Finite Group Databasebeta

← C47×#19766 #26059464

Subgroups — C47×#19766 #26059464

Order 12032.

650 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3384C211yesmaximal, characteristic, complemented
2C47×#3335C211yesmaximal, characteristic, complemented
3C47×#3298C211yesmaximal, characteristic, complemented
4C47×#3283C211yesmaximal, characteristic
5C47×#1716C211yesmaximal, characteristic, complemented
6C47×#1690C211yesmaximal, characteristic, complemented
7C47×#1679C211yesmaximal, characteristic, complemented
8C47×#1671C211yesmaximal, characteristic, complemented
9C47×#1671C211yesmaximal, characteristic, complemented
10C47×#1654C211yesmaximal, characteristic, complemented
11C47×#1651C211yesmaximal, characteristic, complemented
12C47×#1643C211yesmaximal, characteristic, complemented
13C47×#1635C211yesmaximal, characteristic, complemented
14C47×#1582C211yesmaximal, characteristic, complemented
15C47×#1580C211yesmaximal, characteristic, complemented
16C2×#135×C47—21no—
17C47×#554C2211yescharacteristic
18D4×Q8×C47C2211yescharacteristic
19C47×#547C2211yescharacteristic
20C47×#547C2211yescharacteristic
21C47×#501—21no—
22C47×#498C2211yescharacteristic
23C47×#498C2211yescharacteristic
24C47×#498C2211yescharacteristic
25C47×#494C2211yescharacteristic
26C47×#487C2211yescharacteristic
27C47×#487C2211yescharacteristic
28C47×#483—21no—
29C47×#483—21no—
30C47×#481—21no—
31C47×#478—21no—
32C47×#476—21no—
33C47×#476C2211yescharacteristic
34C47×#476C2211yescharacteristic
35C47×#475C2211yescharacteristic
36C47×#475C2211yescharacteristic
37C47×#474C2211yescharacteristic
38C47×#467—21no—
39C47×#465—21no—
40C47×#465—21no—
41C47×#461C2211yescharacteristic
42C47×#461C2211yescharacteristic
43C47×#461C2211yescharacteristic
44C47×#452—21no—
45C47×#452—21no—
46C47×#448—21no—
47C47×#446C2211yescharacteristic
48C47×#442—21no—
49C4×SD16×C47C2211yescharacteristic
50C4×D8×C47C2211yescharacteristic
51C8×D4×C47C2211yescharacteristic
52C8×D4×C47C2211yescharacteristic
53C8×D4×C47C2211yescharacteristic
54C2×#106×C47—21no—
55C2×#103×C47—21no—
56C47×#334C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#333C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#332C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×D4⋊C8C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×#41×C47—21no—
68C2×#41×C47—21no—
69C22×Q8×C47—21no—
70#135×C47—44no—
71C2×Q16×C47—21no—
72C2×Q16×C47—21no—
73C2×SD16×C47—21no—
74C2×SD16×C47—21no—
75C2×SD16×C47—21no—
76C2×SD16×C47D411yescharacteristic
77C2×D8×C47D411yescharacteristic
78C22×C8×C47—21no—
79C22×C8×C47—21no—
80C22×C8×C47—21no—
81C4⋊Q8×C47—21no—
82C4⋊Q8×C47C2311yescharacteristic
83C4⋊Q8×C47C2311yescharacteristic
84C4⋊Q8×C47C2311yescharacteristic
85C4⋊Q8×C47C2311yescharacteristic
86#125×C47—21no—
87#123×C47—41no—
88#123×C47—41no—
89C22⋊Q8×C47—21no—
90C22⋊Q8×C47—21no—
91C22⋊Q8×C47—21no—
92C22⋊Q8×C47—21no—
93C22⋊Q8×C47—41no—
94C22⋊Q8×C47—41no—
95#121×C47—21no—
96#121×C47—21no—
97C4×Q8×C47C2311yescharacteristic
98C4×D4×C47—21no—
99C4×D4×C47—21no—
100C4×D4×C47C2311yescharacteristic
101C4×D4×C47C2311yescharacteristic
102C4×D4×C47C2311yescharacteristic
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×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×C47—21no—
112#106×C47—21no—
113#106×C47—21no—
114#106×C47—21no—
115#106×C47—21no—
116#106×C47—41no—
117#106×C47D411yescharacteristic
118C4⋊C8×C47—21no—
119C4⋊C8×C47C2311yescharacteristic
120C4⋊C8×C47C2311yescharacteristic
121C4⋊C8×C47C2311yescharacteristic
122C4⋊C8×C47C2311yescharacteristic
123#103×C47—21no—
124#103×C47—21no—
125#103×C47—21no—
126#103×C47—21no—
127#103×C47—21no—
128#103×C47—21no—
129#103×C47—21no—
130#103×C47—41no—
131#103×C47D411yescharacteristic
132#102×C47—21no—
133#102×C47—21no—
134#102×C47—21no—
135#102×C47D411yescharacteristic
136#102×C47D411yescharacteristic
137#102×C47D411yescharacteristic
138C22⋊C8×C47—21no—
139C22⋊C8×C47—21no—
140C22⋊C8×C47—21no—
141#97×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×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47—41no—
154C2×Q8×C47—42no—
155C2×Q8×C47—81no—
156C2×Q8×C47C2×D411yescharacteristic
157C2×D4×C47—41no—
158C2×D4×C47—41no—
159C2×D4×C47C2×D411yescharacteristic
160C2×D4×C47C2×D411yescharacteristic
161C2×D4×C47C2×D411yescharacteristic
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—41no—
166C22×C4×C47—41no—
167C22×C4×C47—41no—
168C22×C4×C47—41no—
169Q16×C47—42no—
170Q16×C47—81no—
171SD16×C47—41no—
172SD16×C47—42no—
173SD16×C47—42no—
174SD16×C47—81no—
175D8×C47SD1614yescomplemented
176C2×C8×C47—21no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47—42no—
182C2×C8×C47—42no—
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—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—41no—
198C4⋊C4×C47—41no—
199C4⋊C4×C47—41no—
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—21no—
209C22⋊C4×C47—41no—
210C22⋊C4×C47—41no—
211C22⋊C4×C47—41no—
212C22⋊C4×C47—41no—
213C42×C47—21no—
214C42×C47C2411yescharacteristic
215C23×C47—21no—
216C23×C47—21no—
217C23×C47—21no—
218Q8×C47—21no—
219Q8×C47—21no—
220Q8×C47—41no—
221Q8×C47—41no—
222Q8×C47—41no—
223Q8×C47—41no—
224Q8×C47—41no—
225Q8×C47—41no—
226Q8×C47—81no—
227Q8×C47—82no—
228D4×C47—21no—
229D4×C47—21no—
230D4×C47—21no—
231D4×C47—21no—
232D4×C47—82no—
233D4×C47—82no—
234D4×C47C2×SD1612yes—
235D4×C47C2×SD1612yes—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
247C2×C4×C47—41no—
248C2×C4×C47—41no—
249C2×C4×C47—41no—
250C2×C4×C47—41no—
251C2×C4×C47—82no—
252C2×C4×C47—82no—
253C2×C4×C47—82no—
254C2×C4×C47—161no—
255C2×C4×C47C22×D411yescharacteristic
256C2×C4×C47C22×D411yescharacteristic
257C2×C4×C47H(5,𝔽2)11yescharacteristic
258C8×C47—21no—
259C8×C47—21no—
260C8×C47—21no—
261C8×C47—41no—
262C8×C47—41no—
263C8×C47—41no—
264C8×C47—41no—
265C8×C47—41no—
266C8×C47C2×SD1612yes—
267#19766C4711yesmaximal, characteristic, direct product factor, Sylow
268C22×C47—22no—
269C22×C47—22no—
270C22×C47—41no—
271C22×C47—41no—
272C22×C47—41no—
273C22×C47—41no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47D4211yescharacteristic
278C4×C47—21no—
279C4×C47—41no—
280C4×C47—41no—
281C4×C47—41no—
282C4×C47—41no—
283C4×C47—41no—
284C4×C47—81no—
285C4×C47—81no—
286C4×C47—81no—
287C4×C47—81no—
288C4×C47C22×SD1611yescharacteristic
289C4×C47#57511yescharacteristic
290C4×C47#57711yescharacteristic
291C4×C47#57711yescharacteristic
292#3384C2×C4711yescharacteristic, complemented
293#3335C2×C4711yescharacteristic, complemented
294#3298C2×C4711yescharacteristic, complemented
295#3283C2×C4711yescharacteristic
296#1716C2×C4711yescharacteristic, complemented
297#1690C2×C4711yescharacteristic, complemented
298#1679C2×C4711yescharacteristic, complemented
299#1671C2×C4711yescharacteristic, complemented
300#1671C2×C4711yescharacteristic, complemented
301#1654C2×C4711yescharacteristic, complemented
302#1651C2×C4711yescharacteristic, complemented
303#1643C2×C4711yescharacteristic, complemented
304#1635C2×C4711yescharacteristic, complemented
305#1582C2×C4711yescharacteristic, complemented
306#1580C2×C4711yescharacteristic, complemented
307C2×C47—42no—
308C2×C47—42no—
309C2×C47—81no—
310C2×C47#326711yescharacteristic
311C2×C47D4×SD1611yescharacteristic
312C2×C47#328911yescharacteristic
313C2×#135—21no—
314#554C22×C4711yescharacteristic
315D4×Q8C22×C4711yescharacteristic
316#547C22×C4711yescharacteristic
317#547C22×C4711yescharacteristic
318#501—21no—
319#498C22×C4711yescharacteristic
320#498C22×C4711yescharacteristic
321#498C22×C4711yescharacteristic
322#494C22×C4711yescharacteristic
323#487C22×C4711yescharacteristic
324#487C22×C4711yescharacteristic
325#483—21no—
326#483—21no—
327#481—21no—
328#478—21no—
329#476—21no—
330#476C22×C4711yescharacteristic
331#476C22×C4711yescharacteristic
332#475C22×C4711yescharacteristic
333#475C22×C4711yescharacteristic
334#474C22×C4711yescharacteristic
335#467—21no—
336#465—21no—
337#465—21no—
338#461C22×C4711yescharacteristic
339#461C22×C4711yescharacteristic
340#461C22×C4711yescharacteristic
341#452—21no—
342#452—21no—
343#448—21no—
344#446C22×C4711yescharacteristic
345#442—21no—
346C4×SD16C22×C4711yescharacteristic
347C4×D8C22×C4711yescharacteristic
348C8×D4C22×C4711yescharacteristic
349C8×D4C22×C4711yescharacteristic
350C8×D4C22×C4711yescharacteristic
351C2×#106—21no—
352C2×#103—21no—
353#334C22×C4711yescharacteristic
354#334C22×C4711yescharacteristic
355#333C22×C4711yescharacteristic
356#332C22×C4711yescharacteristic
357#332C22×C4711yescharacteristic
358#332C22×C4711yescharacteristic
359Q8⋊C8C22×C4711yescharacteristic
360D4⋊C8C22×C4711yescharacteristic
361D4⋊C8C22×C4711yescharacteristic
362D4⋊C8C22×C4711yescharacteristic
363#322C22×C4711yescharacteristic
364C47#1976611yescharacteristic, direct product factor, Sylow
365C2×#41—21no—
366C2×#41—21no—
367C22×Q8—21no—
368#135—44no—
369C2×Q16—21no—
370C2×Q16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16D4×C4711yescharacteristic
375C2×D8D4×C4711yescharacteristic
376C22×C8—21no—
377C22×C8—21no—
378C22×C8—21no—
379C4⋊Q8—21no—
380C4⋊Q8C23×C4711yescharacteristic
381C4⋊Q8C23×C4711yescharacteristic
382C4⋊Q8C23×C4711yescharacteristic
383C4⋊Q8C23×C4711yescharacteristic
384#125—21no—
385#123—41no—
386#123—41no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—21no—
390C22⋊Q8—21no—
391C22⋊Q8—41no—
392C22⋊Q8—41no—
393#121—21no—
394#121—21no—
395C4×Q8C23×C4711yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4C23×C4711yescharacteristic
399C4×D4C23×C4711yescharacteristic
400C4×D4C23×C4711yescharacteristic
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404#107—21no—
405#107D4×C4711yescharacteristic
406#106—21no—
407#106—21no—
408#106—21no—
409#106—21no—
410#106—21no—
411#106—21no—
412#106—21no—
413#106—21no—
414#106—41no—
415#106D4×C4711yescharacteristic
416C4⋊C8—21no—
417C4⋊C8C23×C4711yescharacteristic
418C4⋊C8C23×C4711yescharacteristic
419C4⋊C8C23×C4711yescharacteristic
420C4⋊C8C23×C4711yescharacteristic
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#103—21no—
428#103—41no—
429#103D4×C4711yescharacteristic
430#102—21no—
431#102—21no—
432#102—21no—
433#102D4×C4711yescharacteristic
434#102D4×C4711yescharacteristic
435#102D4×C4711yescharacteristic
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439#97—21no—
440C4×C8C23×C4711yescharacteristic
441C4×C8C23×C4711yescharacteristic
442C4×C8C23×C4711yescharacteristic
443#41—42no—
444#41—42no—
445#41—81no—
446#41—81no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—41no—
452C2×Q8—42no—
453C2×Q8—81no—
454C2×Q8C2×D4×C4711yescharacteristic
455C2×D4—41no—
456C2×D4—41no—
457C2×D4C2×D4×C4711yescharacteristic
458C2×D4C2×D4×C4711yescharacteristic
459C2×D4C2×D4×C4711yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467Q16—42no—
468Q16—81no—
469SD16—41no—
470SD16—42no—
471SD16—42no—
472SD16—81no—
473D8SD16×C4714yescomplemented
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—42no—
480C2×C8—42no—
481C2×C8—81no—
482C2×C8C2×D4×C4711yescharacteristic
483C2×C8C2×D4×C4711yescharacteristic
484C2×C8C2×D4×C4711yescharacteristic
485C2×C8C2×D4×C4711yescharacteristic
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4C2×D4×C4711yescharacteristic
501C4⋊C4C2×D4×C4711yescharacteristic
502C4⋊C4C2×D4×C4711yescharacteristic
503C4⋊C4C2×D4×C4711yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C42—21no—
512C42C24×C4711yescharacteristic
513C23—21no—
514C23—21no—
515C23—21no—
516Q8—21no—
517Q8—21no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—81no—
525Q8—82no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—82no—
531D4—82no—
532D4C2×SD16×C4712yes—
533D4C2×SD16×C4712yes—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—82no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4—161no—
553C2×C4C22×D4×C4711yescharacteristic
554C2×C4C22×D4×C4711yescharacteristic
555C2×C4H(5,𝔽2)×C4711yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8C2×SD16×C4712yes—
565C22—22no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22D42×C4711yescharacteristic
575C4—21no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4C22×SD16×C4711yescharacteristic
586C4C47×#57511yescharacteristic
587C4C47×#57711yescharacteristic
588C4C47×#57711yescharacteristic
589C2—42no—
590C2—42no—
591C2—81no—
592C2C47×#326711yescharacteristic
593C2D4×SD16×C4711yescharacteristic
594C2C47×#328911yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3283C2
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×#3384C2semidirect
2. C47×#3335C2semidirect
3. C47×#3298C2semidirect
5. C47×#1716C2semidirect
6. C47×#1690C2semidirect
7. C47×#1679C2semidirect
8. C47×#1671C2semidirect
9. C47×#1671C2semidirect
10. C47×#1654C2semidirect
11. C47×#1651C2semidirect
12. C47×#1643C2semidirect
13. C47×#1635C2semidirect
14. C47×#1582C2semidirect
15. C47×#1580C2semidirect
175. D8×C47SD16semidirect
267. #19766C47direct (N × H)
292. #3384C2×C47semidirect
293. #3335C2×C47semidirect
294. #3298C2×C47semidirect
296. #1716C2×C47semidirect
297. #1690C2×C47semidirect
298. #1679C2×C47semidirect
299. #1671C2×C47semidirect
300. #1671C2×C47semidirect
301. #1654C2×C47semidirect
302. #1651C2×C47semidirect
303. #1643C2×C47semidirect
304. #1635C2×C47semidirect
305. #1582C2×C47semidirect
306. #1580C2×C47semidirect
364. C47#19766direct (N × H)
473. D8SD16×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#33842
C47×#33352
C47×#32982
C47×#32832
C47×#17162
C47×#16902
C47×#16792
C47×#16712
C47×#16542
C47×#16512
C47×#16432
C47×#16352
C47×#15822
C47×#15802
#1976647