Finite Group Databasebeta

← C47×#19791 #26059489

Subgroups — C47×#19791 #26059489

Order 12032.

606 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3367C211yesmaximal, characteristic, complemented
2C47×#3340C211yesmaximal, characteristic, complemented
3C47×#3303C211yesmaximal, characteristic
4C47×#3298C211yesmaximal, characteristic, complemented
5C47×#1718C211yesmaximal, characteristic, complemented
6C47×#1704C211yesmaximal, characteristic, complemented
7C47×#1679C211yesmaximal, characteristic, complemented
8C47×#1679C211yesmaximal, characteristic, complemented
9C47×#1671C211yesmaximal, characteristic, complemented
10C47×#1650C211yesmaximal, characteristic, complemented
11C47×#1647C211yesmaximal, characteristic, complemented
12C47×#1646C211yesmaximal, characteristic, complemented
13C47×#1637C211yesmaximal, characteristic, complemented
14C47×#1582C211yesmaximal, characteristic, complemented
15C47×#1580C211yesmaximal, characteristic, complemented
16C47×#556C2211yescharacteristic
17C47×#555C2211yescharacteristic
18D4×Q8×C47C2211yescharacteristic
19C47×#547C2211yescharacteristic
20C47×#500C2211yescharacteristic
21C47×#498C2211yescharacteristic
22C47×#489—21no—
23C47×#487C2211yescharacteristic
24C47×#487C2211yescharacteristic
25C47×#487C2211yescharacteristic
26C47×#487C2211yescharacteristic
27C47×#485—21no—
28C47×#485—21no—
29C47×#483—21no—
30C47×#482—21no—
31C47×#477—21no—
32C47×#477C2211yescharacteristic
33C47×#476C2211yescharacteristic
34C47×#475C2211yescharacteristic
35C47×#474C2211yescharacteristic
36C47×#474C2211yescharacteristic
37C47×#465—21no—
38C47×#465—21no—
39C47×#465—21no—
40C47×#463—21no—
41C47×#461C2211yescharacteristic
42C47×#461C2211yescharacteristic
43C47×#461C2211yescharacteristic
44C47×#449—21no—
45C47×#448—21no—
46C47×#446C2211yescharacteristic
47C47×#440—21no—
48C4×SD16×C47C2211yescharacteristic
49C4×D8×C47C2211yescharacteristic
50C8×D4×C47C2211yescharacteristic
51C8×D4×C47C2211yescharacteristic
52C8×D4×C47C2211yescharacteristic
53C47×#427—21no—
54C47×#416—21no—
55C2×#103×C47—21no—
56C47×#334C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#333C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#332C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×D4⋊C8C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×#41×C47—21no—
68C22×Q8×C47—21no—
69C2×SD16×C47—21no—
70C2×SD16×C47—21no—
71C2×SD16×C47—21no—
72C2×SD16×C47D411yescharacteristic
73C2×D8×C47D411yescharacteristic
74C22×C8×C47—21no—
75C22×C8×C47—21no—
76C22×C8×C47—21no—
77C4⋊Q8×C47—21no—
78C4⋊Q8×C47C2311yescharacteristic
79C4⋊Q8×C47C2311yescharacteristic
80C4⋊Q8×C47C2311yescharacteristic
81C4⋊Q8×C47C2311yescharacteristic
82#126×C47—41no—
83#124×C47—21no—
84#124×C47—41no—
85#123×C47—41no—
86C22⋊Q8×C47—21no—
87C22⋊Q8×C47—21no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47—41no—
90#121×C47—21no—
91#121×C47—21no—
92#121×C47—21no—
93C4×Q8×C47—21no—
94C4×Q8×C47C2311yescharacteristic
95C4×D4×C47—21no—
96C4×D4×C47C2311yescharacteristic
97C4×D4×C47C2311yescharacteristic
98C4×D4×C47C2311yescharacteristic
99#117×C47—21no—
100#117×C47—21no—
101#117×C47—21no—
102C2×C4⋊C4×C47—21no—
103#107×C47—21no—
104#107×C47—21no—
105#107×C47—21no—
106#107×C47—41no—
107#107×C47D411yescharacteristic
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×C47—21no—
124#103×C47—21no—
125#103×C47—21no—
126#103×C47—21no—
127#103×C47—21no—
128#103×C47—21no—
129#103×C47—41no—
130#103×C47D411yescharacteristic
131#102×C47—21no—
132#102×C47—21no—
133#102×C47—21no—
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—81no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47—41no—
151C2×Q8×C47—42no—
152C2×Q8×C47—81no—
153C2×Q8×C47C2×D411yescharacteristic
154C2×D4×C47—41no—
155C2×D4×C47—41no—
156C2×D4×C47C2×D411yescharacteristic
157C2×D4×C47C2×D411yescharacteristic
158C2×D4×C47C2×D411yescharacteristic
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—41no—
163C22×C4×C47—41no—
164SD16×C47—41no—
165SD16×C47—42no—
166SD16×C47—81no—
167SD16×C47—81no—
168D8×C47—22no—
169C2×C8×C47—21no—
170C2×C8×C47—21no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—42no—
175C2×C8×C47—81no—
176C2×C8×C47—81no—
177C2×C8×C47C2×D411yescharacteristic
178C2×C8×C47C2×D411yescharacteristic
179C2×C8×C47C2×D411yescharacteristic
180C2×C8×C47C2×D411yescharacteristic
181C4⋊C4×C47—21no—
182C4⋊C4×C47—21no—
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—41no—
191C4⋊C4×C47—41no—
192C4⋊C4×C47—41no—
193C4⋊C4×C47C2×D411yescharacteristic
194C4⋊C4×C47C2×D411yescharacteristic
195C4⋊C4×C47C2×D411yescharacteristic
196C4⋊C4×C47C2×D411yescharacteristic
197C22⋊C4×C47—21no—
198C22⋊C4×C47—21no—
199C22⋊C4×C47—21no—
200C22⋊C4×C47—41no—
201C22⋊C4×C47—41no—
202C22⋊C4×C47—41no—
203C22⋊C4×C47—41no—
204C22⋊C4×C47—41no—
205C22⋊C4×C47—41no—
206C42×C47—21no—
207C42×C47—41no—
208C42×C47—41no—
209C42×C47C2411yescharacteristic
210C23×C47—21no—
211C23×C47—21no—
212C23×C47—21no—
213Q8×C47—21no—
214Q8×C47—21no—
215Q8×C47—41no—
216Q8×C47—41no—
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—21no—
227D4×C47—21no—
228D4×C47—82no—
229D4×C47—161no—
230D4×C47#13512yes—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
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—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—82no—
247C2×C4×C47—82no—
248C2×C4×C47C22×D411yescharacteristic
249C2×C4×C47C22×D411yescharacteristic
250C2×C4×C47H(5,𝔽2)11yescharacteristic
251C8×C47—21no—
252C8×C47—21no—
253C8×C47—21no—
254C8×C47—21no—
255C8×C47—41no—
256C8×C47—41no—
257C8×C47—41no—
258C8×C47—41no—
259C8×C47—41no—
260#19791C4711yesmaximal, characteristic, direct product factor, Sylow
261C22×C47—22no—
262C22×C47—41no—
263C22×C47—41no—
264C22×C47—41no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47—41no—
268C22×C47—41no—
269C22×C47—41no—
270C22×C47D4211yescharacteristic
271C4×C47—21no—
272C4×C47—41no—
273C4×C47—41no—
274C4×C47—41no—
275C4×C47—41no—
276C4×C47—41no—
277C4×C47—81no—
278C4×C47—81no—
279C4×C47—81no—
280C4×C47—81no—
281C4×C47C2×#13511yescharacteristic
282C4×C47#57511yescharacteristic
283C4×C47#57711yescharacteristic
284C4×C47#57711yescharacteristic
285#3367C2×C4711yescharacteristic, complemented
286#3340C2×C4711yescharacteristic, complemented
287#3303C2×C4711yescharacteristic
288#3298C2×C4711yescharacteristic, complemented
289#1718C2×C4711yescharacteristic, complemented
290#1704C2×C4711yescharacteristic, complemented
291#1679C2×C4711yescharacteristic, complemented
292#1679C2×C4711yescharacteristic, complemented
293#1671C2×C4711yescharacteristic, complemented
294#1650C2×C4711yescharacteristic, complemented
295#1647C2×C4711yescharacteristic, complemented
296#1646C2×C4711yescharacteristic, complemented
297#1637C2×C4711yescharacteristic, complemented
298#1582C2×C4711yescharacteristic, complemented
299#1580C2×C4711yescharacteristic, complemented
300C2×C47—42no—
301C2×C47—81no—
302C2×C47—81no—
303C2×C47#326711yescharacteristic
304C2×C47#328211yescharacteristic
305C2×C47#328911yescharacteristic
306#556C22×C4711yescharacteristic
307#555C22×C4711yescharacteristic
308D4×Q8C22×C4711yescharacteristic
309#547C22×C4711yescharacteristic
310#500C22×C4711yescharacteristic
311#498C22×C4711yescharacteristic
312#489—21no—
313#487C22×C4711yescharacteristic
314#487C22×C4711yescharacteristic
315#487C22×C4711yescharacteristic
316#487C22×C4711yescharacteristic
317#485—21no—
318#485—21no—
319#483—21no—
320#482—21no—
321#477—21no—
322#477C22×C4711yescharacteristic
323#476C22×C4711yescharacteristic
324#475C22×C4711yescharacteristic
325#474C22×C4711yescharacteristic
326#474C22×C4711yescharacteristic
327#465—21no—
328#465—21no—
329#465—21no—
330#463—21no—
331#461C22×C4711yescharacteristic
332#461C22×C4711yescharacteristic
333#461C22×C4711yescharacteristic
334#449—21no—
335#448—21no—
336#446C22×C4711yescharacteristic
337#440—21no—
338C4×SD16C22×C4711yescharacteristic
339C4×D8C22×C4711yescharacteristic
340C8×D4C22×C4711yescharacteristic
341C8×D4C22×C4711yescharacteristic
342C8×D4C22×C4711yescharacteristic
343#427—21no—
344#416—21no—
345C2×#103—21no—
346#334C22×C4711yescharacteristic
347#334C22×C4711yescharacteristic
348#333C22×C4711yescharacteristic
349#332C22×C4711yescharacteristic
350#332C22×C4711yescharacteristic
351#332C22×C4711yescharacteristic
352Q8⋊C8C22×C4711yescharacteristic
353D4⋊C8C22×C4711yescharacteristic
354D4⋊C8C22×C4711yescharacteristic
355D4⋊C8C22×C4711yescharacteristic
356#322C22×C4711yescharacteristic
357C47#1979111yescharacteristic, direct product factor, Sylow
358C2×#41—21no—
359C22×Q8—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×SD16—21no—
363C2×SD16D4×C4711yescharacteristic
364C2×D8D4×C4711yescharacteristic
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C4⋊Q8—21no—
369C4⋊Q8C23×C4711yescharacteristic
370C4⋊Q8C23×C4711yescharacteristic
371C4⋊Q8C23×C4711yescharacteristic
372C4⋊Q8C23×C4711yescharacteristic
373#126—41no—
374#124—21no—
375#124—41no—
376#123—41no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380C22⋊Q8—41no—
381#121—21no—
382#121—21no—
383#121—21no—
384C4×Q8—21no—
385C4×Q8C23×C4711yescharacteristic
386C4×D4—21no—
387C4×D4C23×C4711yescharacteristic
388C4×D4C23×C4711yescharacteristic
389C4×D4C23×C4711yescharacteristic
390#117—21no—
391#117—21no—
392#117—21no—
393C2×C4⋊C4—21no—
394#107—21no—
395#107—21no—
396#107—21no—
397#107—41no—
398#107D4×C4711yescharacteristic
399#106—21no—
400#106—21no—
401#106—21no—
402#106—21no—
403#106D4×C4711yescharacteristic
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—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—41no—
421#103D4×C4711yescharacteristic
422#102—21no—
423#102—21no—
424#102—21no—
425#102D4×C4711yescharacteristic
426#102D4×C4711yescharacteristic
427#102D4×C4711yescharacteristic
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431#97—21no—
432C4×C8C23×C4711yescharacteristic
433C4×C8C23×C4711yescharacteristic
434C4×C8C23×C4711yescharacteristic
435#41—42no—
436#41—81no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—41no—
442C2×Q8—42no—
443C2×Q8—81no—
444C2×Q8C2×D4×C4711yescharacteristic
445C2×D4—41no—
446C2×D4—41no—
447C2×D4C2×D4×C4711yescharacteristic
448C2×D4C2×D4×C4711yescharacteristic
449C2×D4C2×D4×C4711yescharacteristic
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—41no—
454C22×C4—41no—
455SD16—41no—
456SD16—42no—
457SD16—81no—
458SD16—81no—
459D8—22no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—42no—
466C2×C8—81no—
467C2×C8—81no—
468C2×C8C2×D4×C4711yescharacteristic
469C2×C8C2×D4×C4711yescharacteristic
470C2×C8C2×D4×C4711yescharacteristic
471C2×C8C2×D4×C4711yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4C2×D4×C4711yescharacteristic
485C4⋊C4C2×D4×C4711yescharacteristic
486C4⋊C4C2×D4×C4711yescharacteristic
487C4⋊C4C2×D4×C4711yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C42—21no—
498C42—41no—
499C42—41no—
500C42C24×C4711yescharacteristic
501C23—21no—
502C23—21no—
503C23—21no—
504Q8—21no—
505Q8—21no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—81no—
513Q8—82no—
514D4—21no—
515D4—21no—
516D4—21no—
517D4—21no—
518D4—21no—
519D4—82no—
520D4—161no—
521D4#135×C4712yes—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4C22×D4×C4711yescharacteristic
540C2×C4C22×D4×C4711yescharacteristic
541C2×C4H(5,𝔽2)×C4711yescharacteristic
542C8—21no—
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C22—22no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22D42×C4711yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4C2×#135×C4711yescharacteristic
572C4C47×#57511yescharacteristic
573C4C47×#57711yescharacteristic
574C4C47×#57711yescharacteristic
575C2—42no—
576C2—81no—
577C2—81no—
578C2C47×#326711yescharacteristic
579C2C47×#328211yescharacteristic
580C2C47×#328911yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3303C2
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×#3367C2semidirect
2. C47×#3340C2semidirect
4. C47×#3298C2semidirect
5. C47×#1718C2semidirect
6. C47×#1704C2semidirect
7. C47×#1679C2semidirect
8. C47×#1679C2semidirect
9. C47×#1671C2semidirect
10. C47×#1650C2semidirect
11. C47×#1647C2semidirect
12. C47×#1646C2semidirect
13. C47×#1637C2semidirect
14. C47×#1582C2semidirect
15. C47×#1580C2semidirect
260. #19791C47direct (N × H)
285. #3367C2×C47semidirect
286. #3340C2×C47semidirect
288. #3298C2×C47semidirect
289. #1718C2×C47semidirect
290. #1704C2×C47semidirect
291. #1679C2×C47semidirect
292. #1679C2×C47semidirect
293. #1671C2×C47semidirect
294. #1650C2×C47semidirect
295. #1647C2×C47semidirect
296. #1646C2×C47semidirect
297. #1637C2×C47semidirect
298. #1582C2×C47semidirect
299. #1580C2×C47semidirect
357. C47#19791direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33672
C47×#33402
C47×#33032
C47×#32982
C47×#17182
C47×#17042
C47×#16792
C47×#16712
C47×#16502
C47×#16472
C47×#16462
C47×#16372
C47×#15822
C47×#15802
#1979147