—
86	C₄×C₁₉	#120	1	1	yes	characteristic
87	C₄×C₁₉	#121	1	1	yes	characteristic
88	C₄×C₁₉	#121	1	1	yes	characteristic
89	C₄×C₁₉	#124	1	1	yes	characteristic
90	Dic₁₉	—	4	2	no	—
91	Dic₁₉	—	4	2	no	—
92	C₂²×Q₁₆	—	19	1	no	—
93	#424	—	19	1	no	—
94	#419	—	19	1	no	—
95	#419	—	19	1	no	—
96	C₂×#101	—	19	1	no	—
97	C₂×#101	D₁₉	1	1	yes	characteristic
98	#341	—	19	1	no	—
99	C₂×C₁₉	—	2	1	no	—
100	C₂×C₁₉	—	2	1	no	—
101	C₂×C₁₉	#394	1	1	yes	characteristic
102	C₂×C₁₉	#473	1	2	yes	—
103	C₂²×Q₈	—	19	1	no	—
104	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
105	C₂×Q₁₆	—	38	2	no	—
106	C₂×Q₁₆	—	38	2	no	—
107	C₂×Q₁₆	—	38	2	no	—
108	C₂×M₁₆	—	19	1	no	—
109	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
110	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
111	C₂²×C₈	—	19	1	no	—
112	#117	—	19	1	no	—
113	C₄⋊C₈	—	38	2	no	—
114	#103	—	38	2	no	—
115	#103	—	38	2	no	—
116	#101	—	2	2	no	—
117	#101	—	38	2	no	—
118	C₁₉	#2047	1	1	yes	characteristic, complemented, Sylow
119	C₂×Q₈	—	2	1	no	—
120	C₂×Q₈	—	2	1	no	—
121	C₂×Q₈	—	2	1	no	—
122	C₂×Q₈	—	2	1	no	—
123	C₂×Q₈	—	2	1	no	—
124	C₂×Q₈	—	19	2	no	—
125	C₂×Q₈	—	38	1	no	—
126	C₂×Q₈	—	38	1	no	—
127	C₂×Q₈	—	38	1	no	—
128	C₂×Q₈	—	38	1	no	—
129	C₂×Q₈	—	38	1	no	—
130	C₂×Q₈	C₂²⋊D₁₉	1	2	yes	—
131	C₂²×C₄	—	2	1	no	—
132	C₂²×C₄	—	38	1	no	—
133	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
134	Q₁₆	—	38	8	no	—
135	M₁₆	—	2	1	no	—
136	M₁₆	—	2	1	no	—
137	M₁₆	—	2	1	no	—
138	M₁₆	—	2	1	no	—
139	M₁₆	—	38	1	no	—
140	M₁₆	—	38	1	no	—
141	C₂×C₈	—	2	1	no	—
142	C₂×C₈	—	2	1	no	—
143	C₂×C₈	—	19	2	no	—
144	C₂×C₈	—	38	1	no	—
145	C₂×C₈	—	38	1	no	—
146	C₂×C₈	—	38	1	no	—
147	C₄⋊C₄	—	19	2	no	—
148	C₂²⋊C₄	—	38	1	no	—
149	C₄²	—	38	1	no	—
150	C₂³	#64541	1	1	yes	characteristic
151	Q₈	—	2	2	no	—
152	Q₈	—	2	2	no	—
153	Q₈	—	4	1	no	—
154	Q₈	—	4	1	no	—
155	Q₈	—	38	2	no	—
156	Q₈	—	38	2	no	—
157	Q₈	—	76	1	no	—
158	Q₈	—	76	1	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	4	1	no	—
161	C₂×C₄	—	4	1	no	—
162	C₂×C₄	—	38	2	no	—
163	C₂×C₄	—	38	2	no	—
164	C₂×C₄	—	76	1	no	—
165	C₂×C₄	—	76	1	no	—
166	C₂×C₄	#64541	1	1	yes	characteristic
167	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
168	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
169	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
170	C₂×C₄	#64543	1	1	yes	characteristic
171	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
172	C₈	—	4	1	no	—
173	C₈	—	4	1	no	—
174	C₈	—	38	2	no	—
175	C₈	—	76	1	no	—
176	C₂²	—	2	2	no	—
177	C₂²	#10597329	1	1	yes	characteristic
178	C₂²	#10597330	1	1	yes	characteristic
179	C₂²	#10597375	1	1	yes	characteristic
180	C₄	—	4	2	no	—
181	C₄	—	76	2	no	—
182	C₄	—	76	2	no	—
183	C₄	#10597330	1	1	yes	characteristic
184	C₄	#10597331	1	1	yes	characteristic
185	C₄	#10597383	1	1	yes	characteristic
186	C₄	#10597385	1	1	yes	characteristic
187	C₂	—	2	1	no	—
188	C₂	—	2	1	no	—
189	C₂	#11926459	1	1	yes	characteristic
190	C₂	#11926818	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64528

C₂

yes

maximal, characteristic

#11926572

C₂

yes

maximal, characteristic

#11926554

C₂

yes

maximal, characteristic

#11926553

C₂

yes

maximal, characteristic

C₂×#10597281

C₂

yes

maximal, characteristic

#11926308

C₂

yes

maximal, characteristic

C₂×C₁₉×#101

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

—

—

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#101

—

#10597292

—

#10597281

—

#10597273

—

Dic₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂²⋊Dic₁₉

—

#64528

—

C₄⋊Dic₁₉

D₄

yes

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

#41

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2047

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₂²×Q₁₆

—

—

—

—

—

D₁₉

yes

characteristic

#341

—

C₂×C₁₉

—

100

C₂×C₁₉

—

101

C₂×C₁₉

#394

yes

characteristic

102

C₂×C₁₉

#473

yes

—

103

C₂²×Q₈

—

104

C₂²×Q₈

C₂×D₁₉

yes

characteristic

105

C₂×Q₁₆

—

106

C₂×Q₁₆

—

107

C₂×Q₁₆

—

108

C₂×M₁₆

—

109

C₂×M₁₆

C₂×D₁₉

yes

characteristic

110

C₂×M₁₆

C₂×D₁₉

yes

characteristic

111

C₂²×C₈

—

112

#117

—

113

C₄⋊C₈

—

114

#103

—

115

#103

—

116

#101

—

117

#101

—

118

C₁₉

#2047

yes

characteristic, complemented, Sylow

119

C₂×Q₈

—

120

C₂×Q₈

—

121

C₂×Q₈

—

122

C₂×Q₈

—

123

C₂×Q₈

—

124

C₂×Q₈

—

125

C₂×Q₈

—

126

C₂×Q₈

—

127

C₂×Q₈

—

128

C₂×Q₈

—

129

C₂×Q₈

—

130

C₂×Q₈

C₂²⋊D₁₉

yes

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

C₂²×D₁₉

yes

characteristic

134

Q₁₆

—

135

M₁₆

—

136

M₁₆

—

137

M₁₆

—

138

M₁₆

—

139

M₁₆

—

140

M₁₆

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

—

147

C₄⋊C₄

—

148

C₂²⋊C₄

—

149

C₄²

—

150

C₂³

#64541

yes

characteristic

151

Q₈

—

152

Q₈

—

153

Q₈

—

154

Q₈

—

155

Q₈

—

156

Q₈

—

157

Q₈

—

158

Q₈

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

#64541

yes

characteristic

167

C₂×C₄

D₄×D₁₉

yes

characteristic

168

C₂×C₄

D₄×D₁₉

yes

characteristic

169

C₂×C₄

D₄×D₁₉

yes

characteristic

170

C₂×C₄

#64543

yes

characteristic

171

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

172

C₈

—

173

C₈

—

174

C₈

—

175

C₈

—

176

C₂²

—

177

C₂²

#10597329

yes

characteristic

178

C₂²

#10597330

yes

characteristic

179

C₂²

#10597375

yes

characteristic

180

C₄

—

181

C₄

—

182

C₄

—

183

C₄

#10597330

yes

characteristic

184

C₄

#10597331

yes

characteristic

185

C₄

#10597383

yes

characteristic

186

C₄

#10597385

yes

characteristic

187

C₂

—

188

C₂

—

189

C₂

#11926459

yes

characteristic

190

C₂

#11926818

yes

—

	subgroup	G/H
center	C₂²	#10597330
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#101	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂³×C₁₉	#41
hypercenter	C₂×#101	D₁₉
hypocenter	C₁₉	#2047
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#101

subgroup

G/H

center

C₂²

#10597330

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#101

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#101

N	H ≅ G/N	type
118. C₁₉	#2047	semidirect

H ≅ G/N

type

118. C₁₉

#2047

semidirect

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

subgroup	index
C₂²×#64528	2
#11926572	2
#11926554	2
#11926553	2
C₂×#10597281	2
#11926308	2
C₂×C₁₉×#101	2
#2047	19

subgroup

index

C₂²×#64528

C₂×C₁₉×#101

Subgroups — #14564901

Conjugacy classes of subgroups

Complements

Maximal subgroups