Finite Group Databasebeta

← C47×#19768 #26059466

Subgroups — C47×#19768 #26059466

Order 12032.

642 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3385C211yesmaximal, characteristic, complemented
2C47×#3362C211yesmaximal, characteristic, complemented
3C47×#3335C211yesmaximal, characteristic, complemented
4C47×#3284C211yesmaximal, characteristic
5C47×#1714C211yesmaximal, characteristic, complemented
6C47×#1686C211yesmaximal, characteristic, complemented
7C47×#1677C211yesmaximal, characteristic, complemented
8C47×#1675C211yesmaximal, characteristic, complemented
9C47×#1672C211yesmaximal, characteristic, complemented
10C47×#1645C211yesmaximal, characteristic, complemented
11C47×#1635C211yesmaximal, characteristic, complemented
12C47×#1631C211yesmaximal, characteristic, complemented
13C47×#1622C211yesmaximal, characteristic, complemented
14C47×#1582C211yesmaximal, characteristic, complemented
15C47×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×#135×C47—21no—
17Q82×C47C2211yescharacteristic
18C47×#554C2211yescharacteristic
19C47×#550C2211yescharacteristic
20C47×#547C2211yescharacteristic
21C47×#501—21no—
22C47×#500C2211yescharacteristic
23C47×#498C2211yescharacteristic
24C47×#492C2211yescharacteristic
25C47×#492C2211yescharacteristic
26C47×#487C2211yescharacteristic
27C47×#486—21no—
28C47×#486C2211yescharacteristic
29C47×#483—21no—
30C47×#481—21no—
31C47×#479—21no—
32C47×#477C2211yescharacteristic
33C47×#476—21no—
34C47×#476C2211yescharacteristic
35C47×#476C2211yescharacteristic
36C47×#476C2211yescharacteristic
37C47×#475C2211yescharacteristic
38C47×#474—21no—
39C47×#465—21no—
40C47×#465—21no—
41C47×#462C2211yescharacteristic
42C47×#460—21no—
43C47×#460C2211yescharacteristic
44C47×#459C2211yescharacteristic
45C47×#452—21no—
46C47×#449—21no—
47C47×#446C2211yescharacteristic
48C8×Q8×C47C2211yescharacteristic
49C47×#440—21no—
50C4×SD16×C47—21no—
51C4×SD16×C47C2211yescharacteristic
52C4×SD16×C47C2211yescharacteristic
53C8×D4×C47C2211yescharacteristic
54C8×D4×C47C2211yescharacteristic
55C2×#106×C47—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×#41×C47—21no—
69#135×C47—44no—
70C2×Q16×C47—21no—
71C2×SD16×C47—21no—
72C2×SD16×C47—21no—
73C2×SD16×C47—21no—
74C2×SD16×C47—41no—
75C2×SD16×C47D411yescharacteristic
76C2×SD16×C47D411yescharacteristic
77C2×D8×C47—21no—
78C22×C8×C47—21no—
79C22×C8×C47—21no—
80C4⋊Q8×C47—21no—
81C4⋊Q8×C47—21no—
82C4⋊Q8×C47—41no—
83C4⋊Q8×C47C2311yescharacteristic
84C4⋊Q8×C47C2311yescharacteristic
85C4⋊Q8×C47C2311yescharacteristic
86#127×C47—21no—
87#127×C47C2311yescharacteristic
88#125×C47—21no—
89#123×C47—41no—
90C22⋊Q8×C47—21no—
91C22⋊Q8×C47—21no—
92C22⋊Q8×C47—41no—
93#121×C47—21no—
94#121×C47—21no—
95#121×C47—41no—
96C4×Q8×C47—21no—
97C4×Q8×C47—21no—
98C4×Q8×C47C2311yescharacteristic
99C4×Q8×C47C2311yescharacteristic
100C4×D4×C47—21no—
101C4×D4×C47—21no—
102C4×D4×C47C2311yescharacteristic
103C4×D4×C47C2311yescharacteristic
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106#107×C47—21no—
107#107×C47—21no—
108#107×C47—21no—
109#106×C47—21no—
110#106×C47—21no—
111#106×C47—21no—
112#106×C47—21no—
113#106×C47—21no—
114#106×C47—21no—
115#106×C47D411yescharacteristic
116#106×C47D411yescharacteristic
117C4⋊C8×C47—21no—
118C4⋊C8×C47—21no—
119C4⋊C8×C47C2311yescharacteristic
120C4⋊C8×C47C2311yescharacteristic
121C4⋊C8×C47C2311yescharacteristic
122C4⋊C8×C47C2311yescharacteristic
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×C47—21no—
136#102×C47D411yescharacteristic
137#102×C47D411yescharacteristic
138C22⋊C8×C47—21no—
139C22⋊C8×C47—21no—
140#97×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
145#41×C47—42no—
146#41×C47—42no—
147#41×C47—81no—
148#41×C47—81no—
149C2×Q8×C47—21no—
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C2×Q8×C47—41no—
153C2×Q8×C47C2×D411yescharacteristic
154C2×Q8×C47C2×D411yescharacteristic
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—41no—
159C2×D4×C47—41no—
160C2×D4×C47—41no—
161C2×D4×C47C2×D411yescharacteristic
162C2×D4×C47C2×D411yescharacteristic
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—41no—
166C22×C4×C47—41no—
167C22×C4×C47—41no—
168Q16×C47—42no—
169SD16×C47—41no—
170SD16×C47—42no—
171SD16×C47—42no—
172SD16×C47—81no—
173SD16×C47—82no—
174SD16×C47SD1614yescomplemented
175D8×C47—42no—
176C2×C8×C47—21no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47—42no—
182C2×C8×C47—42no—
183C2×C8×C47C2×D411yescharacteristic
184C2×C8×C47C2×D411yescharacteristic
185C2×C8×C47C2×D411yescharacteristic
186C2×C8×C47C2×D411yescharacteristic
187C4⋊C4×C47—21no—
188C4⋊C4×C47—21no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47—21no—
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—41no—
196C4⋊C4×C47—41no—
197C4⋊C4×C47—41no—
198C4⋊C4×C47—41no—
199C4⋊C4×C47—41no—
200C4⋊C4×C47C2×D411yescharacteristic
201C4⋊C4×C47C2×D411yescharacteristic
202C4⋊C4×C47C2×D411yescharacteristic
203C4⋊C4×C47C2×D411yescharacteristic
204C22⋊C4×C47—21no—
205C22⋊C4×C47—21no—
206C22⋊C4×C47—41no—
207C22⋊C4×C47—41no—
208C22⋊C4×C47—41no—
209C42×C47—21no—
210C42×C47—21no—
211C42×C47—41no—
212C42×C47C2411yescharacteristic
213C23×C47—21no—
214C23×C47—21no—
215C23×C47—41no—
216Q8×C47—21no—
217Q8×C47—21no—
218Q8×C47—21no—
219Q8×C47—41no—
220Q8×C47—41no—
221Q8×C47—81no—
222Q8×C47—81no—
223Q8×C47—161no—
224Q8×C47C2×SD1612yes—
225D4×C47—21no—
226D4×C47—21no—
227D4×C47—21no—
228D4×C47—41no—
229D4×C47—41no—
230D4×C47—41no—
231D4×C47—41no—
232D4×C47—82no—
233D4×C47—81no—
234D4×C47—82no—
235D4×C47—161no—
236D4×C47C2×SD1612yes—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
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×C47—82no—
252C2×C4×C47—161no—
253C2×C4×C47C22×D411yescharacteristic
254C2×C4×C47C22×D411yescharacteristic
255C2×C4×C47H(5,𝔽2)11yescharacteristic
256C8×C47—21no—
257C8×C47—21no—
258C8×C47—21no—
259C8×C47—41no—
260C8×C47—41no—
261C8×C47—41no—
262C8×C47—41no—
263C8×C47—41no—
264C8×C47C2×SD1612yes—
265#19768C4711yesmaximal, characteristic, direct product factor, Sylow
266C22×C47—22no—
267C22×C47—41no—
268C22×C47—41no—
269C22×C47—41no—
270C22×C47—41no—
271C22×C47—41no—
272C22×C47—81no—
273C22×C47—81no—
274C22×C47—81no—
275C22×C47D4211yescharacteristic
276C4×C47—22no—
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×C47C22×SD1611yescharacteristic
287C4×C47#57511yescharacteristic
288C4×C47#57711yescharacteristic
289C4×C47#57811yescharacteristic
290#3385C2×C4711yescharacteristic, complemented
291#3362C2×C4711yescharacteristic, complemented
292#3335C2×C4711yescharacteristic, complemented
293#3284C2×C4711yescharacteristic
294#1714C2×C4711yescharacteristic, complemented
295#1686C2×C4711yescharacteristic, complemented
296#1677C2×C4711yescharacteristic, complemented
297#1675C2×C4711yescharacteristic, complemented
298#1672C2×C4711yescharacteristic, complemented
299#1645C2×C4711yescharacteristic, complemented
300#1635C2×C4711yescharacteristic, complemented
301#1631C2×C4711yescharacteristic, complemented
302#1622C2×C4711yescharacteristic, complemented
303#1582C2×C4711yescharacteristic, complemented
304SD16⋊C8C2×C4711yescharacteristic, complemented
305C2×C47—42no—
306C2×C47—81no—
307C2×C47—161no—
308C2×C47#326911yescharacteristic
309C2×C47D4×SD1611yescharacteristic
310C2×C47#328811yescharacteristic
311C2×#135—21no—
312Q82C22×C4711yescharacteristic
313#554C22×C4711yescharacteristic
314#550C22×C4711yescharacteristic
315#547C22×C4711yescharacteristic
316#501—21no—
317#500C22×C4711yescharacteristic
318#498C22×C4711yescharacteristic
319#492C22×C4711yescharacteristic
320#492C22×C4711yescharacteristic
321#487C22×C4711yescharacteristic
322#486—21no—
323#486C22×C4711yescharacteristic
324#483—21no—
325#481—21no—
326#479—21no—
327#477C22×C4711yescharacteristic
328#476—21no—
329#476C22×C4711yescharacteristic
330#476C22×C4711yescharacteristic
331#476C22×C4711yescharacteristic
332#475C22×C4711yescharacteristic
333#474—21no—
334#465—21no—
335#465—21no—
336#462C22×C4711yescharacteristic
337#460—21no—
338#460C22×C4711yescharacteristic
339#459C22×C4711yescharacteristic
340#452—21no—
341#449—21no—
342#446C22×C4711yescharacteristic
343C8×Q8C22×C4711yescharacteristic
344#440—21no—
345C4×SD16—21no—
346C4×SD16C22×C4711yescharacteristic
347C4×SD16C22×C4711yescharacteristic
348C8×D4C22×C4711yescharacteristic
349C8×D4C22×C4711yescharacteristic
350C2×#106—21no—
351#335C22×C4711yescharacteristic
352#334C22×C4711yescharacteristic
353#333C22×C4711yescharacteristic
354#333C22×C4711yescharacteristic
355#332C22×C4711yescharacteristic
356#331C22×C4711yescharacteristic
357Q8⋊C8C22×C4711yescharacteristic
358Q8⋊C8C22×C4711yescharacteristic
359D4⋊C8C22×C4711yescharacteristic
360D4⋊C8C22×C4711yescharacteristic
361#322C22×C4711yescharacteristic
362C47#1976811yescharacteristic, direct product factor, Sylow
363C2×#41—21no—
364C2×#41—21no—
365#135—44no—
366C2×Q16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—41no—
371C2×SD16D4×C4711yescharacteristic
372C2×SD16D4×C4711yescharacteristic
373C2×D8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C4⋊Q8—21no—
377C4⋊Q8—21no—
378C4⋊Q8—41no—
379C4⋊Q8C23×C4711yescharacteristic
380C4⋊Q8C23×C4711yescharacteristic
381C4⋊Q8C23×C4711yescharacteristic
382#127—21no—
383#127C23×C4711yescharacteristic
384#125—21no—
385#123—41no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—41no—
389#121—21no—
390#121—21no—
391#121—41no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8C23×C4711yescharacteristic
395C4×Q8C23×C4711yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4C23×C4711yescharacteristic
399C4×D4C23×C4711yescharacteristic
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402#107—21no—
403#107—21no—
404#107—21no—
405#106—21no—
406#106—21no—
407#106—21no—
408#106—21no—
409#106—21no—
410#106—21no—
411#106D4×C4711yescharacteristic
412#106D4×C4711yescharacteristic
413C4⋊C8—21no—
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#103D4×C4711yescharacteristic
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102D4×C4711yescharacteristic
433#102D4×C4711yescharacteristic
434C22⋊C8—21no—
435C22⋊C8—21no—
436#97—21no—
437C4×C8—21no—
438C4×C8C23×C4711yescharacteristic
439C4×C8C23×C4711yescharacteristic
440C4×C8C23×C4711yescharacteristic
441#41—42no—
442#41—42no—
443#41—81no—
444#41—81no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—41no—
449C2×Q8C2×D4×C4711yescharacteristic
450C2×Q8C2×D4×C4711yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4C2×D4×C4711yescharacteristic
458C2×D4C2×D4×C4711yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464Q16—42no—
465SD16—41no—
466SD16—42no—
467SD16—42no—
468SD16—81no—
469SD16—82no—
470SD16SD16×C4714yescomplemented
471D8—42no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—42no—
478C2×C8—42no—
479C2×C8C2×D4×C4711yescharacteristic
480C2×C8C2×D4×C4711yescharacteristic
481C2×C8C2×D4×C4711yescharacteristic
482C2×C8C2×D4×C4711yescharacteristic
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4C2×D4×C4711yescharacteristic
497C4⋊C4C2×D4×C4711yescharacteristic
498C4⋊C4C2×D4×C4711yescharacteristic
499C4⋊C4C2×D4×C4711yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C42—21no—
506C42—21no—
507C42—41no—
508C42C24×C4711yescharacteristic
509C23—21no—
510C23—21no—
511C23—41no—
512Q8—21no—
513Q8—21no—
514Q8—21no—
515Q8—41no—
516Q8—41no—
517Q8—81no—
518Q8—81no—
519Q8—161no—
520Q8C2×SD16×C4712yes—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—82no—
529D4—81no—
530D4—82no—
531D4—161no—
532D4C2×SD16×C4712yes—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—82no—
547C2×C4—82no—
548C2×C4—161no—
549C2×C4C22×D4×C4711yescharacteristic
550C2×C4C22×D4×C4711yescharacteristic
551C2×C4H(5,𝔽2)×C4711yescharacteristic
552C8—21no—
553C8—21no—
554C8—21no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8C2×SD16×C4712yes—
561C22—22no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22D42×C4711yescharacteristic
571C4—21no—
572C4—22no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4C22×SD16×C4711yescharacteristic
582C4C47×#57511yescharacteristic
583C4C47×#57711yescharacteristic
584C4C47×#57811yescharacteristic
585C2—42no—
586C2—81no—
587C2—161no—
588C2C47×#326911yescharacteristic
589C2D4×SD16×C4711yescharacteristic
590C2C47×#328811yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3284C2
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×#3385C2semidirect
2. C47×#3362C2semidirect
3. C47×#3335C2semidirect
5. C47×#1714C2semidirect
6. C47×#1686C2semidirect
7. C47×#1677C2semidirect
8. C47×#1675C2semidirect
9. C47×#1672C2semidirect
10. C47×#1645C2semidirect
11. C47×#1635C2semidirect
12. C47×#1631C2semidirect
13. C47×#1622C2semidirect
14. C47×#1582C2semidirect
15. C47×SD16⋊C8C2semidirect
174. SD16×C47SD16semidirect
265. #19768C47direct (N × H)
290. #3385C2×C47semidirect
291. #3362C2×C47semidirect
292. #3335C2×C47semidirect
294. #1714C2×C47semidirect
295. #1686C2×C47semidirect
296. #1677C2×C47semidirect
297. #1675C2×C47semidirect
298. #1672C2×C47semidirect
299. #1645C2×C47semidirect
300. #1635C2×C47semidirect
301. #1631C2×C47semidirect
302. #1622C2×C47semidirect
303. #1582C2×C47semidirect
304. SD16⋊C8C2×C47semidirect
362. C47#19768direct (N × H)
470. SD16SD16×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#33852
C47×#33622
C47×#33352
C47×#32842
C47×#17142
C47×#16862
C47×#16772
C47×#16752
C47×#16722
C47×#16452
C47×#16352
C47×#16312
C47×#16222
C47×#15822
C47×SD16⋊C82
#1976847