Finite Group Databasebeta

← C47×#19825 #26059523

Subgroups — C47×#19825 #26059523

Order 12032.

642 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3394C211yesmaximal, characteristic, complemented
2C47×#3361C211yesmaximal, characteristic, complemented
3C47×#3324C211yesmaximal, characteristic, complemented
4C47×#3295C211yesmaximal, characteristic, complemented
5C47×#1717C211yesmaximal, characteristic, complemented
6C47×#1697C211yesmaximal, characteristic, complemented
7C47×#1682C211yesmaximal, characteristic, complemented
8C47×#1678C211yesmaximal, characteristic, complemented
9C47×#1665C211yesmaximal, characteristic, complemented
10C47×#1644C211yesmaximal, characteristic, complemented
11C47×#1638C211yesmaximal, characteristic, complemented
12C47×#1620C211yesmaximal, characteristic, complemented
13C47×#1619C211yesmaximal, characteristic
14C47×#1583C211yesmaximal, characteristic, complemented
15C47×SD16⋊C8C211yesmaximal, characteristic, complemented
16C47×#559C2211yescharacteristic, complemented
17C47×#556C2211yescharacteristic
18C47×#554C2211yescharacteristic
19D42×C47C2211yescharacteristic
20C47×#495—21no—
21C47×#493C2211yescharacteristic
22C47×#492C2211yescharacteristic, complemented
23C47×#488—21no—
24C47×#487C2211yescharacteristic, complemented
25C47×#486C2211yescharacteristic
26C47×#486C2211yescharacteristic
27C47×#486C2211yescharacteristic, complemented
28C47×#482—21no—
29C47×#481—21no—
30C47×#478—21no—
31C47×#477C2211yescharacteristic, complemented
32C47×#476C2211yescharacteristic
33C47×#474C2211yescharacteristic
34C47×#468—21no—
35C47×#465—21no—
36C47×#464—21no—
37C47×#463—21no—
38C47×#463—21no—
39C47×#462C2211yescharacteristic, complemented
40C47×#460C2211yescharacteristic
41C47×#460C2211yescharacteristic
42C47×#459C2211yescharacteristic
43C47×#459C2211yescharacteristic
44C47×#450—21no—
45C47×#450—21no—
46C8×Q8×C47C2211yescharacteristic, complemented
47C8×Q8×C47C2211yescharacteristic, complemented
48C4×SD16×C47—21no—
49C4×SD16×C47C2211yescharacteristic
50C4×SD16×C47C2211yescharacteristic
51C4×D8×C47—21no—
52C47×#436C2211yescharacteristic
53C8×D4×C47C2211yescharacteristic
54C47×#418—21no—
55C2×#102×C47—21no—
56C47×#335C2211yescharacteristic, complemented
57C47×#334C2211yescharacteristic, complemented
58C47×#333C2211yescharacteristic, complemented
59C47×#332C2211yescharacteristic, complemented
60C47×#331C2211yescharacteristic
61C47×#331C2211yescharacteristic, complemented
62C47×Q8⋊C8C2211yescharacteristic, complemented
63C47×Q8⋊C8C2211yescharacteristic, complemented
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic, complemented
67C22×D4×C47—21no—
68C22×D4×C47—21no—
69C2×Q16×C47—21no—
70C2×SD16×C47—21no—
71C2×SD16×C47—21no—
72C2×SD16×C47—21no—
73C2×SD16×C47—21no—
74C2×SD16×C47D411yescharacteristic
75C2×SD16×C47D411yescharacteristic
76C2×D8×C47—21no—
77C2×D8×C47—21no—
78C2×D8×C47—41no—
79C2×M16×C47—21no—
80C22×C8×C47—21no—
81C4⋊Q8×C47C2311yescharacteristic
82C4⋊Q8×C47C2311yescharacteristic
83#127×C47C2311yescharacteristic
84#127×C47C2311yescharacteristic
85#126×C47—41no—
86#125×C47—21no—
87#124×C47—21no—
88#124×C47—21no—
89#124×C47—21no—
90#123×C47—41no—
91C22⋊Q8×C47—21no—
92C22⋊Q8×C47—21no—
93C22⋊Q8×C47—41no—
94#121×C47—21no—
95#121×C47—21no—
96#120×C47—41no—
97C4×Q8×C47—21no—
98C4×Q8×C47C2311yescharacteristic
99C4×Q8×C47C2311yescharacteristic
100C4×D4×C47—21no—
101C4×D4×C47—21no—
102C4×D4×C47—21no—
103C4×D4×C47C2311yescharacteristic
104C4×D4×C47C2311yescharacteristic
105#117×C47—21no—
106C2×C4⋊C4×C47—21no—
107#107×C47—21no—
108#107×C47—21no—
109#106×C47—21no—
110#106×C47D411yescharacteristic
111#106×C47D411yescharacteristic
112C4⋊C8×C47—21no—
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—41no—
121#103×C47D411yescharacteristic
122#103×C47D411yescharacteristic
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×C47—21no—
135#102×C47D411yescharacteristic
136#102×C47D411yescharacteristic
137C22⋊C8×C47—21no—
138C22⋊C8×C47—21no—
139C4×C8×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C24×C47—41no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47C2×D411yescharacteristic
148C2×Q8×C47C2×D411yescharacteristic
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×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—81no—
160C2×D4×C47—81no—
161C2×D4×C47C2×D411yescharacteristic
162C2×D4×C47C2×D411yescharacteristic
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—41no—
166C22×C4×C47—41no—
167Q16×C47—81no—
168SD16×C47—22no—
169SD16×C47—41no—
170SD16×C47—42no—
171SD16×C47—81no—
172SD16×C47—81no—
173SD16×C47—81no—
174D8×C47—42no—
175D8×C47—81no—
176D8×C47—82no—
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×C47C2×D411yescharacteristic
185C2×C8×C47C2×D411yescharacteristic
186C2×C8×C47C2×D411yescharacteristic
187C2×C8×C47C2×D411yescharacteristic
188C4⋊C4×C47—21no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47—21no—
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—41no—
195C4⋊C4×C47—41no—
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—41no—
204C22⋊C4×C47—41no—
205C22⋊C4×C47—41no—
206C22⋊C4×C47—41no—
207C22⋊C4×C47—41no—
208C22⋊C4×C47—41no—
209C22⋊C4×C47—41no—
210C42×C47—21no—
211C42×C47—21no—
212C42×C47—41no—
213C42×C47C2411yescharacteristic
214C23×C47—21no—
215C23×C47—21no—
216C23×C47—41no—
217C23×C47—41no—
218C23×C47—82no—
219C23×C47—82no—
220C23×C47—161no—
221Q8×C47—21no—
222Q8×C47—21no—
223Q8×C47—21no—
224Q8×C47—21no—
225Q8×C47—41no—
226Q8×C47—41no—
227Q8×C47—81no—
228D4×C47—21no—
229D4×C47—21no—
230D4×C47—21no—
231D4×C47—41no—
232D4×C47—41no—
233D4×C47—41no—
234D4×C47—41no—
235D4×C47—41no—
236D4×C47—41no—
237D4×C47—41no—
238D4×C47—41no—
239D4×C47—81no—
240D4×C47—81no—
241D4×C47—82no—
242D4×C47—82no—
243D4×C47#13512yes—
244C2×C4×C47—21no—
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—161no—
257C2×C4×C47—161no—
258C2×C4×C47C22×D411yescharacteristic
259C2×C4×C47C22×D411yescharacteristic
260C2×C4×C47H(5,𝔽2)11yescharacteristic
261C8×C47—21no—
262C8×C47—21no—
263C8×C47—21no—
264C8×C47—21no—
265C8×C47—41no—
266C8×C47—41no—
267C8×C47—41no—
268C8×C47—41no—
269C8×C47—41no—
270#19825C4711yesmaximal, characteristic, direct product factor, Sylow
271C22×C47—22no—
272C22×C47—41no—
273C22×C47—41no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—81no—
278C22×C47—81no—
279C22×C47—81no—
280C22×C47—81no—
281C22×C47—81no—
282C22×C47—81no—
283C22×C47—164no—
284C22×C47D4211yescharacteristic
285C4×C47—21no—
286C4×C47—41no—
287C4×C47—41no—
288C4×C47—41no—
289C4×C47—41no—
290C4×C47—41no—
291C4×C47—41no—
292C4×C47—81no—
293C4×C47—81no—
294C4×C47C2×#13511yescharacteristic
295C4×C47#57511yescharacteristic
296C4×C47#57611yescharacteristic
297C4×C47#57711yescharacteristic
298#3394C2×C4711yescharacteristic, complemented
299#3361C2×C4711yescharacteristic, complemented
300#3324C2×C4711yescharacteristic, complemented
301#3295C2×C4711yescharacteristic, complemented
302#1717C2×C4711yescharacteristic, complemented
303#1697C2×C4711yescharacteristic, complemented
304#1682C2×C4711yescharacteristic, complemented
305#1678C2×C4711yescharacteristic, complemented
306#1665C2×C4711yescharacteristic, complemented
307#1644C2×C4711yescharacteristic, complemented
308#1638C2×C4711yescharacteristic, complemented
309#1620C2×C4711yescharacteristic, complemented
310#1619C2×C4711yescharacteristic
311#1583C2×C4711yescharacteristic, complemented
312SD16⋊C8C2×C4711yescharacteristic, complemented
313C2×C47—42no—
314C2×C47—81no—
315C2×C47—161no—
316C2×C47—161no—
317C2×C47#326811yescharacteristic
318C2×C47#328211yescharacteristic
319C2×C47#328811yescharacteristic
320#559C22×C4711yescharacteristic, complemented
321#556C22×C4711yescharacteristic
322#554C22×C4711yescharacteristic
323D42C22×C4711yescharacteristic
324#495—21no—
325#493C22×C4711yescharacteristic
326#492C22×C4711yescharacteristic, complemented
327#488—21no—
328#487C22×C4711yescharacteristic, complemented
329#486C22×C4711yescharacteristic
330#486C22×C4711yescharacteristic
331#486C22×C4711yescharacteristic, complemented
332#482—21no—
333#481—21no—
334#478—21no—
335#477C22×C4711yescharacteristic, complemented
336#476C22×C4711yescharacteristic
337#474C22×C4711yescharacteristic
338#468—21no—
339#465—21no—
340#464—21no—
341#463—21no—
342#463—21no—
343#462C22×C4711yescharacteristic, complemented
344#460C22×C4711yescharacteristic
345#460C22×C4711yescharacteristic
346#459C22×C4711yescharacteristic
347#459C22×C4711yescharacteristic
348#450—21no—
349#450—21no—
350C8×Q8C22×C4711yescharacteristic, complemented
351C8×Q8C22×C4711yescharacteristic, complemented
352C4×SD16—21no—
353C4×SD16C22×C4711yescharacteristic
354C4×SD16C22×C4711yescharacteristic
355C4×D8—21no—
356#436C22×C4711yescharacteristic
357C8×D4C22×C4711yescharacteristic
358#418—21no—
359C2×#102—21no—
360#335C22×C4711yescharacteristic, complemented
361#334C22×C4711yescharacteristic, complemented
362#333C22×C4711yescharacteristic, complemented
363#332C22×C4711yescharacteristic, complemented
364#331C22×C4711yescharacteristic
365#331C22×C4711yescharacteristic, complemented
366Q8⋊C8C22×C4711yescharacteristic, complemented
367Q8⋊C8C22×C4711yescharacteristic, complemented
368D4⋊C8C22×C4711yescharacteristic
369D4⋊C8C22×C4711yescharacteristic
370#322C22×C4711yescharacteristic, complemented
371C47#1982511yescharacteristic, direct product factor, Sylow
372C22×D4—21no—
373C22×D4—21no—
374C2×Q16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16D4×C4711yescharacteristic
380C2×SD16D4×C4711yescharacteristic
381C2×D8—21no—
382C2×D8—21no—
383C2×D8—41no—
384C2×M16—21no—
385C22×C8—21no—
386C4⋊Q8C23×C4711yescharacteristic
387C4⋊Q8C23×C4711yescharacteristic
388#127C23×C4711yescharacteristic
389#127C23×C4711yescharacteristic
390#126—41no—
391#125—21no—
392#124—21no—
393#124—21no—
394#124—21no—
395#123—41no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—41no—
399#121—21no—
400#121—21no—
401#120—41no—
402C4×Q8—21no—
403C4×Q8C23×C4711yescharacteristic
404C4×Q8C23×C4711yescharacteristic
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4C23×C4711yescharacteristic
409C4×D4C23×C4711yescharacteristic
410#117—21no—
411C2×C4⋊C4—21no—
412#107—21no—
413#107—21no—
414#106—21no—
415#106D4×C4711yescharacteristic
416#106D4×C4711yescharacteristic
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8C23×C4711yescharacteristic
420C4⋊C8C23×C4711yescharacteristic
421C4⋊C8C23×C4711yescharacteristic
422C4⋊C8C23×C4711yescharacteristic
423#103—21no—
424#103—21no—
425#103—41no—
426#103D4×C4711yescharacteristic
427#103D4×C4711yescharacteristic
428#102—21no—
429#102—21no—
430#102—21no—
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#102D4×C4711yescharacteristic
441#102D4×C4711yescharacteristic
442C22⋊C8—21no—
443C22⋊C8—21no—
444C4×C8—21no—
445C4×C8—21no—
446C4×C8C23×C4711yescharacteristic
447C4×C8C23×C4711yescharacteristic
448C4×C8C23×C4711yescharacteristic
449C24—41no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8C2×D4×C4711yescharacteristic
453C2×Q8C2×D4×C4711yescharacteristic
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4C2×D4×C4711yescharacteristic
467C2×D4C2×D4×C4711yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472Q16—81no—
473SD16—22no—
474SD16—41no—
475SD16—42no—
476SD16—81no—
477SD16—81no—
478SD16—81no—
479D8—42no—
480D8—81no—
481D8—82no—
482M16—81no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—81no—
489C2×C8C2×D4×C4711yescharacteristic
490C2×C8C2×D4×C4711yescharacteristic
491C2×C8C2×D4×C4711yescharacteristic
492C2×C8C2×D4×C4711yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4C2×D4×C4711yescharacteristic
503C4⋊C4C2×D4×C4711yescharacteristic
504C4⋊C4C2×D4×C4711yescharacteristic
505C4⋊C4C2×D4×C4711yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C42—21no—
516C42—21no—
517C42—41no—
518C42C24×C4711yescharacteristic
519C23—21no—
520C23—21no—
521C23—41no—
522C23—41no—
523C23—82no—
524C23—82no—
525C23—161no—
526Q8—21no—
527Q8—21no—
528Q8—21no—
529Q8—21no—
530Q8—41no—
531Q8—41no—
532Q8—81no—
533D4—21no—
534D4—21no—
535D4—21no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—81no—
545D4—81no—
546D4—82no—
547D4—82no—
548D4#135×C4712yes—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—161no—
562C2×C4—161no—
563C2×C4C22×D4×C4711yescharacteristic
564C2×C4C22×D4×C4711yescharacteristic
565C2×C4H(5,𝔽2)×C4711yescharacteristic
566C8—21no—
567C8—21no—
568C8—21no—
569C8—21no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—41no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—164no—
588C22D42×C4711yescharacteristic
589C4—21no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—81no—
597C4—81no—
598C4C2×#135×C4711yescharacteristic
599C4C47×#57511yescharacteristic
600C4C47×#57611yescharacteristic
601C4C47×#57711yescharacteristic
602C2—42no—
603C2—81no—
604C2—161no—
605C2—161no—
606C2C47×#326811yescharacteristic
607C2C47×#328211yescharacteristic
608C2C47×#328811yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#1619C2
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×#3394C2semidirect
2. C47×#3361C2semidirect
3. C47×#3324C2semidirect
4. C47×#3295C2semidirect
5. C47×#1717C2semidirect
6. C47×#1697C2semidirect
7. C47×#1682C2semidirect
8. C47×#1678C2semidirect
9. C47×#1665C2semidirect
10. C47×#1644C2semidirect
11. C47×#1638C2semidirect
12. C47×#1620C2semidirect
14. C47×#1583C2semidirect
15. C47×SD16⋊C8C2semidirect
16. C47×#559C22semidirect
22. C47×#492C22semidirect
24. C47×#487C22semidirect
27. C47×#486C22semidirect
31. C47×#477C22semidirect
39. C47×#462C22semidirect
46. C8×Q8×C47C22semidirect
47. C8×Q8×C47C22semidirect
56. C47×#335C22semidirect
57. C47×#334C22semidirect
58. C47×#333C22semidirect
59. C47×#332C22semidirect
61. C47×#331C22semidirect
62. C47×Q8⋊C8C22semidirect
63. C47×Q8⋊C8C22semidirect
66. C47×#322C22semidirect
270. #19825C47direct (N × H)
298. #3394C2×C47semidirect
299. #3361C2×C47semidirect
300. #3324C2×C47semidirect
301. #3295C2×C47semidirect
302. #1717C2×C47semidirect
303. #1697C2×C47semidirect
304. #1682C2×C47semidirect
305. #1678C2×C47semidirect
306. #1665C2×C47semidirect
307. #1644C2×C47semidirect
308. #1638C2×C47semidirect
309. #1620C2×C47semidirect
311. #1583C2×C47semidirect
312. SD16⋊C8C2×C47semidirect
320. #559C22×C47semidirect
326. #492C22×C47semidirect
328. #487C22×C47semidirect
331. #486C22×C47semidirect
335. #477C22×C47semidirect
343. #462C22×C47semidirect
350. C8×Q8C22×C47semidirect
351. C8×Q8C22×C47semidirect
360. #335C22×C47semidirect
361. #334C22×C47semidirect
362. #333C22×C47semidirect
363. #332C22×C47semidirect
365. #331C22×C47semidirect
366. Q8⋊C8C22×C47semidirect
367. Q8⋊C8C22×C47semidirect
370. #322C22×C47semidirect
371. C47#19825direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33942
C47×#33612
C47×#33242
C47×#32952
C47×#17172
C47×#16972
C47×#16822
C47×#16782
C47×#16652
C47×#16442
C47×#16382
C47×#16202
C47×#16192
C47×#15832
C47×SD16⋊C82
#1982547