Finite Group Databasebeta

← #19144537

Subgroups — #19144537

Order 5504.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063300C211yesmaximal, characteristic
2#117×D43C211yesmaximal, characteristic, complemented
3#14583226C212yesmaximal, complemented
4#14583225C212yesmaximal, complemented
5#14583219C212yesmaximal, complemented
6#14583214C212yesmaximal, complemented
7#14582939C211yesmaximal, characteristic, complemented
8#14582905C211yesmaximal, characteristic, complemented
9#14582903C211yesmaximal, characteristic, complemented
10#14582862C211yesmaximal, characteristic, complemented
11C43×#428C211yesmaximal, characteristic, complemented
12C22×D172—21no—
13C22×D172C2211yescharacteristic
14C22×C4×D43C2211yescharacteristic
15C2×#10621877C2211yescharacteristic
16#13063300—21no—
17#13063300—21no—
18#13063300C2212yes—
19#13063300C2212yes—
20#13063284C2211yescharacteristic
21#13063283C2211yescharacteristic, complemented
22#13063283C2211yescharacteristic, complemented
23#13063282—21no—
24#13063281—21no—
25C4⋊C4×D43C2211yescharacteristic, complemented
26C4⋊C4×D43C2211yescharacteristic, complemented
27C2×(C2×D43)⋊C4—21no—
28C22⋊C4×D43—21no—
29C42×D43—21no—
30#13063258C2212yescomplemented
31#13063256C2212yescomplemented
32#13063247C2212yescomplemented
33#13063247C2212yescomplemented
34#13063245C2212yescomplemented
35#13063245C2212yescomplemented
36(C2×D43)⋊C8C2212yescomplemented
37(C2×D43)⋊C8C2212yescomplemented
38C2×M16×C43C2211yescharacteristic
39#117×C43C2211yescharacteristic
40C2×C4⋊C4×C43C2211yescharacteristic
41#107×C43C2212yescomplemented
42#106×C43C2212yescomplemented
43C23×D43—21no—
44C23×D43D411yescharacteristic
45C22×C4×C43—21no—
46C22×C4×C43C2311yescharacteristic
47C22×Dic43D411yescharacteristic
48C2×D172—21no—
49C2×D172—22no—
50C2×D172—22no—
51C2×D172—22no—
52C2×D172—22no—
53C2×D172—44no—
54C2×D172C2312yes—
55C2×C4×D43—22no—
56C2×C4×D43—22no—
57C2×C4×D43—21no—
58C2×C4×D43—21no—
59C2×C4×D43D411yescharacteristic
60C2×C4×D43D411yescharacteristic
61C2×C4×D43C2311yescharacteristic
62C2×C4×D43C2311yescharacteristic
63M16×C43—22no—
64C2×C8×C43C2312yes—
65C4⋊C4×C43—21no—
66C4⋊C4×C43C2311yescharacteristic
67C4⋊C4×C43C2312yes—
68C4⋊C4×C43C2311yescharacteristic
69C22⋊C4×C43—21no—
70C42×C43—21no—
71C22⋊Dic43—21no—
72(C2×D43)⋊C4—22no—
73(C2×D43)⋊C4—22no—
74(C2×D43)⋊C4—21no—
75(C2×D43)⋊C4—21no—
76C4⋊Dic43C2311yescharacteristic
77C4⋊Dic43C2311yescharacteristic
78Dic43⋊C4—21no—
79Dic43⋊C4—21no—
80C4×Dic43—21no—
81C4×Dic43—21no—
82C4×Dic43—21no—
83#10621877—22no—
84C2×C43⋊C8C2312yes—
85C23×C43C2×D411yescharacteristic
86C22×D43—22no—
87C22×D43—22no—
88C22×D43—22no—
89C22×D43—41no—
90C22×D43—42no—
91C22×D43—42no—
92C22×D43—42no—
93C22×D43C2×D411yescharacteristic
94C22×D43C2×D411yescharacteristic
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—22no—
98C2×C4×C43—42no—
99C2×C4×C43C2×D411yescharacteristic
100C2×C4×C43#4112yes—
101C2×C4×C43#4112yes—
102C2×C4×C43C2411yescharacteristic
103C2×Dic43—22no—
104C2×Dic43—21no—
105C2×Dic43—21no—
106C2×Dic43C2×D411yescharacteristic
107C2×Dic43C2×D411yescharacteristic
108D172—22no—
109D172—22no—
110D172—44no—
111D172—44no—
112D172—42no—
113C4×D43—22no—
114C4×D43—22no—
115C4×D43—21no—
116C4×D43—21no—
117C4×D43—21no—
118C4×D43—21no—
119C4×D43—42no—
120C4×D43—42no—
121C8×C43—22no—
122C43⋊C8—22no—
123C22×C43—21no—
124C22×C43—21no—
125C22×C43#12312yes—
126C22×C43C22×D411yescharacteristic
127C2×D43—21no—
128C2×D43—21no—
129C2×D43—21no—
130C2×D43—21no—
131C2×D43—21no—
132C2×D43—44no—
133C2×D43—42no—
134C2×D43—42no—
135C2×D43—42no—
136C2×D43—84no—
137C2×D43AGL(1,ℤ/8)12yes—
138C4×C43—41no—
139C4×C43—42no—
140C4×C43—41no—
141C4×C43#12312yes—
142C4×C43C2×#4111yescharacteristic
143C4×C43C2×#4111yescharacteristic
144Dic43—21no—
145Dic43—21no—
146Dic43—41no—
147Dic43—41no—
148#3094—431nomaximal, Sylow
149C2×C43—22no—
150C2×C43C2×#12311yescharacteristic
151C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
152C2×C43#57511yescharacteristic
153D43—22no—
154D43—41no—
155D43—82no—
156C2×#121—431no—
157C2×#117—431no—
158#482—432no—
159#482—432no—
160#481—432no—
161#480—432no—
162#428—431no—
163#428D4311yescharacteristic, complemented
164#418—431no—
165#418—431no—
166#407—431no—
167C43#309411yescharacteristic, complemented, Sylow
168C22×D4—431no—
169C22×D4—861no—
170C23×C4—431no—
171C2×M16—431no—
172C2×M16C2×D4311yescharacteristic
173#121—432no—
174#121—432no—
175#121—861no—
176#121—861no—
177#117—431no—
178#117—431no—
179#117—431no—
180#117—861no—
181#117—861no—
182#117C2×D4311yescharacteristic
183C2×C4⋊C4—431no—
184C2×C4⋊C4—431no—
185C2×C4⋊C4C2×D4311yescharacteristic
186C2×C22⋊C4—861no—
187C2×C22⋊C4—861no—
188C2×C42—861no—
189#107—432no—
190#107C2×D4312yescomplemented
191#106—432no—
192#106C2×D4312yescomplemented
193#102—432no—
194#102—432no—
195#102—432no—
196#102—432no—
197C22⋊C8—432no—
198C22⋊C8—432no—
199C24—431no—
200C24—861no—
201C2×D4—432no—
202C2×D4—862no—
203C2×D4—862no—
204C2×D4—862no—
205C2×D4—861no—
206C2×D4—862no—
207C2×D4—1724no—
208C22×C4—21no—
209C22×C4—431no—
210C22×C4—431no—
211C22×C4—431no—
212C22×C4—431no—
213C22×C4—431no—
214C22×C4—861no—
215C22×C4—861no—
216C22×C4—862no—
217C22×C4—862no—
218C22×C4C22×D4311yescharacteristic
219M16—22no—
220M16—862no—
221C2×C8—432no—
222C2×C8C22×D4312yes—
223C4⋊C4—21no—
224C4⋊C4—431no—
225C4⋊C4—431no—
226C4⋊C4—861no—
227C4⋊C4—861no—
228C4⋊C4C22×D4311yescharacteristic
229C4⋊C4C22×D4311yescharacteristic
230C4⋊C4C22×D4312yes—
231C22⋊C4—21no—
232C22⋊C4—862no—
233C22⋊C4—862no—
234C22⋊C4—861no—
235C22⋊C4—861no—
236C22⋊C4—861no—
237C42—21no—
238C42—861no—
239C42—861no—
240C42—861no—
241C23—431no—
242C23—431no—
243C23—862no—
244C23—862no—
245C23—862no—
246C23—1721no—
247C23—1722no—
248C23—1722no—
249C23—1722no—
250C23D4×D4311yescharacteristic
251D4—862no—
252D4—862no—
253D4—1724no—
254D4—1724no—
255D4—1722no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—42no—
260C2×C4—431no—
261C2×C4—431no—
262C2×C4—862no—
263C2×C4—862no—
264C2×C4—862no—
265C2×C4—861no—
266C2×C4—861no—
267C2×C4—861no—
268C2×C4—861no—
269C2×C4—861no—
270C2×C4—861no—
271C2×C4—1722no—
272C2×C4—1722no—
273C2×C4#1062189812yes—
274C2×C4D4×D4311yescharacteristic
275C2×C4#1062190212yes—
276C2×C4C23×D4311yescharacteristic
277C8—22no—
278C8—862no—
279C22—21no—
280C22—21no—
281C22—432no—
282C22—861no—
283C22—861no—
284C22—861no—
285C22—861no—
286C22—861no—
287C22—3444no—
288C22—1724no—
289C22—1722no—
290C22—1722no—
291C22—1722no—
292C22#1306331012yes—
293C22C2×D4×D4311yescharacteristic
294C4—42no—
295C4—41no—
296C4—41no—
297C4—861no—
298C4—861no—
299C4—1721no—
300C4—1721no—
301C4#1306331012yes—
302C4C2×#1062189811yescharacteristic
303C4C2×#1062190211yescharacteristic
304C2—22no—
305C2—862no—
306C2—3442no—
307C2—1721no—
308C2C2×#1306331011yescharacteristic
309C2AGL(1,ℤ/8)×D4311yescharacteristic
310C2#1458369811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#428C2
socleC22×C43C22×D4
hypercenter#428D43
hypocenterC43#3094
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #117×D43C2semidirect
3. #14583226C2semidirect
4. #14583225C2semidirect
5. #14583219C2semidirect
6. #14583214C2semidirect
7. #14582939C2semidirect
8. #14582905C2semidirect
9. #14582903C2semidirect
10. #14582862C2semidirect
11. C43×#428C2semidirect
21. #13063283C22semidirect
22. #13063283C22semidirect
25. C4⋊C4×D43C22semidirect
26. C4⋊C4×D43C22semidirect
30. #13063258C22semidirect
31. #13063256C22semidirect
32. #13063247C22semidirect
33. #13063247C22semidirect
34. #13063245C22semidirect
35. #13063245C22semidirect
36. (C2×D43)⋊C8C22semidirect
37. (C2×D43)⋊C8C22semidirect
41. #107×C43C22semidirect
42. #106×C43C22semidirect
163. #428D43semidirect
167. C43#3094semidirect
190. #107C2×D43semidirect
192. #106C2×D43semidirect