Finite Group Databasebeta

← C47×#19775 #26059473

Subgroups — C47×#19775 #26059473

Order 12032.

656 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3341C211yesmaximal, characteristic, complemented
2C47×#3325C211yesmaximal, characteristic, complemented
3C47×#3303C211yesmaximal, characteristic, complemented
4C47×#3294C211yesmaximal, characteristic, complemented
5C47×#1719C211yesmaximal, characteristic, complemented
6C47×#1703C211yesmaximal, characteristic, complemented
7C47×#1681C211yesmaximal, characteristic, complemented
8C47×#1677C211yesmaximal, characteristic, complemented
9C47×#1675C211yesmaximal, characteristic, complemented
10C47×#1646C211yesmaximal, characteristic, complemented
11C47×#1635C211yesmaximal, characteristic, complemented
12C47×#1629C211yesmaximal, characteristic, complemented
13C47×#1624C211yesmaximal, characteristic, complemented
14C47×#1581C211yesmaximal, characteristic, complemented
15C47×#1580C211yesmaximal, characteristic, complemented
16C47×#555C2211yescharacteristic
17C47×#555C2211yescharacteristic, complemented
18C47×#547C2211yescharacteristic
19D42×C47C2211yescharacteristic
20C47×#500C2211yescharacteristic, complemented
21C47×#492C2211yescharacteristic
22C47×#487C2211yescharacteristic, complemented
23C47×#487C2211yescharacteristic, complemented
24C47×#486C2211yescharacteristic
25C47×#486C2211yescharacteristic
26C47×#485—21no—
27C47×#482—21no—
28C47×#482—21no—
29C47×#482—21no—
30C47×#480—21no—
31C47×#476C2211yescharacteristic
32C47×#476C2211yescharacteristic
33C47×#476C2211yescharacteristic
34C47×#476C2211yescharacteristic, complemented
35C47×#474C2211yescharacteristic
36C47×#469—21no—
37C47×#466—21no—
38C47×#466—21no—
39C47×#465—21no—
40C47×#461C2211yescharacteristic, complemented
41C47×#459C2211yescharacteristic
42C47×#459C2211yescharacteristic
43C47×#449—21no—
44C47×#447—21no—
45C47×#447—21no—
46C4×D8×C47C2211yescharacteristic
47C4×D8×C47C2211yescharacteristic
48C47×#436C2211yescharacteristic
49C8×D4×C47C2211yescharacteristic
50C8×D4×C47C2211yescharacteristic, complemented
51C8×D4×C47C2211yescharacteristic, complemented
52C47×#427—21no—
53C47×#418—21no—
54C47×#416—21no—
55C2×#102×C47—21no—
56C47×#335C2211yescharacteristic, complemented
57C47×#334C2211yescharacteristic, complemented
58C47×#333C2211yescharacteristic, complemented
59C47×#333C2211yescharacteristic, complemented
60C47×#332C2211yescharacteristic, complemented
61C47×#331C2211yescharacteristic
62C47×D4⋊C8C2211yescharacteristic
63C47×D4⋊C8C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic, complemented
65C47×D4⋊C8C2211yescharacteristic, complemented
66C47×#322C2211yescharacteristic, complemented
67C2×#41×C47—21no—
68C22×D4×C47—21no—
69C22×D4×C47—21no—
70C2×SD16×C47—21no—
71C2×SD16×C47—41no—
72C2×D8×C47—21no—
73C2×D8×C47—21no—
74C2×D8×C47D411yescharacteristic
75C2×D8×C47D411yescharacteristic
76C2×M16×C47—21no—
77C22×C8×C47—21no—
78C22×C8×C47—21no—
79C22×C8×C47—21no—
80C4⋊Q8×C47C2311yescharacteristic
81C4⋊Q8×C47C2311yescharacteristic
82C4⋊Q8×C47C2311yescharacteristic
83#127×C47C2311yescharacteristic
84#124×C47—41no—
85#124×C47—41no—
86#123×C47—41no—
87C22⋊Q8×C47—21no—
88#121×C47—21no—
89#121×C47—21no—
90#121×C47—21no—
91#121×C47—21no—
92#121×C47—21no—
93#121×C47—21no—
94#121×C47—21no—
95#120×C47—41no—
96C4×D4×C47C2311yescharacteristic
97C4×D4×C47C2311yescharacteristic
98C4×D4×C47C2311yescharacteristic
99C4×D4×C47C2311yescharacteristic
100#117×C47—21no—
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×C47D411yescharacteristic
109#107×C47D411yescharacteristic
110#106×C47—21no—
111#106×C47—21no—
112#106×C47—21no—
113#106×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—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—21no—
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—81no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—41no—
154C2×D4×C47—41no—
155C2×D4×C47—42no—
156C2×D4×C47—42no—
157C2×D4×C47—41no—
158C2×D4×C47—41no—
159C2×D4×C47—41no—
160C2×D4×C47—81no—
161C2×D4×C47—81no—
162C2×D4×C47C2×D411yescharacteristic
163C2×D4×C47C2×D411yescharacteristic
164C2×D4×C47C2×D411yescharacteristic
165C2×D4×C47C2×D411yescharacteristic
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—41no—
171SD16×C47—81no—
172SD16×C47—82no—
173D8×C47—22no—
174D8×C47—41no—
175D8×C47—81no—
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—42no—
184C2×C8×C47—81no—
185C2×C8×C47—81no—
186C2×C8×C47C2×D411yescharacteristic
187C2×C8×C47C2×D411yescharacteristic
188C2×C8×C47C2×D411yescharacteristic
189C2×C8×C47C2×D411yescharacteristic
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×C47C2×D411yescharacteristic
198C4⋊C4×C47C2×D411yescharacteristic
199C4⋊C4×C47C2×D411yescharacteristic
200C4⋊C4×C47C2×D411yescharacteristic
201C22⋊C4×C47—21no—
202C22⋊C4×C47—21no—
203C22⋊C4×C47—21no—
204C22⋊C4×C47—21no—
205C22⋊C4×C47—41no—
206C22⋊C4×C47—41no—
207C22⋊C4×C47—41no—
208C22⋊C4×C47—41no—
209C22⋊C4×C47—41no—
210C22⋊C4×C47—41no—
211C42×C47—41no—
212C42×C47—41no—
213C42×C47C2411yescharacteristic
214C23×C47—21no—
215C23×C47—21no—
216C23×C47—21no—
217C23×C47—21no—
218C23×C47—41no—
219C23×C47—82no—
220C23×C47—82no—
221C23×C47—161no—
222Q8×C47—41no—
223Q8×C47—41no—
224Q8×C47—81no—
225Q8×C47—81no—
226D4×C47—21no—
227D4×C47—21no—
228D4×C47—21no—
229D4×C47—21no—
230D4×C47—21no—
231D4×C47—21no—
232D4×C47—21no—
233D4×C47—41no—
234D4×C47—41no—
235D4×C47—41no—
236D4×C47—41no—
237D4×C47—81no—
238D4×C47—82no—
239D4×C47—82no—
240D4×C47—82no—
241D4×C47—161no—
242D4×C47—161no—
243D4×C47#13512yes—
244C2×C4×C47—21no—
245C2×C4×C47—21no—
246C2×C4×C47—21no—
247C2×C4×C47—21no—
248C2×C4×C47—41no—
249C2×C4×C47—41no—
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#19775C4711yesmaximal, 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—41no—
283C22×C47—41no—
284C22×C47—41no—
285C22×C47—81no—
286C22×C47—81no—
287C22×C47—81no—
288C22×C47—164no—
289C22×C47D4211yescharacteristic
290C4×C47—21no—
291C4×C47—41no—
292C4×C47—41no—
293C4×C47—41no—
294C4×C47—41no—
295C4×C47—81no—
296C4×C47—81no—
297C4×C47—81no—
298C4×C47C2×#13511yescharacteristic
299C4×C47#57511yescharacteristic
300C4×C47#57611yescharacteristic
301C4×C47#57711yescharacteristic
302#3341C2×C4711yescharacteristic, complemented
303#3325C2×C4711yescharacteristic, complemented
304#3303C2×C4711yescharacteristic, complemented
305#3294C2×C4711yescharacteristic, complemented
306#1719C2×C4711yescharacteristic, complemented
307#1703C2×C4711yescharacteristic, complemented
308#1681C2×C4711yescharacteristic, complemented
309#1677C2×C4711yescharacteristic, complemented
310#1675C2×C4711yescharacteristic, complemented
311#1646C2×C4711yescharacteristic, complemented
312#1635C2×C4711yescharacteristic, complemented
313#1629C2×C4711yescharacteristic, complemented
314#1624C2×C4711yescharacteristic, complemented
315#1581C2×C4711yescharacteristic, complemented
316#1580C2×C4711yescharacteristic, complemented
317C2×C47—42no—
318C2×C47—81no—
319C2×C47—81no—
320C2×C47—81no—
321C2×C47—161no—
322C2×C47#326711yescharacteristic
323C2×C47#328011yescharacteristic
324C2×C47#328811yescharacteristic
325#555C22×C4711yescharacteristic
326#555C22×C4711yescharacteristic, complemented
327#547C22×C4711yescharacteristic
328D42C22×C4711yescharacteristic
329#500C22×C4711yescharacteristic, complemented
330#492C22×C4711yescharacteristic
331#487C22×C4711yescharacteristic, complemented
332#487C22×C4711yescharacteristic, complemented
333#486C22×C4711yescharacteristic
334#486C22×C4711yescharacteristic
335#485—21no—
336#482—21no—
337#482—21no—
338#482—21no—
339#480—21no—
340#476C22×C4711yescharacteristic
341#476C22×C4711yescharacteristic
342#476C22×C4711yescharacteristic
343#476C22×C4711yescharacteristic, complemented
344#474C22×C4711yescharacteristic
345#469—21no—
346#466—21no—
347#466—21no—
348#465—21no—
349#461C22×C4711yescharacteristic, complemented
350#459C22×C4711yescharacteristic
351#459C22×C4711yescharacteristic
352#449—21no—
353#447—21no—
354#447—21no—
355C4×D8C22×C4711yescharacteristic
356C4×D8C22×C4711yescharacteristic
357#436C22×C4711yescharacteristic
358C8×D4C22×C4711yescharacteristic
359C8×D4C22×C4711yescharacteristic, complemented
360C8×D4C22×C4711yescharacteristic, complemented
361#427—21no—
362#418—21no—
363#416—21no—
364C2×#102—21no—
365#335C22×C4711yescharacteristic, complemented
366#334C22×C4711yescharacteristic, complemented
367#333C22×C4711yescharacteristic, complemented
368#333C22×C4711yescharacteristic, complemented
369#332C22×C4711yescharacteristic, complemented
370#331C22×C4711yescharacteristic
371D4⋊C8C22×C4711yescharacteristic
372D4⋊C8C22×C4711yescharacteristic
373D4⋊C8C22×C4711yescharacteristic, complemented
374D4⋊C8C22×C4711yescharacteristic, complemented
375#322C22×C4711yescharacteristic, complemented
376C47#1977511yescharacteristic, direct product factor, Sylow
377C2×#41—21no—
378C22×D4—21no—
379C22×D4—21no—
380C2×SD16—21no—
381C2×SD16—41no—
382C2×D8—21no—
383C2×D8—21no—
384C2×D8D4×C4711yescharacteristic
385C2×D8D4×C4711yescharacteristic
386C2×M16—21no—
387C22×C8—21no—
388C22×C8—21no—
389C22×C8—21no—
390C4⋊Q8C23×C4711yescharacteristic
391C4⋊Q8C23×C4711yescharacteristic
392C4⋊Q8C23×C4711yescharacteristic
393#127C23×C4711yescharacteristic
394#124—41no—
395#124—41no—
396#123—41no—
397C22⋊Q8—21no—
398#121—21no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121—21no—
403#121—21no—
404#121—21no—
405#120—41no—
406C4×D4C23×C4711yescharacteristic
407C4×D4C23×C4711yescharacteristic
408C4×D4C23×C4711yescharacteristic
409C4×D4C23×C4711yescharacteristic
410#117—21no—
411#117—21no—
412#117—21no—
413#117—21no—
414C2×C4⋊C4—21no—
415#107—21no—
416#107—21no—
417#107—21no—
418#107D4×C4711yescharacteristic
419#107D4×C4711yescharacteristic
420#106—21no—
421#106—21no—
422#106—21no—
423#106—21no—
424C4⋊C8C23×C4711yescharacteristic
425C4⋊C8C23×C4711yescharacteristic
426C4⋊C8C23×C4711yescharacteristic
427C4⋊C8C23×C4711yescharacteristic
428#103—21no—
429#103—21no—
430#103—21no—
431#103—41no—
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#102D4×C4711yescharacteristic
444#102D4×C4711yescharacteristic
445#102D4×C4711yescharacteristic
446#102D4×C4711yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C4×C8C23×C4711yescharacteristic
452C4×C8C23×C4711yescharacteristic
453C4×C8C23×C4711yescharacteristic
454C24—41no—
455#41—42no—
456#41—81no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—81no—
471C2×D4—81no—
472C2×D4C2×D4×C4711yescharacteristic
473C2×D4C2×D4×C4711yescharacteristic
474C2×D4C2×D4×C4711yescharacteristic
475C2×D4C2×D4×C4711yescharacteristic
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—41no—
481SD16—81no—
482SD16—82no—
483D8—22no—
484D8—41no—
485D8—81no—
486D8—81no—
487M16—81no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—42no—
494C2×C8—81no—
495C2×C8—81no—
496C2×C8C2×D4×C4711yescharacteristic
497C2×C8C2×D4×C4711yescharacteristic
498C2×C8C2×D4×C4711yescharacteristic
499C2×C8C2×D4×C4711yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—41no—
507C4⋊C4C2×D4×C4711yescharacteristic
508C4⋊C4C2×D4×C4711yescharacteristic
509C4⋊C4C2×D4×C4711yescharacteristic
510C4⋊C4C2×D4×C4711yescharacteristic
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C42—41no—
522C42—41no—
523C42C24×C4711yescharacteristic
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—41no—
529C23—82no—
530C23—82no—
531C23—161no—
532Q8—41no—
533Q8—41no—
534Q8—81no—
535Q8—81no—
536D4—21no—
537D4—21no—
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—161no—
552D4—161no—
553D4#135×C4712yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
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—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—82no—
570C2×C4C22×D4×C4711yescharacteristic
571C2×C4C22×D4×C4711yescharacteristic
572C2×C4H(5,𝔽2)×C4711yescharacteristic
573C8—21no—
574C8—21no—
575C8—21no—
576C8—21no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—164no—
598C22D42×C4711yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4C2×#135×C4711yescharacteristic
608C4C47×#57511yescharacteristic
609C4C47×#57611yescharacteristic
610C4C47×#57711yescharacteristic
611C2—42no—
612C2—81no—
613C2—81no—
614C2—81no—
615C2—161no—
616C2C47×#326711yescharacteristic
617C2C47×#328011yescharacteristic
618C2C47×#328811yescharacteristic
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×#3341C2semidirect
2. C47×#3325C2semidirect
3. C47×#3303C2semidirect
4. C47×#3294C2semidirect
5. C47×#1719C2semidirect
6. C47×#1703C2semidirect
7. C47×#1681C2semidirect
8. C47×#1677C2semidirect
9. C47×#1675C2semidirect
10. C47×#1646C2semidirect
11. C47×#1635C2semidirect
12. C47×#1629C2semidirect
13. C47×#1624C2semidirect
14. C47×#1581C2semidirect
15. C47×#1580C2semidirect
17. C47×#555C22semidirect
20. C47×#500C22semidirect
22. C47×#487C22semidirect
23. C47×#487C22semidirect
34. C47×#476C22semidirect
40. C47×#461C22semidirect
50. C8×D4×C47C22semidirect
51. C8×D4×C47C22semidirect
56. C47×#335C22semidirect
57. C47×#334C22semidirect
58. C47×#333C22semidirect
59. C47×#333C22semidirect
60. C47×#332C22semidirect
64. C47×D4⋊C8C22semidirect
65. C47×D4⋊C8C22semidirect
66. C47×#322C22semidirect
272. #19775C47direct (N × H)
302. #3341C2×C47semidirect
303. #3325C2×C47semidirect
304. #3303C2×C47semidirect
305. #3294C2×C47semidirect
306. #1719C2×C47semidirect
307. #1703C2×C47semidirect
308. #1681C2×C47semidirect
309. #1677C2×C47semidirect
310. #1675C2×C47semidirect
311. #1646C2×C47semidirect
312. #1635C2×C47semidirect
313. #1629C2×C47semidirect
314. #1624C2×C47semidirect
315. #1581C2×C47semidirect
316. #1580C2×C47semidirect
326. #555C22×C47semidirect
329. #500C22×C47semidirect
331. #487C22×C47semidirect
332. #487C22×C47semidirect
343. #476C22×C47semidirect
349. #461C22×C47semidirect
359. C8×D4C22×C47semidirect
360. C8×D4C22×C47semidirect
365. #335C22×C47semidirect
366. #334C22×C47semidirect
367. #333C22×C47semidirect
368. #333C22×C47semidirect
369. #332C22×C47semidirect
373. D4⋊C8C22×C47semidirect
374. D4⋊C8C22×C47semidirect
375. #322C22×C47semidirect
376. C47#19775direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33412
C47×#33252
C47×#33032
C47×#32942
C47×#17192
C47×#17032
C47×#16812
C47×#16772
C47×#16752
C47×#16462
C47×#16352
C47×#16292
C47×#16242
C47×#15812
C47×#15802
#1977547