Finite Group Databasebeta

← C47×#19880 #26059578

Subgroups — C47×#19880 #26059578

Order 12032.

588 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3394C211yesmaximal, characteristic, complemented
2C47×#3361C211yesmaximal, characteristic, complemented
3C47×#3357C211yesmaximal, characteristic, complemented
4C47×#3340C211yesmaximal, characteristic, complemented
5C47×#1714C211yesmaximal, characteristic, complemented
6C47×#1685C211yesmaximal, characteristic, complemented
7C47×#1677C211yesmaximal, characteristic, complemented
8C47×#1676C211yesmaximal, characteristic, complemented
9C47×#1672C211yesmaximal, characteristic, complemented
10C47×#1644C211yesmaximal, characteristic, complemented
11C47×#1638C211yesmaximal, characteristic, complemented
12C47×#1630C211yesmaximal, characteristic, complemented
13C47×#1624C211yesmaximal, characteristic
14C47×#1583C211yesmaximal, characteristic, complemented
15C47×SD16⋊C8C211yesmaximal, characteristic, complemented
16C47×#559C2211yescharacteristic
17C47×#556C2211yescharacteristic
18C47×#555C2211yescharacteristic
19C47×#554C2211yescharacteristic
20C47×#500C2211yescharacteristic
21C47×#498C2211yescharacteristic
22C47×#495—21no—
23C47×#492C2211yescharacteristic
24C47×#492C2211yescharacteristic
25C47×#488—21no—
26C47×#487C2211yescharacteristic
27C47×#486C2211yescharacteristic
28C47×#485—21no—
29C47×#485—21no—
30C47×#482—21no—
31C47×#480—21no—
32C47×#478—21no—
33C47×#477C2211yescharacteristic
34C47×#477C2211yescharacteristic
35C47×#477C2211yescharacteristic
36C47×#476C2211yescharacteristic
37C47×#474C2211yescharacteristic
38C47×#468—21no—
39C47×#465—21no—
40C47×#464—21no—
41C47×#463—21no—
42C47×#463—21no—
43C47×#462C2211yescharacteristic
44C47×#459C2211yescharacteristic
45C47×#459C2211yescharacteristic
46C8×Q8×C47C2211yescharacteristic
47C8×Q8×C47C2211yescharacteristic
48C4×SD16×C47—21no—
49C4×SD16×C47C2211yescharacteristic
50C4×SD16×C47C2211yescharacteristic
51C4×D8×C47—21no—
52C47×#436C2211yescharacteristic
53C8×D4×C47C2211yescharacteristic
54C47×#428—21no—
55C47×#427—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×Q16×C47—21no—
68C2×SD16×C47—21no—
69C2×SD16×C47—21no—
70C2×SD16×C47—41no—
71C2×SD16×C47D411yescharacteristic
72C2×SD16×C47D411yescharacteristic
73C2×D8×C47—21no—
74C2×D8×C47—21no—
75C2×M16×C47—21no—
76C22×C8×C47—21no—
77C4⋊Q8×C47C2311yescharacteristic
78C4⋊Q8×C47C2311yescharacteristic
79C4⋊Q8×C47C2311yescharacteristic
80#127×C47C2311yescharacteristic
81#126×C47—41no—
82#125×C47—21no—
83#124×C47—21no—
84#124×C47—21no—
85#124×C47—21no—
86#124×C47—41no—
87#123×C47—41no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47—21no—
90C22⋊Q8×C47—41no—
91#121×C47—21no—
92#121×C47—21no—
93C4×Q8×C47—21no—
94C4×Q8×C47C2311yescharacteristic
95C4×Q8×C47C2311yescharacteristic
96C4×D4×C47—21no—
97C4×D4×C47—21no—
98C4×D4×C47—21no—
99C4×D4×C47C2311yescharacteristic
100C4×D4×C47C2311yescharacteristic
101#117×C47—21no—
102#117×C47—21no—
103#117×C47—21no—
104C2×C4⋊C4×C47—21no—
105#107×C47—21no—
106#107×C47—21no—
107#107×C47—21no—
108#107×C47—21no—
109#107×C47—21no—
110#107×C47—21no—
111#106×C47—21no—
112#106×C47—21no—
113#106×C47—21no—
114#106×C47D411yescharacteristic
115#106×C47D411yescharacteristic
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×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×C47D411yescharacteristic
136#102×C47D411yescharacteristic
137C22⋊C8×C47—21no—
138C22⋊C8×C47—21no—
139C4×C8×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47C2×D411yescharacteristic
148C2×Q8×C47C2×D411yescharacteristic
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—41no—
153C2×D4×C47C2×D411yescharacteristic
154C2×D4×C47C2×D411yescharacteristic
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—41no—
158C22×C4×C47—41no—
159Q16×C47—81no—
160SD16×C47—22no—
161SD16×C47—41no—
162SD16×C47—42no—
163SD16×C47—81no—
164SD16×C47—82no—
165D8×C47—42no—
166D8×C47—81no—
167M16×C47—42no—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C2×C8×C47—21no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—42no—
174C2×C8×C47C2×D411yescharacteristic
175C2×C8×C47C2×D411yescharacteristic
176C2×C8×C47C2×D411yescharacteristic
177C2×C8×C47C2×D411yescharacteristic
178C4⋊C4×C47—21no—
179C4⋊C4×C47—21no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—21no—
182C4⋊C4×C47—21no—
183C4⋊C4×C47—21no—
184C4⋊C4×C47—21no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—41no—
187C4⋊C4×C47—41no—
188C4⋊C4×C47—41no—
189C4⋊C4×C47C2×D411yescharacteristic
190C4⋊C4×C47C2×D411yescharacteristic
191C4⋊C4×C47C2×D411yescharacteristic
192C4⋊C4×C47C2×D411yescharacteristic
193C22⋊C4×C47—21no—
194C22⋊C4×C47—21no—
195C22⋊C4×C47—41no—
196C22⋊C4×C47—41no—
197C22⋊C4×C47—41no—
198C22⋊C4×C47—41no—
199C22⋊C4×C47—41no—
200C22⋊C4×C47—41no—
201C22⋊C4×C47—41no—
202C22⋊C4×C47—41no—
203C42×C47—21no—
204C42×C47—21no—
205C42×C47—41no—
206C42×C47—41no—
207C42×C47C2411yescharacteristic
208C23×C47—21no—
209C23×C47—21no—
210C23×C47—41no—
211Q8×C47—21no—
212Q8×C47—21no—
213Q8×C47—21no—
214Q8×C47—21no—
215Q8×C47—41no—
216Q8×C47—41no—
217Q8×C47—81no—
218Q8×C47—81no—
219D4×C47—21no—
220D4×C47—21no—
221D4×C47—21no—
222D4×C47—21no—
223D4×C47—41no—
224D4×C47—41no—
225D4×C47—41no—
226D4×C47—41no—
227D4×C47—81no—
228D4×C47—161no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—161no—
243C2×C4×C47—161no—
244C2×C4×C47C22×D411yescharacteristic
245C2×C4×C47C22×D411yescharacteristic
246C2×C4×C47H(5,𝔽2)11yescharacteristic
247C8×C47—21no—
248C8×C47—21no—
249C8×C47—21no—
250C8×C47—41no—
251C8×C47—41no—
252C8×C47—41no—
253C8×C47—41no—
254C8×C47—41no—
255C8×C47#13512yes—
256#19880C4711yesmaximal, characteristic, direct product factor, Sylow
257C22×C47—41no—
258C22×C47—41no—
259C22×C47—41no—
260C22×C47—41no—
261C22×C47—41no—
262C22×C47—41no—
263C22×C47—81no—
264C22×C47—81no—
265C22×C47—81no—
266C22×C47D4211yescharacteristic
267C4×C47—21no—
268C4×C47—41no—
269C4×C47—41no—
270C4×C47—41no—
271C4×C47—41no—
272C4×C47—41no—
273C4×C47—41no—
274C4×C47—81no—
275C4×C47—81no—
276C4×C47—81no—
277C4×C47C2×#13511yescharacteristic
278C4×C47#57511yescharacteristic
279C4×C47#57711yescharacteristic
280C4×C47#57811yescharacteristic
281#3394C2×C4711yescharacteristic, complemented
282#3361C2×C4711yescharacteristic, complemented
283#3357C2×C4711yescharacteristic, complemented
284#3340C2×C4711yescharacteristic, complemented
285#1714C2×C4711yescharacteristic, complemented
286#1685C2×C4711yescharacteristic, complemented
287#1677C2×C4711yescharacteristic, complemented
288#1676C2×C4711yescharacteristic, complemented
289#1672C2×C4711yescharacteristic, complemented
290#1644C2×C4711yescharacteristic, complemented
291#1638C2×C4711yescharacteristic, complemented
292#1630C2×C4711yescharacteristic, complemented
293#1624C2×C4711yescharacteristic
294#1583C2×C4711yescharacteristic, complemented
295SD16⋊C8C2×C4711yescharacteristic, complemented
296C2×C47—81no—
297C2×C47—81no—
298C2×C47—161no—
299C2×C47#326911yescharacteristic
300C2×C47#328411yescharacteristic
301C2×C47#328811yescharacteristic
302#559C22×C4711yescharacteristic
303#556C22×C4711yescharacteristic
304#555C22×C4711yescharacteristic
305#554C22×C4711yescharacteristic
306#500C22×C4711yescharacteristic
307#498C22×C4711yescharacteristic
308#495—21no—
309#492C22×C4711yescharacteristic
310#492C22×C4711yescharacteristic
311#488—21no—
312#487C22×C4711yescharacteristic
313#486C22×C4711yescharacteristic
314#485—21no—
315#485—21no—
316#482—21no—
317#480—21no—
318#478—21no—
319#477C22×C4711yescharacteristic
320#477C22×C4711yescharacteristic
321#477C22×C4711yescharacteristic
322#476C22×C4711yescharacteristic
323#474C22×C4711yescharacteristic
324#468—21no—
325#465—21no—
326#464—21no—
327#463—21no—
328#463—21no—
329#462C22×C4711yescharacteristic
330#459C22×C4711yescharacteristic
331#459C22×C4711yescharacteristic
332C8×Q8C22×C4711yescharacteristic
333C8×Q8C22×C4711yescharacteristic
334C4×SD16—21no—
335C4×SD16C22×C4711yescharacteristic
336C4×SD16C22×C4711yescharacteristic
337C4×D8—21no—
338#436C22×C4711yescharacteristic
339C8×D4C22×C4711yescharacteristic
340#428—21no—
341#427—21no—
342#335C22×C4711yescharacteristic
343#334C22×C4711yescharacteristic
344#333C22×C4711yescharacteristic
345#333C22×C4711yescharacteristic
346#332C22×C4711yescharacteristic
347#331C22×C4711yescharacteristic
348Q8⋊C8C22×C4711yescharacteristic
349Q8⋊C8C22×C4711yescharacteristic
350D4⋊C8C22×C4711yescharacteristic
351D4⋊C8C22×C4711yescharacteristic
352#322C22×C4711yescharacteristic
353C47#1988011yescharacteristic, direct product factor, Sylow
354C2×Q16—21no—
355C2×SD16—21no—
356C2×SD16—21no—
357C2×SD16—41no—
358C2×SD16D4×C4711yescharacteristic
359C2×SD16D4×C4711yescharacteristic
360C2×D8—21no—
361C2×D8—21no—
362C2×M16—21no—
363C22×C8—21no—
364C4⋊Q8C23×C4711yescharacteristic
365C4⋊Q8C23×C4711yescharacteristic
366C4⋊Q8C23×C4711yescharacteristic
367#127C23×C4711yescharacteristic
368#126—41no—
369#125—21no—
370#124—21no—
371#124—21no—
372#124—21no—
373#124—41no—
374#123—41no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—41no—
378#121—21no—
379#121—21no—
380C4×Q8—21no—
381C4×Q8C23×C4711yescharacteristic
382C4×Q8C23×C4711yescharacteristic
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4C23×C4711yescharacteristic
387C4×D4C23×C4711yescharacteristic
388#117—21no—
389#117—21no—
390#117—21no—
391C2×C4⋊C4—21no—
392#107—21no—
393#107—21no—
394#107—21no—
395#107—21no—
396#107—21no—
397#107—21no—
398#106—21no—
399#106—21no—
400#106—21no—
401#106D4×C4711yescharacteristic
402#106D4×C4711yescharacteristic
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8C23×C4711yescharacteristic
406C4⋊C8C23×C4711yescharacteristic
407C4⋊C8C23×C4711yescharacteristic
408C4⋊C8C23×C4711yescharacteristic
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—41no—
414#103D4×C4711yescharacteristic
415#103D4×C4711yescharacteristic
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102D4×C4711yescharacteristic
423#102D4×C4711yescharacteristic
424C22⋊C8—21no—
425C22⋊C8—21no—
426C4×C8—21no—
427C4×C8—21no—
428C4×C8C23×C4711yescharacteristic
429C4×C8C23×C4711yescharacteristic
430C4×C8C23×C4711yescharacteristic
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8C2×D4×C4711yescharacteristic
435C2×Q8C2×D4×C4711yescharacteristic
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—41no—
440C2×D4C2×D4×C4711yescharacteristic
441C2×D4C2×D4×C4711yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—41no—
445C22×C4—41no—
446Q16—81no—
447SD16—22no—
448SD16—41no—
449SD16—42no—
450SD16—81no—
451SD16—82no—
452D8—42no—
453D8—81no—
454M16—42no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—42no—
461C2×C8C2×D4×C4711yescharacteristic
462C2×C8C2×D4×C4711yescharacteristic
463C2×C8C2×D4×C4711yescharacteristic
464C2×C8C2×D4×C4711yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4C2×D4×C4711yescharacteristic
477C4⋊C4C2×D4×C4711yescharacteristic
478C4⋊C4C2×D4×C4711yescharacteristic
479C4⋊C4C2×D4×C4711yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C42—21no—
491C42—21no—
492C42—41no—
493C42—41no—
494C42C24×C4711yescharacteristic
495C23—21no—
496C23—21no—
497C23—41no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—21no—
502Q8—41no—
503Q8—41no—
504Q8—81no—
505Q8—81no—
506D4—21no—
507D4—21no—
508D4—21no—
509D4—21no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—81no—
515D4—161no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—161no—
530C2×C4—161no—
531C2×C4C22×D4×C4711yescharacteristic
532C2×C4C22×D4×C4711yescharacteristic
533C2×C4H(5,𝔽2)×C4711yescharacteristic
534C8—21no—
535C8—21no—
536C8—21no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8#135×C4712yes—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22D42×C4711yescharacteristic
553C4—21no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4C2×#135×C4711yescharacteristic
564C4C47×#57511yescharacteristic
565C4C47×#57711yescharacteristic
566C4C47×#57811yescharacteristic
567C2—81no—
568C2—81no—
569C2—161no—
570C2C47×#326911yescharacteristic
571C2C47×#328411yescharacteristic
572C2C47×#328811yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#1624C2
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×#3394C2semidirect
2. C47×#3361C2semidirect
3. C47×#3357C2semidirect
4. C47×#3340C2semidirect
5. C47×#1714C2semidirect
6. C47×#1685C2semidirect
7. C47×#1677C2semidirect
8. C47×#1676C2semidirect
9. C47×#1672C2semidirect
10. C47×#1644C2semidirect
11. C47×#1638C2semidirect
12. C47×#1630C2semidirect
14. C47×#1583C2semidirect
15. C47×SD16⋊C8C2semidirect
256. #19880C47direct (N × H)
281. #3394C2×C47semidirect
282. #3361C2×C47semidirect
283. #3357C2×C47semidirect
284. #3340C2×C47semidirect
285. #1714C2×C47semidirect
286. #1685C2×C47semidirect
287. #1677C2×C47semidirect
288. #1676C2×C47semidirect
289. #1672C2×C47semidirect
290. #1644C2×C47semidirect
291. #1638C2×C47semidirect
292. #1630C2×C47semidirect
294. #1583C2×C47semidirect
295. SD16⋊C8C2×C47semidirect
353. C47#19880direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33942
C47×#33612
C47×#33572
C47×#33402
C47×#17142
C47×#16852
C47×#16772
C47×#16762
C47×#16722
C47×#16442
C47×#16382
C47×#16302
C47×#16242
C47×#15832
C47×SD16⋊C82
#1988047