Finite Group Databasebeta

← C47×#19871 #26059569

Subgroups — C47×#19871 #26059569

Order 12032.

632 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3399C211yesmaximal, characteristic, complemented
2C47×#3396C211yesmaximal, characteristic, complemented
3C47×#3394C211yesmaximal, characteristic, complemented
4C47×#3304C211yesmaximal, characteristic, complemented
5C47×#1721C211yesmaximal, characteristic, complemented
6C47×#1686C211yesmaximal, characteristic, complemented
7C47×#1682C211yesmaximal, characteristic, complemented
8C47×#1668C211yesmaximal, characteristic, complemented
9C47×#1667C211yesmaximal, characteristic, complemented
10C47×#1640C211yesmaximal, characteristic, complemented
11C47×#1628C211yesmaximal, characteristic, complemented
12C47×#1621C211yesmaximal, characteristic, complemented
13C47×#1620C211yesmaximal, characteristic, complemented
14C47×#1584C211yesmaximal, characteristic, complemented
15C47×SD16⋊C8C211yesmaximal, characteristic, complemented
16C47×#559C2211yescharacteristic
17C47×#559C2211yescharacteristic
18C47×#556C2211yescharacteristic
19C47×#550C2211yescharacteristic
20C47×#496—21no—
21C47×#495—21no—
22C47×#495—21no—
23C47×#493C2211yescharacteristic
24C47×#493C2211yescharacteristic
25C47×#493C2211yescharacteristic
26C47×#492C2211yescharacteristic
27C47×#486C2211yescharacteristic
28C47×#486C2211yescharacteristic
29C47×#482—21no—
30C47×#475C2211yescharacteristic
31C47×#465—21no—
32C47×#464—21no—
33C47×#463—21no—
34C47×#463—21no—
35C47×#463—21no—
36C47×#463—21no—
37C47×#462C2211yescharacteristic
38C47×#460C2211yescharacteristic
39C47×#460C2211yescharacteristic
40C47×#460C2211yescharacteristic
41C47×#460C2211yescharacteristic
42C47×#459—21no—
43C47×#459C2211yescharacteristic
44C47×#459C2211yescharacteristic
45C47×#452—21no—
46C47×#446C2211yescharacteristic
47C8×Q8×C47C2211yescharacteristic
48C8×Q8×C47C2211yescharacteristic
49C47×#442—21no—
50C4×Q16×C47C2211yescharacteristic
51C4×SD16×C47—21no—
52C4×SD16×C47C2211yescharacteristic
53C4×D8×C47—21no—
54C8×D4×C47C2211yescharacteristic
55C47×#416—21no—
56C47×#335C2211yescharacteristic
57C47×#335C2211yescharacteristic
58C47×#332C2211yescharacteristic
59C47×#331C2211yescharacteristic
60C47×#331C2211yescharacteristic
61C47×#331C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×#41×C47—21no—
68C2×Q16×C47—21no—
69C2×Q16×C47D411yescharacteristic
70C2×SD16×C47—21no—
71C2×SD16×C47—21no—
72C2×SD16×C47—21no—
73C2×SD16×C47—21no—
74C2×SD16×C47—21no—
75C2×SD16×C47—21no—
76C2×SD16×C47D411yescharacteristic
77C2×D8×C47—21no—
78C2×D8×C47—21no—
79C2×D8×C47—21no—
80C2×D8×C47—21no—
81C2×D8×C47—21no—
82C2×D8×C47—21no—
83C2×D8×C47—41no—
84C22×C8×C47—21no—
85C4⋊Q8×C47C2311yescharacteristic
86#127×C47—21no—
87#127×C47C2311yescharacteristic
88#127×C47C2311yescharacteristic
89#127×C47C2311yescharacteristic
90#126×C47—41no—
91#124×C47—21no—
92#124×C47—21no—
93#124×C47—21no—
94#124×C47—21no—
95#124×C47—21no—
96#123×C47—41no—
97#123×C47—41no—
98C22⋊Q8×C47—21no—
99#121×C47—21no—
100#121×C47—41no—
101C4×Q8×C47—21no—
102C4×Q8×C47C2311yescharacteristic
103C4×Q8×C47C2311yescharacteristic
104C4×Q8×C47C2311yescharacteristic
105C4×D4×C47—21no—
106C4×D4×C47—21no—
107C4×D4×C47—21no—
108C4×D4×C47—21no—
109C4×D4×C47—21no—
110C4×D4×C47C2311yescharacteristic
111#117×C47—21no—
112#107×C47D411yescharacteristic
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×C47D411yescharacteristic
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—21no—
135#102×C47—41no—
136#102×C47D411yescharacteristic
137C22⋊C8×C47—21no—
138#97×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×C47C2×D411yescharacteristic
148C2×Q8×C47C2×D411yescharacteristic
149C2×Q8×C47C2×D411yescharacteristic
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—41no—
160C2×D4×C47—41no—
161C2×D4×C47C2×D411yescharacteristic
162C22×C4×C47—21no—
163C22×C4×C47—41no—
164C22×C4×C47—41no—
165C22×C4×C47—41no—
166Q16×C47—41no—
167Q16×C47—81no—
168SD16×C47—22no—
169SD16×C47—42no—
170SD16×C47—81no—
171SD16×C47—81no—
172SD16×C47—81no—
173SD16×C47—81no—
174SD16×C47—81no—
175D8×C47—42no—
176D8×C47—42no—
177D8×C47—81no—
178D8×C47—81no—
179D8×C47—81no—
180D8×C47—81no—
181D8×C47—82no—
182C2×C8×C47—21no—
183C2×C8×C47—21no—
184C2×C8×C47—21no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—81no—
188C2×C8×C47C2×D411yescharacteristic
189C2×C8×C47C2×D411yescharacteristic
190C2×C8×C47C2×D411yescharacteristic
191C2×C8×C47C2×D411yescharacteristic
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—41no—
198C4⋊C4×C47C2×D411yescharacteristic
199C4⋊C4×C47C2×D411yescharacteristic
200C4⋊C4×C47C2×D411yescharacteristic
201C4⋊C4×C47C2×D411yescharacteristic
202C22⋊C4×C47—21no—
203C22⋊C4×C47—41no—
204C22⋊C4×C47—41no—
205C22⋊C4×C47—41no—
206C22⋊C4×C47—41no—
207C22⋊C4×C47—41no—
208C22⋊C4×C47—41no—
209C22⋊C4×C47—41no—
210C22⋊C4×C47—41no—
211C22⋊C4×C47—41no—
212C42×C47—21no—
213C42×C47—21no—
214C42×C47—21no—
215C42×C47—41no—
216C42×C47C2411yescharacteristic
217C23×C47—21no—
218C23×C47—41no—
219C23×C47—41no—
220C23×C47—41no—
221Q8×C47—21no—
222Q8×C47—21no—
223Q8×C47—21no—
224Q8×C47—21no—
225Q8×C47—21no—
226Q8×C47—21no—
227Q8×C47—41no—
228Q8×C47—41no—
229D4×C47—21no—
230D4×C47—21no—
231D4×C47—41no—
232D4×C47—41no—
233D4×C47—41no—
234D4×C47—41no—
235D4×C47—41no—
236D4×C47—41no—
237D4×C47—41no—
238D4×C47—41no—
239D4×C47—41no—
240D4×C47—41no—
241D4×C47—41no—
242D4×C47—41no—
243D4×C47—81no—
244D4×C47—81no—
245D4×C47—81no—
246D4×C47—82no—
247D4×C47—161no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47—41no—
258C2×C4×C47—82no—
259C2×C4×C47—161no—
260C2×C4×C47—161no—
261C2×C4×C47C22×D411yescharacteristic
262C2×C4×C47C22×D411yescharacteristic
263C2×C4×C47H(5,𝔽2)11yescharacteristic
264C8×C47—21no—
265C8×C47—21no—
266C8×C47—21no—
267C8×C47—41no—
268C8×C47—41no—
269C8×C47—41no—
270C8×C47—41no—
271C8×C47—41no—
272C8×C47#13512yes—
273#19871C4711yesmaximal, characteristic, direct product factor, Sylow
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—81no—
278C22×C47—81no—
279C22×C47—81no—
280C22×C47—81no—
281C22×C47—81no—
282C22×C47—81no—
283C22×C47—81no—
284C22×C47—81no—
285C22×C47—81no—
286C22×C47D4211yescharacteristic
287C4×C47—21no—
288C4×C47—41no—
289C4×C47—41no—
290C4×C47—41no—
291C4×C47—41no—
292C4×C47—41no—
293C4×C47—41no—
294C4×C47—41no—
295C4×C47—81no—
296C4×C47C2×#13511yescharacteristic
297C4×C47#57511yescharacteristic
298C4×C47#57611yescharacteristic
299C4×C47#57611yescharacteristic
300#3399C2×C4711yescharacteristic, complemented
301#3396C2×C4711yescharacteristic, complemented
302#3394C2×C4711yescharacteristic, complemented
303#3304C2×C4711yescharacteristic, complemented
304#1721C2×C4711yescharacteristic, complemented
305#1686C2×C4711yescharacteristic, complemented
306#1682C2×C4711yescharacteristic, complemented
307#1668C2×C4711yescharacteristic, complemented
308#1667C2×C4711yescharacteristic, complemented
309#1640C2×C4711yescharacteristic, complemented
310#1628C2×C4711yescharacteristic, complemented
311#1621C2×C4711yescharacteristic, complemented
312#1620C2×C4711yescharacteristic, complemented
313#1584C2×C4711yescharacteristic, complemented
314SD16⋊C8C2×C4711yescharacteristic, complemented
315C2×C47—81no—
316C2×C47—161no—
317C2×C47—161no—
318C2×C47—161no—
319C2×C47#326811yescharacteristic
320C2×C47#328711yescharacteristic
321C2×C47#328811yescharacteristic
322#559C22×C4711yescharacteristic
323#559C22×C4711yescharacteristic
324#556C22×C4711yescharacteristic
325#550C22×C4711yescharacteristic
326#496—21no—
327#495—21no—
328#495—21no—
329#493C22×C4711yescharacteristic
330#493C22×C4711yescharacteristic
331#493C22×C4711yescharacteristic
332#492C22×C4711yescharacteristic
333#486C22×C4711yescharacteristic
334#486C22×C4711yescharacteristic
335#482—21no—
336#475C22×C4711yescharacteristic
337#465—21no—
338#464—21no—
339#463—21no—
340#463—21no—
341#463—21no—
342#463—21no—
343#462C22×C4711yescharacteristic
344#460C22×C4711yescharacteristic
345#460C22×C4711yescharacteristic
346#460C22×C4711yescharacteristic
347#460C22×C4711yescharacteristic
348#459—21no—
349#459C22×C4711yescharacteristic
350#459C22×C4711yescharacteristic
351#452—21no—
352#446C22×C4711yescharacteristic
353C8×Q8C22×C4711yescharacteristic
354C8×Q8C22×C4711yescharacteristic
355#442—21no—
356C4×Q16C22×C4711yescharacteristic
357C4×SD16—21no—
358C4×SD16C22×C4711yescharacteristic
359C4×D8—21no—
360C8×D4C22×C4711yescharacteristic
361#416—21no—
362#335C22×C4711yescharacteristic
363#335C22×C4711yescharacteristic
364#332C22×C4711yescharacteristic
365#331C22×C4711yescharacteristic
366#331C22×C4711yescharacteristic
367#331C22×C4711yescharacteristic
368Q8⋊C8C22×C4711yescharacteristic
369Q8⋊C8C22×C4711yescharacteristic
370Q8⋊C8C22×C4711yescharacteristic
371D4⋊C8C22×C4711yescharacteristic
372#322C22×C4711yescharacteristic
373C47#1987111yescharacteristic, direct product factor, Sylow
374C2×#41—21no—
375C2×Q16—21no—
376C2×Q16D4×C4711yescharacteristic
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16D4×C4711yescharacteristic
384C2×D8—21no—
385C2×D8—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—41no—
391C22×C8—21no—
392C4⋊Q8C23×C4711yescharacteristic
393#127—21no—
394#127C23×C4711yescharacteristic
395#127C23×C4711yescharacteristic
396#127C23×C4711yescharacteristic
397#126—41no—
398#124—21no—
399#124—21no—
400#124—21no—
401#124—21no—
402#124—21no—
403#123—41no—
404#123—41no—
405C22⋊Q8—21no—
406#121—21no—
407#121—41no—
408C4×Q8—21no—
409C4×Q8C23×C4711yescharacteristic
410C4×Q8C23×C4711yescharacteristic
411C4×Q8C23×C4711yescharacteristic
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4C23×C4711yescharacteristic
418#117—21no—
419#107D4×C4711yescharacteristic
420#106—21no—
421#106D4×C4711yescharacteristic
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8—21no—
425C4⋊C8C23×C4711yescharacteristic
426C4⋊C8C23×C4711yescharacteristic
427C4⋊C8C23×C4711yescharacteristic
428C4⋊C8C23×C4711yescharacteristic
429#103—21no—
430#103—21no—
431#103D4×C4711yescharacteristic
432#103D4×C4711yescharacteristic
433#103D4×C4711yescharacteristic
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—41no—
443#102D4×C4711yescharacteristic
444C22⋊C8—21no—
445#97—21no—
446C4×C8—21no—
447C4×C8—21no—
448C4×C8C23×C4711yescharacteristic
449C4×C8C23×C4711yescharacteristic
450C4×C8C23×C4711yescharacteristic
451#41—42no—
452#41—81no—
453C2×Q8—21no—
454C2×Q8C2×D4×C4711yescharacteristic
455C2×Q8C2×D4×C4711yescharacteristic
456C2×Q8C2×D4×C4711yescharacteristic
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4C2×D4×C4711yescharacteristic
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473Q16—41no—
474Q16—81no—
475SD16—22no—
476SD16—42no—
477SD16—81no—
478SD16—81no—
479SD16—81no—
480SD16—81no—
481SD16—81no—
482D8—42no—
483D8—42no—
484D8—81no—
485D8—81no—
486D8—81no—
487D8—81no—
488D8—82no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—81no—
495C2×C8C2×D4×C4711yescharacteristic
496C2×C8C2×D4×C4711yescharacteristic
497C2×C8C2×D4×C4711yescharacteristic
498C2×C8C2×D4×C4711yescharacteristic
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4C2×D4×C4711yescharacteristic
506C4⋊C4C2×D4×C4711yescharacteristic
507C4⋊C4C2×D4×C4711yescharacteristic
508C4⋊C4C2×D4×C4711yescharacteristic
509C22⋊C4—21no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—41no—
523C42C24×C4711yescharacteristic
524C23—21no—
525C23—41no—
526C23—41no—
527C23—41no—
528Q8—21no—
529Q8—21no—
530Q8—21no—
531Q8—21no—
532Q8—21no—
533Q8—21no—
534Q8—41no—
535Q8—41no—
536D4—21no—
537D4—21no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—81no—
551D4—81no—
552D4—81no—
553D4—82no—
554D4—161no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—82no—
566C2×C4—161no—
567C2×C4—161no—
568C2×C4C22×D4×C4711yescharacteristic
569C2×C4C22×D4×C4711yescharacteristic
570C2×C4H(5,𝔽2)×C4711yescharacteristic
571C8—21no—
572C8—21no—
573C8—21no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8#135×C4712yes—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22D42×C4711yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—81no—
602C4C2×#135×C4711yescharacteristic
603C4C47×#57511yescharacteristic
604C4C47×#57611yescharacteristic
605C4C47×#57611yescharacteristic
606C2—81no—
607C2—161no—
608C2—161no—
609C2—161no—
610C2C47×#326811yescharacteristic
611C2C47×#328711yescharacteristic
612C2C47×#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×#3399C2semidirect
2. C47×#3396C2semidirect
3. C47×#3394C2semidirect
4. C47×#3304C2semidirect
5. C47×#1721C2semidirect
6. C47×#1686C2semidirect
7. C47×#1682C2semidirect
8. C47×#1668C2semidirect
9. C47×#1667C2semidirect
10. C47×#1640C2semidirect
11. C47×#1628C2semidirect
12. C47×#1621C2semidirect
13. C47×#1620C2semidirect
14. C47×#1584C2semidirect
15. C47×SD16⋊C8C2semidirect
273. #19871C47direct (N × H)
300. #3399C2×C47semidirect
301. #3396C2×C47semidirect
302. #3394C2×C47semidirect
303. #3304C2×C47semidirect
304. #1721C2×C47semidirect
305. #1686C2×C47semidirect
306. #1682C2×C47semidirect
307. #1668C2×C47semidirect
308. #1667C2×C47semidirect
309. #1640C2×C47semidirect
310. #1628C2×C47semidirect
311. #1621C2×C47semidirect
312. #1620C2×C47semidirect
313. #1584C2×C47semidirect
314. SD16⋊C8C2×C47semidirect
373. C47#19871direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33992
C47×#33962
C47×#33942
C47×#33042
C47×#17212
C47×#16862
C47×#16822
C47×#16682
C47×#16672
C47×#16402
C47×#16282
C47×#16212
C47×#16202
C47×#15842
C47×SD16⋊C82
#1987147