Finite Group Databasebeta

← C47×#19777 #26059475

Subgroups — C47×#19777 #26059475

Order 12032.

648 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×#3393C211yesmaximal, characteristic, complemented
2C47×#3324C211yesmaximal, characteristic, complemented
3C47×#3302C211yesmaximal, characteristic, complemented
4C47×#3294C211yesmaximal, characteristic
5C47×#1720C211yesmaximal, characteristic, complemented
6C47×#1699C211yesmaximal, characteristic, complemented
7C47×#1682C211yesmaximal, characteristic, complemented
8C47×#1681C211yesmaximal, characteristic, complemented
9C47×#1669C211yesmaximal, characteristic, complemented
10C47×#1654C211yesmaximal, characteristic, complemented
11C47×#1652C211yesmaximal, characteristic, complemented
12C47×#1639C211yesmaximal, characteristic, complemented
13C47×#1628C211yesmaximal, characteristic, complemented
14C47×#1581C211yesmaximal, characteristic, complemented
15C47×SD16⋊C8C211yesmaximal, characteristic, complemented
16C47×#556C2211yescharacteristic
17C47×#556C2211yescharacteristic, complemented
18C47×#547C2211yescharacteristic
19D42×C47C2211yescharacteristic
20C47×#498C2211yescharacteristic, complemented
21C47×#495—21no—
22C47×#494C2211yescharacteristic, complemented
23C47×#487C2211yescharacteristic, complemented
24C47×#486C2211yescharacteristic
25C47×#486C2211yescharacteristic
26C47×#486C2211yescharacteristic
27C47×#485—21no—
28C47×#482—21no—
29C47×#480—21no—
30C47×#474C2211yescharacteristic
31C47×#474C2211yescharacteristic
32C47×#474C2211yescharacteristic
33C47×#468—21no—
34C47×#467—21no—
35C47×#466—21no—
36C47×#464—21no—
37C47×#464—21no—
38C47×#462C2211yescharacteristic, complemented
39C47×#461C2211yescharacteristic
40C47×#461C2211yescharacteristic, complemented
41C47×#460C2211yescharacteristic
42C47×#459C2211yescharacteristic
43C47×#452—21no—
44C47×#450—21no—
45C47×#447—21no—
46C8×Q8×C47C2211yescharacteristic, complemented
47C4×Q16×C47—21no—
48C4×SD16×C47C2211yescharacteristic
49C4×D8×C47C2211yescharacteristic
50C47×#436C2211yescharacteristic
51C8×D4×C47C2211yescharacteristic
52C8×D4×C47C2211yescharacteristic, complemented
53C47×#418—21no—
54C47×#416—21no—
55C2×#102×C47—21no—
56C47×#335C2211yescharacteristic, complemented
57C47×#335C2211yescharacteristic, complemented
58C47×#332C2211yescharacteristic, complemented
59C47×#332C2211yescharacteristic, complemented
60C47×#332C2211yescharacteristic, complemented
61C47×#331C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic, complemented
63C47×D4⋊C8C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic, complemented
66C47×#322C2211yescharacteristic, complemented
67C2×#41×C47—21no—
68C22×D4×C47—21no—
69C22×D4×C47—21no—
70C2×Q16×C47—21no—
71C2×Q16×C47—21no—
72C2×Q16×C47—21no—
73C2×SD16×C47—21no—
74C2×SD16×C47—21no—
75C2×SD16×C47—21no—
76C2×SD16×C47D411yescharacteristic
77C2×D8×C47—21no—
78C2×D8×C47D411yescharacteristic
79C2×M16×C47—21no—
80C22×C8×C47—21no—
81C22×C8×C47—21no—
82C4⋊Q8×C47C2311yescharacteristic
83C4⋊Q8×C47C2311yescharacteristic
84C4⋊Q8×C47C2311yescharacteristic
85#127×C47C2311yescharacteristic
86#126×C47—41no—
87#126×C47—41no—
88#124×C47—21no—
89#124×C47—21no—
90#123×C47—41no—
91C22⋊Q8×C47—21no—
92C22⋊Q8×C47—21no—
93C22⋊Q8×C47—21no—
94#121×C47—21no—
95#121×C47—21no—
96#121×C47—21no—
97#120×C47—41no—
98C4×Q8×C47—21no—
99C4×Q8×C47—21no—
100C4×Q8×C47C2311yescharacteristic
101C4×D4×C47C2311yescharacteristic
102C4×D4×C47C2311yescharacteristic
103C4×D4×C47C2311yescharacteristic
104#117×C47—21no—
105#117×C47—21no—
106C2×C4⋊C4×C47—21no—
107#107×C47—21no—
108#107×C47—21no—
109#107×C47—21no—
110#107×C47D411yescharacteristic
111#106×C47—41no—
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—
140C4×C8×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C24×C47—41no—
145#41×C47—42no—
146#41×C47—81no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47C2×D411yescharacteristic
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—41no—
155C2×D4×C47—41no—
156C2×D4×C47—42no—
157C2×D4×C47—42no—
158C2×D4×C47—41no—
159C2×D4×C47—81no—
160C2×D4×C47—81no—
161C2×D4×C47C2×D411yescharacteristic
162C2×D4×C47C2×D411yescharacteristic
163C2×D4×C47C2×D411yescharacteristic
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—41no—
168Q16×C47—42no—
169Q16×C47—81no—
170Q16×C47—81no—
171SD16×C47—22no—
172SD16×C47—81no—
173SD16×C47—81no—
174SD16×C47—81no—
175D8×C47—41no—
176D8×C47—81no—
177M16×C47—81no—
178C2×C8×C47—21no—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47—21no—
182C2×C8×C47—21no—
183C2×C8×C47—81no—
184C2×C8×C47—81no—
185C2×C8×C47C2×D411yescharacteristic
186C2×C8×C47C2×D411yescharacteristic
187C2×C8×C47C2×D411yescharacteristic
188C2×C8×C47C2×D411yescharacteristic
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—21no—
196C4⋊C4×C47—41no—
197C4⋊C4×C47—41no—
198C4⋊C4×C47—41no—
199C4⋊C4×C47C2×D411yescharacteristic
200C4⋊C4×C47C2×D411yescharacteristic
201C4⋊C4×C47C2×D411yescharacteristic
202C4⋊C4×C47C2×D411yescharacteristic
203C22⋊C4×C47—21no—
204C22⋊C4×C47—21no—
205C22⋊C4×C47—21no—
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—41no—
214C42×C47—41no—
215C42×C47C2411yescharacteristic
216C23×C47—21no—
217C23×C47—21no—
218C23×C47—21no—
219C23×C47—41no—
220C23×C47—82no—
221C23×C47—82no—
222C23×C47—161no—
223Q8×C47—21no—
224Q8×C47—21no—
225Q8×C47—41no—
226Q8×C47—41no—
227Q8×C47—41no—
228Q8×C47—41no—
229Q8×C47—41no—
230Q8×C47—41no—
231D4×C47—21no—
232D4×C47—21no—
233D4×C47—21no—
234D4×C47—21no—
235D4×C47—21no—
236D4×C47—41no—
237D4×C47—41no—
238D4×C47—41no—
239D4×C47—41no—
240D4×C47—81no—
241D4×C47—82no—
242D4×C47—82no—
243D4×C47—82no—
244D4×C47#13512yes—
245C2×C4×C47—21no—
246C2×C4×C47—21no—
247C2×C4×C47—21no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47—41no—
253C2×C4×C47—41no—
254C2×C4×C47—41no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47—41no—
258C2×C4×C47—41no—
259C2×C4×C47—82no—
260C2×C4×C47C22×D411yescharacteristic
261C2×C4×C47C22×D411yescharacteristic
262C2×C4×C47H(5,𝔽2)11yescharacteristic
263C8×C47—21no—
264C8×C47—21no—
265C8×C47—21no—
266C8×C47—21no—
267C8×C47—41no—
268C8×C47—41no—
269C8×C47—41no—
270C8×C47—41no—
271C8×C47—41no—
272#19777C4711yesmaximal, characteristic, direct product factor, Sylow
273C22×C47—22no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—41no—
278C22×C47—41no—
279C22×C47—41no—
280C22×C47—41no—
281C22×C47—41no—
282C22×C47—81no—
283C22×C47—81no—
284C22×C47—81no—
285C22×C47—164no—
286C22×C47D4211yescharacteristic
287C4×C47—21no—
288C4×C47—41no—
289C4×C47—41no—
290C4×C47—41no—
291C4×C47—41no—
292C4×C47—41no—
293C4×C47—81no—
294C4×C47—81no—
295C4×C47—81no—
296C4×C47C2×#13511yescharacteristic
297C4×C47#57511yescharacteristic
298C4×C47#57611yescharacteristic
299C4×C47#57611yescharacteristic
300#3393C2×C4711yescharacteristic, complemented
301#3324C2×C4711yescharacteristic, complemented
302#3302C2×C4711yescharacteristic, complemented
303#3294C2×C4711yescharacteristic
304#1720C2×C4711yescharacteristic, complemented
305#1699C2×C4711yescharacteristic, complemented
306#1682C2×C4711yescharacteristic, complemented
307#1681C2×C4711yescharacteristic, complemented
308#1669C2×C4711yescharacteristic, complemented
309#1654C2×C4711yescharacteristic, complemented
310#1652C2×C4711yescharacteristic, complemented
311#1639C2×C4711yescharacteristic, complemented
312#1628C2×C4711yescharacteristic, complemented
313#1581C2×C4711yescharacteristic, complemented
314SD16⋊C8C2×C4711yescharacteristic, complemented
315C2×C47—42no—
316C2×C47—81no—
317C2×C47—81no—
318C2×C47—161no—
319C2×C47#326811yescharacteristic
320C2×C47#328011yescharacteristic
321C2×C47#328911yescharacteristic
322#556C22×C4711yescharacteristic
323#556C22×C4711yescharacteristic, complemented
324#547C22×C4711yescharacteristic
325D42C22×C4711yescharacteristic
326#498C22×C4711yescharacteristic, complemented
327#495—21no—
328#494C22×C4711yescharacteristic, complemented
329#487C22×C4711yescharacteristic, complemented
330#486C22×C4711yescharacteristic
331#486C22×C4711yescharacteristic
332#486C22×C4711yescharacteristic
333#485—21no—
334#482—21no—
335#480—21no—
336#474C22×C4711yescharacteristic
337#474C22×C4711yescharacteristic
338#474C22×C4711yescharacteristic
339#468—21no—
340#467—21no—
341#466—21no—
342#464—21no—
343#464—21no—
344#462C22×C4711yescharacteristic, complemented
345#461C22×C4711yescharacteristic
346#461C22×C4711yescharacteristic, complemented
347#460C22×C4711yescharacteristic
348#459C22×C4711yescharacteristic
349#452—21no—
350#450—21no—
351#447—21no—
352C8×Q8C22×C4711yescharacteristic, complemented
353C4×Q16—21no—
354C4×SD16C22×C4711yescharacteristic
355C4×D8C22×C4711yescharacteristic
356#436C22×C4711yescharacteristic
357C8×D4C22×C4711yescharacteristic
358C8×D4C22×C4711yescharacteristic, complemented
359#418—21no—
360#416—21no—
361C2×#102—21no—
362#335C22×C4711yescharacteristic, complemented
363#335C22×C4711yescharacteristic, complemented
364#332C22×C4711yescharacteristic, complemented
365#332C22×C4711yescharacteristic, complemented
366#332C22×C4711yescharacteristic, complemented
367#331C22×C4711yescharacteristic
368Q8⋊C8C22×C4711yescharacteristic, complemented
369D4⋊C8C22×C4711yescharacteristic
370D4⋊C8C22×C4711yescharacteristic
371D4⋊C8C22×C4711yescharacteristic, complemented
372#322C22×C4711yescharacteristic, complemented
373C47#1977711yescharacteristic, direct product factor, Sylow
374C2×#41—21no—
375C22×D4—21no—
376C22×D4—21no—
377C2×Q16—21no—
378C2×Q16—21no—
379C2×Q16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16D4×C4711yescharacteristic
384C2×D8—21no—
385C2×D8D4×C4711yescharacteristic
386C2×M16—21no—
387C22×C8—21no—
388C22×C8—21no—
389C4⋊Q8C23×C4711yescharacteristic
390C4⋊Q8C23×C4711yescharacteristic
391C4⋊Q8C23×C4711yescharacteristic
392#127C23×C4711yescharacteristic
393#126—41no—
394#126—41no—
395#124—21no—
396#124—21no—
397#123—41no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401#121—21no—
402#121—21no—
403#121—21no—
404#120—41no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8C23×C4711yescharacteristic
408C4×D4C23×C4711yescharacteristic
409C4×D4C23×C4711yescharacteristic
410C4×D4C23×C4711yescharacteristic
411#117—21no—
412#117—21no—
413C2×C4⋊C4—21no—
414#107—21no—
415#107—21no—
416#107—21no—
417#107D4×C4711yescharacteristic
418#106—41no—
419#106D4×C4711yescharacteristic
420C4⋊C8—21no—
421C4⋊C8C23×C4711yescharacteristic
422C4⋊C8C23×C4711yescharacteristic
423C4⋊C8C23×C4711yescharacteristic
424C4⋊C8C23×C4711yescharacteristic
425#103—21no—
426#103—21no—
427#103—21no—
428#103—21no—
429#103—21no—
430#103D4×C4711yescharacteristic
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—41no—
441#102D4×C4711yescharacteristic
442#102D4×C4711yescharacteristic
443#102D4×C4711yescharacteristic
444C22⋊C8—21no—
445C22⋊C8—21no—
446C22⋊C8—21no—
447C4×C8—21no—
448C4×C8C23×C4711yescharacteristic
449C4×C8C23×C4711yescharacteristic
450C4×C8C23×C4711yescharacteristic
451C24—41no—
452#41—42no—
453#41—81no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8C2×D4×C4711yescharacteristic
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—41no—
466C2×D4—81no—
467C2×D4—81no—
468C2×D4C2×D4×C4711yescharacteristic
469C2×D4C2×D4×C4711yescharacteristic
470C2×D4C2×D4×C4711yescharacteristic
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—41no—
475Q16—42no—
476Q16—81no—
477Q16—81no—
478SD16—22no—
479SD16—81no—
480SD16—81no—
481SD16—81no—
482D8—41no—
483D8—81no—
484M16—81no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—81no—
491C2×C8—81no—
492C2×C8C2×D4×C4711yescharacteristic
493C2×C8C2×D4×C4711yescharacteristic
494C2×C8C2×D4×C4711yescharacteristic
495C2×C8C2×D4×C4711yescharacteristic
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4C2×D4×C4711yescharacteristic
507C4⋊C4C2×D4×C4711yescharacteristic
508C4⋊C4C2×D4×C4711yescharacteristic
509C4⋊C4C2×D4×C4711yescharacteristic
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C42—21no—
520C42—41no—
521C42—41no—
522C42C24×C4711yescharacteristic
523C23—21no—
524C23—21no—
525C23—21no—
526C23—41no—
527C23—82no—
528C23—82no—
529C23—161no—
530Q8—21no—
531Q8—21no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537Q8—41no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—81no—
548D4—82no—
549D4—82no—
550D4—82no—
551D4#135×C4712yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—82no—
567C2×C4C22×D4×C4711yescharacteristic
568C2×C4C22×D4×C4711yescharacteristic
569C2×C4H(5,𝔽2)×C4711yescharacteristic
570C8—21no—
571C8—21no—
572C8—21no—
573C8—21no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8—41no—
579C22—22no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—164no—
592C22D42×C4711yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4C2×#135×C4711yescharacteristic
603C4C47×#57511yescharacteristic
604C4C47×#57611yescharacteristic
605C4C47×#57611yescharacteristic
606C2—42no—
607C2—81no—
608C2—81no—
609C2—161no—
610C2C47×#326811yescharacteristic
611C2C47×#328011yescharacteristic
612C2C47×#328911yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3294C2
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×#3393C2semidirect
2. C47×#3324C2semidirect
3. C47×#3302C2semidirect
5. C47×#1720C2semidirect
6. C47×#1699C2semidirect
7. C47×#1682C2semidirect
8. C47×#1681C2semidirect
9. C47×#1669C2semidirect
10. C47×#1654C2semidirect
11. C47×#1652C2semidirect
12. C47×#1639C2semidirect
13. C47×#1628C2semidirect
14. C47×#1581C2semidirect
15. C47×SD16⋊C8C2semidirect
17. C47×#556C22semidirect
20. C47×#498C22semidirect
22. C47×#494C22semidirect
23. C47×#487C22semidirect
38. C47×#462C22semidirect
40. C47×#461C22semidirect
46. C8×Q8×C47C22semidirect
52. C8×D4×C47C22semidirect
56. C47×#335C22semidirect
57. C47×#335C22semidirect
58. C47×#332C22semidirect
59. C47×#332C22semidirect
60. C47×#332C22semidirect
62. C47×Q8⋊C8C22semidirect
65. C47×D4⋊C8C22semidirect
66. C47×#322C22semidirect
272. #19777C47direct (N × H)
300. #3393C2×C47semidirect
301. #3324C2×C47semidirect
302. #3302C2×C47semidirect
304. #1720C2×C47semidirect
305. #1699C2×C47semidirect
306. #1682C2×C47semidirect
307. #1681C2×C47semidirect
308. #1669C2×C47semidirect
309. #1654C2×C47semidirect
310. #1652C2×C47semidirect
311. #1639C2×C47semidirect
312. #1628C2×C47semidirect
313. #1581C2×C47semidirect
314. SD16⋊C8C2×C47semidirect
323. #556C22×C47semidirect
326. #498C22×C47semidirect
328. #494C22×C47semidirect
329. #487C22×C47semidirect
344. #462C22×C47semidirect
346. #461C22×C47semidirect
352. C8×Q8C22×C47semidirect
358. C8×D4C22×C47semidirect
362. #335C22×C47semidirect
363. #335C22×C47semidirect
364. #332C22×C47semidirect
365. #332C22×C47semidirect
366. #332C22×C47semidirect
368. Q8⋊C8C22×C47semidirect
371. D4⋊C8C22×C47semidirect
372. #322C22×C47semidirect
373. C47#19777direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33932
C47×#33242
C47×#33022
C47×#32942
C47×#17202
C47×#16992
C47×#16822
C47×#16812
C47×#16692
C47×#16542
C47×#16522
C47×#16392
C47×#16282
C47×#15812
C47×SD16⋊C82
#1977747