Finite Group Databasebeta

← C47×#19947 #26059645

Subgroups — C47×#19947 #26059645

Order 12032.

658 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3399C211yesmaximal, characteristic, complemented
2C47×#3394C211yesmaximal, characteristic, complemented
3C47×#3353C211yesmaximal, characteristic, complemented
4C47×#3284C211yesmaximal, characteristic, complemented
5C47×#1706C211yesmaximal, characteristic, complemented
6C47×#1694C211yesmaximal, characteristic, complemented
7C47×#1687C211yesmaximal, characteristic, complemented
8C47×#1666C211yesmaximal, characteristic, complemented
9C47×#1665C211yesmaximal, characteristic, complemented
10C47×#1641C211yesmaximal, characteristic, complemented
11C47×#1640C211yesmaximal, characteristic, complemented
12C47×#1628C211yesmaximal, characteristic, complemented
13C47×#1625C211yesmaximal, characteristic, complemented
14C47×#1590C211yesmaximal, characteristic, complemented
15C8×SD16×C47C211yesmaximal, characteristic, complemented
16C2×#135×C47—21no—
17C47×#559C2211yescharacteristic
18C47×#556C2211yescharacteristic
19C47×#550C2211yescharacteristic
20C47×#547C2211yescharacteristic
21C47×#500C2211yescharacteristic
22C47×#496—21no—
23C47×#495—21no—
24C47×#493C2211yescharacteristic
25C47×#492C2211yescharacteristic
26C47×#492C2211yescharacteristic
27C47×#486C2211yescharacteristic
28C47×#486C2211yescharacteristic
29C47×#484—21no—
30C47×#482—21no—
31C47×#475C2211yescharacteristic
32C47×#474C2211yescharacteristic
33C47×#468—21no—
34C47×#465—21no—
35C47×#464—21no—
36C47×#463—21no—
37C47×#463—21no—
38C47×#462C2211yescharacteristic
39C47×#462C2211yescharacteristic
40C47×#460C2211yescharacteristic
41C47×#459—21no—
42C47×#459C2211yescharacteristic
43C47×#459C2211yescharacteristic
44C47×#459C2211yescharacteristic
45C47×#452—21no—
46C47×#449—21no—
47C47×#446C2211yescharacteristic
48C8×Q8×C47C2211yescharacteristic
49C47×#442—21no—
50C4×SD16×C47—21no—
51C4×SD16×C47C2211yescharacteristic
52C4×SD16×C47C2211yescharacteristic
53C47×#436C2211yescharacteristic
54C8×D4×C47C2211yescharacteristic
55C47×#428—21no—
56C47×#334C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#332C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#331C2211yescharacteristic
61C47×#331C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C82×C47C2211yescharacteristic
67C2×#41×C47—21no—
68C2×#41×C47—21no—
69#135×C47—44no—
70C2×Q16×C47—21no—
71C2×Q16×C47—21no—
72C2×SD16×C47—21no—
73C2×SD16×C47—21no—
74C2×SD16×C47—21no—
75C2×SD16×C47—21no—
76C2×SD16×C47—21no—
77C2×SD16×C47D411yescharacteristic
78C2×SD16×C47D411yescharacteristic
79C2×D8×C47—21no—
80C2×D8×C47—21no—
81C2×D8×C47—21no—
82C2×D8×C47—21no—
83C2×D8×C47—21no—
84C2×M16×C47—21no—
85C22×C8×C47—21no—
86C4⋊Q8×C47C2311yescharacteristic
87C4⋊Q8×C47C2311yescharacteristic
88#127×C47—21no—
89#127×C47C2311yescharacteristic
90#127×C47C2311yescharacteristic
91#126×C47—41no—
92#124×C47—21no—
93#124×C47—21no—
94#124×C47—21no—
95#123×C47—41no—
96#123×C47—41no—
97C22⋊Q8×C47—21no—
98C22⋊Q8×C47—21no—
99#121×C47—21no—
100#121×C47—21no—
101#121×C47—41no—
102C4×Q8×C47—21no—
103C4×Q8×C47C2311yescharacteristic
104C4×Q8×C47C2311yescharacteristic
105C4×D4×C47—21no—
106C4×D4×C47—21no—
107C4×D4×C47—21no—
108C4×D4×C47C2311yescharacteristic
109C4×D4×C47C2311yescharacteristic
110#117×C47—21no—
111C2×C4⋊C4×C47—21no—
112#107×C47—21no—
113#107×C47—21no—
114#107×C47—21no—
115#106×C47—21no—
116#106×C47D411yescharacteristic
117#106×C47D411yescharacteristic
118C4⋊C8×C47—21no—
119C4⋊C8×C47—21no—
120C4⋊C8×C47C2311yescharacteristic
121C4⋊C8×C47C2311yescharacteristic
122C4⋊C8×C47C2311yescharacteristic
123C4⋊C8×C47C2311yescharacteristic
124#103×C47—21no—
125#103×C47—21no—
126#103×C47—21no—
127#103×C47D411yescharacteristic
128#103×C47D411yescharacteristic
129#102×C47—21no—
130#102×C47—21no—
131#102×C47—21no—
132#102×C47—21no—
133#102×C47—21no—
134#102×C47—41no—
135#102×C47—41no—
136#102×C47D411yescharacteristic
137#102×C47D411yescharacteristic
138C22⋊C8×C47—21no—
139C22⋊C8×C47—21no—
140#97×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
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×C47C2×D411yescharacteristic
152C2×Q8×C47C2×D411yescharacteristic
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—41no—
160C2×D4×C47—41no—
161C2×D4×C47—41no—
162C2×D4×C47C2×D411yescharacteristic
163C2×D4×C47C2×D411yescharacteristic
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—41no—
167C22×C4×C47—41no—
168C22×C4×C47—41no—
169Q16×C47—42no—
170Q16×C47—81no—
171SD16×C47—22no—
172SD16×C47—22no—
173SD16×C47—42no—
174SD16×C47—42no—
175SD16×C47—81no—
176SD16×C47—81no—
177SD16×C47—81no—
178D8×C47—42no—
179D8×C47—42no—
180D8×C47—81no—
181D8×C47—81no—
182D8×C47—81no—
183M16×C47—42no—
184C2×C8×C47—21no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—42no—
190C2×C8×C47C2×D411yescharacteristic
191C2×C8×C47C2×D411yescharacteristic
192C2×C8×C47C2×D411yescharacteristic
193C2×C8×C47C2×D411yescharacteristic
194C4⋊C4×C47—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—21no—
198C4⋊C4×C47—21no—
199C4⋊C4×C47—21no—
200C4⋊C4×C47—41no—
201C4⋊C4×C47—41no—
202C4⋊C4×C47C2×D411yescharacteristic
203C4⋊C4×C47C2×D411yescharacteristic
204C4⋊C4×C47C2×D411yescharacteristic
205C4⋊C4×C47C2×D411yescharacteristic
206C22⋊C4×C47—21no—
207C22⋊C4×C47—21no—
208C22⋊C4×C47—41no—
209C22⋊C4×C47—41no—
210C22⋊C4×C47—41no—
211C22⋊C4×C47—41no—
212C22⋊C4×C47—41no—
213C22⋊C4×C47—41no—
214C22⋊C4×C47—41no—
215C42×C47—21no—
216C42×C47—21no—
217C42×C47—41no—
218C42×C47C2411yescharacteristic
219C23×C47—21no—
220C23×C47—21no—
221C23×C47—41no—
222C23×C47—41no—
223Q8×C47—21no—
224Q8×C47—21no—
225Q8×C47—21no—
226Q8×C47—21no—
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—41no—
236D4×C47—41no—
237D4×C47—41no—
238D4×C47—41no—
239D4×C47—41no—
240D4×C47—41no—
241D4×C47—41no—
242D4×C47—41no—
243D4×C47—81no—
244D4×C47—81no—
245D4×C47—82no—
246D4×C47—82no—
247D4×C47—161no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
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—82no—
261C2×C4×C47—82no—
262C2×C4×C47—161no—
263C2×C4×C47C22×D411yescharacteristic
264C2×C4×C47C22×D411yescharacteristic
265C2×C4×C47H(5,𝔽2)11yescharacteristic
266C8×C47—21no—
267C8×C47—21no—
268C8×C47—41no—
269C8×C47—41no—
270C8×C47—41no—
271C8×C47—41no—
272C8×C47—41no—
273C8×C47#13512yescomplemented
274C8×C47AGL(1,ℤ/8)12yes—
275#19947C4711yesmaximal, characteristic, direct product factor, Sylow
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—81no—
286C22×C47—81no—
287C22×C47—81no—
288C22×C47D4211yescharacteristic
289C4×C47—21no—
290C4×C47—41no—
291C4×C47—41no—
292C4×C47—41no—
293C4×C47—41no—
294C4×C47—41no—
295C4×C47—41no—
296C4×C47—81no—
297C4×C47—81no—
298C4×C47C2×#13511yescharacteristic
299C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C47#57611yescharacteristic
301C4×C47#57711yescharacteristic
302#3399C2×C4711yescharacteristic, complemented
303#3394C2×C4711yescharacteristic, complemented
304#3353C2×C4711yescharacteristic, complemented
305#3284C2×C4711yescharacteristic, complemented
306#1706C2×C4711yescharacteristic, complemented
307#1694C2×C4711yescharacteristic, complemented
308#1687C2×C4711yescharacteristic, complemented
309#1666C2×C4711yescharacteristic, complemented
310#1665C2×C4711yescharacteristic, complemented
311#1641C2×C4711yescharacteristic, complemented
312#1640C2×C4711yescharacteristic, complemented
313#1628C2×C4711yescharacteristic, complemented
314#1625C2×C4711yescharacteristic, complemented
315#1590C2×C4711yescharacteristic, complemented
316C8×SD16C2×C4711yescharacteristic, complemented
317C2×C47—81no—
318C2×C47—81no—
319C2×C47—161no—
320C2×C47—161no—
321C2×C47#327411yescharacteristic
322C2×C47#328411yescharacteristic
323C2×C47#329011yescharacteristic
324C2×#135—21no—
325#559C22×C4711yescharacteristic
326#556C22×C4711yescharacteristic
327#550C22×C4711yescharacteristic
328#547C22×C4711yescharacteristic
329#500C22×C4711yescharacteristic
330#496—21no—
331#495—21no—
332#493C22×C4711yescharacteristic
333#492C22×C4711yescharacteristic
334#492C22×C4711yescharacteristic
335#486C22×C4711yescharacteristic
336#486C22×C4711yescharacteristic
337#484—21no—
338#482—21no—
339#475C22×C4711yescharacteristic
340#474C22×C4711yescharacteristic
341#468—21no—
342#465—21no—
343#464—21no—
344#463—21no—
345#463—21no—
346#462C22×C4711yescharacteristic
347#462C22×C4711yescharacteristic
348#460C22×C4711yescharacteristic
349#459—21no—
350#459C22×C4711yescharacteristic
351#459C22×C4711yescharacteristic
352#459C22×C4711yescharacteristic
353#452—21no—
354#449—21no—
355#446C22×C4711yescharacteristic
356C8×Q8C22×C4711yescharacteristic
357#442—21no—
358C4×SD16—21no—
359C4×SD16C22×C4711yescharacteristic
360C4×SD16C22×C4711yescharacteristic
361#436C22×C4711yescharacteristic
362C8×D4C22×C4711yescharacteristic
363#428—21no—
364#334C22×C4711yescharacteristic
365#334C22×C4711yescharacteristic
366#332C22×C4711yescharacteristic
367#332C22×C4711yescharacteristic
368#331C22×C4711yescharacteristic
369#331C22×C4711yescharacteristic
370Q8⋊C8C22×C4711yescharacteristic
371Q8⋊C8C22×C4711yescharacteristic
372D4⋊C8C22×C4711yescharacteristic
373D4⋊C8C22×C4711yescharacteristic
374C82C22×C4711yescharacteristic
375C47#1994711yescharacteristic, direct product factor, Sylow
376C2×#41—21no—
377C2×#41—21no—
378#135—44no—
379C2×Q16—21no—
380C2×Q16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16D4×C4711yescharacteristic
387C2×SD16D4×C4711yescharacteristic
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—21no—
391C2×D8—21no—
392C2×D8—21no—
393C2×M16—21no—
394C22×C8—21no—
395C4⋊Q8C23×C4711yescharacteristic
396C4⋊Q8C23×C4711yescharacteristic
397#127—21no—
398#127C23×C4711yescharacteristic
399#127C23×C4711yescharacteristic
400#126—41no—
401#124—21no—
402#124—21no—
403#124—21no—
404#123—41no—
405#123—41no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408#121—21no—
409#121—21no—
410#121—41no—
411C4×Q8—21no—
412C4×Q8C23×C4711yescharacteristic
413C4×Q8C23×C4711yescharacteristic
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4C23×C4711yescharacteristic
418C4×D4C23×C4711yescharacteristic
419#117—21no—
420C2×C4⋊C4—21no—
421#107—21no—
422#107—21no—
423#107—21no—
424#106—21no—
425#106D4×C4711yescharacteristic
426#106D4×C4711yescharacteristic
427C4⋊C8—21no—
428C4⋊C8—21no—
429C4⋊C8C23×C4711yescharacteristic
430C4⋊C8C23×C4711yescharacteristic
431C4⋊C8C23×C4711yescharacteristic
432C4⋊C8C23×C4711yescharacteristic
433#103—21no—
434#103—21no—
435#103—21no—
436#103D4×C4711yescharacteristic
437#103D4×C4711yescharacteristic
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—41no—
444#102—41no—
445#102D4×C4711yescharacteristic
446#102D4×C4711yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—21no—
449#97—21no—
450C4×C8—21no—
451C4×C8C23×C4711yescharacteristic
452C4×C8C23×C4711yescharacteristic
453C4×C8C23×C4711yescharacteristic
454#41—42no—
455#41—42no—
456#41—81no—
457#41—81no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8C2×D4×C4711yescharacteristic
461C2×Q8C2×D4×C4711yescharacteristic
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4C2×D4×C4711yescharacteristic
472C2×D4C2×D4×C4711yescharacteristic
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478Q16—42no—
479Q16—81no—
480SD16—22no—
481SD16—22no—
482SD16—42no—
483SD16—42no—
484SD16—81no—
485SD16—81no—
486SD16—81no—
487D8—42no—
488D8—42no—
489D8—81no—
490D8—81no—
491D8—81no—
492M16—42no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—42no—
499C2×C8C2×D4×C4711yescharacteristic
500C2×C8C2×D4×C4711yescharacteristic
501C2×C8C2×D4×C4711yescharacteristic
502C2×C8C2×D4×C4711yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4C2×D4×C4711yescharacteristic
512C4⋊C4C2×D4×C4711yescharacteristic
513C4⋊C4C2×D4×C4711yescharacteristic
514C4⋊C4C2×D4×C4711yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C42—21no—
525C42—21no—
526C42—41no—
527C42C24×C4711yescharacteristic
528C23—21no—
529C23—21no—
530C23—41no—
531C23—41no—
532Q8—21no—
533Q8—21no—
534Q8—21no—
535Q8—21no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—81no—
553D4—81no—
554D4—82no—
555D4—82no—
556D4—161no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4—161no—
572C2×C4C22×D4×C4711yescharacteristic
573C2×C4C22×D4×C4711yescharacteristic
574C2×C4H(5,𝔽2)×C4711yescharacteristic
575C8—21no—
576C8—21no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8#135×C4712yescomplemented
583C8AGL(1,ℤ/8)×C4712yes—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22D42×C4711yescharacteristic
597C4—21no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4C2×#135×C4711yescharacteristic
607C4C2×AGL(1,ℤ/8)×C4711yescharacteristic
608C4C47×#57611yescharacteristic
609C4C47×#57711yescharacteristic
610C2—81no—
611C2—81no—
612C2—161no—
613C2—161no—
614C2C47×#327411yescharacteristic
615C2C47×#328411yescharacteristic
616C2C47×#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×#3399C2semidirect
2. C47×#3394C2semidirect
3. C47×#3353C2semidirect
4. C47×#3284C2semidirect
5. C47×#1706C2semidirect
6. C47×#1694C2semidirect
7. C47×#1687C2semidirect
8. C47×#1666C2semidirect
9. C47×#1665C2semidirect
10. C47×#1641C2semidirect
11. C47×#1640C2semidirect
12. C47×#1628C2semidirect
13. C47×#1625C2semidirect
14. C47×#1590C2semidirect
15. C8×SD16×C47C2semidirect
273. C8×C47#135semidirect
275. #19947C47direct (N × H)
302. #3399C2×C47semidirect
303. #3394C2×C47semidirect
304. #3353C2×C47semidirect
305. #3284C2×C47semidirect
306. #1706C2×C47semidirect
307. #1694C2×C47semidirect
308. #1687C2×C47semidirect
309. #1666C2×C47semidirect
310. #1665C2×C47semidirect
311. #1641C2×C47semidirect
312. #1640C2×C47semidirect
313. #1628C2×C47semidirect
314. #1625C2×C47semidirect
315. #1590C2×C47semidirect
316. C8×SD16C2×C47semidirect
375. C47#19947direct (N × H)
582. C8#135×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#33992
C47×#33942
C47×#33532
C47×#32842
C47×#17062
C47×#16942
C47×#16872
C47×#16662
C47×#16652
C47×#16412
C47×#16402
C47×#16282
C47×#16252
C47×#15902
C8×SD16×C472
#1994747