Finite Group Databasebeta

← C47×#19916 #26059614

Subgroups — C47×#19916 #26059614

Order 12032.

610 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3373C211yesmaximal, characteristic, complemented
2C47×#3361C211yesmaximal, characteristic, complemented
3C47×#3331C211yesmaximal, characteristic, complemented
4C47×#3298C211yesmaximal, characteristic, complemented
5C47×#1711C211yesmaximal, characteristic, complemented
6C47×#1704C211yesmaximal, characteristic, complemented
7C47×#1701C211yesmaximal, characteristic, complemented
8C47×#1680C211yesmaximal, characteristic, complemented
9C47×#1677C211yesmaximal, characteristic, complemented
10C47×#1643C211yesmaximal, characteristic, complemented
11C47×#1640C211yesmaximal, characteristic, complemented
12C47×#1637C211yesmaximal, characteristic, complemented
13C47×#1625C211yesmaximal, characteristic
14C47×#1590C211yesmaximal, characteristic, complemented
15C8×SD16×C47C211yesmaximal, characteristic, complemented
16C47×#559C2211yescharacteristic
17C47×#554C2211yescharacteristic
18D4×Q8×C47C2211yescharacteristic
19C47×#547C2211yescharacteristic
20C47×#489—21no—
21C47×#488—21no—
22C47×#487C2211yescharacteristic
23C47×#487C2211yescharacteristic
24C47×#487C2211yescharacteristic
25C47×#486C2211yescharacteristic
26C47×#486C2211yescharacteristic
27C47×#486C2211yescharacteristic
28C47×#483—21no—
29C47×#483—21no—
30C47×#478—21no—
31C47×#477C2211yescharacteristic
32C47×#476—21no—
33C47×#476C2211yescharacteristic
34C47×#475C2211yescharacteristic
35C47×#475C2211yescharacteristic
36C47×#470—21no—
37C47×#465—21no—
38C47×#463—21no—
39C47×#463—21no—
40C47×#462C2211yescharacteristic
41C47×#461C2211yescharacteristic
42C47×#459C2211yescharacteristic
43C47×#459C2211yescharacteristic
44C47×#452—21no—
45C47×#448—21no—
46C47×#446C2211yescharacteristic
47C8×Q8×C47C2211yescharacteristic
48C47×#442—21no—
49C4×SD16×C47C2211yescharacteristic
50C4×SD16×C47C2211yescharacteristic
51C4×D8×C47—21no—
52C47×#436C2211yescharacteristic
53C8×D4×C47C2211yescharacteristic
54C47×#417—21no—
55C2×#103×C47—21no—
56C47×#334C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#333C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#331C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C82×C47C2211yescharacteristic
67C2×#41×C47—21no—
68C22×Q8×C47—21no—
69C2×Q16×C47—21no—
70C2×SD16×C47—21no—
71C2×SD16×C47D411yescharacteristic
72C2×SD16×C47D411yescharacteristic
73C2×D8×C47—21no—
74C2×D8×C47—21no—
75C2×M16×C47—21no—
76C22×C8×C47—21no—
77C4⋊Q8×C47—21no—
78C4⋊Q8×C47C2311yescharacteristic
79C4⋊Q8×C47C2311yescharacteristic
80C4⋊Q8×C47C2311yescharacteristic
81#127×C47C2311yescharacteristic
82#125×C47—21no—
83#124×C47—21no—
84#124×C47—21no—
85#123×C47—41no—
86#123×C47—41no—
87C22⋊Q8×C47—21no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47—21no—
90C22⋊Q8×C47—41no—
91C22⋊Q8×C47—41no—
92#121×C47—21no—
93C4×Q8×C47C2311yescharacteristic
94C4×Q8×C47C2311yescharacteristic
95C4×D4×C47—21no—
96C4×D4×C47—21no—
97C4×D4×C47—21no—
98C4×D4×C47—21no—
99C4×D4×C47C2311yescharacteristic
100C4×D4×C47C2311yescharacteristic
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103#107×C47—21no—
104#106×C47—21no—
105#106×C47—21no—
106#106×C47—21no—
107#106×C47D411yescharacteristic
108#106×C47D411yescharacteristic
109C4⋊C8×C47—21no—
110C4⋊C8×C47—21no—
111C4⋊C8×C47C2311yescharacteristic
112C4⋊C8×C47C2311yescharacteristic
113C4⋊C8×C47C2311yescharacteristic
114C4⋊C8×C47C2311yescharacteristic
115#103×C47—21no—
116#103×C47—21no—
117#103×C47—21no—
118#103×C47—21no—
119#103×C47—21no—
120#103×C47—21no—
121#103×C47—21no—
122#103×C47—21no—
123#103×C47—21no—
124#103×C47—41no—
125#103×C47D411yescharacteristic
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×C47—41no—
135#102×C47D411yescharacteristic
136#102×C47D411yescharacteristic
137C22⋊C8×C47—21no—
138C22⋊C8×C47—21no—
139#97×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×C47—41no—
150C2×Q8×C47—42no—
151C2×Q8×C47—81no—
152C2×Q8×C47C2×D411yescharacteristic
153C2×Q8×C47C2×D411yescharacteristic
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—41no—
158C2×D4×C47C2×D411yescharacteristic
159C2×D4×C47C2×D411yescharacteristic
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—41no—
163C22×C4×C47—41no—
164C22×C4×C47—41no—
165C22×C4×C47—41no—
166Q16×C47—81no—
167SD16×C47—22no—
168SD16×C47—41no—
169SD16×C47—81no—
170D8×C47—42no—
171D8×C47—42no—
172M16×C47—81no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—21no—
178C2×C8×C47—81no—
179C2×C8×C47C2×D411yescharacteristic
180C2×C8×C47C2×D411yescharacteristic
181C2×C8×C47C2×D411yescharacteristic
182C2×C8×C47C2×D411yescharacteristic
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—21no—
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—
205C22⋊C4×C47—41no—
206C22⋊C4×C47—41no—
207C42×C47—21no—
208C42×C47—21no—
209C42×C47C2411yescharacteristic
210C23×C47—21no—
211C23×C47—21no—
212C23×C47—41no—
213Q8×C47—21no—
214Q8×C47—21no—
215Q8×C47—21no—
216Q8×C47—21no—
217Q8×C47—41no—
218Q8×C47—41no—
219Q8×C47—41no—
220Q8×C47—41no—
221Q8×C47—81no—
222Q8×C47—82no—
223D4×C47—21no—
224D4×C47—21no—
225D4×C47—21no—
226D4×C47—41no—
227D4×C47—41no—
228D4×C47—41no—
229D4×C47—41no—
230D4×C47—81no—
231D4×C47—82no—
232D4×C47#13512yes—
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—82no—
248C2×C4×C47—161no—
249C2×C4×C47—161no—
250C2×C4×C47C22×D411yescharacteristic
251C2×C4×C47C22×D411yescharacteristic
252C2×C4×C47H(5,𝔽2)11yescharacteristic
253C8×C47—21no—
254C8×C47—21no—
255C8×C47—21no—
256C8×C47—21no—
257C8×C47—41no—
258C8×C47—41no—
259C8×C47—41no—
260C8×C47—41no—
261C8×C47—41no—
262#19916C4711yesmaximal, characteristic, direct product factor, Sylow
263C22×C47—22no—
264C22×C47—41no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47—41no—
268C22×C47—41no—
269C22×C47—81no—
270C22×C47—81no—
271C22×C47—81no—
272C22×C47D4211yescharacteristic
273C4×C47—21no—
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×C47—81no—
283C4×C47C2×#13511yescharacteristic
284C4×C47#57511yescharacteristic
285C4×C47#57711yescharacteristic
286C4×C47#57711yescharacteristic
287#3373C2×C4711yescharacteristic, complemented
288#3361C2×C4711yescharacteristic, complemented
289#3331C2×C4711yescharacteristic, complemented
290#3298C2×C4711yescharacteristic, complemented
291#1711C2×C4711yescharacteristic, complemented
292#1704C2×C4711yescharacteristic, complemented
293#1701C2×C4711yescharacteristic, complemented
294#1680C2×C4711yescharacteristic, complemented
295#1677C2×C4711yescharacteristic, complemented
296#1643C2×C4711yescharacteristic, complemented
297#1640C2×C4711yescharacteristic, complemented
298#1637C2×C4711yescharacteristic, complemented
299#1625C2×C4711yescharacteristic
300#1590C2×C4711yescharacteristic, complemented
301C8×SD16C2×C4711yescharacteristic, complemented
302C2×C47—42no—
303C2×C47—81no—
304C2×C47—161no—
305C2×C47#327511yescharacteristic
306C2×C47#328211yescharacteristic
307C2×C47#329011yescharacteristic
308#559C22×C4711yescharacteristic
309#554C22×C4711yescharacteristic
310D4×Q8C22×C4711yescharacteristic
311#547C22×C4711yescharacteristic
312#489—21no—
313#488—21no—
314#487C22×C4711yescharacteristic
315#487C22×C4711yescharacteristic
316#487C22×C4711yescharacteristic
317#486C22×C4711yescharacteristic
318#486C22×C4711yescharacteristic
319#486C22×C4711yescharacteristic
320#483—21no—
321#483—21no—
322#478—21no—
323#477C22×C4711yescharacteristic
324#476—21no—
325#476C22×C4711yescharacteristic
326#475C22×C4711yescharacteristic
327#475C22×C4711yescharacteristic
328#470—21no—
329#465—21no—
330#463—21no—
331#463—21no—
332#462C22×C4711yescharacteristic
333#461C22×C4711yescharacteristic
334#459C22×C4711yescharacteristic
335#459C22×C4711yescharacteristic
336#452—21no—
337#448—21no—
338#446C22×C4711yescharacteristic
339C8×Q8C22×C4711yescharacteristic
340#442—21no—
341C4×SD16C22×C4711yescharacteristic
342C4×SD16C22×C4711yescharacteristic
343C4×D8—21no—
344#436C22×C4711yescharacteristic
345C8×D4C22×C4711yescharacteristic
346#417—21no—
347C2×#103—21no—
348#334C22×C4711yescharacteristic
349#334C22×C4711yescharacteristic
350#333C22×C4711yescharacteristic
351#332C22×C4711yescharacteristic
352#332C22×C4711yescharacteristic
353#331C22×C4711yescharacteristic
354Q8⋊C8C22×C4711yescharacteristic
355Q8⋊C8C22×C4711yescharacteristic
356D4⋊C8C22×C4711yescharacteristic
357D4⋊C8C22×C4711yescharacteristic
358C82C22×C4711yescharacteristic
359C47#1991611yescharacteristic, direct product factor, Sylow
360C2×#41—21no—
361C22×Q8—21no—
362C2×Q16—21no—
363C2×SD16—21no—
364C2×SD16D4×C4711yescharacteristic
365C2×SD16D4×C4711yescharacteristic
366C2×D8—21no—
367C2×D8—21no—
368C2×M16—21no—
369C22×C8—21no—
370C4⋊Q8—21no—
371C4⋊Q8C23×C4711yescharacteristic
372C4⋊Q8C23×C4711yescharacteristic
373C4⋊Q8C23×C4711yescharacteristic
374#127C23×C4711yescharacteristic
375#125—21no—
376#124—21no—
377#124—21no—
378#123—41no—
379#123—41no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—41no—
384C22⋊Q8—41no—
385#121—21no—
386C4×Q8C23×C4711yescharacteristic
387C4×Q8C23×C4711yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4C23×C4711yescharacteristic
393C4×D4C23×C4711yescharacteristic
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396#107—21no—
397#106—21no—
398#106—21no—
399#106—21no—
400#106D4×C4711yescharacteristic
401#106D4×C4711yescharacteristic
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8C23×C4711yescharacteristic
405C4⋊C8C23×C4711yescharacteristic
406C4⋊C8C23×C4711yescharacteristic
407C4⋊C8C23×C4711yescharacteristic
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
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#102—21no—
427#102—41no—
428#102D4×C4711yescharacteristic
429#102D4×C4711yescharacteristic
430C22⋊C8—21no—
431C22⋊C8—21no—
432#97—21no—
433C4×C8—21no—
434C4×C8C23×C4711yescharacteristic
435C4×C8C23×C4711yescharacteristic
436C4×C8C23×C4711yescharacteristic
437#41—42no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—41no—
443C2×Q8—42no—
444C2×Q8—81no—
445C2×Q8C2×D4×C4711yescharacteristic
446C2×Q8C2×D4×C4711yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4C2×D4×C4711yescharacteristic
452C2×D4C2×D4×C4711yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459Q16—81no—
460SD16—22no—
461SD16—41no—
462SD16—81no—
463D8—42no—
464D8—42no—
465M16—81no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—81no—
472C2×C8C2×D4×C4711yescharacteristic
473C2×C8C2×D4×C4711yescharacteristic
474C2×C8C2×D4×C4711yescharacteristic
475C2×C8C2×D4×C4711yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4C2×D4×C4711yescharacteristic
489C4⋊C4C2×D4×C4711yescharacteristic
490C4⋊C4C2×D4×C4711yescharacteristic
491C4⋊C4C2×D4×C4711yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C42—21no—
501C42—21no—
502C42C24×C4711yescharacteristic
503C23—21no—
504C23—21no—
505C23—41no—
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—81no—
515Q8—82no—
516D4—21no—
517D4—21no—
518D4—21no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—81no—
524D4—82no—
525D4#135×C4712yes—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4—161no—
542C2×C4—161no—
543C2×C4C22×D4×C4711yescharacteristic
544C2×C4C22×D4×C4711yescharacteristic
545C2×C4H(5,𝔽2)×C4711yescharacteristic
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C22—22no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22D42×C4711yescharacteristic
565C4—21no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C2×#135×C4711yescharacteristic
576C4C47×#57511yescharacteristic
577C4C47×#57711yescharacteristic
578C4C47×#57711yescharacteristic
579C2—42no—
580C2—81no—
581C2—161no—
582C2C47×#327511yescharacteristic
583C2C47×#328211yescharacteristic
584C2C47×#329011yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#1625C2
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×#3373C2semidirect
2. C47×#3361C2semidirect
3. C47×#3331C2semidirect
4. C47×#3298C2semidirect
5. C47×#1711C2semidirect
6. C47×#1704C2semidirect
7. C47×#1701C2semidirect
8. C47×#1680C2semidirect
9. C47×#1677C2semidirect
10. C47×#1643C2semidirect
11. C47×#1640C2semidirect
12. C47×#1637C2semidirect
14. C47×#1590C2semidirect
15. C8×SD16×C47C2semidirect
262. #19916C47direct (N × H)
287. #3373C2×C47semidirect
288. #3361C2×C47semidirect
289. #3331C2×C47semidirect
290. #3298C2×C47semidirect
291. #1711C2×C47semidirect
292. #1704C2×C47semidirect
293. #1701C2×C47semidirect
294. #1680C2×C47semidirect
295. #1677C2×C47semidirect
296. #1643C2×C47semidirect
297. #1640C2×C47semidirect
298. #1637C2×C47semidirect
300. #1590C2×C47semidirect
301. C8×SD16C2×C47semidirect
359. C47#19916direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33732
C47×#33612
C47×#33312
C47×#32982
C47×#17112
C47×#17042
C47×#17012
C47×#16802
C47×#16772
C47×#16432
C47×#16402
C47×#16372
C47×#16252
C47×#15902
C8×SD16×C472
#1991647