Finite Group Databasebeta

← C47×#19911 #26059609

Subgroups — C47×#19911 #26059609

Order 12032.

666 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3366C211yesmaximal, characteristic, complemented
2C47×#3325C211yesmaximal, characteristic, complemented
3C47×#3305C211yesmaximal, characteristic, complemented
4C47×#3295C211yesmaximal, characteristic, complemented
5C47×#1709C211yesmaximal, characteristic, complemented
6C47×#1698C211yesmaximal, characteristic, complemented
7C47×#1697C211yesmaximal, characteristic, complemented
8C47×#1677C211yesmaximal, characteristic, complemented
9C47×#1677C211yesmaximal, characteristic, complemented
10C47×#1634C211yesmaximal, characteristic, complemented
11C47×#1632C211yesmaximal, characteristic, complemented
12C47×#1621C211yesmaximal, characteristic, complemented
13C47×#1619C211yesmaximal, characteristic, complemented
14C47×#1590C211yesmaximal, characteristic, complemented
15C8×D8×C47C211yesmaximal, characteristic, complemented
16C47×#555C2211yescharacteristic
17C47×#554C2211yescharacteristic
18C47×#550C2211yescharacteristic, complemented
19D42×C47C2211yescharacteristic
20C47×#494C2211yescharacteristic, complemented
21C47×#493C2211yescharacteristic
22C47×#490—21no—
23C47×#486C2211yescharacteristic
24C47×#486C2211yescharacteristic
25C47×#486C2211yescharacteristic, complemented
26C47×#486C2211yescharacteristic, complemented
27C47×#482—21no—
28C47×#482—21no—
29C47×#481—21no—
30C47×#478—21no—
31C47×#477C2211yescharacteristic, complemented
32C47×#476C2211yescharacteristic
33C47×#476C2211yescharacteristic
34C47×#476C2211yescharacteristic, complemented
35C47×#469—21no—
36C47×#466—21no—
37C47×#465—21no—
38C47×#460C2211yescharacteristic
39C47×#459—21no—
40C47×#459C2211yescharacteristic
41C47×#459C2211yescharacteristic
42C47×#459C2211yescharacteristic
43C47×#450—21no—
44C47×#449—21no—
45C47×#447—21no—
46C47×#446C2211yescharacteristic, complemented
47C47×#442—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×#334C2211yescharacteristic, complemented
58C47×#333C2211yescharacteristic, complemented
59C47×#333C2211yescharacteristic, complemented
60C47×#331C2211yescharacteristic
61C47×#331C2211yescharacteristic, complemented
62C47×Q8⋊C8C2211yescharacteristic, complemented
63C47×D4⋊C8C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic, complemented
66C82×C47C2211yescharacteristic, complemented
67C2×#41×C47—21no—
68C22×D4×C47—21no—
69C22×D4×C47—21no—
70C2×Q16×C47—41no—
71C2×SD16×C47—21no—
72C2×SD16×C47D411yescharacteristic
73C2×D8×C47—21no—
74C2×D8×C47—21no—
75C2×D8×C47—21no—
76C2×D8×C47—41no—
77C2×D8×C47D411yescharacteristic
78C2×M16×C47—21no—
79C22×C8×C47—21no—
80C22×C8×C47—21no—
81C4⋊Q8×C47C2311yescharacteristic
82C4⋊Q8×C47C2311yescharacteristic
83#127×C47—21no—
84#127×C47C2311yescharacteristic
85#127×C47C2311yescharacteristic
86#125×C47—21no—
87#124×C47—41no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47—41no—
90#121×C47—21no—
91#121×C47—21no—
92#121×C47—21no—
93#121×C47—21no—
94#121×C47—21no—
95#121×C47—41no—
96#120×C47—41no—
97C4×Q8×C47C2311yescharacteristic
98C4×D4×C47—21no—
99C4×D4×C47—21no—
100C4×D4×C47C2311yescharacteristic
101C4×D4×C47C2311yescharacteristic
102C4×D4×C47C2311yescharacteristic
103#117×C47—21no—
104#117×C47—21no—
105C2×C4⋊C4×C47—21no—
106#107×C47—21no—
107#107×C47D411yescharacteristic
108#106×C47—21no—
109#106×C47—21no—
110#106×C47—21no—
111#106×C47D411yescharacteristic
112C4⋊C8×C47—21no—
113C4⋊C8×C47C2311yescharacteristic
114C4⋊C8×C47C2311yescharacteristic
115C4⋊C8×C47C2311yescharacteristic
116C4⋊C8×C47C2311yescharacteristic
117#103×C47—21no—
118#103×C47D411yescharacteristic
119#102×C47—21no—
120#102×C47—21no—
121#102×C47—21no—
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—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
144C24×C47—41no—
145#41×C47—42no—
146#41×C47—81no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47C2×D411yescharacteristic
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—41no—
157C2×D4×C47—41no—
158C2×D4×C47—41no—
159C2×D4×C47—41no—
160C2×D4×C47—42no—
161C2×D4×C47—42no—
162C2×D4×C47—41no—
163C2×D4×C47—81no—
164C2×D4×C47—81no—
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—41no—
172C22×C4×C47—41no—
173Q16×C47—82no—
174SD16×C47—41no—
175SD16×C47—81no—
176D8×C47—22no—
177D8×C47—42no—
178D8×C47—82no—
179D8×C47—81no—
180D8×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—41no—
199C4⋊C4×C47—41no—
200C4⋊C4×C47C2×D411yescharacteristic
201C4⋊C4×C47C2×D411yescharacteristic
202C4⋊C4×C47C2×D411yescharacteristic
203C4⋊C4×C47C2×D411yescharacteristic
204C22⋊C4×C47—21no—
205C22⋊C4×C47—21no—
206C22⋊C4×C47—21no—
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×C47C2411yescharacteristic
215C23×C47—21no—
216C23×C47—21no—
217C23×C47—21no—
218C23×C47—41no—
219C23×C47—41no—
220C23×C47—82no—
221C23×C47—82no—
222C23×C47—161no—
223Q8×C47—21no—
224Q8×C47—21no—
225Q8×C47—81no—
226Q8×C47—81no—
227D4×C47—21no—
228D4×C47—21no—
229D4×C47—21no—
230D4×C47—21no—
231D4×C47—21no—
232D4×C47—41no—
233D4×C47—41no—
234D4×C47—41no—
235D4×C47—41no—
236D4×C47—41no—
237D4×C47—41no—
238D4×C47—41no—
239D4×C47—41no—
240D4×C47—81no—
241D4×C47—81no—
242D4×C47—82no—
243D4×C47—82no—
244D4×C47—82no—
245D4×C47—161no—
246D4×C47—161no—
247D4×C47#13512yes—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
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—82no—
262C2×C4×C47—161no—
263C2×C4×C47C22×D411yescharacteristic
264C2×C4×C47C22×D411yescharacteristic
265C2×C4×C47H(5,𝔽2)11yescharacteristic
266C8×C47—22no—
267C8×C47—21no—
268C8×C47—21no—
269C8×C47—21no—
270C8×C47—21no—
271C8×C47—41no—
272C8×C47—41no—
273C8×C47—41no—
274C8×C47—41no—
275#19911C4711yesmaximal, characteristic, direct product factor, Sylow
276C22×C47—22no—
277C22×C47—41no—
278C22×C47—41no—
279C22×C47—41no—
280C22×C47—41no—
281C22×C47—41no—
282C22×C47—41no—
283C22×C47—41no—
284C22×C47—41no—
285C22×C47—81no—
286C22×C47—81no—
287C22×C47—81no—
288C22×C47—81no—
289C22×C47—81no—
290C22×C47—81no—
291C22×C47—164no—
292C22×C47D4211yescharacteristic
293C4×C47—21no—
294C4×C47—41no—
295C4×C47—41no—
296C4×C47—41no—
297C4×C47—41no—
298C4×C47—41no—
299C4×C47—81no—
300C4×C47—81no—
301C4×C47C2×#13511yescharacteristic
302C4×C47#57511yescharacteristic
303C4×C47#57611yescharacteristic
304C4×C47#57711yescharacteristic
305#3366C2×C4711yescharacteristic, complemented
306#3325C2×C4711yescharacteristic, complemented
307#3305C2×C4711yescharacteristic, complemented
308#3295C2×C4711yescharacteristic, complemented
309#1709C2×C4711yescharacteristic, complemented
310#1698C2×C4711yescharacteristic, complemented
311#1697C2×C4711yescharacteristic, complemented
312#1677C2×C4711yescharacteristic, complemented
313#1677C2×C4711yescharacteristic, complemented
314#1634C2×C4711yescharacteristic, complemented
315#1632C2×C4711yescharacteristic, complemented
316#1621C2×C4711yescharacteristic, complemented
317#1619C2×C4711yescharacteristic, complemented
318#1590C2×C4711yescharacteristic, complemented
319C8×D8C2×C4711yescharacteristic, complemented
320C2×C47—42no—
321C2×C47—81no—
322C2×C47—81no—
323C2×C47—161no—
324C2×C47—161no—
325C2×C47#327311yescharacteristic
326C2×C47#328211yescharacteristic
327C2×C47#329211yescharacteristic
328#555C22×C4711yescharacteristic
329#554C22×C4711yescharacteristic
330#550C22×C4711yescharacteristic, complemented
331D42C22×C4711yescharacteristic
332#494C22×C4711yescharacteristic, complemented
333#493C22×C4711yescharacteristic
334#490—21no—
335#486C22×C4711yescharacteristic
336#486C22×C4711yescharacteristic
337#486C22×C4711yescharacteristic, complemented
338#486C22×C4711yescharacteristic, complemented
339#482—21no—
340#482—21no—
341#481—21no—
342#478—21no—
343#477C22×C4711yescharacteristic, complemented
344#476C22×C4711yescharacteristic
345#476C22×C4711yescharacteristic
346#476C22×C4711yescharacteristic, complemented
347#469—21no—
348#466—21no—
349#465—21no—
350#460C22×C4711yescharacteristic
351#459—21no—
352#459C22×C4711yescharacteristic
353#459C22×C4711yescharacteristic
354#459C22×C4711yescharacteristic
355#450—21no—
356#449—21no—
357#447—21no—
358#446C22×C4711yescharacteristic, complemented
359#442—21no—
360C4×SD16C22×C4711yescharacteristic
361C4×D8C22×C4711yescharacteristic
362#436C22×C4711yescharacteristic
363C8×D4C22×C4711yescharacteristic
364C8×D4C22×C4711yescharacteristic, complemented
365#418—21no—
366#416—21no—
367C2×#102—21no—
368#335C22×C4711yescharacteristic, complemented
369#334C22×C4711yescharacteristic, complemented
370#333C22×C4711yescharacteristic, complemented
371#333C22×C4711yescharacteristic, complemented
372#331C22×C4711yescharacteristic
373#331C22×C4711yescharacteristic, complemented
374Q8⋊C8C22×C4711yescharacteristic, complemented
375D4⋊C8C22×C4711yescharacteristic
376D4⋊C8C22×C4711yescharacteristic
377D4⋊C8C22×C4711yescharacteristic, complemented
378C82C22×C4711yescharacteristic, complemented
379C47#1991111yescharacteristic, direct product factor, Sylow
380C2×#41—21no—
381C22×D4—21no—
382C22×D4—21no—
383C2×Q16—41no—
384C2×SD16—21no—
385C2×SD16D4×C4711yescharacteristic
386C2×D8—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8—41no—
390C2×D8D4×C4711yescharacteristic
391C2×M16—21no—
392C22×C8—21no—
393C22×C8—21no—
394C4⋊Q8C23×C4711yescharacteristic
395C4⋊Q8C23×C4711yescharacteristic
396#127—21no—
397#127C23×C4711yescharacteristic
398#127C23×C4711yescharacteristic
399#125—21no—
400#124—41no—
401C22⋊Q8—21no—
402C22⋊Q8—41no—
403#121—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—41no—
409#120—41no—
410C4×Q8C23×C4711yescharacteristic
411C4×D4—21no—
412C4×D4—21no—
413C4×D4C23×C4711yescharacteristic
414C4×D4C23×C4711yescharacteristic
415C4×D4C23×C4711yescharacteristic
416#117—21no—
417#117—21no—
418C2×C4⋊C4—21no—
419#107—21no—
420#107D4×C4711yescharacteristic
421#106—21no—
422#106—21no—
423#106—21no—
424#106D4×C4711yescharacteristic
425C4⋊C8—21no—
426C4⋊C8C23×C4711yescharacteristic
427C4⋊C8C23×C4711yescharacteristic
428C4⋊C8C23×C4711yescharacteristic
429C4⋊C8C23×C4711yescharacteristic
430#103—21no—
431#103D4×C4711yescharacteristic
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—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#102D4×C4711yescharacteristic
448#102D4×C4711yescharacteristic
449#102D4×C4711yescharacteristic
450C22⋊C8—21no—
451C22⋊C8—21no—
452C22⋊C8—21no—
453#97—21no—
454C4×C8C23×C4711yescharacteristic
455C4×C8C23×C4711yescharacteristic
456C4×C8C23×C4711yescharacteristic
457C24—41no—
458#41—42no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8C2×D4×C4711yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—41no—
476C2×D4—81no—
477C2×D4—81no—
478C2×D4C2×D4×C4711yescharacteristic
479C2×D4C2×D4×C4711yescharacteristic
480C2×D4C2×D4×C4711yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485C22×C4—41no—
486Q16—82no—
487SD16—41no—
488SD16—81no—
489D8—22no—
490D8—42no—
491D8—82no—
492D8—81no—
493D8—81no—
494M16—81no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—81no—
501C2×C8—81no—
502C2×C8C2×D4×C4711yescharacteristic
503C2×C8C2×D4×C4711yescharacteristic
504C2×C8C2×D4×C4711yescharacteristic
505C2×C8C2×D4×C4711yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4C2×D4×C4711yescharacteristic
514C4⋊C4C2×D4×C4711yescharacteristic
515C4⋊C4C2×D4×C4711yescharacteristic
516C4⋊C4C2×D4×C4711yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C42—21no—
526C42—41no—
527C42C24×C4711yescharacteristic
528C23—21no—
529C23—21no—
530C23—21no—
531C23—41no—
532C23—41no—
533C23—82no—
534C23—82no—
535C23—161no—
536Q8—21no—
537Q8—21no—
538Q8—81no—
539Q8—81no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—81no—
554D4—81no—
555D4—82no—
556D4—82no—
557D4—82no—
558D4—161no—
559D4—161no—
560D4#135×C4712yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
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—82no—
575C2×C4—161no—
576C2×C4C22×D4×C4711yescharacteristic
577C2×C4C22×D4×C4711yescharacteristic
578C2×C4H(5,𝔽2)×C4711yescharacteristic
579C8—22no—
580C8—21no—
581C8—21no—
582C8—21no—
583C8—21no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—164no—
604C22D42×C4711yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4—81no—
613C4C2×#135×C4711yescharacteristic
614C4C47×#57511yescharacteristic
615C4C47×#57611yescharacteristic
616C4C47×#57711yescharacteristic
617C2—42no—
618C2—81no—
619C2—81no—
620C2—161no—
621C2—161no—
622C2C47×#327311yescharacteristic
623C2C47×#328211yescharacteristic
624C2C47×#329211yescharacteristic
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×#3325C2semidirect
3. C47×#3305C2semidirect
4. C47×#3295C2semidirect
5. C47×#1709C2semidirect
6. C47×#1698C2semidirect
7. C47×#1697C2semidirect
8. C47×#1677C2semidirect
9. C47×#1677C2semidirect
10. C47×#1634C2semidirect
11. C47×#1632C2semidirect
12. C47×#1621C2semidirect
13. C47×#1619C2semidirect
14. C47×#1590C2semidirect
15. C8×D8×C47C2semidirect
18. C47×#550C22semidirect
20. C47×#494C22semidirect
25. C47×#486C22semidirect
26. C47×#486C22semidirect
31. C47×#477C22semidirect
34. C47×#476C22semidirect
46. C47×#446C22semidirect
52. C8×D4×C47C22semidirect
56. C47×#335C22semidirect
57. C47×#334C22semidirect
58. C47×#333C22semidirect
59. C47×#333C22semidirect
61. C47×#331C22semidirect
62. C47×Q8⋊C8C22semidirect
65. C47×D4⋊C8C22semidirect
66. C82×C47C22semidirect
275. #19911C47direct (N × H)
305. #3366C2×C47semidirect
306. #3325C2×C47semidirect
307. #3305C2×C47semidirect
308. #3295C2×C47semidirect
309. #1709C2×C47semidirect
310. #1698C2×C47semidirect
311. #1697C2×C47semidirect
312. #1677C2×C47semidirect
313. #1677C2×C47semidirect
314. #1634C2×C47semidirect
315. #1632C2×C47semidirect
316. #1621C2×C47semidirect
317. #1619C2×C47semidirect
318. #1590C2×C47semidirect
319. C8×D8C2×C47semidirect
330. #550C22×C47semidirect
332. #494C22×C47semidirect
337. #486C22×C47semidirect
338. #486C22×C47semidirect
343. #477C22×C47semidirect
346. #476C22×C47semidirect
358. #446C22×C47semidirect
364. C8×D4C22×C47semidirect
368. #335C22×C47semidirect
369. #334C22×C47semidirect
370. #333C22×C47semidirect
371. #333C22×C47semidirect
373. #331C22×C47semidirect
374. Q8⋊C8C22×C47semidirect
377. D4⋊C8C22×C47semidirect
378. C82C22×C47semidirect
379. C47#19911direct (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×#33252
C47×#33052
C47×#32952
C47×#17092
C47×#16982
C47×#16972
C47×#16772
C47×#16342
C47×#16322
C47×#16212
C47×#16192
C47×#15902
C8×D8×C472
#1991147