Group #19142645 — subgroups

Subgroups — #19142645

Order 5504.

464 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13063313	C₂	1	1	yes	maximal, characteristic
2	#14582834	C₂	1	2	yes	maximal, complemented
3	#14582825	C₂	1	2	yes	maximal, complemented
4	#14582821	C₂	1	4	yes	maximal, complemented
5	#14582819	C₂	1	2	yes	maximal, complemented
6	#14582816	C₂	1	2	yes	maximal
7	#14582765	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#125×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
10	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
11	#13063313	—	2	4	no	—
12	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
13	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
14	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	—
15	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	—
16	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	4	yes	—
17	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	4	yes	—
18	C₄₃⋊#95	C₂²	1	2	yes	—
19	C₄₃⋊#95	C₂²	1	4	yes	—
20	C₄₃⋊#95	C₂²	1	2	yes	—
21	#125×C₄₃	—	2	4	no	—
22	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
23	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
24	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
27	C₂³×D₄₃	C₂³	1	2	yes	—
28	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
29	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
30	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
31	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
33	C₂²×Dic₄₃	C₂³	1	4	yes	—
34	C₂²×Dic₄₃	C₂³	1	2	yes	—
35	C₂×D₁₇₂	—	2	2	no	—
36	C₂×D₁₇₂	—	4	2	no	—
37	C₂×Dic₈₆	—	2	2	no	—
38	C₂×Dic₈₆	—	4	2	no	—
39	C₄⋊C₄×C₄₃	—	2	4	no	—
40	C₄⋊C₄×C₄₃	—	2	2	no	—
41	C₄⋊C₄×C₄₃	—	2	2	no	—
42	C₄⋊C₄×C₄₃	—	2	4	no	—
43	C₄²×C₄₃	D₄	1	4	yes	—
44	(C₂×D₄₃)⋊C₄	—	2	4	no	—
45	(C₂×D₄₃)⋊C₄	—	2	4	no	—
46	(C₂×D₄₃)⋊C₄	—	4	4	no	—
47	(C₂×D₄₃)⋊C₄	—	4	4	no	—
48	C₄⋊Dic₄₃	—	4	2	no	—
49	Dic₄₃⋊C₄	—	4	4	no	—
50	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
51	C₂²×D₄₃	—	2	2	no	—
52	C₂²×D₄₃	—	2	2	no	—
53	C₂²×D₄₃	—	2	4	no	—
54	C₂²×D₄₃	—	2	2	no	—
55	C₂²×D₄₃	—	2	4	no	—
56	C₂×C₄×C₄₃	—	2	1	no	—
57	C₂×C₄×C₄₃	—	2	2	no	—
58	C₂×C₄×C₄₃	—	2	1	no	—
59	C₂×C₄×C₄₃	—	2	2	no	—
60	C₂×C₄×C₄₃	—	2	2	no	—
61	C₂×C₄×C₄₃	—	2	2	no	—
62	C₂×C₄×C₄₃	—	2	4	no	—
63	C₂×C₄×C₄₃	—	2	2	no	—
64	C₂×C₄×C₄₃	—	2	2	no	—
65	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
66	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
67	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
68	C₂×Dic₄₃	—	2	2	no	—
69	C₂×Dic₄₃	—	2	4	no	—
70	C₂×Dic₄₃	—	2	4	no	—
71	C₂×Dic₄₃	—	2	4	no	—
72	C₂×Dic₄₃	—	2	4	no	—
73	D₁₇₂	—	4	4	no	—
74	Dic₈₆	—	4	4	no	—
75	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
76	C₂²×C₄₃	H(5,𝔽₂)	1	2	yes	—
77	C₂²×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
78	C₂²×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
79	C₂²×C₄₃	2₋¹⁺⁴	1	2	yes	—
80	C₂×D₄₃	—	4	2	no	—
81	C₂×D₄₃	—	4	2	no	—
82	C₂×D₄₃	—	4	2	no	—
83	C₂×D₄₃	—	4	4	no	—
84	C₂×D₄₃	—	4	4	no	—
85	C₄×C₄₃	—	2	2	no	—
86	C₄×C₄₃	—	2	2	no	—
87	C₄×C₄₃	—	2	2	no	—
88	C₄×C₄₃	—	4	2	no	—
89	C₄×C₄₃	—	4	2	no	—
90	Dic₄₃	—	4	2	no	—
91	Dic₄₃	—	4	4	no	—
92	#2820	—	43	1	no	maximal, Sylow
93	C₂×C₄₃	#535	1	1	yes	characteristic
94	C₂×C₄₃	#536	1	1	yes	characteristic
95	C₂×C₄₃	#537	1	1	yes	characteristic
96	C₂×C₄₃	#562	1	2	yes	—
97	C₂×C₄₃	#563	1	2	yes	—
98	D₄₃	—	8	2	no	—
99	C₂×#125	D₄₃	1	1	yes	characteristic, complemented
100	C₂×#124	—	43	1	no	—
101	#399	—	43	2	no	—
102	#397	—	43	2	no	—
103	#396	—	43	4	no	—
104	#395	—	43	2	no	—
105	#394	—	43	2	no	—
106	#382	—	43	1	no	—
107	C₄₃	#2820	1	1	yes	characteristic, complemented, Sylow
108	C₂²×Q₈	—	43	1	no	—
109	C₂²×D₄	—	43	1	no	—
110	#125	—	2	4	no	—
111	#124	—	86	4	no	—
112	C₂×C₄⋊C₄	—	43	4	no	—
113	C₂×C₄⋊C₄	—	43	2	no	—
114	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
115	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
116	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
117	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
118	C₂×C₂²⋊C₄	—	43	2	no	—
119	C₂×C₂²⋊C₄	—	43	2	no	—
120	C₂×C₂²⋊C₄	—	43	4	no	—
121	C₂×C₂²⋊C₄	—	43	4	no	—
122	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
123	#95	—	43	2	no	—
124	#95	—	43	2	no	—
125	#95	—	43	4	no	—
126	C₂⁴	—	43	2	no	—
127	C₂×Q₈	—	86	2	no	—
128	C₂×Q₈	—	172	2	no	—
129	C₂×D₄	—	86	2	no	—
130	C₂×D₄	—	172	2	no	—
131	C₂²×C₄	—	43	4	no	—
132	C₂²×C₄	—	43	2	no	—
133	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
134	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
135	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
136	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
137	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
138	C₄⋊C₄	—	2	4	no	—
139	C₄⋊C₄	—	2	2	no	—
140	C₄⋊C₄	—	2	2	no	—
141	C₄⋊C₄	—	2	4	no	—
142	C₄⋊C₄	—	172	4	no	—
143	C₄⋊C₄	—	172	2	no	—
144	C₂²⋊C₄	—	86	4	no	—
145	C₂²⋊C₄	—	86	4	no	—
146	C₂²⋊C₄	—	172	4	no	—
147	C₂²⋊C₄	—	172	4	no	—
148	C₄²	C₂²⋊D₄₃	1	4	yes	—
149	C₂³	—	86	2	no	—
150	C₂³	—	86	2	no	—
151	C₂³	—	86	4	no	—
152	C₂³	—	86	2	no	—
153	C₂³	—	86	4	no	—
154	C₂³	C₂³×D₄₃	1	1	yes	characteristic
155	Q₈	—	172	4	no	—
156	D₄	—	172	4	no	—
157	C₂×C₄	—	2	1	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	1	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	4	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	86	2	no	—
167	C₂×C₄	—	86	4	no	—
168	C₂×C₄	—	86	4	no	—
169	C₂×C₄	—	86	4	no	—
170	C₂×C₄	—	86	4	no	—
171	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
172	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
173	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
174	C₂²	—	172	4	no	—
175	C₂²	—	172	4	no	—
176	C₂²	—	172	2	no	—
177	C₂²	—	172	2	no	—
178	C₂²	—	172	2	no	—
179	C₂²	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
180	C₂²	#13063371	1	1	yes	characteristic
181	C₂²	#13063371	1	2	yes	—
182	C₂²	#13063372	1	1	yes	characteristic
183	C₂²	#13063373	1	2	yes	—
184	C₄	—	2	2	no	—
185	C₄	—	2	2	no	—
186	C₄	—	2	2	no	—
187	C₄	—	4	2	no	—
188	C₄	—	4	2	no	—
189	C₄	—	172	4	no	—
190	C₄	—	172	2	no	—
191	C₂	—	344	2	no	—
192	C₂	#14583463	1	1	yes	characteristic
193	C₂	#14583473	1	1	yes	characteristic
194	C₂	#14583477	1	1	yes	characteristic
195	C₂	#14583647	1	2	yes	—
196	C₂	#14583653	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063313

C₂

yes

maximal, characteristic

#14582834

C₂

yes

maximal, complemented

#14582825

C₂

yes

maximal, complemented

#14582821

C₂

yes

maximal, complemented

#14582819

C₂

yes

maximal, complemented

#14582816

C₂

yes

maximal

#14582765

C₂

yes

maximal, characteristic, complemented

C₂×#125×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₈₆

C₂²

yes

characteristic

C₂²×D₁₇₂

C₂²

yes

characteristic

#13063313

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

#125×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂³×D₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

D₄

yes

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

Dic₈₆

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

H(5,𝔽₂)

yes

—

C₂²×C₄₃

H(5,𝔽₂)

yes

characteristic

C₂²×C₄₃

2₋¹⁺⁴

yes

characteristic

C₂²×C₄₃

2₋¹⁺⁴

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#563

yes

—

D₄₃

—

C₂×#125

D₄₃

yes

characteristic, complemented

100

C₂×#124

—

101

#399

—

102

#397

—

103

#396

—

104

#395

—

105

#394

—

106

#382

—

107

C₄₃

#2820

yes

characteristic, complemented, Sylow

108

C₂²×Q₈

—

109

C₂²×D₄

—

110

#125

—

111

#124

—

112

C₂×C₄⋊C₄

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

115

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

116

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

117

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

118

C₂×C₂²⋊C₄

—

119

C₂×C₂²⋊C₄

—

120

C₂×C₂²⋊C₄

—

121

C₂×C₂²⋊C₄

—

122

C₂×C₄²

C₂×D₄₃

yes

characteristic

123

#95

—

124

#95

—

125

#95

—

126

C₂⁴

—

127

C₂×Q₈

—

128

C₂×Q₈

—

172

—

129

C₂×D₄

—

130

C₂×D₄

—

172

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

C₂²×D₄₃

yes

—

134

C₂²×C₄

C₂²×D₄₃

yes

—

135

C₂²×C₄

C₂²×D₄₃

yes

characteristic

136

C₂²×C₄

C₂²×D₄₃

yes

characteristic

137

C₂²×C₄

C₂²×D₄₃

yes

characteristic

138

C₄⋊C₄

—

139

C₄⋊C₄

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄⋊C₄

—

172

—

143

C₄⋊C₄

—

172

—

144

C₂²⋊C₄

—

145

C₂²⋊C₄

—

146

C₂²⋊C₄

—

172

—

147

C₂²⋊C₄

—

172

—

148

C₄²

C₂²⋊D₄₃

yes

—

149

C₂³

—

150

C₂³

—

151

C₂³

—

152

C₂³

—

153

C₂³

—

154

C₂³

C₂³×D₄₃

yes

characteristic

155

Q₈

—

172

—

156

D₄

—

172

—

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

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

172

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

173

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

174

C₂²

—

172

—

175

C₂²

—

172

—

176

C₂²

—

172

—

177

C₂²

—

172

—

178

C₂²

—

172

—

179

C₂²

C₂²×C₂²⋊D₄₃

yes

characteristic

180

C₂²

#13063371

yes

characteristic

181

C₂²

#13063371

yes

—

182

C₂²

#13063372

yes

characteristic

183

C₂²

#13063373

yes

—

184

C₄

—

185

C₄

—

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

—

172

—

190

C₄

—

172

—

191

C₂

—

344

—

192

C₂

#14583463

yes

characteristic

193

C₂

#14583473

yes

characteristic

194

C₂

#14583477

yes

characteristic

195

C₂

#14583647

yes

—

196

C₂

#14583653

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₂×#125×C₄₃	C₂
hypercenter	C₂×#125	D₄₃
hypocenter	C₄₃	#2820
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#125

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₂×#125×C₄₃

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ C₂×#125

N	H ≅ G/N	type
2. #14582834	C₂	semidirect
3. #14582825	C₂	semidirect
4. #14582821	C₂	semidirect
5. #14582819	C₂	semidirect
7. #14582765	C₂	semidirect
8. C₂×#125×C₄₃	C₂	semidirect
99. C₂×#125	D₄₃	semidirect
107. C₄₃	#2820	semidirect

H ≅ G/N

type

2. #14582834

C₂

semidirect

3. #14582825

C₂

semidirect

4. #14582821

C₂

semidirect

5. #14582819

C₂

semidirect

7. #14582765

C₂

semidirect

8. C₂×#125×C₄₃

C₂

semidirect

99. C₂×#125

D₄₃

semidirect

107. C₄₃

#2820

semidirect

Subgroups — #19142645

Conjugacy classes of subgroups

Complements