Finite Group Databasebeta

← #20252653

Subgroups — #20252653

Order 6016.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094070C211yesmaximal, characteristic, complemented
2C2×#13094051C211yesmaximal, characteristic, complemented
3C2×D8×D47C211yesmaximal, characteristic, complemented
4#15689689C211yesmaximal, characteristic, complemented
5#15689271C211yesmaximal, characteristic, complemented
6#15689268C211yesmaximal, characteristic, complemented
7#15689267C211yesmaximal, characteristic, complemented
8#15689259C211yesmaximal, characteristic, complemented
9#15689258C211yesmaximal, characteristic, complemented
10#15689256C211yesmaximal, characteristic, complemented
11#15689255C211yesmaximal, characteristic, complemented
12#15689126C211yesmaximal, characteristic, complemented
13#15689118C211yesmaximal, characteristic, complemented
14#15689088C211yesmaximal, characteristic, complemented
15C47×#449C211yesmaximal, characteristic, complemented
16#13094070—24no—
17#13094070—24no—
18C2×#10625354C2211yescharacteristic
19C2×#10625354C2211yescharacteristic, complemented
20C2×#10625350—21no—
21C2×#10625350C2211yescharacteristic
22C22×D188—21no—
23C22×D188C2211yescharacteristic, complemented
24C2×D4×D47—21no—
25C2×D4×D47—21no—
26C2×D4×D47C2211yescharacteristic
27C2×D4×D47C2211yescharacteristic, complemented
28C2×D4×D47C2211yescharacteristic, complemented
29#13094051—24no—
30C2×#10625336C2211yescharacteristic, complemented
31C2×D376C2211yescharacteristic, complemented
32C2×D376C2211yescharacteristic, complemented
33C2×#10625334C2211yescharacteristic, complemented
34C2×#10625334C2211yescharacteristic, complemented
35C2×#10625334C2211yescharacteristic, complemented
36D8×D47—24no—
37C2×#10625324C2211yescharacteristic, complemented
38C2×C8×D47C2211yescharacteristic, complemented
39#13094020—21no—
40#13094010—21no—
41#13093999C2211yescharacteristic, complemented
42#13093998C2211yescharacteristic, complemented
43#13093995C2211yescharacteristic, complemented
44#13093994—21no—
45#13093992—21no—
46#13093982C2211yescharacteristic, complemented
47#13093948C2211yescharacteristic, complemented
48#13093946C2211yescharacteristic, complemented
49#13093946C2211yescharacteristic, complemented
50#13093945C2211yescharacteristic, complemented
51#13093944C2211yescharacteristic, complemented
52#13093944C2211yescharacteristic, complemented
53C22⋊(C47⋊C8)C2211yescharacteristic, complemented
54(C2×D47)⋊C8C2211yescharacteristic, complemented
55(C2×D47)⋊C8C2211yescharacteristic, complemented
56C2×#41×C47C2211yescharacteristic, complemented
57C2×SD16×C47C2211yescharacteristic, complemented
58C2×D8×C47C2211yescharacteristic, complemented
59#121×C47C2211yescharacteristic, complemented
60#103×C47C2211yescharacteristic, complemented
61#102×C47C2211yescharacteristic, complemented
62C22⋊C8×C47C2211yescharacteristic, complemented
63C23×D47—21no—
64C23×D47—21no—
65C23×D47—21no—
66C23×D47—21no—
67#41×C47—22no—
68#41×C47—22no—
69C2×Q8×C47C2311yescharacteristic
70C2×D4×C47—21no—
71C2×D4×C47—21no—
72C2×D4×C47C2311yescharacteristic
73C2×D4×C47C2311yescharacteristic
74C22×C4×C47—21no—
75C22×C4×C47C2311yescharacteristic
76C2×C22⋊D47—21no—
77C2×C22⋊D47—21no—
78C2×C22⋊D47—21no—
79C2×C22⋊D47—21no—
80C2×C22⋊D47—21no—
81C2×C22⋊D47D411yescharacteristic
82C2×C22⋊D47D411yescharacteristic
83#10625354—22no—
84#10625354—22no—
85#10625354—22no—
86#10625354D414yescomplemented
87D4×D47—28no—
88D4×D47—28no—
89D4×D47—22no—
90D4×D47—22no—
91D4×D47—22no—
92D4×D47—22no—
93D4×D47—22no—
94D4×D47D414yescomplemented
95#10625350—28no—
96#10625350—22no—
97#10625350—22no—
98C2×D188—28no—
99C2×D188—21no—
100C2×D188—21no—
101C2×D188—21no—
102C2×D188—22no—
103C2×D188—22no—
104C2×D188—21no—
105C2×D188D411yescharacteristic
106C2×D188C2311yescharacteristic
107C2×D188C2311yescharacteristic
108C2×D188C2311yescharacteristic
109C2×C4×D47—21no—
110C2×C4×D47—21no—
111C2×C4×D47C2311yescharacteristic
112C2×C4×D47C2311yescharacteristic
113C2×Dic94D411yescharacteristic
114SD16×C47—22no—
115D8×C47—22no—
116C2×C8×C47C2311yescharacteristic
117C2×C8×C47C2311yescharacteristic
118C4⋊C4×C47C2311yescharacteristic
119C22⋊C4×C47—21no—
120C22⋊Dic47—21no—
121#10625336—22no—
122#10625334—22no—
123#10625334—22no—
124#10625334—22no—
125(C2×D47)⋊C4—21no—
126(C2×D47)⋊C4—21no—
127(C2×D47)⋊C4—21no—
128C4⋊Dic47C2311yescharacteristic
129C4×Dic47—21no—
130C2×C47⋊C8C2311yescharacteristic
131C2×C47⋊C8C2311yescharacteristic
132D376—22no—
133D376—22no—
134#10625324—22no—
135C8×D47—22no—
136C23×C47—21no—
137C23×C47—21no—
138C23×C47C2×D411yescharacteristic
139C22×D47—21no—
140C22×D47—21no—
141C22×D47—24no—
142C22×D47—24no—
143C22×D47—24no—
144C22×D47—21no—
145C22×D47—42no—
146C22×D47—81no—
147C22×D47—81no—
148C22×D47—81no—
149C22×D47—81no—
150C22×D47—81no—
151C22×D47—81no—
152C22×D47—81no—
153C22×D47—81no—
154C22×D47C2×D411yescharacteristic
155C22×D47C2×D411yescharacteristic
156Q8×C47—21no—
157Q8×C47C2×D412yes—
158D4×C47—24no—
159D4×C47—21no—
160D4×C47—21no—
161D4×C47—21no—
162D4×C47—81no—
163D4×C47C2×D412yes—
164C2×C4×C47—24no—
165C2×C4×C47—21no—
166C2×C4×C47—21no—
167C2×C4×C47—21no—
168C2×C4×C47—21no—
169C2×C4×C47C2×D411yescharacteristic
170C2×C4×C47C2411yescharacteristic
171C22⋊D47—24no—
172C22⋊D47—22no—
173C22⋊D47—22no—
174C22⋊D47—24no—
175C22⋊D47—42no—
176C22⋊D47—81no—
177C22⋊D47—81no—
178C2×Dic47—21no—
179C2×Dic47C2×D411yescharacteristic
180C2×Dic47C2×D411yescharacteristic
181D188—24no—
182D188—24no—
183D188—22no—
184D188—24no—
185D188—21no—
186D188—21no—
187D188—21no—
188D188—21no—
189D188—81no—
190D188C2×D412yes—
191D188C2×D412yes—
192C4×D47—24no—
193C4×D47—21no—
194C4×D47—21no—
195C4×D47—24no—
196C4×D47C2×D412yes—
197C4×D47C2×D412yes—
198Dic94—22no—
199C8×C47—21no—
200C8×C47—21no—
201C47⋊C8—21no—
202C47⋊C8—21no—
203C22×C47—21no—
204C22×C47—22no—
205C22×C47—21no—
206C22×C47—21no—
207C22×C47—41no—
208C22×C47—41no—
209C22×C47—41no—
210C22×C47—41no—
211C22×C47—41no—
212C22×C47C22×D411yescharacteristic
213C2×D47—21no—
214C2×D47—21no—
215C2×D47—21no—
216C2×D47—22no—
217C2×D47—22no—
218C2×D47—21no—
219C2×D47—21no—
220C2×D47—41no—
221C2×D47—41no—
222C2×D47—41no—
223C2×D47—41no—
224C2×D47—41no—
225C2×D47—41no—
226C2×D47—41no—
227C2×D47—84no—
228C2×D47—84no—
229C2×D47—84no—
230C2×D47—84no—
231C2×D47#12012yes—
232C4×C47—21no—
233C4×C47—22no—
234C4×C47—41no—
235C4×C47C22×D411yescharacteristic
236C4×C47C22×D411yescharacteristic
237Dic47—21no—
238Dic47—41no—
239Dic47#12012yes—
240#3008—471nomaximal, Sylow
241C2×C47—41no—
242C2×C47—42no—
243C2×C47—81no—
244C2×C47C2×#12011yescharacteristic
245C2×C47#57611yescharacteristic
246C2×C47#57611yescharacteristic
247D47—22no—
248D47—41no—
249D47—42no—
250D47—42no—
251D47—81no—
252C2×H(5,𝔽2)—471no—
253C2×AGL(1,ℤ/8)—471no—
254C22×D8—471no—
255#535—471no—
256#449—471no—
257#449—471no—
258#449—471no—
259#449D4711yescharacteristic, complemented
260#447—471no—
261#447—471no—
262#447—471no—
263#447—471no—
264#418—471no—
265#416—471no—
266#408—471no—
267C47#300811yescharacteristic, complemented, Sylow
268H(5,𝔽2)—944no—
269H(5,𝔽2)—944no—
270C2×#41—471no—
271C2×#41—471no—
272C2×#41—471no—
273C2×#41—941no—
274C2×#41C2×D4711yescharacteristic, complemented
275C22×D4—471no—
276C22×D4—471no—
277C22×D4—471no—
278C22×D4—471no—
279C22×D4—941no—
280C22×D4—941no—
281C22×D4—941no—
282AGL(1,ℤ/8)—944no—
283C2×SD16—471no—
284C2×SD16C2×D4711yescharacteristic, complemented
285C2×D8—471no—
286C2×D8—471no—
287C2×D8—471no—
288C2×D8—471no—
289C2×D8—471no—
290C2×D8—944no—
291C2×D8C2×D4711yescharacteristic, complemented
292C2×M16—471no—
293C22×C8—471no—
294#127—941no—
295#124—941no—
296#121—471no—
297#121—471no—
298#121—471no—
299#121C2×D4711yescharacteristic, complemented
300#120—941no—
301#120—941no—
302#117—471no—
303#103—471no—
304#103C2×D4711yescharacteristic, complemented
305#102—471no—
306#102—471no—
307#102—471no—
308#102—471no—
309#102—471no—
310#102C2×D4711yescharacteristic, complemented
311C22⋊C8—471no—
312C22⋊C8—471no—
313C22⋊C8—471no—
314C22⋊C8C2×D4711yescharacteristic, complemented
315C24—941no—
316C24—941no—
317C24—941no—
318C24—941no—
319#41—22no—
320#41—22no—
321#41—474no—
322#41—942no—
323#41—942no—
324#41—948no—
325#41—942no—
326#41—942no—
327#41—942no—
328C2×Q8—471no—
329C2×Q8C22×D4711yescharacteristic
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—474no—
333C2×D4—471no—
334C2×D4—471no—
335C2×D4—471no—
336C2×D4—471no—
337C2×D4—471no—
338C2×D4—471no—
339C2×D4—942no—
340C2×D4—942no—
341C2×D4—941no—
342C2×D4—941no—
343C2×D4—948no—
344C2×D4—941no—
345C2×D4—942no—
346C2×D4—942no—
347C2×D4—942no—
348C2×D4—941no—
349C2×D4—941no—
350C2×D4—941no—
351C2×D4—942no—
352C2×D4—948no—
353C2×D4—948no—
354C2×D4—942no—
355C2×D4—941no—
356C2×D4—941no—
357C2×D4—941no—
358C2×D4C22×D4711yescharacteristic
359C2×D4C22×D4711yescharacteristic
360C22×C4—21no—
361C22×C4—471no—
362C22×C4—471no—
363C22×C4—941no—
364C22×C4—941no—
365C22×C4C22×D4711yescharacteristic
366SD16—22no—
367SD16—942no—
368D8—22no—
369D8—942no—
370D8—942no—
371D8—942no—
372D8—942no—
373D8—942no—
374M16—942no—
375C2×C8—471no—
376C2×C8—471no—
377C2×C8—942no—
378C2×C8C22×D4711yescharacteristic
379C2×C8C22×D4711yescharacteristic
380C4⋊C4—471no—
381C4⋊C4C22×D4711yescharacteristic
382C22⋊C4—21no—
383C22⋊C4—941no—
384C22⋊C4—941no—
385C22⋊C4—941no—
386C22⋊C4—941no—
387C42—941no—
388C23—21no—
389C23—21no—
390C23—471no—
391C23—471no—
392C23—944no—
393C23—944no—
394C23—944no—
395C23—941no—
396C23—941no—
397C23—941no—
398C23—3761no—
399C23—3761no—
400C23—3761no—
401C23—3761no—
402C23—3761no—
403C23—3761no—
404C23—3761no—
405C23—3761no—
406C23—1882no—
407C23D4×D4711yescharacteristic
408Q8—21no—
409Q8—942no—
410Q8D4×D4712yes—
411D4—24no—
412D4—21no—
413D4—21no—
414D4—21no—
415D4—81no—
416D4—472no—
417D4—472no—
418D4—942no—
419D4—944no—
420D4—944no—
421D4—944no—
422D4—942no—
423D4—944no—
424D4—942no—
425D4—944no—
426D4—941no—
427D4—941no—
428D4—941no—
429D4—941no—
430D4—3761no—
431D4—3761no—
432D4—3761no—
433D4—1882no—
434D4D4×D4712yes—
435C2×C4—24no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—471no—
441C2×C4—472no—
442C2×C4—472no—
443C2×C4—471no—
444C2×C4—944no—
445C2×C4—944no—
446C2×C4—941no—
447C2×C4—941no—
448C2×C4—941no—
449C2×C4D4×D4711yescharacteristic
450C2×C4C23×D4711yescharacteristic
451C8—21no—
452C8—21no—
453C8—941no—
454C8—941no—
455C22—21no—
456C22—22no—
457C22—21no—
458C22—21no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—472no—
465C22—941no—
466C22—941no—
467C22—942no—
468C22—942no—
469C22—941no—
470C22—941no—
471C22—941no—
472C22—3764no—
473C22—3764no—
474C22—3764no—
475C22—3764no—
476C22—1881no—
477C22—1881no—
478C22—1881no—
479C22—1881no—
480C22—1881no—
481C22—1881no—
482C22—1881no—
483C22C2×D4×D4711yescharacteristic
484C4—21no—
485C4—22no—
486C4—41no—
487C4—472no—
488C4—941no—
489C4—1881no—
490C4C2×D4×D4711yescharacteristic
491C4C2×D4×D4711yescharacteristic
492C2—41no—
493C2—42no—
494C2—81no—
495C2—942no—
496C2—3761no—
497C2—1881no—
498C2—1882no—
499C2—1882no—
500C2#120×D4711yescharacteristic
501C2#1568992511yescharacteristic
502C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#449C2
socleC22×C47C22×D4
hypercenter#449D47
hypocenterC47#3008
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#13094070C2semidirect
2. C2×#13094051C2semidirect
3. C2×D8×D47C2semidirect
4. #15689689C2semidirect
5. #15689271C2semidirect
6. #15689268C2semidirect
7. #15689267C2semidirect
8. #15689259C2semidirect
9. #15689258C2semidirect
10. #15689256C2semidirect
11. #15689255C2semidirect
12. #15689126C2semidirect
13. #15689118C2semidirect
14. #15689088C2semidirect
15. C47×#449C2semidirect
19. C2×#10625354C22semidirect
23. C22×D188C22semidirect
27. C2×D4×D47C22semidirect
28. C2×D4×D47C22semidirect
30. C2×#10625336C22semidirect
31. C2×D376C22semidirect
32. C2×D376C22semidirect
33. C2×#10625334C22semidirect
34. C2×#10625334C22semidirect
35. C2×#10625334C22semidirect
37. C2×#10625324C22semidirect
38. C2×C8×D47C22semidirect
41. #13093999C22semidirect
42. #13093998C22semidirect
43. #13093995C22semidirect
46. #13093982C22semidirect
47. #13093948C22semidirect
48. #13093946C22semidirect
49. #13093946C22semidirect
50. #13093945C22semidirect
51. #13093944C22semidirect
52. #13093944C22semidirect
53. C22⋊(C47⋊C8)C22semidirect
54. (C2×D47)⋊C8C22semidirect
55. (C2×D47)⋊C8C22semidirect
56. C2×#41×C47C22semidirect
57. C2×SD16×C47C22semidirect
58. C2×D8×C47C22semidirect
59. #121×C47C22semidirect
60. #103×C47C22semidirect
61. #102×C47C22semidirect
62. C22⋊C8×C47C22semidirect
86. #10625354D4semidirect
94. D4×D47D4semidirect
259. #449D47semidirect
267. C47#3008semidirect
274. C2×#41C2×D47semidirect
284. C2×SD16C2×D47semidirect
291. C2×D8C2×D47semidirect
299. #121C2×D47semidirect
304. #103C2×D47semidirect
310. #102C2×D47semidirect
314. C22⋊C8C2×D47semidirect