Finite Group Databasebeta

← C47×#19792 #26059490

Subgroups — C47×#19792 #26059490

Order 12032.

624 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3366C211yesmaximal, characteristic, complemented
2C47×#3335C211yesmaximal, characteristic, complemented
3C47×#3305C211yesmaximal, characteristic, complemented
4C47×#3303C211yesmaximal, characteristic, complemented
5C47×#1720C211yesmaximal, characteristic, complemented
6C47×#1704C211yesmaximal, characteristic, complemented
7C47×#1677C211yesmaximal, characteristic, complemented
8C47×#1677C211yesmaximal, characteristic, complemented
9C47×#1671C211yesmaximal, characteristic, complemented
10C47×#1642C211yesmaximal, characteristic, complemented
11C47×#1634C211yesmaximal, characteristic, complemented
12C47×#1632C211yesmaximal, characteristic, complemented
13C47×#1625C211yesmaximal, characteristic, complemented
14C47×#1582C211yesmaximal, characteristic, complemented
15C47×#1580C211yesmaximal, characteristic, complemented
16C47×#555C2211yescharacteristic
17C47×#554C2211yescharacteristic
18C47×#550C2211yescharacteristic
19C47×#547C2211yescharacteristic
20C47×#498C2211yescharacteristic
21C47×#494C2211yescharacteristic
22C47×#490—21no—
23C47×#487C2211yescharacteristic
24C47×#486C2211yescharacteristic
25C47×#486C2211yescharacteristic
26C47×#486C2211yescharacteristic
27C47×#485—21no—
28C47×#483—21no—
29C47×#482—21no—
30C47×#481—21no—
31C47×#478—21no—
32C47×#477C2211yescharacteristic
33C47×#476C2211yescharacteristic
34C47×#476C2211yescharacteristic
35C47×#476C2211yescharacteristic
36C47×#475C2211yescharacteristic
37C47×#466—21no—
38C47×#465—21no—
39C47×#465—21no—
40C47×#461C2211yescharacteristic
41C47×#459—21no—
42C47×#459C2211yescharacteristic
43C47×#459C2211yescharacteristic
44C47×#449—21no—
45C47×#449—21no—
46C47×#446C2211yescharacteristic
47C47×#442—21no—
48C4×SD16×C47C2211yescharacteristic
49C4×D8×C47C2211yescharacteristic
50C8×D4×C47C2211yescharacteristic
51C8×D4×C47C2211yescharacteristic
52C8×D4×C47C2211yescharacteristic
53C2×#106×C47—21no—
54C47×#416—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×#41×C47—21no—
69C2×Q16×C47—41no—
70C2×SD16×C47—21no—
71C2×SD16×C47D411yescharacteristic
72C2×D8×C47—21no—
73C2×D8×C47—21no—
74C2×D8×C47D411yescharacteristic
75C22×C8×C47—21no—
76C22×C8×C47—21no—
77C22×C8×C47—21no—
78C4⋊Q8×C47C2311yescharacteristic
79C4⋊Q8×C47C2311yescharacteristic
80C4⋊Q8×C47C2311yescharacteristic
81#127×C47—21no—
82#127×C47C2311yescharacteristic
83#125×C47—21no—
84#124×C47—41no—
85#123×C47—41no—
86C22⋊Q8×C47—21no—
87C22⋊Q8×C47—21no—
88C22⋊Q8×C47—41no—
89#121×C47—21no—
90#121×C47—21no—
91#121×C47—21no—
92#121×C47—21no—
93#121×C47—41no—
94C4×Q8×C47C2311yescharacteristic
95C4×D4×C47—21no—
96C4×D4×C47—21no—
97C4×D4×C47C2311yescharacteristic
98C4×D4×C47C2311yescharacteristic
99C4×D4×C47C2311yescharacteristic
100#117×C47—21no—
101#117×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104#107×C47—21no—
105#107×C47D411yescharacteristic
106#106×C47—21no—
107#106×C47—21no—
108#106×C47—21no—
109#106×C47—21no—
110#106×C47—21no—
111#106×C47—21no—
112#106×C47D411yescharacteristic
113C4⋊C8×C47—21no—
114C4⋊C8×C47C2311yescharacteristic
115C4⋊C8×C47C2311yescharacteristic
116C4⋊C8×C47C2311yescharacteristic
117C4⋊C8×C47C2311yescharacteristic
118#103×C47—21no—
119#103×C47—21no—
120#103×C47—21no—
121#103×C47—21no—
122#103×C47—21no—
123#103×C47D411yescharacteristic
124#102×C47—21no—
125#102×C47—21no—
126#102×C47—21no—
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—41no—
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—42no—
146#41×C47—81no—
147#41×C47—81no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47—21no—
151C2×Q8×C47C2×D411yescharacteristic
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—41no—
156C2×D4×C47—41no—
157C2×D4×C47—41no—
158C2×D4×C47—41no—
159C2×D4×C47C2×D411yescharacteristic
160C2×D4×C47C2×D411yescharacteristic
161C2×D4×C47C2×D411yescharacteristic
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—41no—
166C22×C4×C47—41no—
167C22×C4×C47—41no—
168Q16×C47—82no—
169SD16×C47—41no—
170SD16×C47—81no—
171D8×C47—22no—
172D8×C47—42no—
173D8×C47—81no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47—42no—
180C2×C8×C47—81no—
181C2×C8×C47—81no—
182C2×C8×C47C2×D411yescharacteristic
183C2×C8×C47C2×D411yescharacteristic
184C2×C8×C47C2×D411yescharacteristic
185C2×C8×C47C2×D411yescharacteristic
186C4⋊C4×C47—21no—
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—41no—
194C4⋊C4×C47—41no—
195C4⋊C4×C47—41no—
196C4⋊C4×C47C2×D411yescharacteristic
197C4⋊C4×C47C2×D411yescharacteristic
198C4⋊C4×C47C2×D411yescharacteristic
199C4⋊C4×C47C2×D411yescharacteristic
200C22⋊C4×C47—21no—
201C22⋊C4×C47—21no—
202C22⋊C4×C47—21no—
203C22⋊C4×C47—41no—
204C22⋊C4×C47—41no—
205C22⋊C4×C47—41no—
206C22⋊C4×C47—41no—
207C22⋊C4×C47—41no—
208C42×C47—21no—
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—41no—
227D4×C47—41no—
228D4×C47—41no—
229D4×C47—41no—
230D4×C47—81no—
231D4×C47—82no—
232D4×C47—82no—
233D4×C47—161no—
234D4×C47—161no—
235D4×C47#13512yes—
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×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—21no—
260C8×C47—41no—
261C8×C47—41no—
262C8×C47—41no—
263C8×C47—41no—
264C8×C47—41no—
265#19792C4711yesmaximal, 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—41no—
273C22×C47—41no—
274C22×C47—41no—
275C22×C47—81no—
276C22×C47—81no—
277C22×C47—81no—
278C22×C47D4211yescharacteristic
279C4×C47—21no—
280C4×C47—41no—
281C4×C47—41no—
282C4×C47—41no—
283C4×C47—41no—
284C4×C47—41no—
285C4×C47—81no—
286C4×C47—81no—
287C4×C47—81no—
288C4×C47C2×#13511yescharacteristic
289C4×C47#57511yescharacteristic
290C4×C47#57711yescharacteristic
291C4×C47#57711yescharacteristic
292#3366C2×C4711yescharacteristic, complemented
293#3335C2×C4711yescharacteristic, complemented
294#3305C2×C4711yescharacteristic, complemented
295#3303C2×C4711yescharacteristic, complemented
296#1720C2×C4711yescharacteristic, complemented
297#1704C2×C4711yescharacteristic, complemented
298#1677C2×C4711yescharacteristic, complemented
299#1677C2×C4711yescharacteristic, complemented
300#1671C2×C4711yescharacteristic, complemented
301#1642C2×C4711yescharacteristic, complemented
302#1634C2×C4711yescharacteristic, complemented
303#1632C2×C4711yescharacteristic, complemented
304#1625C2×C4711yescharacteristic, complemented
305#1582C2×C4711yescharacteristic, complemented
306#1580C2×C4711yescharacteristic, complemented
307C2×C47—42no—
308C2×C47—81no—
309C2×C47—81no—
310C2×C47—161no—
311C2×C47#326711yescharacteristic
312C2×C47#328211yescharacteristic
313C2×C47#328811yescharacteristic
314#555C22×C4711yescharacteristic
315#554C22×C4711yescharacteristic
316#550C22×C4711yescharacteristic
317#547C22×C4711yescharacteristic
318#498C22×C4711yescharacteristic
319#494C22×C4711yescharacteristic
320#490—21no—
321#487C22×C4711yescharacteristic
322#486C22×C4711yescharacteristic
323#486C22×C4711yescharacteristic
324#486C22×C4711yescharacteristic
325#485—21no—
326#483—21no—
327#482—21no—
328#481—21no—
329#478—21no—
330#477C22×C4711yescharacteristic
331#476C22×C4711yescharacteristic
332#476C22×C4711yescharacteristic
333#476C22×C4711yescharacteristic
334#475C22×C4711yescharacteristic
335#466—21no—
336#465—21no—
337#465—21no—
338#461C22×C4711yescharacteristic
339#459—21no—
340#459C22×C4711yescharacteristic
341#459C22×C4711yescharacteristic
342#449—21no—
343#449—21no—
344#446C22×C4711yescharacteristic
345#442—21no—
346C4×SD16C22×C4711yescharacteristic
347C4×D8C22×C4711yescharacteristic
348C8×D4C22×C4711yescharacteristic
349C8×D4C22×C4711yescharacteristic
350C8×D4C22×C4711yescharacteristic
351C2×#106—21no—
352#416—21no—
353#416—21no—
354#334C22×C4711yescharacteristic
355#334C22×C4711yescharacteristic
356#333C22×C4711yescharacteristic
357#333C22×C4711yescharacteristic
358#332C22×C4711yescharacteristic
359#331C22×C4711yescharacteristic
360Q8⋊C8C22×C4711yescharacteristic
361D4⋊C8C22×C4711yescharacteristic
362D4⋊C8C22×C4711yescharacteristic
363D4⋊C8C22×C4711yescharacteristic
364#322C22×C4711yescharacteristic
365C47#1979211yescharacteristic, direct product factor, Sylow
366C2×#41—21no—
367C2×#41—21no—
368C2×Q16—41no—
369C2×SD16—21no—
370C2×SD16D4×C4711yescharacteristic
371C2×D8—21no—
372C2×D8—21no—
373C2×D8D4×C4711yescharacteristic
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C4⋊Q8C23×C4711yescharacteristic
378C4⋊Q8C23×C4711yescharacteristic
379C4⋊Q8C23×C4711yescharacteristic
380#127—21no—
381#127C23×C4711yescharacteristic
382#125—21no—
383#124—41no—
384#123—41no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—41no—
388#121—21no—
389#121—21no—
390#121—21no—
391#121—21no—
392#121—41no—
393C4×Q8C23×C4711yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C23×C4711yescharacteristic
397C4×D4C23×C4711yescharacteristic
398C4×D4C23×C4711yescharacteristic
399#117—21no—
400#117—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403#107—21no—
404#107D4×C4711yescharacteristic
405#106—21no—
406#106—21no—
407#106—21no—
408#106—21no—
409#106—21no—
410#106—21no—
411#106D4×C4711yescharacteristic
412C4⋊C8—21no—
413C4⋊C8C23×C4711yescharacteristic
414C4⋊C8C23×C4711yescharacteristic
415C4⋊C8C23×C4711yescharacteristic
416C4⋊C8C23×C4711yescharacteristic
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103D4×C4711yescharacteristic
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—41no—
433#102D4×C4711yescharacteristic
434#102D4×C4711yescharacteristic
435#102D4×C4711yescharacteristic
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439#97—21no—
440C4×C8C23×C4711yescharacteristic
441C4×C8C23×C4711yescharacteristic
442C4×C8C23×C4711yescharacteristic
443#41—42no—
444#41—42no—
445#41—81no—
446#41—81no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8C2×D4×C4711yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4C2×D4×C4711yescharacteristic
459C2×D4C2×D4×C4711yescharacteristic
460C2×D4C2×D4×C4711yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467Q16—82no—
468SD16—41no—
469SD16—81no—
470D8—22no—
471D8—42no—
472D8—81no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—42no—
479C2×C8—81no—
480C2×C8—81no—
481C2×C8C2×D4×C4711yescharacteristic
482C2×C8C2×D4×C4711yescharacteristic
483C2×C8C2×D4×C4711yescharacteristic
484C2×C8C2×D4×C4711yescharacteristic
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4C2×D4×C4711yescharacteristic
496C4⋊C4C2×D4×C4711yescharacteristic
497C4⋊C4C2×D4×C4711yescharacteristic
498C4⋊C4C2×D4×C4711yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C42—21no—
508C42—41no—
509C42C24×C4711yescharacteristic
510C23—21no—
511C23—21no—
512C23—21no—
513C23—41no—
514Q8—21no—
515Q8—21no—
516Q8—41no—
517Q8—41no—
518Q8—81no—
519Q8—81no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—81no—
530D4—82no—
531D4—82no—
532D4—161no—
533D4—161no—
534D4#135×C4712yes—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—82no—
550C2×C4—82no—
551C2×C4—161no—
552C2×C4C22×D4×C4711yescharacteristic
553C2×C4C22×D4×C4711yescharacteristic
554C2×C4H(5,𝔽2)×C4711yescharacteristic
555C8—21no—
556C8—21no—
557C8—21no—
558C8—21no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—41no—
564C22—22no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22D42×C4711yescharacteristic
577C4—21no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4C2×#135×C4711yescharacteristic
587C4C47×#57511yescharacteristic
588C4C47×#57711yescharacteristic
589C4C47×#57711yescharacteristic
590C2—42no—
591C2—81no—
592C2—81no—
593C2—161no—
594C2C47×#326711yescharacteristic
595C2C47×#328211yescharacteristic
596C2C47×#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×#3366C2semidirect
2. C47×#3335C2semidirect
3. C47×#3305C2semidirect
4. C47×#3303C2semidirect
5. C47×#1720C2semidirect
6. C47×#1704C2semidirect
7. C47×#1677C2semidirect
8. C47×#1677C2semidirect
9. C47×#1671C2semidirect
10. C47×#1642C2semidirect
11. C47×#1634C2semidirect
12. C47×#1632C2semidirect
13. C47×#1625C2semidirect
14. C47×#1582C2semidirect
15. C47×#1580C2semidirect
265. #19792C47direct (N × H)
292. #3366C2×C47semidirect
293. #3335C2×C47semidirect
294. #3305C2×C47semidirect
295. #3303C2×C47semidirect
296. #1720C2×C47semidirect
297. #1704C2×C47semidirect
298. #1677C2×C47semidirect
299. #1677C2×C47semidirect
300. #1671C2×C47semidirect
301. #1642C2×C47semidirect
302. #1634C2×C47semidirect
303. #1632C2×C47semidirect
304. #1625C2×C47semidirect
305. #1582C2×C47semidirect
306. #1580C2×C47semidirect
365. C47#19792direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33662
C47×#33352
C47×#33052
C47×#33032
C47×#17202
C47×#17042
C47×#16772
C47×#16712
C47×#16422
C47×#16342
C47×#16322
C47×#16252
C47×#15822
C47×#15802
#1979247