Group #24989935 — subgroups

Subgroups — #24989935

Order 11008.

530 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 139 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	#19134663	C₂	1	2	yes	maximal
2	#19132438	C₂	1	4	yes	maximal
3	C₂×C₄₃×#382	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
5	#14582654	—	2	2	no	—
6	#14582654	—	2	2	no	—
7	C₂²×C₄⋊C₄×C₄₃	C₄	1	2	yes	—
8	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
9	C₄₃×#382	—	2	2	no	—
10	C₄₃×#382	—	2	2	no	—
11	C₂×#95×C₄₃	C₄	1	2	yes	—
12	C₂×#95×C₄₃	C₂²	1	2	yes	—
13	C₂²×C₄₃⋊C₈	—	2	4	no	—
14	C₂²⋊(C₄₃⋊C₈)	—	2	8	no	—
15	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂³×C₄×C₄₃	C₂×C₄	1	4	yes	—
18	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
20	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
21	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
22	C₂×C₄²×C₄₃	—	2	4	no	—
23	C₂×C₄²×C₄₃	D₄	1	2	yes	—
24	C₂×C₄²×C₄₃	D₄	1	2	yes	—
25	#95×C₄₃	—	2	4	no	—
26	#95×C₄₃	—	2	4	no	—
27	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₄₃	—	2	2	no	—
29	C₂²×C₄×C₄₃	—	2	2	no	—
30	C₂²×C₄×C₄₃	—	2	4	no	—
31	C₂²×C₄×C₄₃	—	2	2	no	—
32	C₂²×C₄×C₄₃	—	2	2	no	—
33	C₂²×C₄×C₄₃	—	2	4	no	—
34	C₂²×C₄×C₄₃	—	2	8	no	—
35	C₂²×C₄×C₄₃	—	4	2	no	—
36	C₂²×C₄×C₄₃	—	4	4	no	—
37	C₂²×C₄×C₄₃	—	4	4	no	—
38	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
39	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
40	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
41	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
42	C₂²×C₄×C₄₃	#41	1	4	yes	—
43	C₄⋊C₄×C₄₃	—	4	4	no	—
44	C₄⋊C₄×C₄₃	—	4	4	no	—
45	C₄²×C₄₃	—	2	4	no	—
46	C₄²×C₄₃	—	2	4	no	—
47	C₂×C₄₃⋊C₈	—	4	8	no	—
48	C₂×C₄₃⋊C₈	—	4	4	no	—
49	C₂³×C₄₃	—	2	2	no	—
50	C₂³×C₄₃	—	2	1	no	—
51	C₂³×C₄₃	—	2	1	no	—
52	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₂³×C₄₃	#117	1	2	yes	—
54	C₂³×C₄₃	#131	1	4	yes	—
55	C₂×C₄×C₄₃	—	2	8	no	—
56	C₂×C₄×C₄₃	—	2	1	no	—
57	C₂×C₄×C₄₃	—	2	1	no	—
58	C₂×C₄×C₄₃	—	2	4	no	—
59	C₂×C₄×C₄₃	—	2	1	no	—
60	C₂×C₄×C₄₃	—	2	1	no	—
61	C₂×C₄×C₄₃	—	2	2	no	—
62	C₂×C₄×C₄₃	—	2	4	no	—
63	C₂×C₄×C₄₃	—	4	4	no	—
64	C₂×C₄×C₄₃	—	4	4	no	—
65	C₂×C₄×C₄₃	—	4	4	no	—
66	C₂×C₄×C₄₃	—	4	4	no	—
67	C₂×C₄×C₄₃	—	4	4	no	—
68	C₂×C₄×C₄₃	—	8	8	no	—
69	C₂×C₄×C₄₃	#100	1	2	yes	—
70	C₂×C₄×C₄₃	#101	1	2	yes	—
71	C₂×C₄×C₄₃	#123	1	4	yes	—
72	C₄₃⋊C₈	—	8	4	no	—
73	#8703	—	43	1	no	maximal, Sylow
74	C₂²×C₄₃	—	2	2	no	—
75	C₂²×C₄₃	—	2	2	no	—
76	C₂²×C₄₃	—	2	4	no	—
77	C₂²×C₄₃	—	2	4	no	—
78	C₂²×C₄₃	#381	1	1	yes	characteristic
79	C₂²×C₄₃	#408	1	2	yes	—
80	C₂²×C₄₃	#410	1	2	yes	—
81	C₂²×C₄₃	C₂×#100	1	1	yes	characteristic
82	C₂²×C₄₃	C₂×#101	1	1	yes	characteristic
83	C₂²×C₄₃	#433	1	4	yes	—
84	C₄×C₄₃	—	2	4	no	—
85	C₄×C₄₃	—	2	2	no	—
86	C₄×C₄₃	—	2	2	no	—
87	C₄×C₄₃	—	4	2	no	—
88	C₄×C₄₃	—	8	4	no	—
89	C₂×#382	D₄₃	1	1	yes	characteristic
90	#1817	—	43	2	no	—
91	#1280	—	43	4	no	—
92	C₂×C₄₃	—	2	4	no	—
93	C₂×C₄₃	#1469	1	2	yes	—
94	C₂×C₄₃	#1470	1	2	yes	—
95	C₂×C₄₃	#1818	1	1	yes	characteristic
96	C₂×C₄₃	#1820	1	1	yes	characteristic
97	C₂×C₄₃	#1821	1	1	yes	characteristic
98	C₂²×C₄⋊C₄	Dic₄₃	1	2	yes	—
99	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
100	C₂×C₂²⋊C₈	—	43	4	no	—
101	#382	—	2	2	no	—
102	#382	—	2	2	no	—
103	C₂×#95	Dic₄₃	1	2	yes	—
104	C₂×#95	C₂×D₄₃	1	2	yes	—
105	#336	—	86	2	no	—
106	#336	—	86	2	no	—
107	C₄₃	#8703	1	1	yes	characteristic, complemented, Sylow
108	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
109	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
110	C₂³×C₄	C₂×Dic₄₃	1	4	yes	—
111	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
112	C₂²×C₈	—	86	4	no	—
113	C₂×C₄⋊C₄	—	2	2	no	—
114	C₂×C₄⋊C₄	—	2	2	no	—
115	C₂×C₄⋊C₄	—	4	4	no	—
116	C₂×C₄²	—	2	4	no	—
117	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
118	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
119	C₂²⋊C₈	—	86	8	no	—
120	#95	—	2	4	no	—
121	#95	—	2	4	no	—
122	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
123	C₂²×C₄	—	2	2	no	—
124	C₂²×C₄	—	2	2	no	—
125	C₂²×C₄	—	2	2	no	—
126	C₂²×C₄	—	2	2	no	—
127	C₂²×C₄	—	2	4	no	—
128	C₂²×C₄	—	2	4	no	—
129	C₂²×C₄	—	2	8	no	—
130	C₂²×C₄	—	4	2	no	—
131	C₂²×C₄	—	4	4	no	—
132	C₂²×C₄	—	4	4	no	—
133	C₂²×C₄	C₂²⋊Dic₄₃	1	2	yes	—
134	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
135	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
136	C₂²×C₄	#10621898	1	4	yes	—
137	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
138	C₂×C₈	—	172	8	no	—
139	C₂×C₈	—	172	4	no	—
140	C₄⋊C₄	—	4	4	no	—
141	C₄⋊C₄	—	4	4	no	—
142	C₄²	—	2	4	no	—
143	C₄²	—	2	4	no	—
144	C₂³	—	2	2	no	—
145	C₂³	—	2	1	no	—
146	C₂³	—	2	1	no	—
147	C₂³	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
148	C₂³	#13063284	1	2	yes	—
149	C₂³	#13063332	1	4	yes	—
150	C₂×C₄	—	2	8	no	—
151	C₂×C₄	—	2	4	no	—
152	C₂×C₄	—	2	1	no	—
153	C₂×C₄	—	2	1	no	—
154	C₂×C₄	—	2	1	no	—
155	C₂×C₄	—	2	1	no	—
156	C₂×C₄	—	2	4	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	4	4	no	—
159	C₂×C₄	—	4	4	no	—
160	C₂×C₄	—	4	4	no	—
161	C₂×C₄	—	4	4	no	—
162	C₂×C₄	—	4	4	no	—
163	C₂×C₄	—	8	8	no	—
164	C₂×C₄	#13063242	1	2	yes	—
165	C₂×C₄	#13063244	1	2	yes	—
166	C₂×C₄	#13063308	1	4	yes	—
167	C₈	—	344	4	no	—
168	C₂²	—	2	4	no	—
169	C₂²	—	2	4	no	—
170	C₂²	—	2	2	no	—
171	C₂²	—	2	2	no	—
172	C₂²	#14582762	1	1	yes	characteristic
173	C₂²	#14582866	1	2	yes	—
174	C₂²	#14582873	1	2	yes	—
175	C₂²	C₂×#13063242	1	1	yes	characteristic
176	C₂²	C₂×#13063244	1	1	yes	characteristic
177	C₂²	#14582960	1	4	yes	—
178	C₄	—	2	4	no	—
179	C₄	—	2	2	no	—
180	C₄	—	2	2	no	—
181	C₄	—	4	2	no	—
182	C₄	—	8	4	no	—
183	C₂	—	2	4	no	—
184	C₂	#19132947	1	2	yes	—
185	C₂	#19132951	1	2	yes	—
186	C₂	#19134666	1	1	yes	characteristic
187	C₂	#19134672	1	1	yes	characteristic
188	C₂	#19134675	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19134663

C₂

yes

maximal

#19132438

C₂

yes

maximal

C₂×C₄₃×#382

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₄₃⋊C₈)

C₂²

yes

—

#14582654

—

#14582654

—

C₂²×C₄⋊C₄×C₄₃

C₄

yes

—

C₂²×C₄²×C₄₃

C₂²

yes

characteristic

C₄₃×#382

—

C₄₃×#382

—

C₂×#95×C₄₃

C₄

yes

—

C₂×#95×C₄₃

C₂²

yes

—

C₂²×C₄₃⋊C₈

—

C₂²⋊(C₄₃⋊C₈)

—

C₂³×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₃

C₂×C₄

yes

—

C₂³×C₄×C₄₃

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

D₄

yes

—

#95×C₄₃

—

#95×C₄₃

—

C₂⁴×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

#41

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₄₃

#117

yes

—

C₂³×C₄₃

#131

yes

—

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×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#100

yes

—

C₂×C₄×C₄₃

#101

yes

—

C₂×C₄×C₄₃

#123

yes

—

C₄₃⋊C₈

—

#8703

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#381

yes

characteristic

C₂²×C₄₃

#408

yes

—

C₂²×C₄₃

#410

yes

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₂×#382

D₄₃

yes

characteristic

#1817

—

#1280

—

C₂×C₄₃

—

C₂×C₄₃

#1469

yes

—

C₂×C₄₃

#1470

yes

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂²×C₄⋊C₄

Dic₄₃

yes

—

C₂²×C₄²

C₂×D₄₃

yes

characteristic

100

C₂×C₂²⋊C₈

—

101

#382

—

102

#382

—

103

C₂×#95

Dic₄₃

yes

—

104

C₂×#95

C₂×D₄₃

yes

—

105

#336

—

106

#336

—

107

C₄₃

#8703

yes

characteristic, complemented, Sylow

108

C₂³×C₄

C₂×Dic₄₃

yes

characteristic

109

C₂³×C₄

C₂×Dic₄₃

yes

characteristic

110

C₂³×C₄

C₂×Dic₄₃

yes

—

111

C₂³×C₄

C₂²×D₄₃

yes

characteristic

112

C₂²×C₈

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄⋊C₄

—

115

C₂×C₄⋊C₄

—

116

C₂×C₄²

—

117

C₂×C₄²

C₂²⋊D₄₃

yes

—

118

C₂×C₄²

C₂²⋊D₄₃

yes

—

119

C₂²⋊C₈

—

120

#95

—

121

#95

—

122

C₂⁴

C₂²×Dic₄₃

yes

characteristic

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

C₂²⋊Dic₄₃

yes

—

134

C₂²×C₄

C₂²⋊Dic₄₃

yes

characteristic

135

C₂²×C₄

C₂²⋊Dic₄₃

yes

characteristic

136

C₂²×C₄

#10621898

yes

—

137

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

138

C₂×C₈

—

172

—

139

C₂×C₈

—

172

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄²

—

143

C₄²

—

144

C₂³

—

145

C₂³

—

146

C₂³

—

147

C₂³

C₂×C₂²⋊Dic₄₃

yes

characteristic

148

C₂³

#13063284

yes

—

149

C₂³

#13063332

yes

—

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

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

#13063242

yes

—

165

C₂×C₄

#13063244

yes

—

166

C₂×C₄

#13063308

yes

—

167

C₈

—

344

—

168

C₂²

—

169

C₂²

—

170

C₂²

—

171

C₂²

—

172

C₂²

#14582762

yes

characteristic

173

C₂²

#14582866

yes

—

174

C₂²

#14582873

yes

—

175

C₂²

C₂×#13063242

yes

characteristic

176

C₂²

C₂×#13063244

yes

characteristic

177

C₂²

#14582960

yes

—

178

C₄

—

179

C₄

—

180

C₄

—

181

C₄

—

182

C₄

—

183

C₂

—

184

C₂

#19132947

yes

—

185

C₂

#19132951

yes

—

186

C₂

#19134666

yes

characteristic

187

C₂

#19134672

yes

characteristic

188

C₂

#19134675

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₃
commutator, prime radical	C₂⁴×C₄₃	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₂×C₄₃×#382	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×#382	D₄₃
hypocenter	C₄₃	#8703
LCS	G ▷ C₂⁴×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#382

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₄₃

commutator, prime radical

C₂⁴×C₄₃

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₄₃

Fitting

C₂×C₄₃×#382

C₂

socle

C₂³×C₄₃

C₂×C₂²⋊C₄

cosocle

C₂³×C₄×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂⁴×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#382

N	H ≅ G/N	type
107. C₄₃	#8703	semidirect

H ≅ G/N

type

107. C₄₃

#8703

semidirect

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

subgroup	index
#19134663	2
#19132438	2
C₂×C₄₃×#382	2
#8703	43

subgroup

index

#19134663

#19132438

C₂×C₄₃×#382

#8703

Subgroups — #24989935

Conjugacy classes of subgroups

Complements

Maximal subgroups