Finite Group Databasebeta

← D47×#3531 #27123175

Subgroups — D47×#3531 #27123175

Order 12032.

6554 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257536C211yesmaximal, characteristic, complemented
2#20257535C215yesmaximal, complemented
3#20257534C2110yesmaximal, complemented
4#20257533C2110yesmaximal, complemented
5#20257532C215yesmaximal, complemented
6#564×D47C211yesmaximal, characteristic, complemented
7#563×D47C2110yesmaximal, complemented
8#562×D47C215yesmaximal, complemented
9#533×D47C215yesmaximal, complemented
10#529×D47C2110yesmaximal, complemented
11C47×#3531C211yesmaximal, characteristic, complemented
12C47⋊#564C2215yescomplemented
13C47⋊#564C22110yescomplemented
14#15689877C22110yescomplemented
15#15689877C22110yescomplemented
16#15689876C22120yescomplemented
17#15689875C22120yescomplemented
18#15689875C22120yescomplemented
19#15689874C22120yescomplemented
20#15689874C22120yescomplemented
21#15689873C22110yescomplemented
22#15689872C22120yescomplemented
23#15689871C2215yescomplemented
24#15689870C22120yescomplemented
25#15689869C22120yescomplemented
26#15689868C22120yescomplemented
27#15689867C22110yescomplemented
28#15689680C2215yescomplemented
29#15689679C2215yescomplemented
30#15689679C2215yescomplemented
31#15689678C22110yescomplemented
32#15689677C22120yescomplemented
33#15689676C22110yescomplemented
34#15689675C22120yescomplemented
35C4⋊Q8×D47C22110yes—
36#15689660C22110yescomplemented
37#15689659C22110yescomplemented
38#15689658C22110yescomplemented
39#15689657C22110yescomplemented
40#15689656C22120yescomplemented
41#15689655C22110yescomplemented
42#15689654C22110yescomplemented
43#15689653C22120yescomplemented
44#15689652C22110yescomplemented
45#15689651C22120yescomplemented
46#15689650C22120yescomplemented
47#126×D47C22120yes—
48#125×D47C22110yes—
49#125×D47C2215yes—
50#125×D47C2215yes—
51#124×D47C22110yes—
52#123×D47C22120yes—
53C22⋊Q8×D47C22110yes—
54C22⋊Q8×D47C22120yes—
55#121×D47C22110yes—
56C4×Q8×D47C22110yes—
57C4×D4×D47C22110yes—
58#117×D47C22110yes—
59C2×C42×D47C2215yes—
60C47×#564C2211yescharacteristic, complemented
61C47×#563C22110yescomplemented
62C47×#562C2215yescomplemented
63C47×#533C2215yescomplemented
64C47×#529C22110yescomplemented
65C2×Q8×D47C23110yes—
66C2×D4×D47C23110yes—
67C22×C4×D47C2315yes—
68C22×C4×D47C23110yes—
69#13094024C23110yes—
70#13094023C23110yes—
71#13094023C23120yes—
72#13094023C23110yes—
73#13094022C23120yes—
74#13094019C23120yes—
75#13094019C23120yes—
76#13094019C23120yes—
77#13094018C23120yes—
78#13094017C23120yes—
79#13094017C23120yes—
80#13094017C23120yes—
81#13094016C2315yes—
82#13094016C2315yes—
83#13094016C23110yes—
84#13094015C23110yes—
85#13094015C23110yes—
86#13094015C23110yes—
87#13094015C23110yes—
88#13094014C23120yes—
89#13094014C23120yes—
90#13094014C23120yes—
91#13094014C23120yes—
92#13094013C23110yes—
93#13094012C23110yes—
94#13094011C23110yes—
95#13094010C23120yes—
96#13094010C23120yes—
97#13094009C23120yes—
98#13094009C23120yes—
99#13094008C23120yes—
100#13094007C23120yes—
101#13094006C23120yes—
102#13094006C23120yes—
103#13094005C23120yes—
104#13094004C23120yes—
105#13094004C23110yes—
106#13094003C23120yes—
107#13094003C23110yes—
108#13094002C23120yes—
109#13094002C23120yes—
110#13094002C23120yes—
111#13094001C23120yes—
112#13094001C23120yes—
113#13094001C23120yes—
114#13094000C23120yes—
115#13094000C23110yes—
116#13093999C23110yes—
117#13093998C23110yes—
118#13093997C23120yes—
119#13093996C23120yes—
120#13093995C23110yes—
121Q8×Dic47C23110yes—
122C4×Dic94C23120yes—
123C4×Dic94C23110yes—
124#13093989C23120yes—
125#13093989C23110yes—
126C4×D188C23110yes—
127D4×Dic47C23110yes—
128#13093986C23110yes—
129C4×C22⋊D47C23120yes—
130(C22⋊D47)⋊C4C23120yes—
131#13093983C23110yes—
132#13093982C23110yes—
133#13093982C23110yes—
134#13093981C23120yes—
135#13093980C23120yes—
136C4⋊C4×D47C23110yes—
137C4⋊C4×D47C23110yes—
138C4⋊C4×D47C23110yes—
139C4⋊C4×D47C23110yes—
140C4⋊C4×D47C23120yes—
141C22⋊C4×D47C23120yes—
142C22⋊C4×D47C23120yes—
143C2×C4×Dic47C23110yes—
144C2×C4×Dic47C2315yes—
145C42×D47C23110yes—
146C42×D47C2315yes—
147C42×D47C2315yes—
148C42×D47C23110yes—
149C42×D47C2315yes—
150C42×D47C2315yes—
151C4⋊Q8×C47C23110yes—
152#126×C47C23120yes—
153#125×C47C23110yes—
154#125×C47C2315yes—
155#125×C47C2315yes—
156#124×C47C23110yes—
157#123×C47C23120yes—
158C22⋊Q8×C47C23110yes—
159C22⋊Q8×C47C23120yes—
160#121×C47C23110yes—
161C4×Q8×C47C23110yes—
162C4×D4×C47C23110yes—
163#117×C47C23110yes—
164C2×C42×C47C2315yes—
165C23×D47C2415yes—
166C2×Q8×C47C24110yes—
167C2×D4×C47C24110yes—
168C22×C4×C47C2415yes—
169C22×C4×C47C24110yes—
170C2×C22⋊D47C24120yes—
171C22×Dic47C2415yes—
172C22×Dic47C24110yes—
173Q8×D47—420no—
174D4×D47—420no—
175C2×D188C24110yes—
176C2×C4×D47—220no—
177C2×C4×D47—420no—
178C2×C4×D47C2415yes—
179C2×C4×D47C24110yes—
180C2×C4×D47C24110yes—
181C2×C4×D47C2415yes—
182C2×C4×D47C2415yes—
183C2×C4×D47C24110yes—
184C2×C4×D47C24110yes—
185C2×C4×D47C2411yescharacteristic
186C2×Dic94C24120yes—
187C2×Dic94C24110yes—
188C4⋊C4×C47C24110yes—
189C4⋊C4×C47C24110yes—
190C4⋊C4×C47C24110yes—
191C4⋊C4×C47C24110yes—
192C4⋊C4×C47C24120yes—
193C22⋊C4×C47C24120yes—
194C22⋊C4×C47C24120yes—
195C42×C47C24110yes—
196C42×C47C2415yes—
197C42×C47C2415yes—
198C22⋊Dic47C24120yes—
199C22⋊Dic47C24120yes—
200(C2×D47)⋊C4C24120yes—
201(C2×D47)⋊C4C24120yes—
202(C2×D47)⋊C4C24120yes—
203(C2×D47)⋊C4C24120yes—
204C4⋊Dic47C24110yes—
205C4⋊Dic47C24110yes—
206C4⋊Dic47C24110yes—
207C4⋊Dic47C24110yes—
208C4⋊Dic47C24120yes—
209Dic47⋊C4C24120yes—
210Dic47⋊C4C24120yes—
211Dic47⋊C4C24120yes—
212Dic47⋊C4C24120yes—
213Dic47⋊C4C24120yes—
214Dic47⋊C4C24120yes—
215C4×Dic47C24110yes—
216C4×Dic47C24110yes—
217C4×Dic47C24110yes—
218C4×Dic47C2415yes—
219C4×Dic47C24110yes—
220C4×Dic47C24110yes—
221C4×Dic47C2415yes—
222C23×C47C2515yes—
223C22×D47—210no—
224C22×D47—220no—
225C22×D47C2515yes—
226C22×D47C2511yescharacteristic
227Q8×C47—410no—
228D4×C47—410no—
229C2×C4×C47—210no—
230C2×C4×C47—410no—
231C2×C4×C47C25110yes—
232C2×C4×C47C2515yes—
233C2×C4×C47C25110yes—
234C2×C4×C47C2511yescharacteristic
235C22⋊D47—420no—
236C2×Dic47—210no—
237C2×Dic47—410no—
238C2×Dic47C2515yes—
239C2×Dic47C25110yes—
240C2×Dic47C25110yes—
241C2×Dic47C2511yescharacteristic
242D188—410no—
243C4×D47—210no—
244C4×D47—220no—
245C4×D47—220no—
246C4×D47—210no—
247C4×D47—210no—
248C4×D47—410no—
249C4×D47—410no—
250C4×D472−1+414yes—
251Dic94—410no—
252Dic94—420no—
253C2×#3531—471nomaximal, Sylow
254C22×C47—25no—
255C22×C47—210no—
256C22×C47C2611yescharacteristic
257C2×D47—25no—
258C2×D47—210no—
259C2×D47—420no—
260C2×D47C2×2−1+412yes—
261C2×D47#58514yes—
262C4×C47—25no—
263C4×C47—210no—
264C4×C47—210no—
265C4×C47C2×2−1+412yes—
266Dic47—25no—
267Dic47—210no—
268Dic47—210no—
269Dic47C2×2−1+412yes—
270#3531—471no—
271#3531—4710no—
272#3531—475no—
273#3531—475no—
274#3531—4710no—
275#3531D4711yescharacteristic, direct product factor
276C2×#564—471no—
277C2×#563—4710no—
278C2×#562—475no—
279C2×#533—475no—
280C2×#529—4710no—
281C2×C47—45no—
282C2×C47C22×2−1+411yescharacteristic
283C2×C47C2×#58512yes—
284D47—45no—
285D47#353114yesdirect product factor
286#564—4710no—
287#564—475no—
288#564C2×D4711yescharacteristic, complemented
289#563—4720no—
290#563—4720no—
291#563—4720no—
292#563—4710no—
293#563—4710no—
294#563—4710no—
295#563—4720no—
296#563—4720no—
297#563—4720no—
298#563C2×D47110yescomplemented
299#562—475no—
300#562—4710no—
301#562—4720no—
302#562—4720no—
303#562—4720no—
304#562C2×D4715yescomplemented
305#533—4710no—
306#533—475no—
307#533—475no—
308#533—4720no—
309#533—4720no—
310#533—4710no—
311#533—475no—
312#533C2×D4715yescomplemented
313C2×C4⋊Q8—4710no—
314#529—4720no—
315#529—4710no—
316#529—4710no—
317#529—4720no—
318#529—4710no—
319#529—4710no—
320#529—4710no—
321#529—4720no—
322#529—4710no—
323#529—4720no—
324#529—4710no—
325#529C2×D47110yescomplemented
326C2×#126—4720no—
327C2×#125—4710no—
328C2×#125—475no—
329C2×#125—475no—
330C2×#124—4710no—
331C2×#123—4720no—
332C2×C22⋊Q8—4710no—
333C2×C22⋊Q8—4720no—
334C2×#121—4710no—
335C2×C4×Q8—4710no—
336C2×C4×D4—4710no—
337C2×#117—4710no—
338C22×C42—475no—
339C47C2×#353111yescharacteristic, complemented, Sylow
340C22×Q8—4710no—
341C22×D4—4710no—
342C23×C4—475no—
343C23×C4—4710no—
344C4⋊Q8—4720no—
345C4⋊Q8—4720no—
346C4⋊Q8—4710no—
347C4⋊Q8—4710no—
348C4⋊Q8—4710no—
349C4⋊Q8C22×D47110yes—
350#126—4720no—
351#126—4720no—
352#126—4720no—
353#126—4720no—
354#126—4720no—
355#126—4720no—
356#126—4720no—
357#126C22×D47120yes—
358#125—4720no—
359#125—4720no—
360#125—4710no—
361#125—4710no—
362#125—4720no—
363#125—4710no—
364#125—4720no—
365#125—4710no—
366#125—4710no—
367#125—475no—
368#125—475no—
369#125C22×D47110yes—
370#125C22×D4715yes—
371#125C22×D4715yes—
372#124—4710no—
373#124—4710no—
374#124—4720no—
375#124—4720no—
376#124—4710no—
377#124C22×D47110yes—
378#123—4720no—
379#123—4720no—
380#123—4720no—
381#123—4720no—
382#123—4720no—
383#123—4720no—
384#123—4720no—
385#123C22×D47120yes—
386C22⋊Q8—4710no—
387C22⋊Q8—4720no—
388C22⋊Q8—4710no—
389C22⋊Q8—4720no—
390C22⋊Q8—4720no—
391C22⋊Q8—4710no—
392C22⋊Q8—4720no—
393C22⋊Q8—4720no—
394C22⋊Q8—4720no—
395C22⋊Q8—4720no—
396C22⋊Q8—4720no—
397C22⋊Q8—4720no—
398C22⋊Q8C22×D47110yes—
399C22⋊Q8C22×D47120yes—
400#121—4710no—
401#121—4720no—
402#121—4710no—
403#121—4710no—
404#121—4720no—
405#121C22×D47110yes—
406C4×Q8—4710no—
407C4×Q8—4720no—
408C4×Q8—4710no—
409C4×Q8—4720no—
410C4×Q8—4710no—
411C4×Q8C22×D47110yes—
412C4×D4—4710no—
413C4×D4—4720no—
414C4×D4—4710no—
415C4×D4—4720no—
416C4×D4—4710no—
417C4×D4C22×D47110yes—
418#117—4710no—
419#117—4710no—
420#117—4710no—
421#117—4720no—
422#117—4720no—
423#117C22×D47110yes—
424C2×C4⋊C4—4710no—
425C2×C4⋊C4—4710no—
426C2×C4⋊C4—4710no—
427C2×C4⋊C4—4710no—
428C2×C4⋊C4—4720no—
429C2×C22⋊C4—4720no—
430C2×C22⋊C4—4720no—
431C2×C42—4710no—
432C2×C42—475no—
433C2×C42—4710no—
434C2×C42—475no—
435C2×C42—475no—
436C2×C42—475no—
437C2×C42—475no—
438C2×C42—4710no—
439C2×C42C22×D4715yes—
440C24—475no—
441C2×Q8—4710no—
442C2×Q8—4720no—
443C2×Q8—18820no—
444C2×Q8C23×D47110yes—
445C2×D4—4720no—
446C2×D4—4710no—
447C2×D4—18820no—
448C2×D4C23×D47110yes—
449C22×C4—471no—
450C22×C4—475no—
451C22×C4—4710no—
452C22×C4—475no—
453C22×C4—4710no—
454C22×C4—4710no—
455C22×C4—475no—
456C22×C4—475no—
457C22×C4—4710no—
458C22×C4—4710no—
459C22×C4—9420no—
460C22×C4—18820no—
461C22×C4C23×D4715yes—
462C22×C4C23×D47110yes—
463C4⋊C4—4720no—
464C4⋊C4—4720no—
465C4⋊C4—4720no—
466C4⋊C4—4720no—
467C4⋊C4—4720no—
468C4⋊C4—4720no—
469C4⋊C4—4710no—
470C4⋊C4—4710no—
471C4⋊C4—4710no—
472C4⋊C4—4710no—
473C4⋊C4—4720no—
474C4⋊C4C23×D47110yes—
475C4⋊C4C23×D47110yes—
476C4⋊C4C23×D47110yes—
477C4⋊C4C23×D47110yes—
478C4⋊C4C23×D47120yes—
479C22⋊C4—4720no—
480C22⋊C4—4720no—
481C22⋊C4—4720no—
482C22⋊C4—4720no—
483C22⋊C4—4720no—
484C22⋊C4—4720no—
485C22⋊C4C23×D47120yes—
486C22⋊C4C23×D47120yes—
487C42—4710no—
488C42—4710no—
489C42—4710no—
490C42—475no—
491C42—4710no—
492C42—475no—
493C42—4710no—
494C42C23×D4715yes—
495C42C23×D4715yes—
496C42C23×D47110yes—
497C23—471no—
498C23—475no—
499C23—9410no—
500C23—9420no—
501C23C24×D4715yes—
502Q8—410no—
503Q8—18810no—
504Q8—18820no—
505D4—410no—
506D4—18810no—
507D4—18820no—
508C2×C4—210no—
509C2×C4—410no—
510C2×C4—471no—
511C2×C4—474no—
512C2×C4—475no—
513C2×C4—4710no—
514C2×C4—4710no—
515C2×C4—9410no—
516C2×C4—9410no—
517C2×C4—9420no—
518C2×C4—9420no—
519C2×C4—9410no—
520C2×C4—9410no—
521C2×C4—18810no—
522C2×C4—18810no—
523C2×C4—18810no—
524C2×C4C24×D4715yes—
525C2×C4C24×D47110yes—
526C2×C4C24×D47110yes—
527C2×C4C24×D4711yescharacteristic
528C22—25no—
529C22—210no—
530C22—472no—
531C22—474no—
532C22—945no—
533C22—9410no—
534C22—18820no—
535C22C25×D4711yescharacteristic
536C4—25no—
537C4—210no—
538C4—210no—
539C4—472no—
540C4—945no—
541C4—9410no—
542C4—9410no—
543C42−1+4×D4712yes—
544C2—45no—
545C2—474no—
546C2—1885no—
547C2C2×2−1+4×D4711yescharacteristic
548C2#585×D4712yes—
subgroupG/H
centerC2×C4C24×D47
commutator, socle, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC47×#3531C2
hypercenter#3531D47
hypocenterC47C2×#3531
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #3531

Complements

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

NH ≅ G/Ntype
1. #20257536C2semidirect
2. #20257535C2semidirect
3. #20257534C2semidirect
4. #20257533C2semidirect
5. #20257532C2semidirect
6. #564×D47C2semidirect
7. #563×D47C2semidirect
8. #562×D47C2semidirect
9. #533×D47C2semidirect
10. #529×D47C2semidirect
11. C47×#3531C2semidirect
12. C47⋊#564C22semidirect
13. C47⋊#564C22semidirect
14. #15689877C22semidirect
15. #15689877C22semidirect
16. #15689876C22semidirect
17. #15689875C22semidirect
18. #15689875C22semidirect
19. #15689874C22semidirect
20. #15689874C22semidirect
21. #15689873C22semidirect
22. #15689872C22semidirect
23. #15689871C22semidirect
24. #15689870C22semidirect
25. #15689869C22semidirect
26. #15689868C22semidirect
27. #15689867C22semidirect
28. #15689680C22semidirect
29. #15689679C22semidirect
30. #15689679C22semidirect
31. #15689678C22semidirect
32. #15689677C22semidirect
33. #15689676C22semidirect
34. #15689675C22semidirect
36. #15689660C22semidirect
37. #15689659C22semidirect
38. #15689658C22semidirect
39. #15689657C22semidirect
40. #15689656C22semidirect
41. #15689655C22semidirect
42. #15689654C22semidirect
43. #15689653C22semidirect
44. #15689652C22semidirect
45. #15689651C22semidirect
46. #15689650C22semidirect
60. C47×#564C22semidirect
61. C47×#563C22semidirect
62. C47×#562C22semidirect
63. C47×#533C22semidirect
64. C47×#529C22semidirect
275. #3531D47direct (N × H)
285. D47#3531direct (N × H)
288. #564C2×D47semidirect
298. #563C2×D47semidirect
304. #562C2×D47semidirect
312. #533C2×D47semidirect
325. #529C2×D47semidirect
339. C47C2×#3531semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202575362
#202575352
#202575342
#202575332
#202575322
#564×D472
#563×D472
#562×D472
#533×D472
#529×D472
C47×#35312
C2×#353147