Finite Group Databasebeta

← C47×#19843 #26059541

Subgroups — C47×#19843 #26059541

Order 12032.

644 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3368C211yesmaximal, characteristic, complemented
2C47×#3363C211yesmaximal, characteristic, complemented
3C47×#3362C211yesmaximal, characteristic, complemented
4C47×#3287C211yesmaximal, characteristic
5C47×#1717C211yesmaximal, characteristic, complemented
6C47×#1698C211yesmaximal, characteristic, complemented
7C47×#1683C211yesmaximal, characteristic, complemented
8C47×#1682C211yesmaximal, characteristic, complemented
9C47×#1668C211yesmaximal, characteristic, complemented
10C47×#1641C211yesmaximal, characteristic, complemented
11C47×#1631C211yesmaximal, characteristic, complemented
12C47×#1626C211yesmaximal, characteristic, complemented
13C47×#1623C211yesmaximal, characteristic, complemented
14C47×#1584C211yesmaximal, characteristic, complemented
15C47×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×#135×C47—21no—
17Q82×C47C2211yescharacteristic
18C47×#557C2211yescharacteristic
19C47×#550C2211yescharacteristic
20C47×#550C2211yescharacteristic
21C47×#493C2211yescharacteristic
22C47×#492C2211yescharacteristic
23C47×#490—21no—
24C47×#487—21no—
25C47×#487C2211yescharacteristic
26C47×#486—21no—
27C47×#486C2211yescharacteristic
28C47×#486C2211yescharacteristic
29C47×#486C2211yescharacteristic
30C47×#478—21no—
31C47×#477—21no—
32C47×#477C2211yescharacteristic
33C47×#476—21no—
34C47×#476C2211yescharacteristic
35C47×#474C2211yescharacteristic
36C47×#466—21no—
37C47×#462—21no—
38C47×#462C2211yescharacteristic
39C47×#460—21no—
40C47×#460—21no—
41C47×#460C2211yescharacteristic
42C47×#460C2211yescharacteristic
43C47×#460C2211yescharacteristic
44C47×#460C2211yescharacteristic
45C47×#449—21no—
46C47×#449—21no—
47C47×#446C2211yescharacteristic
48C8×Q8×C47C2211yescharacteristic
49C8×Q8×C47C2211yescharacteristic
50C47×#440—21no—
51C4×Q16×C47—21no—
52C4×Q16×C47C2211yescharacteristic
53C4×SD16×C47—21no—
54C4×SD16×C47C2211yescharacteristic
55C8×D4×C47C2211yescharacteristic
56C47×#335C2211yescharacteristic
57C47×#335C2211yescharacteristic
58C47×#333C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#331C2211yescharacteristic
61C47×#331C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×#41×C47—21no—
68C2×#41×C47—21no—
69#135×C47—44no—
70C2×Q16×C47—21no—
71C2×Q16×C47D411yescharacteristic
72C2×SD16×C47—21no—
73C2×SD16×C47—21no—
74C2×SD16×C47—21no—
75C2×SD16×C47—21no—
76C2×SD16×C47—41no—
77C2×SD16×C47D411yescharacteristic
78C2×D8×C47—21no—
79C2×D8×C47—21no—
80C22×C8×C47—21no—
81C4⋊Q8×C47—21no—
82C4⋊Q8×C47—21no—
83C4⋊Q8×C47—21no—
84C4⋊Q8×C47—41no—
85C4⋊Q8×C47C2311yescharacteristic
86C4⋊Q8×C47C2311yescharacteristic
87#127×C47—21no—
88#127×C47—21no—
89#127×C47C2311yescharacteristic
90#127×C47C2311yescharacteristic
91#125×C47—21no—
92#125×C47—41no—
93#121×C47—21no—
94#121×C47—21no—
95#121×C47—41no—
96#121×C47—41no—
97C4×Q8×C47—21no—
98C4×Q8×C47—21no—
99C4×Q8×C47—21no—
100C4×Q8×C47—21no—
101C4×Q8×C47C2311yescharacteristic
102C4×Q8×C47C2311yescharacteristic
103C4×Q8×C47C2311yescharacteristic
104C4×D4×C47—21no—
105C4×D4×C47—21no—
106C4×D4×C47C2311yescharacteristic
107#107×C47—21no—
108#107×C47—21no—
109#107×C47D411yescharacteristic
110#106×C47—21no—
111#106×C47D411yescharacteristic
112C4⋊C8×C47—21no—
113C4⋊C8×C47—21no—
114C4⋊C8×C47—21no—
115C4⋊C8×C47C2311yescharacteristic
116C4⋊C8×C47C2311yescharacteristic
117C4⋊C8×C47C2311yescharacteristic
118C4⋊C8×C47C2311yescharacteristic
119#103×C47—21no—
120#103×C47—21no—
121#103×C47—21no—
122#103×C47—21no—
123#103×C47D411yescharacteristic
124#103×C47D411yescharacteristic
125#103×C47D411yescharacteristic
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×C47—21no—
136#102×C47—41no—
137#102×C47D411yescharacteristic
138C22⋊C8×C47—21no—
139#97×C47—21no—
140C4×C8×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×C47—41no—
152C2×Q8×C47C2×D411yescharacteristic
153C2×Q8×C47C2×D411yescharacteristic
154C2×Q8×C47C2×D411yescharacteristic
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—41no—
162C2×D4×C47—41no—
163C2×D4×C47—41no—
164C2×D4×C47—41no—
165C2×D4×C47C2×D411yescharacteristic
166C22×C4×C47—21no—
167C22×C4×C47—41no—
168C22×C4×C47—41no—
169Q16×C47—22no—
170Q16×C47—42no—
171SD16×C47—22no—
172SD16×C47—42no—
173SD16×C47—42no—
174SD16×C47—42no—
175SD16×C47—42no—
176SD16×C47—82no—
177D8×C47—42no—
178D8×C47—81no—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47—21no—
182C2×C8×C47—21no—
183C2×C8×C47—21no—
184C2×C8×C47—42no—
185C2×C8×C47C2×D411yescharacteristic
186C2×C8×C47C2×D411yescharacteristic
187C2×C8×C47C2×D411yescharacteristic
188C2×C8×C47C2×D411yescharacteristic
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—41no—
197C4⋊C4×C47—41no—
198C4⋊C4×C47—41no—
199C4⋊C4×C47—41no—
200C4⋊C4×C47—41no—
201C4⋊C4×C47C2×D411yescharacteristic
202C4⋊C4×C47C2×D411yescharacteristic
203C4⋊C4×C47C2×D411yescharacteristic
204C4⋊C4×C47C2×D411yescharacteristic
205C22⋊C4×C47—21no—
206C22⋊C4×C47—41no—
207C22⋊C4×C47—41no—
208C42×C47—21no—
209C42×C47—21no—
210C42×C47—21no—
211C42×C47—41no—
212C42×C47—41no—
213C42×C47C2411yescharacteristic
214C23×C47—21no—
215C23×C47—41no—
216C23×C47—41no—
217Q8×C47—21no—
218Q8×C47—21no—
219Q8×C47—21no—
220Q8×C47—21no—
221Q8×C47—41no—
222Q8×C47—41no—
223Q8×C47—81no—
224Q8×C47—161no—
225Q8×C47#13512yescomplemented
226Q8×C47AGL(1,ℤ/8)12yes—
227D4×C47—21no—
228D4×C47—21no—
229D4×C47—41no—
230D4×C47—41no—
231D4×C47—41no—
232D4×C47—41no—
233D4×C47—41no—
234D4×C47—41no—
235D4×C47—41no—
236D4×C47—41no—
237D4×C47—82no—
238D4×C47—81no—
239D4×C47—81no—
240D4×C47—82no—
241D4×C47—161no—
242D4×C47—161no—
243C2×C4×C47—21no—
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—82no—
255C2×C4×C47—82no—
256C2×C4×C47C22×D411yescharacteristic
257C2×C4×C47C22×D411yescharacteristic
258C2×C4×C47H(5,𝔽2)11yescharacteristic
259C8×C47—21no—
260C8×C47—21no—
261C8×C47—21no—
262C8×C47—21no—
263C8×C47—41no—
264C8×C47—41no—
265C8×C47—41no—
266C8×C47—41no—
267C8×C47—41no—
268#19843C4711yesmaximal, characteristic, direct product factor, Sylow
269C22×C47—41no—
270C22×C47—41no—
271C22×C47—41no—
272C22×C47—81no—
273C22×C47—81no—
274C22×C47—81no—
275C22×C47—81no—
276C22×C47—81no—
277C22×C47—81no—
278C22×C47D4211yescharacteristic
279C4×C47—22no—
280C4×C47—22no—
281C4×C47—21no—
282C4×C47—41no—
283C4×C47—41no—
284C4×C47—41no—
285C4×C47—41no—
286C4×C47—41no—
287C4×C47—81no—
288C4×C47—81no—
289C4×C47C2×#13511yescharacteristic
290C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
291C4×C47#57711yescharacteristic
292C4×C47#57811yescharacteristic
293#3368C2×C4711yescharacteristic, complemented
294#3363C2×C4711yescharacteristic, complemented
295#3362C2×C4711yescharacteristic, complemented
296#3287C2×C4711yescharacteristic
297#1717C2×C4711yescharacteristic, complemented
298#1698C2×C4711yescharacteristic, complemented
299#1683C2×C4711yescharacteristic, complemented
300#1682C2×C4711yescharacteristic, complemented
301#1668C2×C4711yescharacteristic, complemented
302#1641C2×C4711yescharacteristic, complemented
303#1631C2×C4711yescharacteristic, complemented
304#1626C2×C4711yescharacteristic, complemented
305#1623C2×C4711yescharacteristic, complemented
306#1584C2×C4711yescharacteristic, complemented
307SD16⋊C8C2×C4711yescharacteristic, complemented
308C2×C47—81no—
309C2×C47—161no—
310C2×C47—161no—
311C2×C47#326511yescharacteristic
312C2×C47#328511yescharacteristic
313C2×C47#328811yescharacteristic
314C2×#135—21no—
315Q82C22×C4711yescharacteristic
316#557C22×C4711yescharacteristic
317#550C22×C4711yescharacteristic
318#550C22×C4711yescharacteristic
319#493C22×C4711yescharacteristic
320#492C22×C4711yescharacteristic
321#490—21no—
322#487—21no—
323#487C22×C4711yescharacteristic
324#486—21no—
325#486C22×C4711yescharacteristic
326#486C22×C4711yescharacteristic
327#486C22×C4711yescharacteristic
328#478—21no—
329#477—21no—
330#477C22×C4711yescharacteristic
331#476—21no—
332#476C22×C4711yescharacteristic
333#474C22×C4711yescharacteristic
334#466—21no—
335#462—21no—
336#462C22×C4711yescharacteristic
337#460—21no—
338#460—21no—
339#460C22×C4711yescharacteristic
340#460C22×C4711yescharacteristic
341#460C22×C4711yescharacteristic
342#460C22×C4711yescharacteristic
343#449—21no—
344#449—21no—
345#446C22×C4711yescharacteristic
346C8×Q8C22×C4711yescharacteristic
347C8×Q8C22×C4711yescharacteristic
348#440—21no—
349C4×Q16—21no—
350C4×Q16C22×C4711yescharacteristic
351C4×SD16—21no—
352C4×SD16C22×C4711yescharacteristic
353C8×D4C22×C4711yescharacteristic
354#335C22×C4711yescharacteristic
355#335C22×C4711yescharacteristic
356#333C22×C4711yescharacteristic
357#332C22×C4711yescharacteristic
358#331C22×C4711yescharacteristic
359#331C22×C4711yescharacteristic
360Q8⋊C8C22×C4711yescharacteristic
361Q8⋊C8C22×C4711yescharacteristic
362Q8⋊C8C22×C4711yescharacteristic
363D4⋊C8C22×C4711yescharacteristic
364#322C22×C4711yescharacteristic
365C47#1984311yescharacteristic, direct product factor, Sylow
366C2×#41—21no—
367C2×#41—21no—
368#135—44no—
369C2×Q16—21no—
370C2×Q16D4×C4711yescharacteristic
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—41no—
376C2×SD16D4×C4711yescharacteristic
377C2×D8—21no—
378C2×D8—21no—
379C22×C8—21no—
380C4⋊Q8—21no—
381C4⋊Q8—21no—
382C4⋊Q8—21no—
383C4⋊Q8—41no—
384C4⋊Q8C23×C4711yescharacteristic
385C4⋊Q8C23×C4711yescharacteristic
386#127—21no—
387#127—21no—
388#127C23×C4711yescharacteristic
389#127C23×C4711yescharacteristic
390#125—21no—
391#125—41no—
392#121—21no—
393#121—21no—
394#121—41no—
395#121—41no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×Q8C23×C4711yescharacteristic
401C4×Q8C23×C4711yescharacteristic
402C4×Q8C23×C4711yescharacteristic
403C4×D4—21no—
404C4×D4—21no—
405C4×D4C23×C4711yescharacteristic
406#107—21no—
407#107—21no—
408#107D4×C4711yescharacteristic
409#106—21no—
410#106D4×C4711yescharacteristic
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8C23×C4711yescharacteristic
415C4⋊C8C23×C4711yescharacteristic
416C4⋊C8C23×C4711yescharacteristic
417C4⋊C8C23×C4711yescharacteristic
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103D4×C4711yescharacteristic
423#103D4×C4711yescharacteristic
424#103D4×C4711yescharacteristic
425#102—21no—
426#102—21no—
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—41no—
436#102D4×C4711yescharacteristic
437C22⋊C8—21no—
438#97—21no—
439C4×C8—21no—
440C4×C8—21no—
441C4×C8C23×C4711yescharacteristic
442C4×C8C23×C4711yescharacteristic
443C4×C8C23×C4711yescharacteristic
444#41—42no—
445#41—42no—
446#41—81no—
447#41—81no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—41no—
451C2×Q8C2×D4×C4711yescharacteristic
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—41no—
463C2×D4—41no—
464C2×D4C2×D4×C4711yescharacteristic
465C22×C4—21no—
466C22×C4—41no—
467C22×C4—41no—
468Q16—22no—
469Q16—42no—
470SD16—22no—
471SD16—42no—
472SD16—42no—
473SD16—42no—
474SD16—42no—
475SD16—82no—
476D8—42no—
477D8—81no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—42no—
484C2×C8C2×D4×C4711yescharacteristic
485C2×C8C2×D4×C4711yescharacteristic
486C2×C8C2×D4×C4711yescharacteristic
487C2×C8C2×D4×C4711yescharacteristic
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—41no—
506C22⋊C4—41no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—41no—
511C42—41no—
512C42C24×C4711yescharacteristic
513C23—21no—
514C23—41no—
515C23—41no—
516Q8—21no—
517Q8—21no—
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—81no—
523Q8—161no—
524Q8#135×C4712yescomplemented
525Q8AGL(1,ℤ/8)×C4712yes—
526D4—21no—
527D4—21no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—82no—
537D4—81no—
538D4—81no—
539D4—82no—
540D4—161no—
541D4—161no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—82no—
554C2×C4—82no—
555C2×C4C22×D4×C4711yescharacteristic
556C2×C4C22×D4×C4711yescharacteristic
557C2×C4H(5,𝔽2)×C4711yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22D42×C4711yescharacteristic
577C4—21no—
578C4—22no—
579C4—22no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—81no—
587C4C2×#135×C4711yescharacteristic
588C4C2×AGL(1,ℤ/8)×C4711yescharacteristic
589C4C47×#57711yescharacteristic
590C4C47×#57811yescharacteristic
591C2—81no—
592C2—161no—
593C2—161no—
594C2C47×#326511yescharacteristic
595C2C47×#328511yescharacteristic
596C2C47×#328811yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3287C2
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×#3368C2semidirect
2. C47×#3363C2semidirect
3. C47×#3362C2semidirect
5. C47×#1717C2semidirect
6. C47×#1698C2semidirect
7. C47×#1683C2semidirect
8. C47×#1682C2semidirect
9. C47×#1668C2semidirect
10. C47×#1641C2semidirect
11. C47×#1631C2semidirect
12. C47×#1626C2semidirect
13. C47×#1623C2semidirect
14. C47×#1584C2semidirect
15. C47×SD16⋊C8C2semidirect
225. Q8×C47#135semidirect
268. #19843C47direct (N × H)
293. #3368C2×C47semidirect
294. #3363C2×C47semidirect
295. #3362C2×C47semidirect
297. #1717C2×C47semidirect
298. #1698C2×C47semidirect
299. #1683C2×C47semidirect
300. #1682C2×C47semidirect
301. #1668C2×C47semidirect
302. #1641C2×C47semidirect
303. #1631C2×C47semidirect
304. #1626C2×C47semidirect
305. #1623C2×C47semidirect
306. #1584C2×C47semidirect
307. SD16⋊C8C2×C47semidirect
365. C47#19843direct (N × H)
524. Q8#135×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#33682
C47×#33632
C47×#33622
C47×#32872
C47×#17172
C47×#16982
C47×#16832
C47×#16822
C47×#16682
C47×#16412
C47×#16312
C47×#16262
C47×#16232
C47×#15842
C47×SD16⋊C82
#1984347