Group #19139067 — subgroups

Subgroups — #19139067

Order 5504.

708 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 181 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×#13063306	C₂	1	4	yes	maximal, complemented
2	C₂²×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582835	C₂	1	4	yes	maximal, complemented
4	#14582802	C₂	1	2	yes	maximal, complemented
5	#14582768	C₂	1	2	yes	maximal, complemented
6	C₄×C₂²⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#121×C₄₃	C₂	1	1	yes	maximal, characteristic
8	C₂³×Dic₄₃	C₂²	1	2	yes	—
9	#13063306	—	2	16	no	—
10	C₂×C₄⋊Dic₄₃	—	2	4	no	—
11	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
12	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
13	C₂×Dic₄₃⋊C₄	C₂²	1	8	yes	—
14	C₂×C₂²⋊Dic₄₃	C₂²	1	8	yes	—
15	C₂×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
16	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
17	C₄₃⋊#95	C₂²	1	2	yes	—
18	C₂²×D₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₄₃	C₂²	1	2	yes	—
20	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
21	#121×C₄₃	—	2	4	no	—
22	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
24	C₂⁴×C₄₃	C₂³	1	2	yes	—
25	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
26	C₂×D₄×C₄₃	—	2	2	no	—
27	C₂×D₄×C₄₃	—	2	4	no	—
28	C₂×D₄×C₄₃	—	2	4	no	—
29	C₂×D₄×C₄₃	—	2	8	no	—
30	C₂²×C₄×C₄₃	—	2	4	no	—
31	C₂²×C₄×C₄₃	D₄	1	4	yes	—
32	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
33	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
34	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
35	C₂²×Dic₄₃	—	2	4	no	—
36	C₂²×Dic₄₃	—	2	8	no	—
37	C₂²×Dic₄₃	C₂³	1	4	yes	—
38	C₂²×Dic₄₃	C₂³	1	4	yes	—
39	C₄⋊C₄×C₄₃	—	2	2	no	—
40	C₂²⋊C₄×C₄₃	—	2	4	no	—
41	C₂²⋊Dic₄₃	—	2	16	no	—
42	C₂²⋊Dic₄₃	D₄	1	8	yes	complemented
43	C₄⋊Dic₄₃	—	2	4	no	—
44	C₄⋊Dic₄₃	—	2	4	no	—
45	Dic₄₃⋊C₄	—	2	16	no	—
46	C₄×Dic₄₃	—	2	4	no	—
47	C₂³×C₄₃	—	2	2	no	—
48	C₂³×C₄₃	—	2	2	no	—
49	C₂³×C₄₃	—	2	4	no	—
50	C₂³×C₄₃	—	2	2	no	—
51	C₂³×C₄₃	—	2	4	no	—
52	C₂³×C₄₃	—	2	4	no	—
53	C₂³×C₄₃	C₂×D₄	1	4	yes	—
54	C₂³×C₄₃	C₂×D₄	1	2	yes	—
55	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
56	D₄×C₄₃	—	4	8	no	—
57	D₄×C₄₃	—	4	4	no	—
58	C₂×C₄×C₄₃	—	2	2	no	—
59	C₂×C₄×C₄₃	—	2	8	no	—
60	C₂×C₄×C₄₃	—	2	4	no	—
61	C₂×C₄×C₄₃	—	2	2	no	—
62	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
63	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
64	C₂×C₄×C₄₃	#41	1	4	yes	—
65	C₂×Dic₄₃	—	2	4	no	—
66	C₂×Dic₄₃	—	2	4	no	—
67	C₂×Dic₄₃	—	2	8	no	—
68	C₂×Dic₄₃	—	2	4	no	—
69	C₂×Dic₄₃	—	4	8	no	—
70	C₂×Dic₄₃	C₂×D₄	1	8	yes	—
71	C₂²×C₄₃	—	2	2	no	—
72	C₂²×C₄₃	—	2	2	no	—
73	C₂²×C₄₃	—	2	8	no	—
74	C₂²×C₄₃	—	4	2	no	—
75	C₂²×C₄₃	—	4	2	no	—
76	C₂²×C₄₃	—	4	2	no	—
77	C₂²×C₄₃	—	4	8	no	—
78	C₂²×C₄₃	#127	1	4	yes	—
79	C₂²×C₄₃	C₂²×D₄	1	2	yes	—
80	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
81	C₂²×C₄₃	C₂×#41	1	2	yes	—
82	C₂²×C₄₃	2₋¹⁺⁴	1	2	yes	—
83	C₄×C₄₃	—	2	2	no	—
84	C₄×C₄₃	—	4	2	no	—
85	C₄×C₄₃	#123	1	4	yes	complemented
86	Dic₄₃	—	2	8	no	—
87	Dic₄₃	—	4	4	no	—
88	#2501	—	43	1	no	maximal, Sylow
89	C₂×C₄₃	—	2	4	no	—
90	C₂×C₄₃	—	8	2	no	—
91	C₂×C₄₃	C₂×#123	1	1	yes	characteristic
92	C₂×C₄₃	C₂×#127	1	1	yes	characteristic
93	C₂×C₄₃	#536	1	1	yes	characteristic
94	C₂×C₄₃	#547	1	4	yes	—
95	C₂×#123	—	43	4	no	—
96	C₂×#121	D₄₃	1	1	yes	characteristic
97	C₂²×C₄⋊C₄	—	43	1	no	—
98	#399	—	43	4	no	—
99	#390	—	43	2	no	—
100	#384	—	43	2	no	—
101	C₄×C₂²⋊C₄	—	43	1	no	—
102	C₄₃	#2501	1	1	yes	characteristic, complemented, Sylow
103	C₂²×D₄	C₂×D₄₃	1	2	yes	—
104	C₂²×D₄	C₂×D₄₃	1	1	yes	characteristic
105	C₂³×C₄	—	43	2	no	—
106	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
107	#123	—	86	16	no	—
108	#121	—	2	4	no	—
109	C₂×C₄⋊C₄	—	43	2	no	—
110	C₂×C₄⋊C₄	—	43	2	no	—
111	C₂×C₄⋊C₄	—	43	8	no	—
112	C₂×C₄⋊C₄	—	86	4	no	—
113	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
114	C₂×C₂²⋊C₄	—	43	2	no	—
115	C₂×C₂²⋊C₄	—	43	8	no	—
116	C₂×C₂²⋊C₄	C₂×D₄₃	1	2	yes	—
117	C₂×C₄²	—	43	2	no	—
118	#95	—	43	2	no	—
119	C₂⁴	C₂²×D₄₃	1	2	yes	—
120	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
121	C₂×D₄	—	2	8	no	—
122	C₂×D₄	—	2	4	no	—
123	C₂×D₄	—	2	4	no	—
124	C₂×D₄	—	2	2	no	—
125	C₂²×C₄	—	2	4	no	—
126	C₂²×C₄	—	43	4	no	—
127	C₂²×C₄	—	43	4	no	—
128	C₂²×C₄	—	86	8	no	—
129	C₂²×C₄	—	86	4	no	—
130	C₂²×C₄	C₂²⋊D₄₃	1	4	yes	—
131	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
132	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
133	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
134	C₄⋊C₄	—	2	2	no	—
135	C₄⋊C₄	—	86	16	no	—
136	C₄⋊C₄	—	86	4	no	—
137	C₄⋊C₄	—	86	4	no	—
138	C₂²⋊C₄	—	2	4	no	—
139	C₂²⋊C₄	—	43	8	no	—
140	C₂²⋊C₄	—	86	16	no	—
141	C₄²	—	86	4	no	—
142	C₂³	—	2	2	no	—
143	C₂³	—	2	2	no	—
144	C₂³	—	2	4	no	—
145	C₂³	—	2	2	no	—
146	C₂³	—	2	4	no	—
147	C₂³	—	2	4	no	—
148	C₂³	D₄×D₄₃	1	4	yes	—
149	C₂³	C₂×C₂²⋊D₄₃	1	2	yes	—
150	C₂³	C₂³×D₄₃	1	1	yes	characteristic
151	D₄	—	4	8	no	—
152	D₄	—	4	4	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	8	no	—
155	C₂×C₄	—	2	4	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	43	8	no	—
158	C₂×C₄	—	86	4	no	—
159	C₂×C₄	—	86	4	no	—
160	C₂×C₄	—	86	8	no	—
161	C₂×C₄	—	86	4	no	—
162	C₂×C₄	—	172	8	no	—
163	C₂×C₄	#10621900	1	4	yes	—
164	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
165	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
166	C₂²	—	2	2	no	—
167	C₂²	—	2	2	no	—
168	C₂²	—	2	8	no	—
169	C₂²	—	4	2	no	—
170	C₂²	—	4	2	no	—
171	C₂²	—	4	2	no	—
172	C₂²	—	4	8	no	—
173	C₂²	#13063321	1	4	yes	—
174	C₂²	C₂×D₄×D₄₃	1	2	yes	—
175	C₂²	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
176	C₂²	C₂×#10621900	1	2	yes	—
177	C₂²	#13063372	1	2	yes	—
178	C₄	—	2	2	no	—
179	C₄	—	4	2	no	—
180	C₄	—	86	8	no	—
181	C₄	—	172	4	no	—
182	C₄	#13063306	1	4	yes	complemented
183	C₂	—	2	4	no	—
184	C₂	—	8	2	no	—
185	C₂	C₂×#13063306	1	1	yes	characteristic
186	C₂	C₂×#13063321	1	1	yes	characteristic
187	C₂	#14583470	1	1	yes	characteristic
188	C₂	#14583549	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063306

C₂

yes

maximal, complemented

C₂²×C₄⋊Dic₄₃

C₂

yes

maximal, characteristic, complemented

#14582835

C₂

yes

maximal, complemented

#14582802

C₂

yes

maximal, complemented

#14582768

C₂

yes

maximal, complemented

C₄×C₂²⋊Dic₄₃

C₂

yes

maximal, characteristic, complemented

C₂×#121×C₄₃

C₂

yes

maximal, characteristic

C₂³×Dic₄₃

C₂²

yes

—

#13063306

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂²×D₄×C₄₃

C₂²

yes

characteristic

C₂²×D₄×C₄₃

C₂²

yes

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

#121×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

—

C₂⁴×C₄₃

C₂³

yes

—

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

D₄

yes

complemented

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

C₂⁴

yes

characteristic

D₄×C₄₃

—

D₄×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

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×D₄

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#127

yes

—

C₂²×C₄₃

C₂²×D₄

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₂²×C₄₃

2₋¹⁺⁴

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#123

yes

complemented

Dic₄₃

—

Dic₄₃

—

#2501

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×#123

—

C₂×#121

D₄₃

yes

characteristic

C₂²×C₄⋊C₄

—

#399

—

#390

—

100

#384

—

101

C₄×C₂²⋊C₄

—

102

C₄₃

#2501

yes

characteristic, complemented, Sylow

103

C₂²×D₄

C₂×D₄₃

yes

—

104

C₂²×D₄

C₂×D₄₃

yes

characteristic

105

C₂³×C₄

—

106

C₂³×C₄

C₂×D₄₃

yes

characteristic

107

#123

—

108

#121

—

109

C₂×C₄⋊C₄

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

—

113

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

114

C₂×C₂²⋊C₄

—

115

C₂×C₂²⋊C₄

—

116

C₂×C₂²⋊C₄

C₂×D₄₃

yes

—

117

C₂×C₄²

—

118

#95

—

119

C₂⁴

C₂²×D₄₃

yes

—

120

C₂⁴

C₂²×D₄₃

yes

characteristic

121

C₂×D₄

—

122

C₂×D₄

—

123

C₂×D₄

—

124

C₂×D₄

—

125

C₂²×C₄

—

126

C₂²×C₄

—

127

C₂²×C₄

—

128

C₂²×C₄

—

129

C₂²×C₄

—

130

C₂²×C₄

C₂²⋊D₄₃

yes

—

131

C₂²×C₄

C₂²×D₄₃

yes

—

132

C₂²×C₄

C₂²×D₄₃

yes

characteristic

133

C₂²×C₄

C₂²×D₄₃

yes

characteristic

134

C₄⋊C₄

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₂²⋊C₄

—

139

C₂²⋊C₄

—

140

C₂²⋊C₄

—

141

C₄²

—

142

C₂³

—

143

C₂³

—

144

C₂³

—

145

C₂³

—

146

C₂³

—

147

C₂³

—

148

C₂³

D₄×D₄₃

yes

—

149

C₂³

C₂×C₂²⋊D₄₃

yes

—

150

C₂³

C₂³×D₄₃

yes

characteristic

151

D₄

—

152

D₄

—

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

—

172

—

163

C₂×C₄

#10621900

yes

—

164

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

165

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

166

C₂²

—

167

C₂²

—

168

C₂²

—

169

C₂²

—

170

C₂²

—

171

C₂²

—

172

C₂²

—

173

C₂²

#13063321

yes

—

174

C₂²

C₂×D₄×D₄₃

yes

—

175

C₂²

C₂²×C₂²⋊D₄₃

yes

characteristic

176

C₂²

C₂×#10621900

yes

—

177

C₂²

#13063372

yes

—

178

C₄

—

179

C₄

—

180

C₄

—

181

C₄

—

172

—

182

C₄

#13063306

yes

complemented

183

C₂

—

184

C₂

—

185

C₂

C₂×#13063306

yes

characteristic

186

C₂

C₂×#13063321

yes

characteristic

187

C₂

#14583470

yes

characteristic

188

C₂

#14583549

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₂×#121×C₄₃	C₂
hypercenter	C₂×#121	D₄₃
hypocenter	C₄₃	#2501
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#121

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₂×#121×C₄₃

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ C₂×#121

N	H ≅ G/N	type
1. C₂×#13063306	C₂	semidirect
2. C₂²×C₄⋊Dic₄₃	C₂	semidirect
3. #14582835	C₂	semidirect
4. #14582802	C₂	semidirect
5. #14582768	C₂	semidirect
6. C₄×C₂²⋊Dic₄₃	C₂	semidirect
42. C₂²⋊Dic₄₃	D₄	semidirect
85. C₄×C₄₃	#123	semidirect
102. C₄₃	#2501	semidirect
182. C₄	#13063306	semidirect

H ≅ G/N

type

1. C₂×#13063306

C₂

semidirect

2. C₂²×C₄⋊Dic₄₃

C₂

semidirect

3. #14582835

C₂

semidirect

4. #14582802

C₂

semidirect

5. #14582768

C₂

semidirect

6. C₄×C₂²⋊Dic₄₃

C₂

semidirect

42. C₂²⋊Dic₄₃

D₄

semidirect

85. C₄×C₄₃

#123

semidirect

102. C₄₃

#2501

semidirect

182. C₄

#13063306

semidirect

Subgroups — #19139067

Conjugacy classes of subgroups

Complements