Finite Group Databasebeta

← C47×#19854 #26059552

Subgroups — C47×#19854 #26059552

Order 12032.

612 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3397C211yesmaximal, characteristic, complemented
2C47×#3341C211yesmaximal, characteristic, complemented
3C47×#3340C211yesmaximal, characteristic, complemented
4C47×#3305C211yesmaximal, characteristic, complemented
5C47×#1714C211yesmaximal, characteristic, complemented
6C47×#1696C211yesmaximal, characteristic, complemented
7C47×#1677C211yesmaximal, characteristic, complemented
8C47×#1671C211yesmaximal, characteristic, complemented
9C47×#1665C211yesmaximal, characteristic, complemented
10C47×#1646C211yesmaximal, characteristic, complemented
11C47×#1638C211yesmaximal, characteristic, complemented
12C47×#1631C211yesmaximal, characteristic, complemented
13C47×#1624C211yesmaximal, characteristic, complemented
14C47×#1582C211yesmaximal, characteristic, complemented
15C47×#1580C211yesmaximal, characteristic, complemented
16C47×#556C2211yescharacteristic
17C47×#555C2211yescharacteristic
18C47×#555C2211yescharacteristic
19C47×#550C2211yescharacteristic
20C47×#500C2211yescharacteristic
21C47×#498C2211yescharacteristic
22C47×#496—21no—
23C47×#492C2211yescharacteristic
24C47×#492C2211yescharacteristic
25C47×#487C2211yescharacteristic
26C47×#486C2211yescharacteristic
27C47×#485—21no—
28C47×#482—21no—
29C47×#482—21no—
30C47×#482—21no—
31C47×#482—21no—
32C47×#477C2211yescharacteristic
33C47×#477C2211yescharacteristic
34C47×#476C2211yescharacteristic
35C47×#476C2211yescharacteristic
36C47×#474C2211yescharacteristic
37C47×#466—21no—
38C47×#466—21no—
39C47×#465—21no—
40C47×#463—21no—
41C47×#461C2211yescharacteristic
42C47×#460—21no—
43C47×#459C2211yescharacteristic
44C47×#459C2211yescharacteristic
45C47×#449—21no—
46C47×#446C2211yescharacteristic
47C47×#440—21no—
48C4×SD16×C47C2211yescharacteristic
49C4×D8×C47C2211yescharacteristic
50C8×D4×C47C2211yescharacteristic
51C8×D4×C47C2211yescharacteristic
52C8×D4×C47C2211yescharacteristic
53C47×#427—21no—
54C47×#427—21no—
55C47×#416—21no—
56C47×#334C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#333C2211yescharacteristic
59C47×#333C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#331C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×D4⋊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—41no—
72C2×SD16×C47D411yescharacteristic
73C2×D8×C47—21no—
74C2×D8×C47—21no—
75C2×D8×C47D411yescharacteristic
76C22×C8×C47—21no—
77C22×C8×C47—21no—
78C22×C8×C47—21no—
79C4⋊Q8×C47C2311yescharacteristic
80C4⋊Q8×C47C2311yescharacteristic
81C4⋊Q8×C47C2311yescharacteristic
82#127×C47—21no—
83#127×C47C2311yescharacteristic
84#126×C47—41no—
85#124×C47—21no—
86#124×C47—41no—
87#124×C47—41no—
88C22⋊Q8×C47—21no—
89#121×C47—21no—
90#121×C47—21no—
91#121×C47—21no—
92#121×C47—21no—
93#121×C47—21no—
94#121×C47—41no—
95C4×Q8×C47—21no—
96C4×Q8×C47C2311yescharacteristic
97C4×D4×C47—21no—
98C4×D4×C47C2311yescharacteristic
99C4×D4×C47C2311yescharacteristic
100C4×D4×C47C2311yescharacteristic
101#117×C47—21no—
102#117×C47—21no—
103#117×C47—21no—
104#117×C47—21no—
105#117×C47—21no—
106#107×C47—21no—
107#107×C47—21no—
108#107×C47—21no—
109#107×C47—21no—
110#107×C47—21no—
111#107×C47D411yescharacteristic
112#106×C47—21no—
113#106×C47—21no—
114#106×C47—21no—
115#106×C47—21no—
116#106×C47D411yescharacteristic
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—41no—
126#103×C47D411yescharacteristic
127#102×C47—21no—
128#102×C47—21no—
129#102×C47—21no—
130#102×C47—21no—
131#102×C47—21no—
132#102×C47—21no—
133#102×C47—21no—
134#102×C47D411yescharacteristic
135#102×C47D411yescharacteristic
136#102×C47D411yescharacteristic
137C22⋊C8×C47—21no—
138C22⋊C8×C47—21no—
139C22⋊C8×C47—21no—
140#97×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×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—41no—
154C2×D4×C47—41no—
155C2×D4×C47—41no—
156C2×D4×C47—41no—
157C2×D4×C47C2×D411yescharacteristic
158C2×D4×C47C2×D411yescharacteristic
159C2×D4×C47C2×D411yescharacteristic
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—41no—
164SD16×C47—41no—
165SD16×C47—42no—
166SD16×C47—81no—
167SD16×C47—81no—
168SD16×C47—82no—
169D8×C47—22no—
170D8×C47—81no—
171D8×C47—81no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—42no—
178C2×C8×C47—42no—
179C2×C8×C47—81no—
180C2×C8×C47C2×D411yescharacteristic
181C2×C8×C47C2×D411yescharacteristic
182C2×C8×C47C2×D411yescharacteristic
183C2×C8×C47C2×D411yescharacteristic
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—21no—
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—21no—
198C22⋊C4×C47—21no—
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—41no—
208C42×C47—41no—
209C42×C47—41no—
210C42×C47C2411yescharacteristic
211C23×C47—21no—
212C23×C47—21no—
213C23×C47—21no—
214C23×C47—41no—
215Q8×C47—21no—
216Q8×C47—21no—
217Q8×C47—41no—
218Q8×C47—41no—
219Q8×C47—81no—
220Q8×C47—81no—
221D4×C47—21no—
222D4×C47—21no—
223D4×C47—21no—
224D4×C47—21no—
225D4×C47—21no—
226D4×C47—21no—
227D4×C47—41no—
228D4×C47—41no—
229D4×C47—41no—
230D4×C47—41no—
231D4×C47—81no—
232D4×C47—82no—
233D4×C47—161no—
234D4×C47—161no—
235D4×C47—161no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
247C2×C4×C47—41no—
248C2×C4×C47—41no—
249C2×C4×C47—41no—
250C2×C4×C47—82no—
251C2×C4×C47C22×D411yescharacteristic
252C2×C4×C47C22×D411yescharacteristic
253C2×C4×C47H(5,𝔽2)11yescharacteristic
254C8×C47—21no—
255C8×C47—21no—
256C8×C47—21no—
257C8×C47—41no—
258C8×C47—41no—
259C8×C47—41no—
260C8×C47—41no—
261C8×C47—41no—
262C8×C47#13512yes—
263#19854C4711yesmaximal, characteristic, direct product factor, Sylow
264C22×C47—41no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47—41no—
268C22×C47—41no—
269C22×C47—41no—
270C22×C47—41no—
271C22×C47—41no—
272C22×C47—41no—
273C22×C47—81no—
274C22×C47—81no—
275C22×C47—81no—
276C22×C47D4211yescharacteristic
277C4×C47—21no—
278C4×C47—41no—
279C4×C47—41no—
280C4×C47—41no—
281C4×C47—41no—
282C4×C47—41no—
283C4×C47—81no—
284C4×C47—81no—
285C4×C47—81no—
286C4×C47C2×#13511yescharacteristic
287C4×C47#57511yescharacteristic
288C4×C47#57711yescharacteristic
289C4×C47#57711yescharacteristic
290#3397C2×C4711yescharacteristic, complemented
291#3341C2×C4711yescharacteristic, complemented
292#3340C2×C4711yescharacteristic, complemented
293#3305C2×C4711yescharacteristic, complemented
294#1714C2×C4711yescharacteristic, complemented
295#1696C2×C4711yescharacteristic, complemented
296#1677C2×C4711yescharacteristic, complemented
297#1671C2×C4711yescharacteristic, complemented
298#1665C2×C4711yescharacteristic, complemented
299#1646C2×C4711yescharacteristic, complemented
300#1638C2×C4711yescharacteristic, complemented
301#1631C2×C4711yescharacteristic, complemented
302#1624C2×C4711yescharacteristic, complemented
303#1582C2×C4711yescharacteristic, complemented
304#1580C2×C4711yescharacteristic, complemented
305C2×C47—81no—
306C2×C47—81no—
307C2×C47—81no—
308C2×C47—161no—
309C2×C47#326711yescharacteristic
310C2×C47#328411yescharacteristic
311C2×C47#328811yescharacteristic
312#556C22×C4711yescharacteristic
313#555C22×C4711yescharacteristic
314#555C22×C4711yescharacteristic
315#550C22×C4711yescharacteristic
316#500C22×C4711yescharacteristic
317#498C22×C4711yescharacteristic
318#496—21no—
319#492C22×C4711yescharacteristic
320#492C22×C4711yescharacteristic
321#487C22×C4711yescharacteristic
322#486C22×C4711yescharacteristic
323#485—21no—
324#482—21no—
325#482—21no—
326#482—21no—
327#482—21no—
328#477C22×C4711yescharacteristic
329#477C22×C4711yescharacteristic
330#476C22×C4711yescharacteristic
331#476C22×C4711yescharacteristic
332#474C22×C4711yescharacteristic
333#466—21no—
334#466—21no—
335#465—21no—
336#463—21no—
337#461C22×C4711yescharacteristic
338#460—21no—
339#459C22×C4711yescharacteristic
340#459C22×C4711yescharacteristic
341#449—21no—
342#446C22×C4711yescharacteristic
343#440—21no—
344C4×SD16C22×C4711yescharacteristic
345C4×D8C22×C4711yescharacteristic
346C8×D4C22×C4711yescharacteristic
347C8×D4C22×C4711yescharacteristic
348C8×D4C22×C4711yescharacteristic
349#427—21no—
350#427—21no—
351#416—21no—
352#334C22×C4711yescharacteristic
353#334C22×C4711yescharacteristic
354#333C22×C4711yescharacteristic
355#333C22×C4711yescharacteristic
356#332C22×C4711yescharacteristic
357#331C22×C4711yescharacteristic
358Q8⋊C8C22×C4711yescharacteristic
359D4⋊C8C22×C4711yescharacteristic
360D4⋊C8C22×C4711yescharacteristic
361D4⋊C8C22×C4711yescharacteristic
362#322C22×C4711yescharacteristic
363C47#1985411yescharacteristic, direct product factor, Sylow
364C2×#41—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—41no—
369C2×SD16D4×C4711yescharacteristic
370C2×D8—21no—
371C2×D8—21no—
372C2×D8D4×C4711yescharacteristic
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C4⋊Q8C23×C4711yescharacteristic
377C4⋊Q8C23×C4711yescharacteristic
378C4⋊Q8C23×C4711yescharacteristic
379#127—21no—
380#127C23×C4711yescharacteristic
381#126—41no—
382#124—21no—
383#124—41no—
384#124—41no—
385C22⋊Q8—21no—
386#121—21no—
387#121—21no—
388#121—21no—
389#121—21no—
390#121—21no—
391#121—41no—
392C4×Q8—21no—
393C4×Q8C23×C4711yescharacteristic
394C4×D4—21no—
395C4×D4C23×C4711yescharacteristic
396C4×D4C23×C4711yescharacteristic
397C4×D4C23×C4711yescharacteristic
398#117—21no—
399#117—21no—
400#117—21no—
401#117—21no—
402#117—21no—
403#107—21no—
404#107—21no—
405#107—21no—
406#107—21no—
407#107—21no—
408#107D4×C4711yescharacteristic
409#106—21no—
410#106—21no—
411#106—21no—
412#106—21no—
413#106D4×C4711yescharacteristic
414C4⋊C8—21no—
415C4⋊C8C23×C4711yescharacteristic
416C4⋊C8C23×C4711yescharacteristic
417C4⋊C8C23×C4711yescharacteristic
418C4⋊C8C23×C4711yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#103—41no—
423#103D4×C4711yescharacteristic
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102D4×C4711yescharacteristic
432#102D4×C4711yescharacteristic
433#102D4×C4711yescharacteristic
434C22⋊C8—21no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437#97—21no—
438C4×C8C23×C4711yescharacteristic
439C4×C8C23×C4711yescharacteristic
440C4×C8C23×C4711yescharacteristic
441#41—42no—
442#41—81no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8C2×D4×C4711yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4C2×D4×C4711yescharacteristic
455C2×D4C2×D4×C4711yescharacteristic
456C2×D4C2×D4×C4711yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—41no—
461SD16—41no—
462SD16—42no—
463SD16—81no—
464SD16—81no—
465SD16—82no—
466D8—22no—
467D8—81no—
468D8—81no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—42no—
475C2×C8—42no—
476C2×C8—81no—
477C2×C8C2×D4×C4711yescharacteristic
478C2×C8C2×D4×C4711yescharacteristic
479C2×C8C2×D4×C4711yescharacteristic
480C2×C8C2×D4×C4711yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—41no—
489C4⋊C4C2×D4×C4711yescharacteristic
490C4⋊C4C2×D4×C4711yescharacteristic
491C4⋊C4C2×D4×C4711yescharacteristic
492C4⋊C4C2×D4×C4711yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C42—21no—
504C42—41no—
505C42—41no—
506C42—41no—
507C42C24×C4711yescharacteristic
508C23—21no—
509C23—21no—
510C23—21no—
511C23—41no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—81no—
517Q8—81no—
518D4—21no—
519D4—21no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—81no—
529D4—82no—
530D4—161no—
531D4—161no—
532D4—161no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—82no—
548C2×C4C22×D4×C4711yescharacteristic
549C2×C4C22×D4×C4711yescharacteristic
550C2×C4H(5,𝔽2)×C4711yescharacteristic
551C8—21no—
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8#135×C4712yes—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22D42×C4711yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4C2×#135×C4711yescharacteristic
583C4C47×#57511yescharacteristic
584C4C47×#57711yescharacteristic
585C4C47×#57711yescharacteristic
586C2—81no—
587C2—81no—
588C2—81no—
589C2—161no—
590C2C47×#326711yescharacteristic
591C2C47×#328411yescharacteristic
592C2C47×#328811yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
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×#3397C2semidirect
2. C47×#3341C2semidirect
3. C47×#3340C2semidirect
4. C47×#3305C2semidirect
5. C47×#1714C2semidirect
6. C47×#1696C2semidirect
7. C47×#1677C2semidirect
8. C47×#1671C2semidirect
9. C47×#1665C2semidirect
10. C47×#1646C2semidirect
11. C47×#1638C2semidirect
12. C47×#1631C2semidirect
13. C47×#1624C2semidirect
14. C47×#1582C2semidirect
15. C47×#1580C2semidirect
263. #19854C47direct (N × H)
290. #3397C2×C47semidirect
291. #3341C2×C47semidirect
292. #3340C2×C47semidirect
293. #3305C2×C47semidirect
294. #1714C2×C47semidirect
295. #1696C2×C47semidirect
296. #1677C2×C47semidirect
297. #1671C2×C47semidirect
298. #1665C2×C47semidirect
299. #1646C2×C47semidirect
300. #1638C2×C47semidirect
301. #1631C2×C47semidirect
302. #1624C2×C47semidirect
303. #1582C2×C47semidirect
304. #1580C2×C47semidirect
363. C47#19854direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33972
C47×#33412
C47×#33402
C47×#33052
C47×#17142
C47×#16962
C47×#16772
C47×#16712
C47×#16652
C47×#16462
C47×#16382
C47×#16312
C47×#16242
C47×#15822
C47×#15802
#1985447