Finite Group Databasebeta

← C47×#19899 #26059597

Subgroups — C47×#19899 #26059597

Order 12032.

666 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3330C211yesmaximal, characteristic, complemented
2C47×#3325C211yesmaximal, characteristic, complemented
3C47×#3303C211yesmaximal, characteristic, complemented
4C47×#3294C211yesmaximal, characteristic, complemented
5C47×#1711C211yesmaximal, characteristic, complemented
6C47×#1699C211yesmaximal, characteristic, complemented
7C47×#1697C211yesmaximal, characteristic, complemented
8C47×#1683C211yesmaximal, characteristic, complemented
9C47×#1681C211yesmaximal, characteristic, complemented
10C47×#1646C211yesmaximal, characteristic, complemented
11C47×#1639C211yesmaximal, characteristic, complemented
12C47×#1635C211yesmaximal, characteristic, complemented
13C47×#1625C211yesmaximal, characteristic, complemented
14C47×#1589C211yesmaximal, characteristic, complemented
15C8×D8×C47C211yesmaximal, characteristic, complemented
16C47×#555C2211yescharacteristic
17C47×#547C2211yescharacteristic
18C47×#547C2211yescharacteristic, complemented
19D42×C47C2211yescharacteristic
20C47×#487C2211yescharacteristic, complemented
21C47×#487C2211yescharacteristic, complemented
22C47×#487C2211yescharacteristic, complemented
23C47×#486C2211yescharacteristic
24C47×#486C2211yescharacteristic
25C47×#486C2211yescharacteristic
26C47×#485—21no—
27C47×#484—21no—
28C47×#482—21no—
29C47×#480—21no—
30C47×#476C2211yescharacteristic
31C47×#476C2211yescharacteristic, complemented
32C47×#474C2211yescharacteristic
33C47×#474C2211yescharacteristic
34C47×#469—21no—
35C47×#468—21no—
36C47×#466—21no—
37C47×#465—21no—
38C47×#461C2211yescharacteristic
39C47×#461C2211yescharacteristic, complemented
40C47×#459C2211yescharacteristic
41C47×#459C2211yescharacteristic
42C47×#449—21no—
43C47×#449—21no—
44C47×#447—21no—
45C47×#447—21no—
46C4×D8×C47C2211yescharacteristic
47C4×D8×C47C2211yescharacteristic
48C47×#436C2211yescharacteristic
49C47×#436C2211yescharacteristic, complemented
50C8×D4×C47C2211yescharacteristic
51C8×D4×C47C2211yescharacteristic, complemented
52C47×#418—21no—
53C47×#417—21no—
54C47×#416—21no—
55C2×#102×C47—21no—
56C47×#335C2211yescharacteristic, complemented
57C47×#335C2211yescharacteristic, complemented
58C47×#333C2211yescharacteristic, complemented
59C47×#332C2211yescharacteristic, complemented
60C47×#332C2211yescharacteristic, complemented
61C47×#331C2211yescharacteristic
62C47×D4⋊C8C2211yescharacteristic
63C47×D4⋊C8C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic, complemented
65C47×D4⋊C8C2211yescharacteristic, complemented
66C82×C47C2211yescharacteristic, complemented
67C2×#41×C47—21no—
68C2×#41×C47—21no—
69C22×D4×C47—21no—
70C22×D4×C47—21no—
71C2×SD16×C47—21no—
72C2×SD16×C47—21no—
73C2×D8×C47—21no—
74C2×D8×C47—21no—
75C2×D8×C47D411yescharacteristic
76C2×D8×C47D411yescharacteristic
77C2×M16×C47—21no—
78C2×M16×C47—21no—
79C22×C8×C47—21no—
80C22×C8×C47—21no—
81C4⋊Q8×C47C2311yescharacteristic
82C4⋊Q8×C47C2311yescharacteristic
83C4⋊Q8×C47C2311yescharacteristic
84#127×C47C2311yescharacteristic
85#124×C47—41no—
86#123×C47—41no—
87#123×C47—41no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47—21no—
90#121×C47—21no—
91#121×C47—21no—
92#121×C47—21no—
93#121×C47—21no—
94#121×C47—21no—
95#121×C47—21no—
96#120×C47—41no—
97C4×D4×C47C2311yescharacteristic
98C4×D4×C47C2311yescharacteristic
99C4×D4×C47C2311yescharacteristic
100C4×D4×C47C2311yescharacteristic
101#117×C47—21no—
102#117×C47—21no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47—21no—
105#107×C47—21no—
106#107×C47—21no—
107#107×C47D411yescharacteristic
108#107×C47D411yescharacteristic
109#106×C47—21no—
110#106×C47—21no—
111C4⋊C8×C47C2311yescharacteristic
112C4⋊C8×C47C2311yescharacteristic
113C4⋊C8×C47C2311yescharacteristic
114C4⋊C8×C47C2311yescharacteristic
115#103×C47—21no—
116#103×C47—21no—
117#103×C47—21no—
118#103×C47—21no—
119#103×C47—21no—
120#103×C47—21no—
121#103×C47—41no—
122#102×C47—21no—
123#102×C47—21no—
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—41no—
133#102×C47D411yescharacteristic
134#102×C47D411yescharacteristic
135#102×C47D411yescharacteristic
136#102×C47D411yescharacteristic
137C22⋊C8×C47—21no—
138C22⋊C8×C47—21no—
139C22⋊C8×C47—21no—
140C22⋊C8×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C24×C47—41no—
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×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—41no—
156C2×D4×C47—41no—
157C2×D4×C47—42no—
158C2×D4×C47—42no—
159C2×D4×C47—41no—
160C2×D4×C47—41no—
161C2×D4×C47—41no—
162C2×D4×C47—81no—
163C2×D4×C47—81no—
164C2×D4×C47C2×D411yescharacteristic
165C2×D4×C47C2×D411yescharacteristic
166C2×D4×C47C2×D411yescharacteristic
167C2×D4×C47C2×D411yescharacteristic
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—41no—
173C22×C4×C47—41no—
174SD16×C47—81no—
175SD16×C47—81no—
176D8×C47—22no—
177D8×C47—41no—
178D8×C47—81no—
179D8×C47—81no—
180M16×C47—81no—
181M16×C47—81no—
182C2×C8×C47—21no—
183C2×C8×C47—21no—
184C2×C8×C47—21no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—81no—
188C2×C8×C47—81no—
189C2×C8×C47C2×D411yescharacteristic
190C2×C8×C47C2×D411yescharacteristic
191C2×C8×C47C2×D411yescharacteristic
192C2×C8×C47C2×D411yescharacteristic
193C4⋊C4×C47—21no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—21no—
198C4⋊C4×C47—21no—
199C4⋊C4×C47—41no—
200C4⋊C4×C47—41no—
201C4⋊C4×C47C2×D411yescharacteristic
202C4⋊C4×C47C2×D411yescharacteristic
203C4⋊C4×C47C2×D411yescharacteristic
204C4⋊C4×C47C2×D411yescharacteristic
205C22⋊C4×C47—21no—
206C22⋊C4×C47—21no—
207C22⋊C4×C47—21no—
208C22⋊C4×C47—21no—
209C22⋊C4×C47—41no—
210C22⋊C4×C47—41no—
211C22⋊C4×C47—41no—
212C22⋊C4×C47—41no—
213C22⋊C4×C47—41no—
214C42×C47—41no—
215C42×C47C2411yescharacteristic
216C23×C47—21no—
217C23×C47—21no—
218C23×C47—21no—
219C23×C47—21no—
220C23×C47—41no—
221C23×C47—82no—
222C23×C47—82no—
223C23×C47—161no—
224Q8×C47—41no—
225Q8×C47—41no—
226Q8×C47—41no—
227Q8×C47—41no—
228Q8×C47—81no—
229D4×C47—21no—
230D4×C47—21no—
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—82no—
245D4×C47—161no—
246D4×C47#13512yes—
247C2×C4×C47—21no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
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—41no—
260C2×C4×C47—41no—
261C2×C4×C47—41no—
262C2×C4×C47—82no—
263C2×C4×C47—82no—
264C2×C4×C47C22×D411yescharacteristic
265C2×C4×C47C22×D411yescharacteristic
266C2×C4×C47H(5,𝔽2)11yescharacteristic
267C8×C47—21no—
268C8×C47—21no—
269C8×C47—21no—
270C8×C47—21no—
271C8×C47—41no—
272C8×C47—41no—
273C8×C47—41no—
274C8×C47—41no—
275C8×C47—41no—
276#19899C4711yesmaximal, characteristic, direct product factor, Sylow
277C22×C47—22no—
278C22×C47—41no—
279C22×C47—41no—
280C22×C47—41no—
281C22×C47—41no—
282C22×C47—41no—
283C22×C47—41no—
284C22×C47—41no—
285C22×C47—41no—
286C22×C47—41no—
287C22×C47—41no—
288C22×C47—41no—
289C22×C47—81no—
290C22×C47—81no—
291C22×C47—81no—
292C22×C47—164no—
293C22×C47D4211yescharacteristic
294C4×C47—21no—
295C4×C47—41no—
296C4×C47—41no—
297C4×C47—41no—
298C4×C47—41no—
299C4×C47—81no—
300C4×C47—81no—
301C4×C47—81no—
302C4×C47C2×#13511yescharacteristic
303C4×C47#57511yescharacteristic
304C4×C47#57611yescharacteristic
305C4×C47#57611yescharacteristic
306#3330C2×C4711yescharacteristic, complemented
307#3325C2×C4711yescharacteristic, complemented
308#3303C2×C4711yescharacteristic, complemented
309#3294C2×C4711yescharacteristic, complemented
310#1711C2×C4711yescharacteristic, complemented
311#1699C2×C4711yescharacteristic, complemented
312#1697C2×C4711yescharacteristic, complemented
313#1683C2×C4711yescharacteristic, complemented
314#1681C2×C4711yescharacteristic, complemented
315#1646C2×C4711yescharacteristic, complemented
316#1639C2×C4711yescharacteristic, complemented
317#1635C2×C4711yescharacteristic, complemented
318#1625C2×C4711yescharacteristic, complemented
319#1589C2×C4711yescharacteristic, complemented
320C8×D8C2×C4711yescharacteristic, complemented
321C2×C47—42no—
322C2×C47—81no—
323C2×C47—81no—
324C2×C47—81no—
325C2×C47—161no—
326C2×C47#327311yescharacteristic
327C2×C47#328011yescharacteristic
328C2×C47#329011yescharacteristic
329#555C22×C4711yescharacteristic
330#547C22×C4711yescharacteristic
331#547C22×C4711yescharacteristic, complemented
332D42C22×C4711yescharacteristic
333#487C22×C4711yescharacteristic, complemented
334#487C22×C4711yescharacteristic, complemented
335#487C22×C4711yescharacteristic, complemented
336#486C22×C4711yescharacteristic
337#486C22×C4711yescharacteristic
338#486C22×C4711yescharacteristic
339#485—21no—
340#484—21no—
341#482—21no—
342#480—21no—
343#476C22×C4711yescharacteristic
344#476C22×C4711yescharacteristic, complemented
345#474C22×C4711yescharacteristic
346#474C22×C4711yescharacteristic
347#469—21no—
348#468—21no—
349#466—21no—
350#465—21no—
351#461C22×C4711yescharacteristic
352#461C22×C4711yescharacteristic, complemented
353#459C22×C4711yescharacteristic
354#459C22×C4711yescharacteristic
355#449—21no—
356#449—21no—
357#447—21no—
358#447—21no—
359C4×D8C22×C4711yescharacteristic
360C4×D8C22×C4711yescharacteristic
361#436C22×C4711yescharacteristic
362#436C22×C4711yescharacteristic, complemented
363C8×D4C22×C4711yescharacteristic
364C8×D4C22×C4711yescharacteristic, complemented
365#418—21no—
366#417—21no—
367#416—21no—
368C2×#102—21no—
369#335C22×C4711yescharacteristic, complemented
370#335C22×C4711yescharacteristic, complemented
371#333C22×C4711yescharacteristic, complemented
372#332C22×C4711yescharacteristic, complemented
373#332C22×C4711yescharacteristic, complemented
374#331C22×C4711yescharacteristic
375D4⋊C8C22×C4711yescharacteristic
376D4⋊C8C22×C4711yescharacteristic
377D4⋊C8C22×C4711yescharacteristic, complemented
378D4⋊C8C22×C4711yescharacteristic, complemented
379C82C22×C4711yescharacteristic, complemented
380C47#1989911yescharacteristic, direct product factor, Sylow
381C2×#41—21no—
382C2×#41—21no—
383C22×D4—21no—
384C22×D4—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8D4×C4711yescharacteristic
390C2×D8D4×C4711yescharacteristic
391C2×M16—21no—
392C2×M16—21no—
393C22×C8—21no—
394C22×C8—21no—
395C4⋊Q8C23×C4711yescharacteristic
396C4⋊Q8C23×C4711yescharacteristic
397C4⋊Q8C23×C4711yescharacteristic
398#127C23×C4711yescharacteristic
399#124—41no—
400#123—41no—
401#123—41no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—21no—
409#121—21no—
410#120—41no—
411C4×D4C23×C4711yescharacteristic
412C4×D4C23×C4711yescharacteristic
413C4×D4C23×C4711yescharacteristic
414C4×D4C23×C4711yescharacteristic
415#117—21no—
416#117—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419#107—21no—
420#107—21no—
421#107D4×C4711yescharacteristic
422#107D4×C4711yescharacteristic
423#106—21no—
424#106—21no—
425C4⋊C8C23×C4711yescharacteristic
426C4⋊C8C23×C4711yescharacteristic
427C4⋊C8C23×C4711yescharacteristic
428C4⋊C8C23×C4711yescharacteristic
429#103—21no—
430#103—21no—
431#103—21no—
432#103—21no—
433#103—21no—
434#103—21no—
435#103—41no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—41no—
447#102D4×C4711yescharacteristic
448#102D4×C4711yescharacteristic
449#102D4×C4711yescharacteristic
450#102D4×C4711yescharacteristic
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455C4×C8C23×C4711yescharacteristic
456C4×C8C23×C4711yescharacteristic
457C4×C8C23×C4711yescharacteristic
458C24—41no—
459#41—42no—
460#41—42no—
461#41—81no—
462#41—81no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—81no—
477C2×D4—81no—
478C2×D4C2×D4×C4711yescharacteristic
479C2×D4C2×D4×C4711yescharacteristic
480C2×D4C2×D4×C4711yescharacteristic
481C2×D4C2×D4×C4711yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—41no—
487C22×C4—41no—
488SD16—81no—
489SD16—81no—
490D8—22no—
491D8—41no—
492D8—81no—
493D8—81no—
494M16—81no—
495M16—81no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—81no—
502C2×C8—81no—
503C2×C8C2×D4×C4711yescharacteristic
504C2×C8C2×D4×C4711yescharacteristic
505C2×C8C2×D4×C4711yescharacteristic
506C2×C8C2×D4×C4711yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4C2×D4×C4711yescharacteristic
516C4⋊C4C2×D4×C4711yescharacteristic
517C4⋊C4C2×D4×C4711yescharacteristic
518C4⋊C4C2×D4×C4711yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C42—41no—
529C42C24×C4711yescharacteristic
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—41no—
535C23—82no—
536C23—82no—
537C23—161no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—81no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—81no—
555D4—82no—
556D4—82no—
557D4—82no—
558D4—82no—
559D4—161no—
560D4#135×C4712yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4C22×D4×C4711yescharacteristic
579C2×C4C22×D4×C4711yescharacteristic
580C2×C4H(5,𝔽2)×C4711yescharacteristic
581C8—21no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8—41no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—164no—
606C22D42×C4711yescharacteristic
607C4—21no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—81no—
613C4—81no—
614C4—81no—
615C4C2×#135×C4711yescharacteristic
616C4C47×#57511yescharacteristic
617C4C47×#57611yescharacteristic
618C4C47×#57611yescharacteristic
619C2—42no—
620C2—81no—
621C2—81no—
622C2—81no—
623C2—161no—
624C2C47×#327311yescharacteristic
625C2C47×#328011yescharacteristic
626C2C47×#329011yescharacteristic
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×#3330C2semidirect
2. C47×#3325C2semidirect
3. C47×#3303C2semidirect
4. C47×#3294C2semidirect
5. C47×#1711C2semidirect
6. C47×#1699C2semidirect
7. C47×#1697C2semidirect
8. C47×#1683C2semidirect
9. C47×#1681C2semidirect
10. C47×#1646C2semidirect
11. C47×#1639C2semidirect
12. C47×#1635C2semidirect
13. C47×#1625C2semidirect
14. C47×#1589C2semidirect
15. C8×D8×C47C2semidirect
18. C47×#547C22semidirect
20. C47×#487C22semidirect
21. C47×#487C22semidirect
22. C47×#487C22semidirect
31. C47×#476C22semidirect
39. C47×#461C22semidirect
49. C47×#436C22semidirect
51. C8×D4×C47C22semidirect
56. C47×#335C22semidirect
57. C47×#335C22semidirect
58. C47×#333C22semidirect
59. C47×#332C22semidirect
60. C47×#332C22semidirect
64. C47×D4⋊C8C22semidirect
65. C47×D4⋊C8C22semidirect
66. C82×C47C22semidirect
276. #19899C47direct (N × H)
306. #3330C2×C47semidirect
307. #3325C2×C47semidirect
308. #3303C2×C47semidirect
309. #3294C2×C47semidirect
310. #1711C2×C47semidirect
311. #1699C2×C47semidirect
312. #1697C2×C47semidirect
313. #1683C2×C47semidirect
314. #1681C2×C47semidirect
315. #1646C2×C47semidirect
316. #1639C2×C47semidirect
317. #1635C2×C47semidirect
318. #1625C2×C47semidirect
319. #1589C2×C47semidirect
320. C8×D8C2×C47semidirect
331. #547C22×C47semidirect
333. #487C22×C47semidirect
334. #487C22×C47semidirect
335. #487C22×C47semidirect
344. #476C22×C47semidirect
352. #461C22×C47semidirect
362. #436C22×C47semidirect
364. C8×D4C22×C47semidirect
369. #335C22×C47semidirect
370. #335C22×C47semidirect
371. #333C22×C47semidirect
372. #332C22×C47semidirect
373. #332C22×C47semidirect
377. D4⋊C8C22×C47semidirect
378. D4⋊C8C22×C47semidirect
379. C82C22×C47semidirect
380. C47#19899direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33302
C47×#33252
C47×#33032
C47×#32942
C47×#17112
C47×#16992
C47×#16972
C47×#16832
C47×#16812
C47×#16462
C47×#16392
C47×#16352
C47×#16252
C47×#15892
C8×D8×C472
#1989947