Finite Group Databasebeta

← #20258173

Subgroups — #20258173

Order 6016.

1412 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
1#15689960C211yesmaximal, characteristic, complemented
22−1+4×D47C211yesmaximal, characteristic, complemented
3#15689939C213yesmaximal, complemented
4#15689938C211yesmaximal, characteristic, complemented
5#15689936C213yesmaximal, complemented
6#15689935C211yesmaximal, characteristic, complemented
7#15689932C213yesmaximal, complemented
8#15689931C211yesmaximal, characteristic, complemented
9#15689930C213yesmaximal, complemented
10#15689922C213yesmaximal, complemented
11#15689920C213yesmaximal, complemented
12C2×#13094056C213yesmaximal, complemented
13#137×D47C213yesmaximal, complemented
14#15689888C211yesmaximal, characteristic, complemented
15C47×#578C211yesmaximal, characteristic, complemented
16#13094072—21no—
17#13094072—21no—
18#13094072C2213yescomplemented
19#13094072C2213yescomplemented
20#13094071—23no—
21#13094071C2213yescomplemented
22#13094071C2211yescharacteristic, complemented
23#13094070—23no—
24#13094070C2213yescomplemented
25#13094070C2211yescharacteristic, complemented
26C2×#10625354—21no—
27C2×#10625354C2213yes—
28#41×D47—23no—
29#41×D47—23no—
30#41×D47C2213yes—
31#41×D47C2211yescharacteristic
32#41×D47C2213yescomplemented
33C2×Q8×D47—21no—
34C2×Q8×D47C2213yescomplemented
35#13094057C2213yescomplemented
36#13094056C2216yescomplemented
37#13094056C2213yescomplemented
38#13094056C2216yescomplemented
39#13094056C2216yescomplemented
40#13094056C2213yescomplemented
41#13094055C2213yescomplemented
42#13094055C2213yescomplemented
43#13094054C2213yescomplemented
44#13094053C2213yescomplemented
45#13094053C2213yescomplemented
46#13094052C2213yescomplemented
47#13094051C2213yescomplemented
48#13094051C2213yescomplemented
49#13094049C2213yescomplemented
50#13094048C2211yescharacteristic, complemented
51#13094048C2213yescomplemented
52#13094047C2216yescomplemented
53#13094046C2213yescomplemented
54#13094045C2216yescomplemented
55#13094044C2213yescomplemented
56#13094044C2213yescomplemented
57C2×#10625337C2213yescomplemented
58Q16×D47C2216yescomplemented
59C2×#10625325C2213yescomplemented
60C2×#10625336C2213yescomplemented
61SD16×D47C2216yescomplemented
62#13094032C2213yescomplemented
63#13094031C2211yescharacteristic, complemented
64#13094030C2213yescomplemented
65C2×#10625324C2213yescomplemented
66M16×D47C2213yescomplemented
672−1+4×C47C2211yescharacteristic, complemented
682−1+4×C47C2211yescharacteristic, complemented
69#137×C47C2213yescomplemented
70#137×C47C2213yescomplemented
71#135×C47C2213yescomplemented
72C2×Q16×C47C2213yescomplemented
73#131×C47C2211yescharacteristic, complemented
74#41×C47—23no—
75#41×C47—23no—
76#41×C47C2313yes—
77#41×C47C2313yes—
78#41×C47C2311yescharacteristic
79C2×Q8×C47—21no—
80C2×Q8×C47—21no—
81C2×Q8×C47C2313yes—
82C2×Q8×C47C2313yes—
83#10625354—21no—
84#10625354—23no—
85#10625354—23no—
86#10625354—23no—
87#10625354—23no—
88#10625354D411yescharacteristic
89#10625354C2316yes—
90#10625354C2313yes—
91#10625354C2313yes—
92Q8×D47—21no—
93Q8×D47—23no—
94Q8×D47—23no—
95Q8×D47—23no—
96Q8×D47—23no—
97Q8×D47D411yescharacteristic
98Q8×D47C2316yes—
99Q8×D47C2313yes—
100Q8×D47C2313yes—
101#10625352—23no—
102#10625352—26no—
103#10625352—23no—
104#10625352—23no—
105#10625352D413yes—
106#10625352C2313yes—
107#10625352C2311yescharacteristic
108D4×D47—23no—
109D4×D47—23no—
110D4×D47—23no—
111D4×D47—26no—
112D4×D47D413yes—
113D4×D47C2313yes—
114D4×D47C2311yescharacteristic
115#10625350—26no—
116#10625350—26no—
117#10625350—23no—
118#10625350—23no—
119#10625350—23no—
120#10625350—23no—
121#10625350C2313yes—
122#10625350C2313yes—
123#10625350C2313yes—
124C2×D188—23no—
125C2×D188—23no—
126C2×D188C2313yes—
127C2×C4×D47—23no—
128C2×C4×D47—23no—
129C2×C4×D47—23no—
130C2×C4×D47—23no—
131C2×C4×D47C2313yes—
132C2×Dic94—23no—
133C2×Dic94—23no—
134C2×Dic94C2313yes—
135Q16×C47C2313yes—
136Q16×C47C2316yes—
137SD16×C47C2313yes—
138SD16×C47C2313yes—
139D8×C47C2311yescharacteristic
140M16×C47C2313yes—
141C2×C8×C47C2313yes—
142#10625337C2313yes—
143#10625337C2316yes—
144#10625337C2313yes—
145#10625336C2316yes—
146#10625336C2313yes—
147#10625336C2313yes—
148#10625335C2313yes—
149#10625335C2311yescharacteristic
150#10625334C2311yescharacteristic
151#10625334C2313yes—
152#10625329C2313yes—
153C2×C47⋊C8C2313yes—
154Dic188C2313yes—
155D376C2313yes—
156#10625325C2316yes—
157#10625325C2313yes—
158#10625325C2311yescharacteristic
159#10625324C2313yes—
160#10625324C2311yescharacteristic
161#10625324C2313yes—
162#10625324C2313yes—
163C8×D47C2316yes—
164C22×D47—23no—
165C22×D47—21no—
166C22×D47—23no—
167C22×D47C2×D413yes—
168Q8×C47—23no—
169Q8×C47—23no—
170Q8×C47C2×D411yescharacteristic
171Q8×C47C2413yes—
172Q8×C47C2413yes—
173D4×C47—23no—
174D4×C47—23no—
175D4×C47C2×D413yes—
176D4×C47C2411yescharacteristic
177D4×C47C2411yescharacteristic
178C2×C4×C47—23no—
179C2×C4×C47—23no—
180C2×C4×C47—23no—
181C2×C4×C47—23no—
182C2×C4×C47C2413yes—
183C22⋊D47—23no—
184C22⋊D47—23no—
185C22⋊D47—21no—
186C22⋊D47—23no—
187C22⋊D47—23no—
188C22⋊D47—21no—
189C22⋊D47C2×D416yes—
190C2×Dic47—23no—
191C2×Dic47—23no—
192C2×Dic47—21no—
193C2×Dic47C2×D413yes—
194D188—23no—
195D188—26no—
196D188—23no—
197D188—23no—
198D188C2×D413yes—
199D188C2413yes—
200D188C2411yescharacteristic
201C4×D47—23no—
202C4×D47—23no—
203C4×D47—26no—
204C4×D47—23no—
205C4×D47—23no—
206C4×D47—23no—
207C4×D47—26no—
208C4×D47—23no—
209C4×D47C2×D413yes—
210C4×D47C2×D413yes—
211C4×D47C2413yes—
212C4×D47C2411yescharacteristic
213Dic94—23no—
214Dic94—26no—
215Dic94—23no—
216Dic94—23no—
217Dic94C2×D413yes—
218Dic94C2413yes—
219Dic94C2411yescharacteristic
220C8×C47C2413yes—
221C8×C47C2411yescharacteristic
222C47⋊C8C2413yes—
223C47⋊C8C2411yescharacteristic
224C22×C47—21no—
225C22×C47—21no—
226C22×C47C22×D413yes—
227C2×D47—21no—
228C2×D47—23no—
229C2×D47—43no—
230C2×D47—42no—
231C2×D47—83no—
232C2×D47—83no—
233C2×D47C22×D411yescharacteristic
234C2×D47C22×D413yes—
235C4×C47—23no—
236C4×C47—23no—
237C4×C47C22×D413yes—
238C4×C47C2511yescharacteristic
239Dic47—23no—
240Dic47—21no—
241Dic47C22×D413yes—
242Dic47C22×D411yescharacteristic
243#3586—471nomaximal, Sylow
244C2×C47—23no—
245C2×C47—41no—
246C2×C47—41no—
247C2×C47C23×D411yescharacteristic
248D47—21no—
249D47—23no—
250D47—41no—
251D47—43no—
252#585—471no—
253C2×2−1+4—471no—
254#578—471no—
255#578—473no—
256#578—473no—
257#578D4711yescharacteristic, complemented
258#577—471no—
259#577—473no—
260#577—473no—
261#577—471no—
262#575—473no—
263#575—473no—
264C2×#137—473no—
265C2×#137—473no—
266#568—471no—
267C47#358611yescharacteristic, complemented, Sylow
2682−1+4—473no—
2692−1+4—471no—
2702−1+4—473no—
2712−1+4—473no—
2722−1+4—941no—
2732−1+4—941no—
2742−1+4—943no—
2752−1+4C2×D4711yescharacteristic, complemented
2762−1+4C2×D4711yescharacteristic, complemented
277H(5,𝔽2)—473no—
278H(5,𝔽2)—471no—
279H(5,𝔽2)—943no—
280C2×#41—471no—
281C2×#41—473no—
282C2×#41—473no—
283C2×#41—473no—
284C2×#41—943no—
285C2×#41—941no—
286C2×#41—943no—
287C22×Q8—473no—
288C22×Q8—941no—
289#137—473no—
290#137—473no—
291#137—473no—
292#137—476no—
293#137—473no—
294#137—476no—
295#137—476no—
296#137—473no—
297#137—473no—
298#137—473no—
299#137—473no—
300#137C2×D4713yescomplemented
301#137C2×D4713yescomplemented
302AGL(1,ℤ/8)—473no—
303AGL(1,ℤ/8)—473no—
304AGL(1,ℤ/8)—473no—
305AGL(1,ℤ/8)—471no—
306AGL(1,ℤ/8)—473no—
307AGL(1,ℤ/8)—473no—
308#135—473no—
309#135—473no—
310#135—476no—
311#135—476no—
312#135—473no—
313#135C2×D4713yescomplemented
314C2×Q16—473no—
315C2×Q16—476no—
316C2×Q16C2×D4713yescomplemented
317C2×SD16—473no—
318C2×SD16—476no—
319C2×SD16—473no—
320#131—471no—
321#131—473no—
322#131—473no—
323#131C2×D4711yescharacteristic, complemented
324C2×M16—473no—
325C2×M16—473no—
326#41—23no—
327#41—23no—
328#41—471no—
329#41—473no—
330#41—473no—
331#41—473no—
332#41—476no—
333#41—473no—
334#41—473no—
335#41—471no—
336#41—473no—
337#41—473no—
338#41—943no—
339#41—943no—
340#41—946no—
341#41—946no—
342#41—943no—
343#41—943no—
344#41—943no—
345#41—943no—
346#41—943no—
347#41—943no—
348#41—946no—
349#41—943no—
350#41—943no—
351#41—941no—
352#41—943no—
353#41C22×D4713yes—
354#41C22×D4713yes—
355#41C22×D4711yescharacteristic
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—471no—
359C2×Q8—476no—
360C2×Q8—473no—
361C2×Q8—473no—
362C2×Q8—473no—
363C2×Q8—943no—
364C2×Q8—943no—
365C2×Q8—943no—
366C2×Q8—943no—
367C2×Q8—943no—
368C2×Q8—943no—
369C2×Q8—941no—
370C2×Q8C22×D4713yes—
371C2×Q8C22×D4713yes—
372C2×D4—473no—
373C2×D4—473no—
374C2×D4—471no—
375C2×D4—473no—
376C2×D4—943no—
377C2×D4—943no—
378C2×D4—946no—
379C2×D4—943no—
380C2×D4—943no—
381C2×D4—943no—
382C22×C4—473no—
383C22×C4—943no—
384C22×C4—943no—
385C22×C4—943no—
386C22×C4—943no—
387Q16—476no—
388Q16—473no—
389Q16—473no—
390Q16—473no—
391Q16C22×D4716yes—
392Q16C22×D4713yes—
393SD16—476no—
394SD16—473no—
395SD16—473no—
396SD16—473no—
397SD16—471no—
398SD16—476no—
399SD16—473no—
400SD16—471no—
401SD16C22×D4713yes—
402SD16C22×D4713yes—
403D8—471no—
404D8—473no—
405D8—473no—
406D8C22×D4711yescharacteristic
407M16—473no—
408M16—473no—
409M16—471no—
410M16—473no—
411M16—473no—
412M16C22×D4713yes—
413C2×C8—473no—
414C2×C8—476no—
415C2×C8C22×D4713yes—
416C23—473no—
417C23—943no—
418C23—941no—
419C23—943no—
420Q8—23no—
421Q8—23no—
422Q8—473no—
423Q8—473no—
424Q8—471no—
425Q8—943no—
426Q8—946no—
427Q8—943no—
428Q8—943no—
429Q8D4×D4711yescharacteristic
430Q8C23×D4713yes—
431Q8C23×D4713yes—
432D4—23no—
433D4—23no—
434D4—476no—
435D4—473no—
436D4—471no—
437D4—473no—
438D4—943no—
439D4—946no—
440D4—943no—
441D4—943no—
442D4—941no—
443D4—941no—
444D4—943no—
445D4—943no—
446D4—943no—
447D4—943no—
448D4D4×D4713yes—
449D4C23×D4711yescharacteristic
450D4C23×D4711yescharacteristic
451C2×C4—23no—
452C2×C4—23no—
453C2×C4—23no—
454C2×C4—23no—
455C2×C4—473no—
456C2×C4—473no—
457C2×C4—473no—
458C2×C4—473no—
459C2×C4—471no—
460C2×C4—943no—
461C2×C4—946no—
462C2×C4—943no—
463C2×C4—943no—
464C2×C4—943no—
465C2×C4—946no—
466C2×C4—941no—
467C2×C4—943no—
468C2×C4—943no—
469C2×C4—943no—
470C2×C4—943no—
471C2×C4C23×D4713yes—
472C8—473no—
473C8—471no—
474C8C23×D4713yes—
475C8C23×D4711yescharacteristic
476C22—21no—
477C22—21no—
478C22—471no—
479C22—473no—
480C22—941no—
481C22—943no—
482C22—3763no—
483C22—3763no—
484C22—1883no—
485C22—1882no—
486C22C2×D4×D4713yes—
487C4—23no—
488C4—23no—
489C4—471no—
490C4—473no—
491C4—941no—
492C4—943no—
493C4C2×D4×D4713yes—
494C4C24×D4711yescharacteristic
495C2—23no—
496C2—41no—
497C2—41no—
498C2—943no—
499C2—941no—
500C2—1883no—
501C2—1881no—
502C2C22×D4×D4711yescharacteristic
subgroupG/H
centerC2C22×D4×D47
commutatorC4×C47C25
FrattiniC4C24×D47
FittingC47×#578C2
socleC2×C47C23×D4
hypercenter#578D47
hypocenterC47#3586
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ #41 ◁ #578

Complements

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

NH ≅ G/Ntype
1. #15689960C2semidirect
2. 2−1+4×D47C2semidirect
3. #15689939C2semidirect
4. #15689938C2semidirect
5. #15689936C2semidirect
6. #15689935C2semidirect
7. #15689932C2semidirect
8. #15689931C2semidirect
9. #15689930C2semidirect
10. #15689922C2semidirect
11. #15689920C2semidirect
12. C2×#13094056C2semidirect
13. #137×D47C2semidirect
14. #15689888C2semidirect
15. C47×#578C2semidirect
18. #13094072C22semidirect
19. #13094072C22semidirect
21. #13094071C22semidirect
22. #13094071C22semidirect
24. #13094070C22semidirect
25. #13094070C22semidirect
32. #41×D47C22semidirect
34. C2×Q8×D47C22semidirect
35. #13094057C22semidirect
36. #13094056C22semidirect
37. #13094056C22semidirect
38. #13094056C22semidirect
39. #13094056C22semidirect
40. #13094056C22semidirect
41. #13094055C22semidirect
42. #13094055C22semidirect
43. #13094054C22semidirect
44. #13094053C22semidirect
45. #13094053C22semidirect
46. #13094052C22semidirect
47. #13094051C22semidirect
48. #13094051C22semidirect
49. #13094049C22semidirect
50. #13094048C22semidirect
51. #13094048C22semidirect
52. #13094047C22semidirect
53. #13094046C22semidirect
54. #13094045C22semidirect
55. #13094044C22semidirect
56. #13094044C22semidirect
57. C2×#10625337C22semidirect
58. Q16×D47C22semidirect
59. C2×#10625325C22semidirect
60. C2×#10625336C22semidirect
61. SD16×D47C22semidirect
62. #13094032C22semidirect
63. #13094031C22semidirect
64. #13094030C22semidirect
65. C2×#10625324C22semidirect
66. M16×D47C22semidirect
67. 2−1+4×C47C22semidirect
68. 2−1+4×C47C22semidirect
69. #137×C47C22semidirect
70. #137×C47C22semidirect
71. #135×C47C22semidirect
72. C2×Q16×C47C22semidirect
73. #131×C47C22semidirect
257. #578D47semidirect
267. C47#3586semidirect
275. 2−1+4C2×D47semidirect
276. 2−1+4C2×D47semidirect
300. #137C2×D47semidirect
301. #137C2×D47semidirect
313. #135C2×D47semidirect
316. C2×Q16C2×D47semidirect
323. #131C2×D47semidirect