Finite Group Databasebeta

← #19146427

Subgroups — #19146427

Order 5504.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583587C211yesmaximal, characteristic, complemented
2#14583544C211yesmaximal, characteristic
3#14583256C211yesmaximal, characteristic, complemented
4#14583231C211yesmaximal, characteristic, complemented
5#14583226C211yesmaximal, characteristic, complemented
6#14583141C211yesmaximal, characteristic, complemented
7#14583129C211yesmaximal, characteristic, complemented
8#14583122C211yesmaximal, characteristic, complemented
9#14583062C211yesmaximal, characteristic, complemented
10#14583051C211yesmaximal, characteristic, complemented
11C4×#10621883C211yesmaximal, characteristic, complemented
12#14582964C211yesmaximal, characteristic, complemented
13#14582892C211yesmaximal, characteristic, complemented
14#102×D43C211yesmaximal, characteristic, complemented
15C43×#478C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×Dic172C2211yescharacteristic, complemented
19C2×#10621873C2211yescharacteristic
20C2×#10621883C2211yescharacteristic
21C2×C8×D43C2211yescharacteristic
22C2×C8×D43C2211yescharacteristic, complemented
23#13063320—21no—
24#13063316—21no—
25#13063313C2211yescharacteristic
26#13063310—21no—
27#13063309—21no—
28#13063305C2211yescharacteristic
29#13063305C2211yescharacteristic
30#13063305C2211yescharacteristic, complemented
31#13063300C2211yescharacteristic
32#13063299—21no—
33#13063295—21no—
34C4×Dic86C2211yescharacteristic, complemented
35C4×D172C2211yescharacteristic
36#13063283—21no—
37#13063283C2211yescharacteristic, complemented
38C4⋊C4×D43C2211yescharacteristic
39C2×(C2×D43)⋊C4—21no—
40#13063256C2211yescharacteristic, complemented
41#13063250C2211yescharacteristic, complemented
42#13063248C2211yescharacteristic, complemented
43#13063248C2211yescharacteristic, complemented
44#13063248C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51C4×C43⋊C8C2211yescharacteristic, complemented
52#125×C43C2211yescharacteristic, complemented
53C4×D4×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic, complemented
55#106×C43C2211yescharacteristic, complemented
56C4⋊C8×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C23×D43—21no—
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C22×Dic43—21no—
65#10621900—22no—
66#10621900—41no—
67D4×D43—22no—
68D4×D43—41no—
69C2×D172—21no—
70C2×D172D411yescharacteristic
71C2×D172C2311yescharacteristic
72C2×C4×D43—21no—
73C2×C4×D43C2311yescharacteristic
74C2×C4×D43C2311yescharacteristic
75C2×Dic86C2311yescharacteristic
76C2×Dic86C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C2×C8×C43C2311yescharacteristic
79C4⋊C4×C43—21no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C22⋊C4×C43—21no—
85C42×C43C2311yescharacteristic
86#10621883—22no—
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4D411yescharacteristic
95(C2×D43)⋊C4D411yescharacteristic
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43D411yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107Dic172—41no—
108#10621873—41no—
109C8×D43—41no—
110C8×D43—41no—
111C23×C43—21no—
112C22×D43—21no—
113C22×D43—42no—
114C22×D43—42no—
115C22×D43—81no—
116C22×D43C2×D411yescharacteristic
117C22×D43C2×D411yescharacteristic
118D4×C43—21no—
119D4×C43#4112yes—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—81no—
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2411yescharacteristic
127C22⋊D43—42no—
128C22⋊D43—42no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—42no—
133C2×Dic43C2×D411yescharacteristic
134C2×Dic43C2×D411yescharacteristic
135D172—22no—
136D172—21no—
137D172—21no—
138D172—81no—
139C4×D43—21no—
140C4×D43—21no—
141C4×D43—21no—
142C4×D43—21no—
143C4×D43—42no—
144Dic86—21no—
145Dic86—21no—
146Dic86—21no—
147Dic86—21no—
148C8×C43—21no—
149C8×C43—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43—22no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43C22×D411yescharacteristic
156C2×D43—21no—
157C2×D43—21no—
158C2×D43—21no—
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—41no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—84no—
165C2×D43#13512yes—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—41no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43C2×#4111yescharacteristic
172C4×C43H(5,𝔽2)11yescharacteristic
173Dic43—21no—
174Dic43—21no—
175Dic43—41no—
176Dic43—41no—
177Dic43—41no—
178#3296—431nomaximal, Sylow
179C2×C43—42no—
180C2×C43#54611yescharacteristic
181C2×C43C2×#13511yescharacteristic
182C2×C43#57711yescharacteristic
183D43—22no—
184D43—41no—
185D43—81no—
186#552—431no—
187#546—431no—
188#488—431no—
189#483—431no—
190#482—431no—
191#478D4311yescharacteristic, complemented
192#467—431no—
193#465—431no—
194#464—431no—
195#452—431no—
196#450—431no—
197C4×SD16—431no—
198C8×D4—431no—
199#416—431no—
200C2×#102—431no—
201C43#329611yescharacteristic, complemented, Sylow
202C2×#41—431no—
203C22×D4—431no—
204C2×Q16—431no—
205C2×SD16—431no—
206C2×SD16—431no—
207C22×C8—431no—
208C22×C8—431no—
209#126—861no—
210#125—861no—
211#125C2×D4311yescharacteristic, complemented
212#124—431no—
213#123—861no—
214#123—861no—
215C22⋊Q8—431no—
216C22⋊Q8—431no—
217C22⋊Q8—431no—
218#121—431no—
219#121—861no—
220#120—861no—
221C4×Q8—431no—
222C4×D4—431no—
223C4×D4C2×D4311yescharacteristic
224#117—431no—
225#117—861no—
226C2×C4⋊C4—431no—
227C2×C22⋊C4—861no—
228#107C2×D4311yescharacteristic, complemented
229#106—431no—
230#106C2×D4311yescharacteristic, complemented
231C4⋊C8C2×D4311yescharacteristic, complemented
232#103—431no—
233#103—431no—
234#103—431no—
235#103—431no—
236#102—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102C2×D4311yescharacteristic
241#102C2×D4311yescharacteristic
242C22⋊C8—431no—
243C22⋊C8—431no—
244C4×C8—431no—
245C24—861no—
246#41—862no—
247#41—1721no—
248C2×Q8—431no—
249C2×Q8—431no—
250C2×D4—431no—
251C2×D4—431no—
252C2×D4—861no—
253C2×D4—861no—
254C2×D4—862no—
255C2×D4—861no—
256C2×D4—1721no—
257C2×D4C22×D4311yescharacteristic
258C22×C4—21no—
259C22×C4—431no—
260C22×C4—431no—
261C22×C4—861no—
262C22×C4—861no—
263Q16—1721no—
264SD16—862no—
265SD16—1721no—
266C2×C8—431no—
267C2×C8—431no—
268C2×C8—1721no—
269C2×C8—1721no—
270C2×C8C22×D4311yescharacteristic
271C2×C8C22×D4311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4C22×D4311yescharacteristic
282C4⋊C4C22×D4311yescharacteristic
283C4⋊C4C22×D4311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—431no—
286C22⋊C4—431no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C42—861no—
295C42—861no—
296C42C22×D4311yescharacteristic
297C23—21no—
298C23—431no—
299C23—431no—
300C23—861no—
301C23—3441no—
302C23—1722no—
303C23—1722no—
304Q8—861no—
305Q8—861no—
306Q8—861no—
307Q8—861no—
308D4—21no—
309D4—862no—
310D4—861no—
311D4—861no—
312D4—3441no—
313D4—1722no—
314D4—1722no—
315D4#1062190212yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—431no—
321C2×C4—431no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—1722no—
330C2×C4—1722no—
331C2×C4D4×D4311yescharacteristic
332C2×C4D4×D4311yescharacteristic
333C2×C4C23×D4311yescharacteristic
334C8—21no—
335C8—21no—
336C8—861no—
337C8—861no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—432no—
342C22—861no—
343C22—861no—
344C22—861no—
345C22—861no—
346C22—861no—
347C22—3444no—
348C22—1721no—
349C22—1721no—
350C22—1721no—
351C22C2×D4×D4311yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—861no—
358C4—861no—
359C4—1721no—
360C4—1721no—
361C4—1721no—
362C4C2×#1062190211yescharacteristic
363C4#1306337111yescharacteristic
364C2—42no—
365C2—862no—
366C2—3441no—
367C2—1721no—
368C2#1458354011yescharacteristic
369C2#135×D4311yescharacteristic
370C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#478C2
socleC22×C43C22×D4
hypercenter#478D43
hypocenterC43#3296
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #14583587C2semidirect
3. #14583256C2semidirect
4. #14583231C2semidirect
5. #14583226C2semidirect
6. #14583141C2semidirect
7. #14583129C2semidirect
8. #14583122C2semidirect
9. #14583062C2semidirect
10. #14583051C2semidirect
11. C4×#10621883C2semidirect
12. #14582964C2semidirect
13. #14582892C2semidirect
14. #102×D43C2semidirect
15. C43×#478C2semidirect
18. C2×Dic172C22semidirect
22. C2×C8×D43C22semidirect
30. #13063305C22semidirect
34. C4×Dic86C22semidirect
37. #13063283C22semidirect
40. #13063256C22semidirect
41. #13063250C22semidirect
42. #13063248C22semidirect
43. #13063248C22semidirect
44. #13063248C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. C4×C43⋊C8C22semidirect
52. #125×C43C22semidirect
54. #107×C43C22semidirect
55. #106×C43C22semidirect
56. C4⋊C8×C43C22semidirect
191. #478D43semidirect
201. C43#3296semidirect
211. #125C2×D43semidirect
228. #107C2×D43semidirect
230. #106C2×D43semidirect
231. C4⋊C8C2×D43semidirect