Finite Group Databasebeta

← C47×#19988 #26059686

Subgroups — C47×#19988 #26059686

Order 12032.

650 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3360C211yesmaximal, characteristic, complemented
2C47×#3302C211yesmaximal, characteristic, complemented
3C47×#3295C211yesmaximal, characteristic, complemented
4C47×#3294C211yesmaximal, characteristic
5C47×#1711C211yesmaximal, characteristic, complemented
6C47×#1683C211yesmaximal, characteristic, complemented
7C47×#1682C211yesmaximal, characteristic, complemented
8C47×#1679C211yesmaximal, characteristic, complemented
9C47×#1677C211yesmaximal, characteristic, complemented
10C47×#1644C211yesmaximal, characteristic, complemented
11C47×#1639C211yesmaximal, characteristic, complemented
12C47×#1635C211yesmaximal, characteristic, complemented
13C47×#1628C211yesmaximal, characteristic, complemented
14C8×SD16×C47C211yesmaximal, characteristic, complemented
15C8×D8×C47C211yesmaximal, characteristic, complemented
16C47×#556C2211yescharacteristic, complemented
17C47×#554C2211yescharacteristic
18C47×#547C2211yescharacteristic
19D42×C47C2211yescharacteristic
20C47×#488—21no—
21C47×#487C2211yescharacteristic, complemented
22C47×#487C2211yescharacteristic, complemented
23C47×#487C2211yescharacteristic, complemented
24C47×#486C2211yescharacteristic
25C47×#486C2211yescharacteristic
26C47×#486C2211yescharacteristic
27C47×#485—21no—
28C47×#481—21no—
29C47×#480—21no—
30C47×#479—21no—
31C47×#476C2211yescharacteristic
32C47×#476C2211yescharacteristic, complemented
33C47×#474C2211yescharacteristic
34C47×#474C2211yescharacteristic
35C47×#467—21no—
36C47×#466—21no—
37C47×#465—21no—
38C47×#463—21no—
39C47×#462C2211yescharacteristic, complemented
40C47×#461C2211yescharacteristic
41C47×#460C2211yescharacteristic
42C47×#459C2211yescharacteristic
43C47×#452—21no—
44C47×#450—21no—
45C47×#447—21no—
46C8×Q8×C47C2211yescharacteristic, complemented
47C4×SD16×C47—21no—
48C4×SD16×C47C2211yescharacteristic
49C4×D8×C47C2211yescharacteristic
50C8×D4×C47C2211yescharacteristic
51C8×D4×C47C2211yescharacteristic
52C8×D4×C47C2211yescharacteristic, complemented
53C47×#416—21no—
54C2×#102×C47—21no—
55C2×#102×C47—21no—
56C47×#335C2211yescharacteristic, complemented
57C47×#334C2211yescharacteristic, complemented
58C47×#333C2211yescharacteristic, complemented
59C47×#332C2211yescharacteristic, complemented
60C47×#332C2211yescharacteristic, complemented
61C47×#331C2211yescharacteristic
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—21no—
71C2×SD16×C47—21no—
72C2×SD16×C47—21no—
73C2×SD16×C47D411yescharacteristic
74C2×D8×C47—21no—
75C2×D8×C47D411yescharacteristic
76C22×C8×C47—21no—
77C22×C8×C47—21no—
78C22×C8×C47—21no—
79C4⋊Q8×C47C2311yescharacteristic
80C4⋊Q8×C47C2311yescharacteristic
81C4⋊Q8×C47C2311yescharacteristic
82#127×C47C2311yescharacteristic
83#126×C47—41no—
84#125×C47—21no—
85#124×C47—21no—
86#123×C47—41no—
87C22⋊Q8×C47—21no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47—21no—
90C22⋊Q8×C47—41no—
91#121×C47—21no—
92#121×C47—21no—
93#121×C47—21no—
94#120×C47—41no—
95C4×Q8×C47—21no—
96C4×Q8×C47C2311yescharacteristic
97C4×D4×C47—21no—
98C4×D4×C47C2311yescharacteristic
99C4×D4×C47C2311yescharacteristic
100C4×D4×C47C2311yescharacteristic
101#117×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104#107×C47—21no—
105#107×C47—21no—
106#107×C47D411yescharacteristic
107#106×C47—21no—
108#106×C47—21no—
109#106×C47D411yescharacteristic
110C4⋊C8×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#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—41no—
134#102×C47D411yescharacteristic
135#102×C47D411yescharacteristic
136#102×C47D411yescharacteristic
137C22⋊C8×C47—21no—
138C22⋊C8×C47—21no—
139C22⋊C8×C47—21no—
140C4×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×Q8×C47C2×D411yescharacteristic
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—41no—
155C2×D4×C47—41no—
156C2×D4×C47—42no—
157C2×D4×C47—42no—
158C2×D4×C47—41no—
159C2×D4×C47—81no—
160C2×D4×C47—81no—
161C2×D4×C47C2×D411yescharacteristic
162C2×D4×C47C2×D411yescharacteristic
163C2×D4×C47C2×D411yescharacteristic
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—41no—
168C22×C4×C47—41no—
169Q16×C47—81no—
170SD16×C47—22no—
171SD16×C47—42no—
172SD16×C47—81no—
173D8×C47—22no—
174D8×C47—81no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47—21no—
180C2×C8×C47—81no—
181C2×C8×C47—81no—
182C2×C8×C47—81no—
183C2×C8×C47C2×D411yescharacteristic
184C2×C8×C47C2×D411yescharacteristic
185C2×C8×C47C2×D411yescharacteristic
186C2×C8×C47C2×D411yescharacteristic
187C4⋊C4×C47—21no—
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×C47—41no—
198C4⋊C4×C47C2×D411yescharacteristic
199C4⋊C4×C47C2×D411yescharacteristic
200C4⋊C4×C47C2×D411yescharacteristic
201C4⋊C4×C47C2×D411yescharacteristic
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—
210C42×C47—21no—
211C42×C47—41no—
212C42×C47C2411yescharacteristic
213C23×C47—21no—
214C23×C47—21no—
215C23×C47—21no—
216C23×C47—41no—
217C23×C47—82no—
218C23×C47—82no—
219C23×C47—161no—
220Q8×C47—21no—
221Q8×C47—21no—
222Q8×C47—41no—
223Q8×C47—41no—
224Q8×C47—41no—
225Q8×C47—41no—
226Q8×C47—81no—
227D4×C47—21no—
228D4×C47—21no—
229D4×C47—21no—
230D4×C47—21no—
231D4×C47—41no—
232D4×C47—41no—
233D4×C47—41no—
234D4×C47—41no—
235D4×C47—81no—
236D4×C47—82no—
237D4×C47—82no—
238D4×C47—82no—
239D4×C47#13512yes—
240D4×C47#13512yes—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—21no—
245C2×C4×C47—21no—
246C2×C4×C47—41no—
247C2×C4×C47—41no—
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—82no—
256C2×C4×C47—161no—
257C2×C4×C47C22×D411yescharacteristic
258C2×C4×C47C22×D411yescharacteristic
259C2×C4×C47H(5,𝔽2)11yescharacteristic
260C8×C47—21no—
261C8×C47—21no—
262C8×C47—21no—
263C8×C47—21no—
264C8×C47—41no—
265C8×C47—41no—
266C8×C47—41no—
267C8×C47—41no—
268C8×C47—41no—
269#19988C4711yesmaximal, characteristic, direct product factor, Sylow
270C22×C47—22no—
271C22×C47—22no—
272C22×C47—41no—
273C22×C47—41no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—41no—
278C22×C47—41no—
279C22×C47—81no—
280C22×C47—81no—
281C22×C47—81no—
282C22×C47—164no—
283C22×C47D4211yescharacteristic
284C4×C47—21no—
285C4×C47—41no—
286C4×C47—41no—
287C4×C47—41no—
288C4×C47—41no—
289C4×C47—41no—
290C4×C47—81no—
291C4×C47—81no—
292C4×C47—81no—
293C4×C47C2×#13511yescharacteristic
294C4×C47C2×#13511yescharacteristic
295C4×C47#57611yescharacteristic
296C4×C47#57711yescharacteristic
297#3360C2×C4711yescharacteristic, complemented
298#3302C2×C4711yescharacteristic, complemented
299#3295C2×C4711yescharacteristic, complemented
300#3294C2×C4711yescharacteristic
301#1711C2×C4711yescharacteristic, complemented
302#1683C2×C4711yescharacteristic, complemented
303#1682C2×C4711yescharacteristic, complemented
304#1679C2×C4711yescharacteristic, complemented
305#1677C2×C4711yescharacteristic, complemented
306#1644C2×C4711yescharacteristic, complemented
307#1639C2×C4711yescharacteristic, complemented
308#1635C2×C4711yescharacteristic, complemented
309#1628C2×C4711yescharacteristic, complemented
310C8×SD16C2×C4711yescharacteristic, complemented
311C8×D8C2×C4711yescharacteristic, complemented
312C2×C47—42no—
313C2×C47—42no—
314C2×C47—81no—
315C2×C47—161no—
316C2×C47#328011yescharacteristic
317C2×C47#328211yescharacteristic
318C2×C47#329011yescharacteristic
319#556C22×C4711yescharacteristic, complemented
320#554C22×C4711yescharacteristic
321#547C22×C4711yescharacteristic
322D42C22×C4711yescharacteristic
323#488—21no—
324#487C22×C4711yescharacteristic, complemented
325#487C22×C4711yescharacteristic, complemented
326#487C22×C4711yescharacteristic, complemented
327#486C22×C4711yescharacteristic
328#486C22×C4711yescharacteristic
329#486C22×C4711yescharacteristic
330#485—21no—
331#481—21no—
332#480—21no—
333#479—21no—
334#476C22×C4711yescharacteristic
335#476C22×C4711yescharacteristic, complemented
336#474C22×C4711yescharacteristic
337#474C22×C4711yescharacteristic
338#467—21no—
339#466—21no—
340#465—21no—
341#463—21no—
342#462C22×C4711yescharacteristic, complemented
343#461C22×C4711yescharacteristic
344#460C22×C4711yescharacteristic
345#459C22×C4711yescharacteristic
346#452—21no—
347#450—21no—
348#447—21no—
349C8×Q8C22×C4711yescharacteristic, complemented
350C4×SD16—21no—
351C4×SD16C22×C4711yescharacteristic
352C4×D8C22×C4711yescharacteristic
353C8×D4C22×C4711yescharacteristic
354C8×D4C22×C4711yescharacteristic
355C8×D4C22×C4711yescharacteristic, complemented
356#416—21no—
357C2×#102—21no—
358C2×#102—21no—
359#335C22×C4711yescharacteristic, complemented
360#334C22×C4711yescharacteristic, complemented
361#333C22×C4711yescharacteristic, complemented
362#332C22×C4711yescharacteristic, complemented
363#332C22×C4711yescharacteristic, complemented
364#331C22×C4711yescharacteristic
365Q8⋊C8C22×C4711yescharacteristic, complemented
366D4⋊C8C22×C4711yescharacteristic
367D4⋊C8C22×C4711yescharacteristic
368D4⋊C8C22×C4711yescharacteristic, complemented
369C82C22×C4711yescharacteristic, complemented
370C47#1998811yescharacteristic, direct product factor, Sylow
371C2×#41—21no—
372C22×D4—21no—
373C22×D4—21no—
374C2×Q16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16D4×C4711yescharacteristic
378C2×D8—21no—
379C2×D8D4×C4711yescharacteristic
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—21no—
383C4⋊Q8C23×C4711yescharacteristic
384C4⋊Q8C23×C4711yescharacteristic
385C4⋊Q8C23×C4711yescharacteristic
386#127C23×C4711yescharacteristic
387#126—41no—
388#125—21no—
389#124—21no—
390#123—41no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8—41no—
395#121—21no—
396#121—21no—
397#121—21no—
398#120—41no—
399C4×Q8—21no—
400C4×Q8C23×C4711yescharacteristic
401C4×D4—21no—
402C4×D4C23×C4711yescharacteristic
403C4×D4C23×C4711yescharacteristic
404C4×D4C23×C4711yescharacteristic
405#117—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408#107—21no—
409#107—21no—
410#107D4×C4711yescharacteristic
411#106—21no—
412#106—21no—
413#106D4×C4711yescharacteristic
414C4⋊C8—21no—
415C4⋊C8C23×C4711yescharacteristic
416C4⋊C8C23×C4711yescharacteristic
417C4⋊C8C23×C4711yescharacteristic
418C4⋊C8C23×C4711yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—41no—
426#103D4×C4711yescharacteristic
427#102—21no—
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—41no—
438#102D4×C4711yescharacteristic
439#102D4×C4711yescharacteristic
440#102D4×C4711yescharacteristic
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8—21no—
444C4×C8—21no—
445C4×C8C23×C4711yescharacteristic
446C4×C8C23×C4711yescharacteristic
447C4×C8C23×C4711yescharacteristic
448C24—41no—
449#41—42no—
450#41—81no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8C2×D4×C4711yescharacteristic
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—41no—
463C2×D4—81no—
464C2×D4—81no—
465C2×D4C2×D4×C4711yescharacteristic
466C2×D4C2×D4×C4711yescharacteristic
467C2×D4C2×D4×C4711yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—41no—
472C22×C4—41no—
473Q16—81no—
474SD16—22no—
475SD16—42no—
476SD16—81no—
477D8—22no—
478D8—81no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—81no—
485C2×C8—81no—
486C2×C8—81no—
487C2×C8C2×D4×C4711yescharacteristic
488C2×C8C2×D4×C4711yescharacteristic
489C2×C8C2×D4×C4711yescharacteristic
490C2×C8C2×D4×C4711yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—41no—
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—21no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C42—21no—
515C42—41no—
516C42C24×C4711yescharacteristic
517C23—21no—
518C23—21no—
519C23—21no—
520C23—41no—
521C23—82no—
522C23—82no—
523C23—161no—
524Q8—21no—
525Q8—21no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—81no—
531D4—21no—
532D4—21no—
533D4—21no—
534D4—21no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—81no—
540D4—82no—
541D4—82no—
542D4—82no—
543D4#135×C4712yes—
544D4#135×C4712yes—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—82no—
560C2×C4—161no—
561C2×C4C22×D4×C4711yescharacteristic
562C2×C4C22×D4×C4711yescharacteristic
563C2×C4H(5,𝔽2)×C4711yescharacteristic
564C8—21no—
565C8—21no—
566C8—21no—
567C8—21no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C22—22no—
574C22—22no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—164no—
586C22D42×C4711yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4C2×#135×C4711yescharacteristic
597C4C2×#135×C4711yescharacteristic
598C4C47×#57611yescharacteristic
599C4C47×#57711yescharacteristic
600C2—42no—
601C2—42no—
602C2—81no—
603C2—161no—
604C2C47×#328011yescharacteristic
605C2C47×#328211yescharacteristic
606C2C47×#329011yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3294C2
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×#3360C2semidirect
2. C47×#3302C2semidirect
3. C47×#3295C2semidirect
5. C47×#1711C2semidirect
6. C47×#1683C2semidirect
7. C47×#1682C2semidirect
8. C47×#1679C2semidirect
9. C47×#1677C2semidirect
10. C47×#1644C2semidirect
11. C47×#1639C2semidirect
12. C47×#1635C2semidirect
13. C47×#1628C2semidirect
14. C8×SD16×C47C2semidirect
15. C8×D8×C47C2semidirect
16. C47×#556C22semidirect
21. C47×#487C22semidirect
22. C47×#487C22semidirect
23. C47×#487C22semidirect
32. C47×#476C22semidirect
39. C47×#462C22semidirect
46. C8×Q8×C47C22semidirect
52. C8×D4×C47C22semidirect
56. C47×#335C22semidirect
57. C47×#334C22semidirect
58. C47×#333C22semidirect
59. C47×#332C22semidirect
60. C47×#332C22semidirect
62. C47×Q8⋊C8C22semidirect
65. C47×D4⋊C8C22semidirect
66. C82×C47C22semidirect
269. #19988C47direct (N × H)
297. #3360C2×C47semidirect
298. #3302C2×C47semidirect
299. #3295C2×C47semidirect
301. #1711C2×C47semidirect
302. #1683C2×C47semidirect
303. #1682C2×C47semidirect
304. #1679C2×C47semidirect
305. #1677C2×C47semidirect
306. #1644C2×C47semidirect
307. #1639C2×C47semidirect
308. #1635C2×C47semidirect
309. #1628C2×C47semidirect
310. C8×SD16C2×C47semidirect
311. C8×D8C2×C47semidirect
319. #556C22×C47semidirect
324. #487C22×C47semidirect
325. #487C22×C47semidirect
326. #487C22×C47semidirect
335. #476C22×C47semidirect
342. #462C22×C47semidirect
349. C8×Q8C22×C47semidirect
355. C8×D4C22×C47semidirect
359. #335C22×C47semidirect
360. #334C22×C47semidirect
361. #333C22×C47semidirect
362. #332C22×C47semidirect
363. #332C22×C47semidirect
365. Q8⋊C8C22×C47semidirect
368. D4⋊C8C22×C47semidirect
369. C82C22×C47semidirect
370. C47#19988direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33602
C47×#33022
C47×#32952
C47×#32942
C47×#17112
C47×#16832
C47×#16822
C47×#16792
C47×#16772
C47×#16442
C47×#16392
C47×#16352
C47×#16282
C8×SD16×C472
C8×D8×C472
#1998847