Finite Group Databasebeta

← C47×#19882 #26059580

Subgroups — C47×#19882 #26059580

Order 12032.

598 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3396C211yesmaximal, characteristic, complemented
2C47×#3394C211yesmaximal, characteristic, complemented
3C47×#3361C211yesmaximal, characteristic, complemented
4C47×#3356C211yesmaximal, characteristic, complemented
5C47×#1715C211yesmaximal, characteristic, complemented
6C47×#1687C211yesmaximal, characteristic
7C47×#1678C211yesmaximal, characteristic, complemented
8C47×#1672C211yesmaximal, characteristic, complemented
9C47×#1666C211yesmaximal, characteristic, complemented
10C47×#1640C211yesmaximal, characteristic, complemented
11C47×#1630C211yesmaximal, characteristic, complemented
12C47×#1628C211yesmaximal, characteristic, complemented
13C47×#1622C211yesmaximal, characteristic, complemented
14C47×#1583C211yesmaximal, characteristic, complemented
15C47×#1579C211yesmaximal, characteristic, complemented
16C47×#559C2211yescharacteristic
17C47×#559C2211yescharacteristic
18C47×#556C2211yescharacteristic
19C47×#554C2211yescharacteristic
20C47×#498C2211yescharacteristic
21C47×#495—21no—
22C47×#495—21no—
23C47×#493C2211yescharacteristic
24C47×#492C2211yescharacteristic
25C47×#492C2211yescharacteristic
26C47×#488—21no—
27C47×#486C2211yescharacteristic
28C47×#486C2211yescharacteristic
29C47×#485—21no—
30C47×#483—21no—
31C47×#478—21no—
32C47×#477C2211yescharacteristic
33C47×#477C2211yescharacteristic
34C47×#475C2211yescharacteristic
35C47×#470—21no—
36C47×#464—21no—
37C47×#463—21no—
38C47×#463—21no—
39C47×#463—21no—
40C47×#463—21no—
41C47×#462C2211yescharacteristic
42C47×#460C2211yescharacteristic
43C47×#460C2211yescharacteristic
44C47×#459C2211yescharacteristic
45C47×#459C2211yescharacteristic
46C8×Q8×C47C2211yescharacteristic
47C8×Q8×C47C2211yescharacteristic
48C8×Q8×C47C2211yescharacteristic
49C4×Q16×C47C2211yescharacteristic
50C4×SD16×C47—21no—
51C4×SD16×C47C2211yescharacteristic
52C4×D8×C47—21no—
53C4×D8×C47—21no—
54C47×#436C2211yescharacteristic
55C47×#428—21no—
56C47×#334C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#333C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#331C2211yescharacteristic
61C47×#331C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×Q16×C47—21no—
68C2×Q16×C47D411yescharacteristic
69C2×SD16×C47—21no—
70C2×SD16×C47—21no—
71C2×SD16×C47—21no—
72C2×SD16×C47—21no—
73C2×SD16×C47—41no—
74C2×SD16×C47D411yescharacteristic
75C2×D8×C47—21no—
76C2×D8×C47—21no—
77C2×D8×C47—21no—
78C2×D8×C47—21no—
79C2×M16×C47—21no—
80C4⋊Q8×C47C2311yescharacteristic
81C4⋊Q8×C47C2311yescharacteristic
82#127×C47C2311yescharacteristic
83#127×C47C2311yescharacteristic
84#126×C47—41no—
85#125×C47—21no—
86#124×C47—21no—
87#124×C47—21no—
88#124×C47—21no—
89#124×C47—21no—
90#124×C47—21no—
91#123×C47—41no—
92#123×C47—41no—
93C22⋊Q8×C47—21no—
94C22⋊Q8×C47—21no—
95C22⋊Q8×C47—41no—
96C4×Q8×C47—21no—
97C4×Q8×C47C2311yescharacteristic
98C4×Q8×C47C2311yescharacteristic
99C4×Q8×C47C2311yescharacteristic
100C4×D4×C47—21no—
101C4×D4×C47—21no—
102C4×D4×C47—21no—
103C4×D4×C47—21no—
104C4×D4×C47—21no—
105C4×D4×C47C2311yescharacteristic
106#117×C47—21no—
107C2×C4⋊C4×C47—21no—
108#107×C47—21no—
109#107×C47—21no—
110#107×C47D411yescharacteristic
111#106×C47—21no—
112#106×C47—21no—
113#106×C47—21no—
114#106×C47D411yescharacteristic
115C4⋊C8×C47—21no—
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×C47D411yescharacteristic
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×C47—41no—
136#102×C47D411yescharacteristic
137C22⋊C8×C47—21no—
138C4×C8×C47—21no—
139C4×C8×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47C2×D411yescharacteristic
147C2×Q8×C47C2×D411yescharacteristic
148C2×Q8×C47C2×D411yescharacteristic
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47C2×D411yescharacteristic
156C22×C4×C47—21no—
157C22×C4×C47—41no—
158C22×C4×C47—41no—
159C22×C4×C47—41no—
160Q16×C47—22no—
161Q16×C47—81no—
162SD16×C47—41no—
163SD16×C47—42no—
164SD16×C47—81no—
165SD16×C47—81no—
166SD16×C47—81no—
167SD16×C47—82no—
168D8×C47—42no—
169D8×C47—42no—
170D8×C47—81no—
171D8×C47—81no—
172M16×C47—42no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—21no—
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—41no—
190C4⋊C4×C47—41no—
191C4⋊C4×C47—41no—
192C4⋊C4×C47C2×D411yescharacteristic
193C4⋊C4×C47C2×D411yescharacteristic
194C4⋊C4×C47C2×D411yescharacteristic
195C4⋊C4×C47C2×D411yescharacteristic
196C22⋊C4×C47—21no—
197C22⋊C4×C47—41no—
198C22⋊C4×C47—41no—
199C22⋊C4×C47—41no—
200C22⋊C4×C47—41no—
201C22⋊C4×C47—41no—
202C22⋊C4×C47—41no—
203C22⋊C4×C47—41no—
204C22⋊C4×C47—41no—
205C22⋊C4×C47—41no—
206C42×C47—21no—
207C42×C47—21no—
208C42×C47—21no—
209C42×C47—41no—
210C42×C47C2411yescharacteristic
211C23×C47—21no—
212C23×C47—41no—
213C23×C47—41no—
214Q8×C47—21no—
215Q8×C47—21no—
216Q8×C47—21no—
217Q8×C47—21no—
218Q8×C47—21no—
219Q8×C47—21no—
220Q8×C47—41no—
221Q8×C47—41no—
222Q8×C47—81no—
223D4×C47—21no—
224D4×C47—21no—
225D4×C47—41no—
226D4×C47—41no—
227D4×C47—41no—
228D4×C47—41no—
229D4×C47—41no—
230D4×C47—41no—
231D4×C47—41no—
232D4×C47—41no—
233D4×C47—81no—
234D4×C47—81no—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—161no—
247C2×C4×C47—161no—
248C2×C4×C47—161no—
249C2×C4×C47C22×D411yescharacteristic
250C2×C4×C47C22×D411yescharacteristic
251C2×C4×C47H(5,𝔽2)11yescharacteristic
252C8×C47—21no—
253C8×C47—21no—
254C8×C47—21no—
255C8×C47—41no—
256C8×C47—41no—
257C8×C47—41no—
258C8×C47—41no—
259C8×C47—41no—
260C8×C47#13512yes—
261#19882C4711yesmaximal, characteristic, direct product factor, Sylow
262C22×C47—41no—
263C22×C47—41no—
264C22×C47—41no—
265C22×C47—81no—
266C22×C47—81no—
267C22×C47—81no—
268C22×C47—81no—
269C22×C47—81no—
270C22×C47—81no—
271C22×C47D4211yescharacteristic
272C4×C47—21no—
273C4×C47—41no—
274C4×C47—41no—
275C4×C47—41no—
276C4×C47—41no—
277C4×C47—41no—
278C4×C47—41no—
279C4×C47—41no—
280C4×C47—81no—
281C4×C47—81no—
282C4×C47C2×#13511yescharacteristic
283C4×C47#57511yescharacteristic
284C4×C47#57711yescharacteristic
285C4×C47#57711yescharacteristic
286#3396C2×C4711yescharacteristic, complemented
287#3394C2×C4711yescharacteristic, complemented
288#3361C2×C4711yescharacteristic, complemented
289#3356C2×C4711yescharacteristic, complemented
290#1715C2×C4711yescharacteristic, complemented
291#1687C2×C4711yescharacteristic
292#1678C2×C4711yescharacteristic, complemented
293#1672C2×C4711yescharacteristic, complemented
294#1666C2×C4711yescharacteristic, complemented
295#1640C2×C4711yescharacteristic, complemented
296#1630C2×C4711yescharacteristic, complemented
297#1628C2×C4711yescharacteristic, complemented
298#1622C2×C4711yescharacteristic, complemented
299#1583C2×C4711yescharacteristic, complemented
300#1579C2×C4711yescharacteristic, complemented
301C2×C47—81no—
302C2×C47—161no—
303C2×C47—161no—
304C2×C47#327111yescharacteristic
305C2×C47#328411yescharacteristic
306C2×C47#328811yescharacteristic
307#559C22×C4711yescharacteristic
308#559C22×C4711yescharacteristic
309#556C22×C4711yescharacteristic
310#554C22×C4711yescharacteristic
311#498C22×C4711yescharacteristic
312#495—21no—
313#495—21no—
314#493C22×C4711yescharacteristic
315#492C22×C4711yescharacteristic
316#492C22×C4711yescharacteristic
317#488—21no—
318#486C22×C4711yescharacteristic
319#486C22×C4711yescharacteristic
320#485—21no—
321#483—21no—
322#478—21no—
323#477C22×C4711yescharacteristic
324#477C22×C4711yescharacteristic
325#475C22×C4711yescharacteristic
326#470—21no—
327#464—21no—
328#463—21no—
329#463—21no—
330#463—21no—
331#463—21no—
332#462C22×C4711yescharacteristic
333#460C22×C4711yescharacteristic
334#460C22×C4711yescharacteristic
335#459C22×C4711yescharacteristic
336#459C22×C4711yescharacteristic
337C8×Q8C22×C4711yescharacteristic
338C8×Q8C22×C4711yescharacteristic
339C8×Q8C22×C4711yescharacteristic
340C4×Q16C22×C4711yescharacteristic
341C4×SD16—21no—
342C4×SD16C22×C4711yescharacteristic
343C4×D8—21no—
344C4×D8—21no—
345#436C22×C4711yescharacteristic
346#428—21no—
347#334C22×C4711yescharacteristic
348#334C22×C4711yescharacteristic
349#333C22×C4711yescharacteristic
350#332C22×C4711yescharacteristic
351#331C22×C4711yescharacteristic
352#331C22×C4711yescharacteristic
353Q8⋊C8C22×C4711yescharacteristic
354Q8⋊C8C22×C4711yescharacteristic
355Q8⋊C8C22×C4711yescharacteristic
356D4⋊C8C22×C4711yescharacteristic
357#322C22×C4711yescharacteristic
358C47#1988211yescharacteristic, direct product factor, Sylow
359C2×Q16—21no—
360C2×Q16D4×C4711yescharacteristic
361C2×SD16—21no—
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—41no—
366C2×SD16D4×C4711yescharacteristic
367C2×D8—21no—
368C2×D8—21no—
369C2×D8—21no—
370C2×D8—21no—
371C2×M16—21no—
372C4⋊Q8C23×C4711yescharacteristic
373C4⋊Q8C23×C4711yescharacteristic
374#127C23×C4711yescharacteristic
375#127C23×C4711yescharacteristic
376#126—41no—
377#125—21no—
378#124—21no—
379#124—21no—
380#124—21no—
381#124—21no—
382#124—21no—
383#123—41no—
384#123—41no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—41no—
388C4×Q8—21no—
389C4×Q8C23×C4711yescharacteristic
390C4×Q8C23×C4711yescharacteristic
391C4×Q8C23×C4711yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4C23×C4711yescharacteristic
398#117—21no—
399C2×C4⋊C4—21no—
400#107—21no—
401#107—21no—
402#107D4×C4711yescharacteristic
403#106—21no—
404#106—21no—
405#106—21no—
406#106D4×C4711yescharacteristic
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8C23×C4711yescharacteristic
411C4⋊C8C23×C4711yescharacteristic
412C4⋊C8C23×C4711yescharacteristic
413C4⋊C8C23×C4711yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103D4×C4711yescharacteristic
419#103D4×C4711yescharacteristic
420#103D4×C4711yescharacteristic
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—41no—
428#102D4×C4711yescharacteristic
429C22⋊C8—21no—
430C4×C8—21no—
431C4×C8—21no—
432C4×C8—21no—
433C4×C8C23×C4711yescharacteristic
434C4×C8C23×C4711yescharacteristic
435C4×C8C23×C4711yescharacteristic
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C2×D4×C4711yescharacteristic
439C2×Q8C2×D4×C4711yescharacteristic
440C2×Q8C2×D4×C4711yescharacteristic
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4C2×D4×C4711yescharacteristic
448C22×C4—21no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452Q16—22no—
453Q16—81no—
454SD16—41no—
455SD16—42no—
456SD16—81no—
457SD16—81no—
458SD16—81no—
459SD16—82no—
460D8—42no—
461D8—42no—
462D8—81no—
463D8—81no—
464M16—42no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8C2×D4×C4711yescharacteristic
471C2×C8C2×D4×C4711yescharacteristic
472C2×C8C2×D4×C4711yescharacteristic
473C2×C8C2×D4×C4711yescharacteristic
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⋊C4C2×D4×C4711yescharacteristic
485C4⋊C4C2×D4×C4711yescharacteristic
486C4⋊C4C2×D4×C4711yescharacteristic
487C4⋊C4C2×D4×C4711yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—41no—
502C42C24×C4711yescharacteristic
503C23—21no—
504C23—41no—
505C23—41no—
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—21no—
512Q8—41no—
513Q8—41no—
514Q8—81no—
515D4—21no—
516D4—21no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—81no—
526D4—81no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—161no—
539C2×C4—161no—
540C2×C4—161no—
541C2×C4C22×D4×C4711yescharacteristic
542C2×C4C22×D4×C4711yescharacteristic
543C2×C4H(5,𝔽2)×C4711yescharacteristic
544C8—21no—
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8#135×C4712yes—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22D42×C4711yescharacteristic
563C4—21no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4C2×#135×C4711yescharacteristic
574C4C47×#57511yescharacteristic
575C4C47×#57711yescharacteristic
576C4C47×#57711yescharacteristic
577C2—81no—
578C2—161no—
579C2—161no—
580C2C47×#327111yescharacteristic
581C2C47×#328411yescharacteristic
582C2C47×#328811yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#1687C2
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×#3396C2semidirect
2. C47×#3394C2semidirect
3. C47×#3361C2semidirect
4. C47×#3356C2semidirect
5. C47×#1715C2semidirect
7. C47×#1678C2semidirect
8. C47×#1672C2semidirect
9. C47×#1666C2semidirect
10. C47×#1640C2semidirect
11. C47×#1630C2semidirect
12. C47×#1628C2semidirect
13. C47×#1622C2semidirect
14. C47×#1583C2semidirect
15. C47×#1579C2semidirect
261. #19882C47direct (N × H)
286. #3396C2×C47semidirect
287. #3394C2×C47semidirect
288. #3361C2×C47semidirect
289. #3356C2×C47semidirect
290. #1715C2×C47semidirect
292. #1678C2×C47semidirect
293. #1672C2×C47semidirect
294. #1666C2×C47semidirect
295. #1640C2×C47semidirect
296. #1630C2×C47semidirect
297. #1628C2×C47semidirect
298. #1622C2×C47semidirect
299. #1583C2×C47semidirect
300. #1579C2×C47semidirect
358. C47#19882direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33962
C47×#33942
C47×#33612
C47×#33562
C47×#17152
C47×#16872
C47×#16782
C47×#16722
C47×#16662
C47×#16402
C47×#16302
C47×#16282
C47×#16222
C47×#15832
C47×#15792
#1988247