Group #19143227 — subgroups

Subgroups — #19143227

Order 5504.

484 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 197 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	C₂×C₄²×D₄₃	C₂	1	1	yes	maximal, characteristic
2	#14582955	C₂	1	4	yes	maximal, complemented
3	#14582951	C₂	1	4	yes	maximal, complemented
4	#14582923	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582862	C₂	1	2	yes	maximal
6	M₁₆×Dic₄₃	C₂	1	2	yes	maximal, complemented
7	C₄₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄₃	C₄	1	2	yes	—
9	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
10	C₂×#10621877	C₂²	1	2	yes	—
11	C₂×C₄×Dic₄₃	C₄	1	2	yes	—
12	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
13	C₄²×D₄₃	C₄	1	2	yes	—
14	C₄²×D₄₃	C₄	1	2	yes	—
15	C₄²×D₄₃	C₂²	1	2	yes	—
16	C₄²×D₄₃	C₂²	1	2	yes	—
17	C₄⋊(C₄₃⋊C₈)	C₂²	1	4	yes	complemented
18	(C₂×D₄₃)⋊C₈	C₂²	1	8	yes	—
19	#13063235	C₂²	1	4	yes	complemented
20	C₈×Dic₄₃	C₂²	1	4	yes	complemented
21	C₂×M₁₆×C₄₃	C₂²	1	2	yes	—
22	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
23	C₄⋊C₈×C₄₃	C₂²	1	4	yes	complemented
24	C₂³×D₄₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
27	C₂²×Dic₄₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×Dic₄₃	C₂×C₄	1	2	yes	—
29	C₂×C₄×D₄₃	—	2	2	no	—
30	C₂×C₄×D₄₃	—	2	2	no	—
31	C₂×C₄×D₄₃	—	2	8	no	—
32	C₂×C₄×D₄₃	C₂×C₄	1	2	yes	—
33	C₂×C₄×D₄₃	C₂×C₄	1	2	yes	—
34	C₂×C₄×D₄₃	C₂×C₄	1	2	yes	—
35	C₂×C₄×D₄₃	C₂×C₄	1	2	yes	—
36	C₂×C₄×D₄₃	C₂×C₄	1	2	yes	—
37	C₂×C₄×D₄₃	C₂³	1	2	yes	—
38	M₁₆×C₄₃	—	2	4	no	—
39	C₂×C₈×C₄₃	C₂³	1	4	yes	—
40	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
41	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
42	C₄²×C₄₃	C₂³	1	2	yes	—
43	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
44	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
45	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
46	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
47	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
48	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
49	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
50	#10621877	—	2	4	no	—
51	C₂×C₄₃⋊C₈	C₂³	1	4	yes	—
52	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
53	C₂²×D₄₃	—	2	2	no	—
54	C₂²×D₄₃	—	2	4	no	—
55	C₂²×D₄₃	C₂²×C₄	1	2	yes	—
56	C₂×C₄×C₄₃	—	2	4	no	—
57	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
58	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
60	C₂×C₄×C₄₃	#41	1	2	yes	—
61	C₂×C₄×C₄₃	#41	1	2	yes	—
62	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
63	C₂×Dic₄₃	—	2	2	no	—
64	C₂×Dic₄₃	—	2	4	no	—
65	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
66	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
67	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
68	C₄×D₄₃	—	2	4	no	—
69	C₄×D₄₃	—	2	4	no	—
70	C₄×D₄₃	—	2	4	no	—
71	C₄×D₄₃	—	2	2	no	—
72	C₄×D₄₃	—	2	2	no	—
73	C₄×D₄₃	—	2	4	no	—
74	C₄×D₄₃	M₁₆	1	8	yes	complemented
75	C₈×C₄₃	—	2	4	no	—
76	C₄₃⋊C₈	—	2	4	no	—
77	C₂²×C₄₃	—	2	2	no	—
78	C₂²×C₄₃	#117	1	2	yes	—
79	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
80	C₂×D₄₃	—	2	8	no	—
81	C₂×D₄₃	—	2	2	no	—
82	C₂×D₄₃	—	2	2	no	—
83	C₂×D₄₃	C₂×M₁₆	1	4	yes	—
84	C₄×C₄₃	—	2	2	no	—
85	C₄×C₄₃	#117	1	2	yes	—
86	C₄×C₄₃	C₂×M₁₆	1	4	yes	—
87	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
88	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
89	Dic₄₃	—	2	2	no	—
90	Dic₄₃	—	2	2	no	—
91	Dic₄₃	C₂×M₁₆	1	4	yes	—
92	#2920	—	43	1	no	maximal, Sylow
93	C₂×C₄₃	—	2	2	no	—
94	C₂×C₄₃	C₂×#117	1	1	yes	characteristic
95	C₂×C₄₃	C₂²×M₁₆	1	2	yes	—
96	D₄₃	—	2	4	no	—
97	C₂²×C₄²	—	43	1	no	—
98	#432	—	43	4	no	—
99	#431	—	43	4	no	—
100	#423	—	43	1	no	—
101	#423	D₄₃	1	1	yes	characteristic, complemented
102	#407	—	43	2	no	—
103	C₄×M₁₆	—	43	2	no	—
104	C₄₃	#2920	1	1	yes	characteristic, complemented, Sylow
105	C₂³×C₄	—	43	1	no	—
106	C₂³×C₄	—	43	2	no	—
107	C₂×M₁₆	—	43	2	no	—
108	C₂×M₁₆	C₂×D₄₃	1	2	yes	—
109	C₂×C₄²	—	43	1	no	—
110	C₂×C₄²	—	43	2	no	—
111	C₂×C₄²	—	43	2	no	—
112	C₂×C₄²	—	43	2	no	—
113	C₂×C₄²	—	43	2	no	—
114	C₂×C₄²	—	43	2	no	—
115	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
116	C₄⋊C₈	—	43	4	no	—
117	C₄⋊C₈	C₂×D₄₃	1	4	yes	complemented
118	C₂²⋊C₈	—	43	8	no	—
119	#97	—	43	4	no	—
120	C₄×C₈	—	43	4	no	—
121	C₂⁴	—	43	1	no	—
122	C₂²×C₄	—	43	2	no	—
123	C₂²×C₄	—	43	2	no	—
124	C₂²×C₄	—	43	1	no	—
125	C₂²×C₄	—	43	2	no	—
126	C₂²×C₄	—	43	2	no	—
127	C₂²×C₄	—	43	2	no	—
128	C₂²×C₄	—	43	2	no	—
129	C₂²×C₄	—	43	2	no	—
130	C₂²×C₄	—	86	8	no	—
131	C₂²×C₄	—	86	2	no	—
132	C₂²×C₄	—	86	2	no	—
133	C₂²×C₄	C₄×D₄₃	1	2	yes	—
134	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
135	M₁₆	—	2	4	no	—
136	M₁₆	—	86	4	no	—
137	C₂×C₈	—	43	4	no	—
138	C₂×C₈	C₂²×D₄₃	1	4	yes	—
139	C₄²	—	43	2	no	—
140	C₄²	—	43	2	no	—
141	C₄²	—	43	2	no	—
142	C₄²	—	43	2	no	—
143	C₄²	—	43	2	no	—
144	C₄²	—	43	1	no	—
145	C₄²	—	43	1	no	—
146	C₄²	C₄×D₄₃	1	1	yes	characteristic
147	C₄²	C₄×D₄₃	1	1	yes	characteristic
148	C₄²	C₂²×D₄₃	1	2	yes	—
149	C₂³	—	43	2	no	—
150	C₂³	—	86	4	no	—
151	C₂³	—	86	2	no	—
152	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
153	C₂×C₄	—	2	4	no	—
154	C₂×C₄	—	43	2	no	—
155	C₂×C₄	—	43	8	no	—
156	C₂×C₄	—	43	2	no	—
157	C₂×C₄	—	43	2	no	—
158	C₂×C₄	—	86	4	no	—
159	C₂×C₄	—	86	4	no	—
160	C₂×C₄	—	86	4	no	—
161	C₂×C₄	—	86	2	no	—
162	C₂×C₄	—	86	4	no	—
163	C₂×C₄	—	86	4	no	—
164	C₂×C₄	—	86	2	no	—
165	C₂×C₄	—	86	2	no	—
166	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
167	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
168	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
169	C₂×C₄	#10621900	1	2	yes	—
170	C₂×C₄	#10621902	1	2	yes	—
171	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
172	C₈	—	2	4	no	—
173	C₈	—	86	4	no	—
174	C₂²	—	2	2	no	—
175	C₂²	—	43	4	no	—
176	C₂²	—	86	8	no	—
177	C₂²	—	86	2	no	—
178	C₂²	—	86	2	no	—
179	C₂²	#13063283	1	2	yes	—
180	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
181	C₄	—	2	2	no	—
182	C₄	—	43	4	no	—
183	C₄	—	86	2	no	—
184	C₄	—	86	2	no	—
185	C₄	#13063283	1	2	yes	—
186	C₄	M₁₆×D₄₃	1	4	yes	—
187	C₄	C₂×#10621900	1	1	yes	characteristic
188	C₄	C₂×#10621902	1	1	yes	characteristic
189	C₂	—	2	2	no	—
190	C₂	—	86	4	no	—
191	C₂	C₂×#13063283	1	1	yes	characteristic
192	C₂	C₂×M₁₆×D₄₃	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄²×D₄₃

C₂

yes

maximal, characteristic

#14582955

C₂

yes

maximal, complemented

#14582951

C₂

yes

maximal, complemented

#14582923

C₂

yes

maximal, characteristic, complemented

#14582862

C₂

yes

maximal

M₁₆×Dic₄₃

C₂

yes

maximal, complemented

C₄₃×#423

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₃

C₄

yes

—

C₂²×C₄×D₄₃

C₂²

yes

characteristic

C₂×#10621877

C₂²

yes

—

C₂×C₄×Dic₄₃

C₄

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

C₄²×D₄₃

C₄

yes

—

C₄²×D₄₃

C₄

yes

—

C₄²×D₄₃

C₂²

yes

—

C₄²×D₄₃

C₂²

yes

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

complemented

(C₂×D₄₃)⋊C₈

C₂²

yes

—

#13063235

C₂²

yes

complemented

C₈×Dic₄₃

C₂²

yes

complemented

C₂×M₁₆×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

complemented

C₂³×D₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

C₂×C₄

yes

—

C₂×C₄×D₄₃

C₂×C₄

yes

—

C₂×C₄×D₄₃

C₂×C₄

yes

—

C₂×C₄×D₄₃

C₂×C₄

yes

—

C₂×C₄×D₄₃

C₂×C₄

yes

—

C₂×C₄×D₄₃

C₂³

yes

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

—

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

C₂³

yes

characteristic

C₄×Dic₄₃

C₂³

yes

characteristic

#10621877

—

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

M₁₆

yes

complemented

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

#117

yes

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

C₂×M₁₆

yes

—

C₄×C₄₃

—

C₄×C₄₃

#117

yes

—

C₄×C₄₃

C₂×M₁₆

yes

—

C₄×C₄₃

C₂×#41

yes

characteristic

C₄×C₄₃

C₂×#41

yes

characteristic

Dic₄₃

—

Dic₄₃

—

Dic₄₃

C₂×M₁₆

yes

—

#2920

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×#117

yes

characteristic

C₂×C₄₃

C₂²×M₁₆

yes

—

D₄₃

—

C₂²×C₄²

—

#432

—

#431

—

100

#423

—

101

#423

D₄₃

yes

characteristic, complemented

102

#407

—

103

C₄×M₁₆

—

104

C₄₃

#2920

yes

characteristic, complemented, Sylow

105

C₂³×C₄

—

106

C₂³×C₄

—

107

C₂×M₁₆

—

108

C₂×M₁₆

C₂×D₄₃

yes

—

109

C₂×C₄²

—

110

C₂×C₄²

—

111

C₂×C₄²

—

112

C₂×C₄²

—

113

C₂×C₄²

—

114

C₂×C₄²

—

115

C₂×C₄²

C₂×D₄₃

yes

characteristic

116

C₄⋊C₈

—

117

C₄⋊C₈

C₂×D₄₃

yes

complemented

118

C₂²⋊C₈

—

119

#97

—

120

C₄×C₈

—

121

C₂⁴

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

—

127

C₂²×C₄

—

128

C₂²×C₄

—

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

C₄×D₄₃

yes

—

134

C₂²×C₄

C₂²×D₄₃

yes

characteristic

135

M₁₆

—

136

M₁₆

—

137

C₂×C₈

—

138

C₂×C₈

C₂²×D₄₃

yes

—

139

C₄²

—

140

C₄²

—

141

C₄²

—

142

C₄²

—

143

C₄²

—

144

C₄²

—

145

C₄²

—

146

C₄²

C₄×D₄₃

yes

characteristic

147

C₄²

C₄×D₄₃

yes

characteristic

148

C₄²

C₂²×D₄₃

yes

—

149

C₂³

—

150

C₂³

—

151

C₂³

—

152

C₂³

C₂×C₄×D₄₃

yes

characteristic

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

C₂×C₄×D₄₃

yes

—

167

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

168

C₂×C₄

C₂×C₄×D₄₃

yes

—

169

C₂×C₄

#10621900

yes

—

170

C₂×C₄

#10621902

yes

—

171

C₂×C₄

C₂³×D₄₃

yes

characteristic

172

C₈

—

173

C₈

—

174

C₂²

—

175

C₂²

—

176

C₂²

—

177

C₂²

—

178

C₂²

—

179

C₂²

#13063283

yes

—

180

C₂²

C₂²×C₄×D₄₃

yes

characteristic

181

C₄

—

182

C₄

—

183

C₄

—

184

C₄

—

185

C₄

#13063283

yes

—

186

C₄

M₁₆×D₄₃

yes

—

187

C₄

C₂×#10621900

yes

characteristic

188

C₄

C₂×#10621902

yes

characteristic

189

C₂

—

190

C₂

—

191

C₂

C₂×#13063283

yes

characteristic

192

C₂

C₂×M₁₆×D₄₃

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₄₃
commutator, socle	C₂²×C₄₃	C₂³×C₄
Fitting	C₄₃×#423	C₂
hypercenter	#423	D₄₃
hypocenter	C₄₃	#2920
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #423

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₄₃

commutator, socle

C₂²×C₄₃

C₂³×C₄

Fitting

C₄₃×#423

C₂

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₄ ◁ #423

N	H ≅ G/N	type
2. #14582955	C₂	semidirect
3. #14582951	C₂	semidirect
4. #14582923	C₂	semidirect
6. M₁₆×Dic₄₃	C₂	semidirect
7. C₄₃×#423	C₂	semidirect
17. C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
19. #13063235	C₂²	semidirect
20. C₈×Dic₄₃	C₂²	semidirect
23. C₄⋊C₈×C₄₃	C₂²	semidirect
74. C₄×D₄₃	M₁₆	semidirect
101. #423	D₄₃	semidirect
104. C₄₃	#2920	semidirect
117. C₄⋊C₈	C₂×D₄₃	semidirect

H ≅ G/N

type

2. #14582955

C₂

semidirect

3. #14582951

C₂

semidirect

4. #14582923

C₂

semidirect

6. M₁₆×Dic₄₃

C₂

semidirect

7. C₄₃×#423

C₂

semidirect

17. C₄⋊(C₄₃⋊C₈)

C₂²

semidirect

19. #13063235

C₂²

semidirect

20. C₈×Dic₄₃

C₂²

semidirect

23. C₄⋊C₈×C₄₃

C₂²

semidirect

74. C₄×D₄₃

M₁₆

semidirect

101. #423

D₄₃

semidirect

104. C₄₃

#2920

semidirect

117. C₄⋊C₈

C₂×D₄₃

semidirect

Subgroups — #19143227

Conjugacy classes of subgroups

Complements