Group #24999628 — subgroups

Subgroups — #24999628

Order 11008.

416 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 121 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	#19139837	C₂	1	1	yes	maximal, characteristic
2	#19135542	C₂	1	2	yes	maximal
3	#19135396	C₂	1	1	yes	maximal, characteristic
4	#19132434	C₂	1	2	yes	maximal
5	C₄₃×#1296	C₂	1	1	yes	maximal, characteristic
6	C₂×#13063325	C₂²	1	1	yes	characteristic
7	C₂×#13063248	—	2	2	no	—
8	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
9	#14582838	—	2	2	no	—
10	#14582798	—	2	2	no	—
11	#14582764	—	2	2	no	—
12	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
13	#14582662	—	2	2	no	—
14	#14582662	—	2	2	no	—
15	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
16	C₄₃×#384	C₂²	1	1	yes	characteristic
17	C₂²×Dic₈₆	—	2	1	no	—
18	C₂²×C₄₃⋊C₈	—	2	1	no	—
19	#13063325	—	2	2	no	—
20	#13063325	—	2	1	no	—
21	#13063325	Q₈	1	2	yes	—
22	C₂×C₄⋊Dic₄₃	—	2	2	no	—
23	C₂×C₄⋊Dic₄₃	—	2	2	no	—
24	C₂×C₄⋊Dic₄₃	D₄	1	2	yes	—
25	C₂×C₄⋊Dic₄₃	D₄	1	2	yes	—
26	C₂×C₄×Dic₄₃	—	2	2	no	—
27	#13063248	—	4	4	no	—
28	C₄×C₄₃⋊C₈	—	2	2	no	—
29	C₄₃⋊#95	—	2	4	no	—
30	C₄₃⋊#95	—	2	2	no	—
31	C₄₃⋊#95	—	2	2	no	—
32	C₂²×C₈×C₄₃	—	2	2	no	—
33	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
34	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
35	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
36	C₄⋊C₈×C₄₃	—	2	2	no	—
37	C₄⋊C₈×C₄₃	—	2	2	no	—
38	C₂²×C₄×C₄₃	—	2	2	no	—
39	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
41	C₂²×Dic₄₃	—	2	2	no	—
42	C₂²×Dic₄₃	—	2	2	no	—
43	C₂²×Dic₄₃	—	4	1	no	—
44	C₂×Dic₈₆	—	2	2	no	—
45	C₂×Dic₈₆	—	4	2	no	—
46	C₂×Dic₈₆	—	4	2	no	—
47	C₂×Dic₈₆	—	4	1	no	—
48	C₂×C₈×C₄₃	—	4	2	no	—
49	C₂×C₈×C₄₃	—	4	2	no	—
50	C₂×C₈×C₄₃	—	4	2	no	—
51	C₄⋊C₄×C₄₃	—	4	2	no	—
52	C₄⋊C₄×C₄₃	—	4	2	no	—
53	C₄⋊C₄×C₄₃	—	4	2	no	—
54	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
55	C₄²×C₄₃	#41	1	2	yes	—
56	C₄²×C₄₃	#41	1	1	yes	characteristic
57	C₄⋊Dic₄₃	—	2	4	no	—
58	C₄⋊Dic₄₃	—	2	2	no	—
59	C₄⋊Dic₄₃	—	2	2	no	—
60	C₄⋊Dic₄₃	—	2	2	no	—
61	C₄⋊Dic₄₃	—	2	2	no	—
62	C₄⋊Dic₄₃	—	4	2	no	—
63	C₄⋊Dic₄₃	—	8	2	no	—
64	C₄×Dic₄₃	—	4	2	no	—
65	C₄×Dic₄₃	—	4	2	no	—
66	C₂×C₄₃⋊C₈	—	2	2	no	—
67	C₂×C₄₃⋊C₈	—	4	1	no	—
68	C₂×C₄₃⋊C₈	—	4	1	no	—
69	C₂³×C₄₃	#120	1	1	yes	characteristic
70	C₂×C₄×C₄₃	—	2	1	no	—
71	C₂×C₄×C₄₃	—	2	1	no	—
72	C₂×C₄×C₄₃	—	4	4	no	—
73	C₂×C₄×C₄₃	—	4	2	no	—
74	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
75	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
76	C₂×C₄×C₄₃	#124	1	2	yes	—
77	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
78	C₂×C₄×C₄₃	#135	1	2	yes	—
79	C₂×C₄×C₄₃	#135	1	2	yes	—
80	C₂×C₄×C₄₃	#137	1	2	yes	—
81	C₂×C₄×C₄₃	#137	1	2	yes	—
82	C₂×Dic₄₃	—	4	2	no	—
83	C₂×Dic₄₃	—	4	2	no	—
84	C₂×Dic₄₃	—	4	2	no	—
85	C₂×Dic₄₃	—	4	2	no	—
86	C₂×Dic₄₃	—	4	2	no	—
87	C₂×Dic₄₃	—	4	2	no	—
88	C₂×Dic₄₃	—	4	2	no	—
89	C₂×Dic₄₃	—	8	1	no	—
90	C₂×Dic₄₃	—	8	1	no	—
91	Dic₈₆	—	4	4	no	—
92	Dic₈₆	—	8	2	no	—
93	C₈×C₄₃	—	8	2	no	—
94	C₄₃⋊C₈	—	4	2	no	—
95	#10352	—	43	1	no	maximal, Sylow
96	C₂²×C₄₃	#393	1	1	yes	characteristic
97	C₂²×C₄₃	#452	1	2	yes	—
98	C₂²×C₄₃	#452	1	2	yes	—
99	C₂²×C₄₃	#453	1	1	yes	characteristic
100	C₂²×C₄₃	#454	1	1	yes	characteristic
101	C₄×C₄₃	—	2	1	no	—
102	C₄×C₄₃	—	2	1	no	—
103	C₄×C₄₃	—	8	2	no	—
104	C₄×C₄₃	#479	1	2	yes	—
105	C₄×C₄₃	#479	1	2	yes	—
106	C₄×C₄₃	#488	1	2	yes	—
107	C₄×C₄₃	#491	1	2	yes	—
108	Dic₄₃	—	8	2	no	—
109	Dic₄₃	—	8	2	no	—
110	Dic₄₃	—	8	2	no	—
111	#2571	—	43	1	no	—
112	#1987	—	43	2	no	—
113	#1956	—	43	1	no	—
114	#1296	D₄₃	1	1	yes	characteristic
115	#1279	—	43	2	no	—
116	C₂×C₄₃	#1630	1	1	yes	characteristic
117	C₂×C₄₃	#1634	1	1	yes	characteristic
118	C₂×C₄₃	#1638	1	2	yes	—
119	C₂×C₄₃	#2026	1	2	yes	—
120	C₂×C₄₃	#2027	1	1	yes	characteristic
121	C₂×C₄⋊Q₈	—	43	1	no	—
122	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
123	C₂×#103	—	86	2	no	—
124	C₂×C₄×C₈	—	43	1	no	—
125	#400	—	86	2	no	—
126	#389	—	86	2	no	—
127	#384	C₂×D₄₃	1	1	yes	characteristic
128	#382	—	86	2	no	—
129	C₄×C₄⋊C₄	—	43	2	no	—
130	#340	—	86	2	no	—
131	#340	—	86	2	no	—
132	C₄₃	#10352	1	1	yes	characteristic, complemented, Sylow
133	C₂²×Q₈	—	86	1	no	—
134	C₂²×C₈	—	2	2	no	—
135	C₂²×C₈	—	86	1	no	—
136	C₄⋊Q₈	—	43	2	no	—
137	C₄⋊Q₈	—	86	2	no	—
138	C₄⋊Q₈	—	86	1	no	—
139	C₂×C₄⋊C₄	—	2	2	no	—
140	C₂×C₄⋊C₄	—	43	2	no	—
141	C₂×C₄⋊C₄	—	43	2	no	—
142	C₂×C₄⋊C₄	—	86	2	no	—
143	C₂×C₄⋊C₄	—	86	2	no	—
144	C₂×C₄⋊C₄	D₁₇₂	1	2	yes	—
145	C₂×C₄²	—	86	2	no	—
146	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
147	C₄⋊C₈	—	2	2	no	—
148	C₄⋊C₈	—	2	2	no	—
149	#103	—	172	4	no	—
150	C₄×C₈	—	86	2	no	—
151	#95	—	86	2	no	—
152	#95	—	86	4	no	—
153	#95	—	86	2	no	—
154	C₂×Q₈	—	86	2	no	—
155	C₂×Q₈	—	172	2	no	—
156	C₂×Q₈	—	172	2	no	—
157	C₂×Q₈	—	172	1	no	—
158	C₂²×C₄	—	2	2	no	—
159	C₂²×C₄	—	86	2	no	—
160	C₂²×C₄	—	86	2	no	—
161	C₂²×C₄	—	172	1	no	—
162	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
163	C₂²×C₄	D₄×D₄₃	1	2	yes	—
164	C₂×C₈	—	4	2	no	—
165	C₂×C₈	—	4	2	no	—
166	C₂×C₈	—	4	2	no	—
167	C₂×C₈	—	86	2	no	—
168	C₂×C₈	—	172	1	no	—
169	C₂×C₈	—	172	1	no	—
170	C₄⋊C₄	—	4	2	no	—
171	C₄⋊C₄	—	4	2	no	—
172	C₄⋊C₄	—	4	2	no	—
173	C₄⋊C₄	—	86	4	no	—
174	C₄⋊C₄	—	86	2	no	—
175	C₄⋊C₄	—	86	2	no	—
176	C₄⋊C₄	—	86	2	no	—
177	C₄⋊C₄	—	86	2	no	—
178	C₄⋊C₄	—	344	2	no	—
179	C₄⋊C₄	—	172	2	no	—
180	C₄²	—	172	2	no	—
181	C₄²	—	172	2	no	—
182	C₄²	#10621898	1	2	yes	—
183	C₄²	#10621900	1	1	yes	characteristic
184	C₄²	Q₈×D₄₃	1	1	yes	characteristic
185	C₂³	#13063295	1	1	yes	characteristic
186	Q₈	—	344	2	no	—
187	Q₈	—	172	4	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	4	4	no	—
191	C₂×C₄	—	4	2	no	—
192	C₂×C₄	—	344	1	no	—
193	C₂×C₄	—	344	1	no	—
194	C₂×C₄	—	172	2	no	—
195	C₂×C₄	—	172	2	no	—
196	C₂×C₄	—	172	2	no	—
197	C₂×C₄	—	172	2	no	—
198	C₂×C₄	—	172	2	no	—
199	C₂×C₄	—	172	2	no	—
200	C₂×C₄	—	172	2	no	—
201	C₂×C₄	#13063303	1	2	yes	—
202	C₂×C₄	#13063305	1	1	yes	characteristic
203	C₂×C₄	#13063311	1	2	yes	—
204	C₂×C₄	#13063313	1	1	yes	characteristic
205	C₂×C₄	#13063344	1	2	yes	—
206	C₂×C₄	#13063346	1	2	yes	—
207	C₂×C₄	#13063354	1	2	yes	—
208	C₂×C₄	#13063357	1	2	yes	—
209	C₈	—	8	2	no	—
210	C₈	—	172	2	no	—
211	C₂²	#14582812	1	1	yes	characteristic
212	C₂²	#14583062	1	2	yes	—
213	C₂²	#14583064	1	2	yes	—
214	C₂²	#14583069	1	1	yes	characteristic
215	C₂²	#14583074	1	1	yes	characteristic
216	C₄	—	2	1	no	—
217	C₄	—	2	1	no	—
218	C₄	—	8	2	no	—
219	C₄	—	344	2	no	—
220	C₄	—	344	2	no	—
221	C₄	—	344	2	no	—
222	C₄	#14583205	1	2	yes	—
223	C₄	#14583209	1	2	yes	—
224	C₄	#14583252	1	2	yes	—
225	C₄	#14583266	1	2	yes	—
226	C₂	#19133717	1	1	yes	characteristic
227	C₂	#19133741	1	1	yes	characteristic
228	C₂	#19133768	1	2	yes	—
229	C₂	#19135745	1	2	yes	—
230	C₂	#19135752	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19139837

C₂

yes

maximal, characteristic

#19135542

C₂

yes

maximal

#19135396

C₂

yes

maximal, characteristic

#19132434

C₂

yes

maximal

C₄₃×#1296

C₂

yes

maximal, characteristic

C₂×#13063325

C₂²

yes

characteristic

C₂×#13063248

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

—

—

C₄×C₄⋊Dic₄₃

C₂²

yes

—

#14582662

—

#14582662

—

C₂×C₄⋊C₈×C₄₃

C₂²

yes

—

C₄₃×#384

C₂²

yes

characteristic

C₂²×Dic₈₆

—

C₂²×C₄₃⋊C₈

—

#13063325

—

#13063325

—

#13063325

Q₈

yes

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

D₄

yes

—

C₂×C₄⋊Dic₄₃

D₄

yes

—

C₂×C₄×Dic₄₃

—

#13063248

—

C₄×C₄₃⋊C₈

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂×Q₈

yes

characteristic

C₄²×C₄₃

#41

yes

—

C₄²×C₄₃

#41

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#120

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₃

#124

yes

—

C₂×C₄×C₄₃

#124

yes

characteristic

C₂×C₄×C₄₃

#135

yes

—

C₂×C₄×C₄₃

#135

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂²×C₄₃

#452

yes

—

C₂²×C₄₃

#453

yes

characteristic

100

C₂²×C₄₃

#454

yes

characteristic

101

C₄×C₄₃

—

102

C₄×C₄₃

—

103

C₄×C₄₃

—

104

C₄×C₄₃

#479

yes

—

105

C₄×C₄₃

#479

yes

—

106

C₄×C₄₃

#488

yes

—

107

C₄×C₄₃

#491

yes

—

108

Dic₄₃

—

109

Dic₄₃

—

110

Dic₄₃

—

111

#2571

—

112

#1987

—

113

#1956

—

114

#1296

D₄₃

yes

characteristic

115

#1279

—

116

C₂×C₄₃

#1630

yes

characteristic

117

C₂×C₄₃

#1634

yes

characteristic

118

C₂×C₄₃

#1638

yes

—

119

C₂×C₄₃

#2026

yes

—

120

C₂×C₄₃

#2027

yes

characteristic

121

C₂×C₄⋊Q₈

—

122

C₂×C₄⋊C₈

C₂×D₄₃

yes

—

123

C₂×#103

—

124

C₂×C₄×C₈

—

125

#400

—

126

#389

—

127

#384

C₂×D₄₃

yes

characteristic

128

#382

—

129

C₄×C₄⋊C₄

—

130

#340

—

131

#340

—

132

C₄₃

#10352

yes

characteristic, complemented, Sylow

133

C₂²×Q₈

—

134

C₂²×C₈

—

135

C₂²×C₈

—

136

C₄⋊Q₈

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

—

139

C₂×C₄⋊C₄

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

D₁₇₂

yes

—

145

C₂×C₄²

—

146

C₂×C₄²

C₂²×D₄₃

yes

characteristic

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

#103

—

172

—

150

C₄×C₈

—

151

#95

—

152

#95

—

153

#95

—

154

C₂×Q₈

—

155

C₂×Q₈

—

172

—

156

C₂×Q₈

—

172

—

157

C₂×Q₈

—

172

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

172

—

162

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

163

C₂²×C₄

D₄×D₄₃

yes

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

172

—

169

C₂×C₈

—

172

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

344

—

179

C₄⋊C₄

—

172

—

180

C₄²

—

172

—

181

C₄²

—

172

—

182

C₄²

#10621898

yes

—

183

C₄²

#10621900

yes

characteristic

184

C₄²

Q₈×D₄₃

yes

characteristic

185

C₂³

#13063295

yes

characteristic

186

Q₈

—

344

—

187

Q₈

—

172

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

344

—

193

C₂×C₄

—

344

—

194

C₂×C₄

—

172

—

195

C₂×C₄

—

172

—

196

C₂×C₄

—

172

—

197

C₂×C₄

—

172

—

198

C₂×C₄

—

172

—

199

C₂×C₄

—

172

—

200

C₂×C₄

—

172

—

201

C₂×C₄

#13063303

yes

—

202

C₂×C₄

#13063305

yes

characteristic

203

C₂×C₄

#13063311

yes

—

204

C₂×C₄

#13063313

yes

characteristic

205

C₂×C₄

#13063344

yes

—

206

C₂×C₄

#13063346

yes

—

207

C₂×C₄

#13063354

yes

—

208

C₂×C₄

#13063357

yes

—

209

C₈

—

210

C₈

—

172

—

211

C₂²

#14582812

yes

characteristic

212

C₂²

#14583062

yes

—

213

C₂²

#14583064

yes

—

214

C₂²

#14583069

yes

characteristic

215

C₂²

#14583074

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

344

—

220

C₄

—

344

—

221

C₄

—

344

—

222

C₄

#14583205

yes

—

223

C₄

#14583209

yes

—

224

C₄

#14583252

yes

—

225

C₄

#14583266

yes

—

226

C₂

#19133717

yes

characteristic

227

C₂

#19133741

yes

characteristic

228

C₂

#19133768

yes

—

229

C₂

#19135745

yes

—

230

C₂

#19135752

yes

characteristic

	subgroup	G/H
center	C₂³	#13063295
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1296	C₂
socle, prime radical	C₂³×C₄₃	#120
hypercenter	#1296	D₄₃
hypocenter	C₄₃	#10352
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

subgroup

G/H

center

C₂³

#13063295

commutator, cosocle

C₂×C₄²×C₄₃

C₂³

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1296

C₂

C₂³×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

N	H ≅ G/N	type
132. C₄₃	#10352	semidirect

H ≅ G/N

type

132. C₄₃

#10352

semidirect

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

subgroup	index
#19139837	2
#19135542	2
#19135396	2
#19132434	2
C₄₃×#1296	2
#10352	43

subgroup

index

C₄₃×#1296

Subgroups — #24999628

Conjugacy classes of subgroups

Complements

Maximal subgroups