Finite Group Databasebeta

← C47×#19877 #26059575

Subgroups — C47×#19877 #26059575

Order 12032.

604 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3392C211yesmaximal, characteristic, complemented
2C47×#3381C211yesmaximal, characteristic, complemented
3C47×#3357C211yesmaximal, characteristic, complemented
4C47×#3305C211yesmaximal, characteristic
5C47×#1714C211yesmaximal, characteristic, complemented
6C47×#1685C211yesmaximal, characteristic, complemented
7C47×#1678C211yesmaximal, characteristic, complemented
8C47×#1676C211yesmaximal, characteristic, complemented
9C47×#1671C211yesmaximal, characteristic, complemented
10C47×#1646C211yesmaximal, characteristic, complemented
11C47×#1636C211yesmaximal, characteristic, complemented
12C47×#1631C211yesmaximal, characteristic, complemented
13C47×#1622C211yesmaximal, characteristic, complemented
14C47×#1583C211yesmaximal, characteristic, complemented
15C47×SD16⋊C8C211yesmaximal, characteristic, complemented
16C47×#557C2211yescharacteristic
17C47×#555C2211yescharacteristic
18C47×#554C2211yescharacteristic
19C47×#550C2211yescharacteristic
20C47×#500C2211yescharacteristic
21C47×#499—21no—
22C47×#498C2211yescharacteristic
23C47×#492—21no—
24C47×#492C2211yescharacteristic
25C47×#492C2211yescharacteristic
26C47×#487C2211yescharacteristic
27C47×#486C2211yescharacteristic
28C47×#485—21no—
29C47×#482—21no—
30C47×#480—21no—
31C47×#479—21no—
32C47×#478—21no—
33C47×#477C2211yescharacteristic
34C47×#477C2211yescharacteristic
35C47×#477C2211yescharacteristic
36C47×#476C2211yescharacteristic
37C47×#474C2211yescharacteristic
38C47×#468—21no—
39C47×#466—21no—
40C47×#461—21no—
41C47×#461C2211yescharacteristic
42C47×#460—21no—
43C47×#460C2211yescharacteristic
44C47×#459C2211yescharacteristic
45C47×#449—21no—
46C8×Q8×C47C2211yescharacteristic
47C8×Q8×C47C2211yescharacteristic
48C4×SD16×C47—21no—
49C4×SD16×C47—21no—
50C4×SD16×C47C2211yescharacteristic
51C4×SD16×C47C2211yescharacteristic
52C47×#436C2211yescharacteristic
53C8×D4×C47C2211yescharacteristic
54C47×#428—21no—
55C47×#416—21no—
56C47×#335C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#333C2211yescharacteristic
59C47×#333C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#331C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×#41×C47—21no—
68C2×SD16×C47—21no—
69C2×SD16×C47—21no—
70C2×SD16×C47—21no—
71C2×SD16×C47—21no—
72C2×SD16×C47—41no—
73C2×SD16×C47D411yescharacteristic
74C2×SD16×C47D411yescharacteristic
75C2×D8×C47—21no—
76C2×M16×C47—21no—
77C22×C8×C47—21no—
78C4⋊Q8×C47—21no—
79C4⋊Q8×C47C2311yescharacteristic
80C4⋊Q8×C47C2311yescharacteristic
81C4⋊Q8×C47C2311yescharacteristic
82#127×C47—21no—
83#127×C47C2311yescharacteristic
84#125×C47—21no—
85#125×C47—21no—
86#125×C47—41no—
87#124×C47—41no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47—41no—
90#121×C47—21no—
91#121×C47—21no—
92#121×C47—21no—
93#121×C47—41no—
94C4×Q8×C47—21no—
95C4×Q8×C47—21no—
96C4×Q8×C47C2311yescharacteristic
97C4×Q8×C47C2311yescharacteristic
98C4×D4×C47—21no—
99C4×D4×C47—21no—
100C4×D4×C47C2311yescharacteristic
101C4×D4×C47C2311yescharacteristic
102#117×C47—21no—
103#117×C47—21no—
104C2×C4⋊C4×C47—21no—
105#107×C47—21no—
106#107×C47—21no—
107#107×C47—21no—
108#107×C47—21no—
109#107×C47—21no—
110#107×C47—21no—
111#106×C47—21no—
112#106×C47—21no—
113#106×C47—21no—
114#106×C47D411yescharacteristic
115#106×C47D411yescharacteristic
116C4⋊C8×C47—21no—
117C4⋊C8×C47—21no—
118C4⋊C8×C47C2311yescharacteristic
119C4⋊C8×C47C2311yescharacteristic
120C4⋊C8×C47C2311yescharacteristic
121C4⋊C8×C47C2311yescharacteristic
122#103×C47—21no—
123#103×C47—21no—
124#103×C47—21no—
125#103×C47—21no—
126#103×C47—41no—
127#103×C47D411yescharacteristic
128#103×C47D411yescharacteristic
129#102×C47—21no—
130#102×C47—21no—
131#102×C47—21no—
132#102×C47—21no—
133#102×C47—21no—
134#102×C47—21no—
135#102×C47D411yescharacteristic
136#102×C47D411yescharacteristic
137C22⋊C8×C47—21no—
138C22⋊C8×C47—21no—
139C4×C8×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144#41×C47—42no—
145#41×C47—81no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47C2×D411yescharacteristic
150C2×Q8×C47C2×D411yescharacteristic
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—41no—
155C2×D4×C47—41no—
156C2×D4×C47—41no—
157C2×D4×C47C2×D411yescharacteristic
158C2×D4×C47C2×D411yescharacteristic
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—41no—
162C22×C4×C47—41no—
163SD16×C47—22no—
164SD16×C47—22no—
165SD16×C47—42no—
166SD16×C47—81no—
167SD16×C47—81no—
168SD16×C47—81no—
169SD16×C47—82no—
170D8×C47—81no—
171M16×C47—42no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—81no—
178C2×C8×C47C2×D411yescharacteristic
179C2×C8×C47C2×D411yescharacteristic
180C2×C8×C47C2×D411yescharacteristic
181C2×C8×C47C2×D411yescharacteristic
182C4⋊C4×C47—21no—
183C4⋊C4×C47—21no—
184C4⋊C4×C47—21no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47—21no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47—41no—
191C4⋊C4×C47—41no—
192C4⋊C4×C47—41no—
193C4⋊C4×C47—41no—
194C4⋊C4×C47—41no—
195C4⋊C4×C47C2×D411yescharacteristic
196C4⋊C4×C47C2×D411yescharacteristic
197C4⋊C4×C47C2×D411yescharacteristic
198C4⋊C4×C47C2×D411yescharacteristic
199C22⋊C4×C47—21no—
200C22⋊C4×C47—21no—
201C22⋊C4×C47—41no—
202C22⋊C4×C47—41no—
203C22⋊C4×C47—41no—
204C22⋊C4×C47—41no—
205C42×C47—21no—
206C42×C47—21no—
207C42×C47—41no—
208C42×C47—41no—
209C42×C47C2411yescharacteristic
210C23×C47—21no—
211C23×C47—21no—
212C23×C47—41no—
213Q8×C47—21no—
214Q8×C47—21no—
215Q8×C47—21no—
216Q8×C47—41no—
217Q8×C47—41no—
218Q8×C47—81no—
219Q8×C47—81no—
220Q8×C47#13712yes—
221D4×C47—21no—
222D4×C47—21no—
223D4×C47—21no—
224D4×C47—21no—
225D4×C47—41no—
226D4×C47—41no—
227D4×C47—41no—
228D4×C47—41no—
229D4×C47—82no—
230D4×C47—81no—
231D4×C47—161no—
232D4×C47—161no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—82no—
247C2×C4×C47—161no—
248C2×C4×C47C22×D411yescharacteristic
249C2×C4×C47C22×D411yescharacteristic
250C2×C4×C47H(5,𝔽2)11yescharacteristic
251C8×C47—21no—
252C8×C47—21no—
253C8×C47—21no—
254C8×C47—41no—
255C8×C47—41no—
256C8×C47—41no—
257C8×C47—41no—
258C8×C47—41no—
259C8×C47#13512yes—
260#19877C4711yesmaximal, characteristic, direct product factor, Sylow
261C22×C47—41no—
262C22×C47—41no—
263C22×C47—41no—
264C22×C47—41no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47—81no—
268C22×C47—81no—
269C22×C47—81no—
270C22×C47D4211yescharacteristic
271C4×C47—22no—
272C4×C47—21no—
273C4×C47—41no—
274C4×C47—41no—
275C4×C47—41no—
276C4×C47—41no—
277C4×C47—41no—
278C4×C47—81no—
279C4×C47—81no—
280C4×C47—81no—
281C4×C47C2×#13511yescharacteristic
282C4×C47C2×#13711yescharacteristic
283C4×C47#57711yescharacteristic
284C4×C47#57711yescharacteristic
285#3392C2×C4711yescharacteristic, complemented
286#3381C2×C4711yescharacteristic, complemented
287#3357C2×C4711yescharacteristic, complemented
288#3305C2×C4711yescharacteristic
289#1714C2×C4711yescharacteristic, complemented
290#1685C2×C4711yescharacteristic, complemented
291#1678C2×C4711yescharacteristic, complemented
292#1676C2×C4711yescharacteristic, complemented
293#1671C2×C4711yescharacteristic, complemented
294#1646C2×C4711yescharacteristic, complemented
295#1636C2×C4711yescharacteristic, complemented
296#1631C2×C4711yescharacteristic, complemented
297#1622C2×C4711yescharacteristic, complemented
298#1583C2×C4711yescharacteristic, complemented
299SD16⋊C8C2×C4711yescharacteristic, complemented
300C2×C47—81no—
301C2×C47—81no—
302C2×C47—161no—
303C2×C47#326611yescharacteristic
304C2×C47#328411yescharacteristic
305C2×C47#328811yescharacteristic
306#557C22×C4711yescharacteristic
307#555C22×C4711yescharacteristic
308#554C22×C4711yescharacteristic
309#550C22×C4711yescharacteristic
310#500C22×C4711yescharacteristic
311#499—21no—
312#498C22×C4711yescharacteristic
313#492—21no—
314#492C22×C4711yescharacteristic
315#492C22×C4711yescharacteristic
316#487C22×C4711yescharacteristic
317#486C22×C4711yescharacteristic
318#485—21no—
319#482—21no—
320#480—21no—
321#479—21no—
322#478—21no—
323#477C22×C4711yescharacteristic
324#477C22×C4711yescharacteristic
325#477C22×C4711yescharacteristic
326#476C22×C4711yescharacteristic
327#474C22×C4711yescharacteristic
328#468—21no—
329#466—21no—
330#461—21no—
331#461C22×C4711yescharacteristic
332#460—21no—
333#460C22×C4711yescharacteristic
334#459C22×C4711yescharacteristic
335#449—21no—
336C8×Q8C22×C4711yescharacteristic
337C8×Q8C22×C4711yescharacteristic
338C4×SD16—21no—
339C4×SD16—21no—
340C4×SD16C22×C4711yescharacteristic
341C4×SD16C22×C4711yescharacteristic
342#436C22×C4711yescharacteristic
343C8×D4C22×C4711yescharacteristic
344#428—21no—
345#416—21no—
346#335C22×C4711yescharacteristic
347#334C22×C4711yescharacteristic
348#333C22×C4711yescharacteristic
349#333C22×C4711yescharacteristic
350#332C22×C4711yescharacteristic
351#331C22×C4711yescharacteristic
352Q8⋊C8C22×C4711yescharacteristic
353Q8⋊C8C22×C4711yescharacteristic
354D4⋊C8C22×C4711yescharacteristic
355D4⋊C8C22×C4711yescharacteristic
356#322C22×C4711yescharacteristic
357C47#1987711yescharacteristic, direct product factor, Sylow
358C2×#41—21no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×SD16—21no—
363C2×SD16—41no—
364C2×SD16D4×C4711yescharacteristic
365C2×SD16D4×C4711yescharacteristic
366C2×D8—21no—
367C2×M16—21no—
368C22×C8—21no—
369C4⋊Q8—21no—
370C4⋊Q8C23×C4711yescharacteristic
371C4⋊Q8C23×C4711yescharacteristic
372C4⋊Q8C23×C4711yescharacteristic
373#127—21no—
374#127C23×C4711yescharacteristic
375#125—21no—
376#125—21no—
377#125—41no—
378#124—41no—
379C22⋊Q8—21no—
380C22⋊Q8—41no—
381#121—21no—
382#121—21no—
383#121—21no—
384#121—41no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8C23×C4711yescharacteristic
388C4×Q8C23×C4711yescharacteristic
389C4×D4—21no—
390C4×D4—21no—
391C4×D4C23×C4711yescharacteristic
392C4×D4C23×C4711yescharacteristic
393#117—21no—
394#117—21no—
395C2×C4⋊C4—21no—
396#107—21no—
397#107—21no—
398#107—21no—
399#107—21no—
400#107—21no—
401#107—21no—
402#106—21no—
403#106—21no—
404#106—21no—
405#106D4×C4711yescharacteristic
406#106D4×C4711yescharacteristic
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8C23×C4711yescharacteristic
410C4⋊C8C23×C4711yescharacteristic
411C4⋊C8C23×C4711yescharacteristic
412C4⋊C8C23×C4711yescharacteristic
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—41no—
418#103D4×C4711yescharacteristic
419#103D4×C4711yescharacteristic
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102D4×C4711yescharacteristic
427#102D4×C4711yescharacteristic
428C22⋊C8—21no—
429C22⋊C8—21no—
430C4×C8—21no—
431C4×C8—21no—
432C4×C8C23×C4711yescharacteristic
433C4×C8C23×C4711yescharacteristic
434C4×C8C23×C4711yescharacteristic
435#41—42no—
436#41—81no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8C2×D4×C4711yescharacteristic
441C2×Q8C2×D4×C4711yescharacteristic
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4C2×D4×C4711yescharacteristic
449C2×D4C2×D4×C4711yescharacteristic
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—41no—
453C22×C4—41no—
454SD16—22no—
455SD16—22no—
456SD16—42no—
457SD16—81no—
458SD16—81no—
459SD16—81no—
460SD16—82no—
461D8—81no—
462M16—42no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—81no—
469C2×C8C2×D4×C4711yescharacteristic
470C2×C8C2×D4×C4711yescharacteristic
471C2×C8C2×D4×C4711yescharacteristic
472C2×C8C2×D4×C4711yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4C2×D4×C4711yescharacteristic
487C4⋊C4C2×D4×C4711yescharacteristic
488C4⋊C4C2×D4×C4711yescharacteristic
489C4⋊C4C2×D4×C4711yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C42—21no—
497C42—21no—
498C42—41no—
499C42—41no—
500C42C24×C4711yescharacteristic
501C23—21no—
502C23—21no—
503C23—41no—
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—41no—
508Q8—41no—
509Q8—81no—
510Q8—81no—
511Q8#137×C4712yes—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—82no—
521D4—81no—
522D4—161no—
523D4—161no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—82no—
538C2×C4—161no—
539C2×C4C22×D4×C4711yescharacteristic
540C2×C4C22×D4×C4711yescharacteristic
541C2×C4H(5,𝔽2)×C4711yescharacteristic
542C8—21no—
543C8—21no—
544C8—21no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8#135×C4712yes—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22D42×C4711yescharacteristic
561C4—21no—
562C4—22no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4C2×#135×C4711yescharacteristic
572C4C2×#137×C4711yescharacteristic
573C4C47×#57711yescharacteristic
574C4C47×#57711yescharacteristic
575C2—81no—
576C2—81no—
577C2—161no—
578C2C47×#326611yescharacteristic
579C2C47×#328411yescharacteristic
580C2C47×#328811yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3305C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3392C2semidirect
2. C47×#3381C2semidirect
3. C47×#3357C2semidirect
5. C47×#1714C2semidirect
6. C47×#1685C2semidirect
7. C47×#1678C2semidirect
8. C47×#1676C2semidirect
9. C47×#1671C2semidirect
10. C47×#1646C2semidirect
11. C47×#1636C2semidirect
12. C47×#1631C2semidirect
13. C47×#1622C2semidirect
14. C47×#1583C2semidirect
15. C47×SD16⋊C8C2semidirect
260. #19877C47direct (N × H)
285. #3392C2×C47semidirect
286. #3381C2×C47semidirect
287. #3357C2×C47semidirect
289. #1714C2×C47semidirect
290. #1685C2×C47semidirect
291. #1678C2×C47semidirect
292. #1676C2×C47semidirect
293. #1671C2×C47semidirect
294. #1646C2×C47semidirect
295. #1636C2×C47semidirect
296. #1631C2×C47semidirect
297. #1622C2×C47semidirect
298. #1583C2×C47semidirect
299. SD16⋊C8C2×C47semidirect
357. C47#19877direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33922
C47×#33812
C47×#33572
C47×#33052
C47×#17142
C47×#16852
C47×#16782
C47×#16762
C47×#16712
C47×#16462
C47×#16362
C47×#16312
C47×#16222
C47×#15832
C47×SD16⋊C82
#1987747