Finite Group Databasebeta

← #20258160

Subgroups — #20258160

Order 6016.

1424 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689960C211yesmaximal, characteristic, complemented
2#15689958C211yesmaximal, characteristic, complemented
3#15689939C213yesmaximal, complemented
4#15689938C211yesmaximal, characteristic, complemented
5#15689935C211yesmaximal, characteristic, complemented
6#15689930C213yesmaximal, complemented
7#15689929C213yesmaximal, complemented
8#15689927C213yesmaximal, complemented
9#15689926C211yesmaximal, characteristic, complemented
10#15689922C213yesmaximal, complemented
11#15689919C213yesmaximal, complemented
12C2×#13094045C213yesmaximal, complemented
13#135×D47C213yesmaximal, complemented
14#131×D47C211yesmaximal, characteristic, complemented
15C47×#577C211yesmaximal, characteristic, complemented
16#13094072—21no—
17#13094072C2213yescomplemented
18#13094071—21no—
19#13094071C2213yescomplemented
20#13094071C2211yescharacteristic, complemented
21#13094070—23no—
22#13094070C2213yescomplemented
23#13094070C2211yescharacteristic, complemented
24#13094069—23no—
25#13094069C2213yescomplemented
26C2×#10625354—21no—
27C2×#10625354C2213yescomplemented
28C2×#10625352—23no—
29C2×#10625352C2213yescomplemented
30#41×D47—21no—
31#41×D47—23no—
32#41×D47C2211yescharacteristic
33#41×D47C2213yescomplemented
34#41×D47C2213yescomplemented
35#13094057C2213yescomplemented
36#13094056C2216yescomplemented
37#13094055C2213yescomplemented
38#13094054C2213yescomplemented
39#13094053C2216yescomplemented
40#13094052C2213yescomplemented
41#13094051C2216yescomplemented
42#13094050C2213yescomplemented
43#13094049C2213yescomplemented
44#13094048C2216yescomplemented
45#13094047C2213yescomplemented
46#13094046C2213yescomplemented
47#13094045C2211yescharacteristic, complemented
48#13094045C2213yescomplemented
49#13094045C2216yescomplemented
50#13094045C2216yescomplemented
51#13094045C2216yescomplemented
52#13094044C2213yescomplemented
53#13094044C2213yescomplemented
54#13094043C2213yescomplemented
55C2×#10625337C2213yescomplemented
56Q16×D47C2213yescomplemented
57C2×#10625325C2213yescomplemented
58SD16×D47C2213yescomplemented
59SD16×D47C2213yescomplemented
60C2×#10625334C2213yescomplemented
61D8×D47C2213yescomplemented
62#13094032C2213yescomplemented
63#13094031C2211yescharacteristic, complemented
64#13094030C2213yescomplemented
65M16×D47C2213yescomplemented
66C2×C8×D47C2213yescomplemented
672−1+4×C47C2211yescharacteristic, complemented
68H(5,𝔽2)×C47C2211yescharacteristic, complemented
69#137×C47C2213yescomplemented
70AGL(1,ℤ/8)×C47C2213yescomplemented
71#135×C47C2213yescomplemented
72C2×SD16×C47C2213yescomplemented
73#131×C47C2211yescharacteristic, complemented
74#41×C47—21no—
75#41×C47—23no—
76#41×C47C2313yes—
77#41×C47C2313yes—
78#41×C47C2311yescharacteristic
79C2×Q8×C47—21no—
80C2×Q8×C47C2313yes—
81C2×D4×C47—23no—
82C2×D4×C47C2313yes—
83C2×C22⋊D47—23no—
84C2×C22⋊D47—26no—
85C22×Dic47—23no—
86#10625354—21no—
87#10625354—23no—
88#10625354—23no—
89#10625354—23no—
90#10625354D411yescharacteristic
91#10625354C2313yes—
92#10625354C2316yes—
93#10625354C2311yescharacteristic
94Q8×D47—21no—
95Q8×D47—23no—
96Q8×D47D411yescharacteristic
97Q8×D47C2313yes—
98Q8×D47C2313yes—
99#10625352—23no—
100#10625352—26no—
101#10625352—23no—
102#10625352—23no—
103#10625352—23no—
104#10625352—23no—
105#10625352—23no—
106#10625352D413yes—
107#10625352C2311yescharacteristic
108#10625352C2313yes—
109#10625352C2316yes—
110D4×D47—23no—
111D4×D47—23no—
112D4×D47—23no—
113D4×D47—26no—
114D4×D47—23no—
115D4×D47D413yes—
116D4×D47C2313yes—
117D4×D47C2313yes—
118#10625350—26no—
119#10625350—23no—
120#10625350—23no—
121#10625350—23no—
122#10625350—23no—
123#10625350C2313yes—
124#10625350C2313yes—
125#10625350C2313yes—
126C2×D188—23no—
127C2×D188—23no—
128C2×D188C2313yes—
129C2×C4×D47—23no—
130C2×C4×D47—23no—
131C2×C4×D47—23no—
132C2×C4×D47C2313yes—
133C2×Dic94—23no—
134C2×Dic94C2313yes—
135Q16×C47C2313yes—
136SD16×C47C2313yes—
137SD16×C47C2316yes—
138SD16×C47C2311yescharacteristic
139D8×C47C2313yes—
140M16×C47C2313yes—
141C2×C8×C47C2313yes—
142#10625337C2311yescharacteristic
143#10625337C2313yes—
144#10625337C2316yes—
145#10625336C2313yes—
146#10625336C2313yes—
147#10625335C2313yes—
148#10625335C2313yes—
149#10625334C2311yescharacteristic
150#10625334C2313yes—
151#10625334C2316yes—
152#10625329C2313yes—
153C2×C47⋊C8C2313yes—
154Dic188C2313yes—
155D376C2313yes—
156#10625325C2311yescharacteristic
157#10625325C2313yes—
158#10625325C2316yes—
159#10625324C2316yes—
160C8×D47C2311yescharacteristic
161C8×D47C2313yes—
162C8×D47C2313yes—
163C8×D47C2313yes—
164C23×C47—23no—
165C22×D47—23no—
166C22×D47—23no—
167C22×D47—23no—
168C22×D47C2×D413yes—
169Q8×C47—23no—
170Q8×C47C2×D411yescharacteristic
171Q8×C47C2411yescharacteristic
172Q8×C47C2413yes—
173D4×C47—23no—
174D4×C47—23no—
175D4×C47—23no—
176D4×C47C2×D413yes—
177D4×C47C2413yes—
178D4×C47C2411yescharacteristic
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—26no—
187C22⋊D47—23no—
188C22⋊D47—23no—
189C22⋊D47—23no—
190C22⋊D47C2×D416yes—
191C2×Dic47—23no—
192C2×Dic47—26no—
193C2×Dic47—21no—
194C2×Dic47—23no—
195C2×Dic47C2×D413yes—
196D188—26no—
197D188—23no—
198D188—21no—
199D188—23no—
200D188C2×D413yes—
201D188C2413yes—
202D188C2411yescharacteristic
203C4×D47—23no—
204C4×D47—23no—
205C4×D47—23no—
206C4×D47—23no—
207C4×D47—21no—
208C4×D47—23no—
209C4×D47—26no—
210C4×D47C2×D413yes—
211C4×D47C2×D413yes—
212C4×D47C2411yescharacteristic
213C4×D47C2413yes—
214Dic94—23no—
215Dic94—23no—
216Dic94—23no—
217Dic94C2×D413yes—
218Dic94C2413yes—
219Dic94C2411yescharacteristic
220C8×C47C2411yescharacteristic
221C8×C47C2413yes—
222C47⋊C8C2411yescharacteristic
223C47⋊C8C2413yes—
224C22×C47—23no—
225C22×C47—21no—
226C22×C47—83no—
227C22×C47C22×D413yes—
228C2×D47—23no—
229C2×D47—21no—
230C2×D47—43no—
231C2×D47—83no—
232C2×D47—83no—
233C2×D47—83no—
234C2×D47C22×D413yes—
235C2×D47C22×D411yescharacteristic
236C4×C47—21no—
237C4×C47—23no—
238C4×C47C22×D413yes—
239C4×C47C2511yescharacteristic
240Dic47—21no—
241Dic47—23no—
242Dic47C22×D413yes—
243Dic47C22×D411yescharacteristic
244#3584—471nomaximal, Sylow
245C2×C47—23no—
246C2×C47—41no—
247C2×C47—43no—
248C2×C47C23×D411yescharacteristic
249D47—21no—
250D47—23no—
251D47—43no—
252D47—41no—
253#585—471no—
254#585—471no—
255#578—471no—
256#578—473no—
257#577—473no—
258#577—473no—
259#577—471no—
260#577D4711yescharacteristic, complemented
261#576—471no—
262#576—473no—
263#575—473no—
264#575—473no—
265C2×#135—473no—
266C2×#135—473no—
267C2×#131—471no—
268C47#358411yescharacteristic, complemented, Sylow
2692−1+4—473no—
2702−1+4—471no—
2712−1+4—473no—
2722−1+4—941no—
2732−1+4—941no—
2742−1+4C2×D4711yescharacteristic, complemented
275H(5,𝔽2)—473no—
276H(5,𝔽2)—471no—
277H(5,𝔽2)—473no—
278H(5,𝔽2)—943no—
279H(5,𝔽2)—943no—
280H(5,𝔽2)C2×D4711yescharacteristic, complemented
281C2×#41—471no—
282C2×#41—473no—
283C2×#41—473no—
284C2×#41—473no—
285C2×#41—473no—
286C2×#41—943no—
287C2×#41—941no—
288C2×#41—941no—
289C2×#41—943no—
290#137—473no—
291#137—473no—
292#137—476no—
293#137—476no—
294#137—473no—
295#137C2×D4713yescomplemented
296AGL(1,ℤ/8)—473no—
297AGL(1,ℤ/8)—473no—
298AGL(1,ℤ/8)—476no—
299AGL(1,ℤ/8)—476no—
300AGL(1,ℤ/8)—473no—
301AGL(1,ℤ/8)C2×D4713yescomplemented
302#135—473no—
303#135—473no—
304#135—473no—
305#135—471no—
306#135—473no—
307#135—476no—
308#135—476no—
309#135—476no—
310#135—473no—
311#135—473no—
312#135C2×D4713yescomplemented
313C2×Q16—473no—
314C2×Q16—473no—
315C2×SD16—473no—
316C2×SD16—473no—
317C2×SD16—473no—
318C2×SD16C2×D4713yescomplemented
319C2×D8—473no—
320C2×D8—473no—
321#131—471no—
322#131—473no—
323#131—473no—
324#131C2×D4711yescharacteristic, complemented
325C2×M16—473no—
326C22×C8—473no—
327#41—21no—
328#41—23no—
329#41—471no—
330#41—473no—
331#41—473no—
332#41—471no—
333#41—473no—
334#41—476no—
335#41—473no—
336#41—471no—
337#41—476no—
338#41—473no—
339#41—473no—
340#41—943no—
341#41—943no—
342#41—946no—
343#41—943no—
344#41—943no—
345#41—943no—
346#41—943no—
347#41—943no—
348#41—943no—
349#41—943no—
350#41—943no—
351#41—946no—
352#41—943no—
353#41—943no—
354#41—941no—
355#41—943no—
356#41C22×D4713yes—
357#41C22×D4713yes—
358#41C22×D4711yescharacteristic
359C2×Q8—21no—
360C2×Q8—471no—
361C2×Q8—473no—
362C2×Q8—473no—
363C2×Q8—473no—
364C2×Q8—943no—
365C2×Q8—943no—
366C2×Q8—941no—
367C2×Q8C22×D4713yes—
368C2×D4—23no—
369C2×D4—473no—
370C2×D4—473no—
371C2×D4—473no—
372C2×D4—473no—
373C2×D4—943no—
374C2×D4—943no—
375C2×D4—946no—
376C2×D4—943no—
377C2×D4—943no—
378C2×D4—943no—
379C2×D4—946no—
380C2×D4—943no—
381C2×D4—943no—
382C2×D4C22×D4713yes—
383C22×C4—473no—
384C22×C4—943no—
385C22×C4—943no—
386C22×C4—943no—
387C22×C4—943no—
388Q16—471no—
389Q16—473no—
390Q16—476no—
391Q16—473no—
392Q16C22×D4713yes—
393SD16—473no—
394SD16—473no—
395SD16—473no—
396SD16—473no—
397SD16—471no—
398SD16—473no—
399SD16—476no—
400SD16C22×D4711yescharacteristic
401SD16C22×D4713yes—
402SD16C22×D4716yes—
403D8—473no—
404D8—471no—
405D8—476no—
406D8—473no—
407D8C22×D4713yes—
408M16—473no—
409M16—476no—
410M16C22×D4713yes—
411C2×C8—473no—
412C2×C8—471no—
413C2×C8—473no—
414C2×C8—473no—
415C2×C8—473no—
416C2×C8C22×D4713yes—
417C23—23no—
418C23—473no—
419C23—943no—
420C23—943no—
421C23—943no—
422Q8—23no—
423Q8—473no—
424Q8—473no—
425Q8—471no—
426Q8—943no—
427Q8—943no—
428Q8—943no—
429Q8D4×D4711yescharacteristic
430Q8C23×D4711yescharacteristic
431Q8C23×D4713yes—
432D4—23no—
433D4—23no—
434D4—23no—
435D4—476no—
436D4—473no—
437D4—473no—
438D4—471no—
439D4—941no—
440D4—943no—
441D4—946no—
442D4—943no—
443D4—943no—
444D4—941no—
445D4—943no—
446D4—946no—
447D4—943no—
448D4—943no—
449D4—943no—
450D4D4×D4713yes—
451D4C23×D4713yes—
452D4C23×D4711yescharacteristic
453C2×C4—23no—
454C2×C4—23no—
455C2×C4—23no—
456C2×C4—473no—
457C2×C4—473no—
458C2×C4—473no—
459C2×C4—471no—
460C2×C4—473no—
461C2×C4—941no—
462C2×C4—943no—
463C2×C4—946no—
464C2×C4—943no—
465C2×C4—943no—
466C2×C4—941no—
467C2×C4—943no—
468C2×C4—946no—
469C2×C4—943no—
470C2×C4—943no—
471C2×C4—943no—
472C2×C4C23×D4713yes—
473C8—471no—
474C8—473no—
475C8C23×D4711yescharacteristic
476C8C23×D4713yes—
477C22—21no—
478C22—23no—
479C22—83no—
480C22—471no—
481C22—473no—
482C22—943no—
483C22—941no—
484C22—3763no—
485C22—3763no—
486C22—3763no—
487C22—1883no—
488C22C2×D4×D4713yes—
489C4—21no—
490C4—23no—
491C4—471no—
492C4—473no—
493C4—941no—
494C4—943no—
495C4C2×D4×D4713yes—
496C4C24×D4711yescharacteristic
497C2—23no—
498C2—43no—
499C2—41no—
500C2—943no—
501C2—941no—
502C2—1883no—
503C2—1881no—
504C2C22×D4×D4711yescharacteristic
subgroupG/H
centerC2C22×D4×D47
commutatorC4×C47C25
FrattiniC4C24×D47
FittingC47×#577C2
socleC2×C47C23×D4
hypercenter#577D47
hypocenterC47#3584
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ #41 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #15689960C2semidirect
2. #15689958C2semidirect
3. #15689939C2semidirect
4. #15689938C2semidirect
5. #15689935C2semidirect
6. #15689930C2semidirect
7. #15689929C2semidirect
8. #15689927C2semidirect
9. #15689926C2semidirect
10. #15689922C2semidirect
11. #15689919C2semidirect
12. C2×#13094045C2semidirect
13. #135×D47C2semidirect
14. #131×D47C2semidirect
15. C47×#577C2semidirect
17. #13094072C22semidirect
19. #13094071C22semidirect
20. #13094071C22semidirect
22. #13094070C22semidirect
23. #13094070C22semidirect
25. #13094069C22semidirect
27. C2×#10625354C22semidirect
29. C2×#10625352C22semidirect
33. #41×D47C22semidirect
34. #41×D47C22semidirect
35. #13094057C22semidirect
36. #13094056C22semidirect
37. #13094055C22semidirect
38. #13094054C22semidirect
39. #13094053C22semidirect
40. #13094052C22semidirect
41. #13094051C22semidirect
42. #13094050C22semidirect
43. #13094049C22semidirect
44. #13094048C22semidirect
45. #13094047C22semidirect
46. #13094046C22semidirect
47. #13094045C22semidirect
48. #13094045C22semidirect
49. #13094045C22semidirect
50. #13094045C22semidirect
51. #13094045C22semidirect
52. #13094044C22semidirect
53. #13094044C22semidirect
54. #13094043C22semidirect
55. C2×#10625337C22semidirect
56. Q16×D47C22semidirect
57. C2×#10625325C22semidirect
58. SD16×D47C22semidirect
59. SD16×D47C22semidirect
60. C2×#10625334C22semidirect
61. D8×D47C22semidirect
62. #13094032C22semidirect
63. #13094031C22semidirect
64. #13094030C22semidirect
65. M16×D47C22semidirect
66. C2×C8×D47C22semidirect
67. 2−1+4×C47C22semidirect
68. H(5,𝔽2)×C47C22semidirect
69. #137×C47C22semidirect
70. AGL(1,ℤ/8)×C47C22semidirect
71. #135×C47C22semidirect
72. C2×SD16×C47C22semidirect
73. #131×C47C22semidirect
260. #577D47semidirect
268. C47#3584semidirect
274. 2−1+4C2×D47semidirect
280. H(5,𝔽2)C2×D47semidirect
295. #137C2×D47semidirect
301. AGL(1,ℤ/8)C2×D47semidirect
312. #135C2×D47semidirect
318. C2×SD16C2×D47semidirect
324. #131C2×D47semidirect