Finite Group Databasebeta

← C83×#19874 #35247698

Subgroups — C83×#19874 #35247698

Order 21248.

608 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3400C211yesmaximal, characteristic, complemented
2C83×#3396C211yesmaximal, characteristic, complemented
3C83×#3396C211yesmaximal, characteristic, complemented
4C83×#3365C211yesmaximal, characteristic, complemented
5C83×#1721C211yesmaximal, characteristic
6C83×#1688C211yesmaximal, characteristic, complemented
7C83×#1682C211yesmaximal, characteristic, complemented
8C83×#1668C211yesmaximal, characteristic, complemented
9C83×#1666C211yesmaximal, characteristic, complemented
10C83×#1640C211yesmaximal, characteristic, complemented
11C83×#1626C211yesmaximal, characteristic, complemented
12C83×#1620C211yesmaximal, characteristic, complemented
13C83×#1620C211yesmaximal, characteristic, complemented
14C83×#1584C211yesmaximal, characteristic, complemented
15C83×#1579C211yesmaximal, characteristic, complemented
16#559×C83C2211yescharacteristic
17#559×C83C2211yescharacteristic
18#559×C83C2211yescharacteristic
19#557×C83C2211yescharacteristic
20#497×C83—21no—
21#495×C83—21no—
22#495×C83—21no—
23#493×C83C2211yescharacteristic
24#493×C83C2211yescharacteristic
25#493×C83C2211yescharacteristic
26#492×C83C2211yescharacteristic
27#488×C83—21no—
28#486×C83C2211yescharacteristic
29#486×C83C2211yescharacteristic
30#478×C83—21no—
31#475×C83C2211yescharacteristic
32#464×C83—21no—
33#464×C83—21no—
34#463×C83—21no—
35#463×C83—21no—
36#463×C83—21no—
37#463×C83—21no—
38#462×C83C2211yescharacteristic
39#461×C83—21no—
40#460×C83C2211yescharacteristic
41#460×C83C2211yescharacteristic
42#460×C83C2211yescharacteristic
43#460×C83C2211yescharacteristic
44#460×C83C2211yescharacteristic
45#460×C83C2211yescharacteristic
46#446×C83C2211yescharacteristic
47C8×Q8×C83C2211yescharacteristic
48C8×Q8×C83C2211yescharacteristic
49C8×Q8×C83C2211yescharacteristic
50#440×C83—21no—
51C4×Q16×C83C2211yescharacteristic
52C4×Q16×C83C2211yescharacteristic
53C4×SD16×C83—21no—
54C4×D8×C83—21no—
55C4×D8×C83—21no—
56#335×C83C2211yescharacteristic
57#334×C83C2211yescharacteristic
58#332×C83C2211yescharacteristic
59#331×C83C2211yescharacteristic
60#331×C83C2211yescharacteristic
61#331×C83C2211yescharacteristic
62Q8⋊C8×C83C2211yescharacteristic
63Q8⋊C8×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65Q8⋊C8×C83C2211yescharacteristic
66#322×C83C2211yescharacteristic
67C2×Q16×C83—21no—
68C2×Q16×C83D411yescharacteristic
69C2×Q16×C83D411yescharacteristic
70C2×SD16×C83—21no—
71C2×SD16×C83—21no—
72C2×SD16×C83—21no—
73C2×SD16×C83—21no—
74C2×SD16×C83—21no—
75C2×SD16×C83—21no—
76C2×SD16×C83—21no—
77C2×SD16×C83—21no—
78C2×D8×C83—21no—
79C2×D8×C83—21no—
80C2×D8×C83—21no—
81C2×D8×C83—21no—
82C2×D8×C83—41no—
83C4⋊Q8×C83—21no—
84C4⋊Q8×C83C2311yescharacteristic
85#127×C83C2311yescharacteristic
86#127×C83C2311yescharacteristic
87#127×C83C2311yescharacteristic
88#125×C83—21no—
89#125×C83—41no—
90#124×C83—21no—
91#124×C83—21no—
92#124×C83—21no—
93#124×C83—21no—
94#124×C83—21no—
95#124×C83—21no—
96#123×C83—41no—
97#123×C83—41no—
98#123×C83—41no—
99C4×Q8×C83—21no—
100C4×Q8×C83—21no—
101C4×Q8×C83C2311yescharacteristic
102C4×Q8×C83C2311yescharacteristic
103C4×Q8×C83C2311yescharacteristic
104C4×Q8×C83C2311yescharacteristic
105C4×D4×C83—21no—
106C4×D4×C83—21no—
107C4×D4×C83—21no—
108C4×D4×C83—21no—
109C4×D4×C83—21no—
110C4×D4×C83—21no—
111#107×C83D411yescharacteristic
112#107×C83D411yescharacteristic
113#106×C83—21no—
114C4⋊C8×C83—21no—
115C4⋊C8×C83—21no—
116C4⋊C8×C83—21no—
117C4⋊C8×C83—21no—
118C4⋊C8×C83C2311yescharacteristic
119C4⋊C8×C83C2311yescharacteristic
120C4⋊C8×C83C2311yescharacteristic
121C4⋊C8×C83C2311yescharacteristic
122#103×C83—21no—
123#103×C83—21no—
124#103×C83D411yescharacteristic
125#103×C83D411yescharacteristic
126#103×C83D411yescharacteristic
127#103×C83D411yescharacteristic
128#102×C83—21no—
129#102×C83—21no—
130#102×C83—21no—
131#102×C83—21no—
132#102×C83—21no—
133#102×C83—21no—
134#102×C83—21no—
135#102×C83—21no—
136#102×C83—41no—
137#97×C83—21no—
138C4×C8×C83—21no—
139C4×C8×C83—21no—
140C4×C8×C83—21no—
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C2×Q8×C83—21no—
145C2×Q8×C83C2×D411yescharacteristic
146C2×Q8×C83C2×D411yescharacteristic
147C2×Q8×C83C2×D411yescharacteristic
148C2×Q8×C83C2×D411yescharacteristic
149C2×D4×C83—21no—
150C2×D4×C83—21no—
151C2×D4×C83—21no—
152C2×D4×C83—21no—
153C2×D4×C83—21no—
154C2×D4×C83—21no—
155C2×D4×C83—21no—
156C2×D4×C83—21no—
157C2×D4×C83—21no—
158C22×C4×C83—41no—
159C22×C4×C83—41no—
160C22×C4×C83—41no—
161Q16×C83—22no—
162Q16×C83—41no—
163Q16×C83—81no—
164SD16×C83—42no—
165SD16×C83—42no—
166SD16×C83—81no—
167SD16×C83—81no—
168SD16×C83—81no—
169SD16×C83—81no—
170SD16×C83—81no—
171SD16×C83—81no—
172D8×C83—42no—
173D8×C83—42no—
174D8×C83—81no—
175D8×C83—81no—
176D8×C83—82no—
177C2×C8×C83—21no—
178C2×C8×C83—21no—
179C2×C8×C83—21no—
180C2×C8×C83—21no—
181C2×C8×C83—21no—
182C2×C8×C83C2×D411yescharacteristic
183C2×C8×C83C2×D411yescharacteristic
184C2×C8×C83C2×D411yescharacteristic
185C2×C8×C83C2×D411yescharacteristic
186C4⋊C4×C83—21no—
187C4⋊C4×C83—21no—
188C4⋊C4×C83—21no—
189C4⋊C4×C83—21no—
190C4⋊C4×C83—21no—
191C4⋊C4×C83—21no—
192C4⋊C4×C83—41no—
193C4⋊C4×C83—41no—
194C4⋊C4×C83—41no—
195C4⋊C4×C83C2×D411yescharacteristic
196C4⋊C4×C83C2×D411yescharacteristic
197C4⋊C4×C83C2×D411yescharacteristic
198C4⋊C4×C83C2×D411yescharacteristic
199C22⋊C4×C83—41no—
200C22⋊C4×C83—41no—
201C22⋊C4×C83—41no—
202C22⋊C4×C83—41no—
203C22⋊C4×C83—41no—
204C22⋊C4×C83—41no—
205C22⋊C4×C83—41no—
206C22⋊C4×C83—41no—
207C22⋊C4×C83—41no—
208C42×C83—21no—
209C42×C83—21no—
210C42×C83—21no—
211C42×C83—21no—
212C42×C83—41no—
213C42×C83C2411yescharacteristic
214C23×C83—41no—
215C23×C83—41no—
216C23×C83—41no—
217Q8×C83—21no—
218Q8×C83—21no—
219Q8×C83—21no—
220Q8×C83—21no—
221Q8×C83—21no—
222Q8×C83—21no—
223Q8×C83—21no—
224Q8×C83—21no—
225Q8×C83—41no—
226Q8×C83—41no—
227D4×C83—41no—
228D4×C83—41no—
229D4×C83—41no—
230D4×C83—41no—
231D4×C83—41no—
232D4×C83—41no—
233D4×C83—41no—
234D4×C83—41no—
235D4×C83—41no—
236D4×C83—41no—
237D4×C83—41no—
238D4×C83—41no—
239D4×C83—81no—
240D4×C83—81no—
241D4×C83—81no—
242C2×C4×C83—21no—
243C2×C4×C83—21no—
244C2×C4×C83—21no—
245C2×C4×C83—21no—
246C2×C4×C83—21no—
247C2×C4×C83—21no—
248C2×C4×C83—21no—
249C2×C4×C83—21no—
250C2×C4×C83—41no—
251C2×C4×C83—161no—
252C2×C4×C83—161no—
253C2×C4×C83—161no—
254C2×C4×C83C22×D411yescharacteristic
255C2×C4×C83C22×D411yescharacteristic
256C2×C4×C83H(5,𝔽2)11yescharacteristic
257C8×C83—21no—
258C8×C83—21no—
259C8×C83—21no—
260C8×C83—41no—
261C8×C83—41no—
262C8×C83—41no—
263C8×C83—41no—
264C8×C83—41no—
265C8×C83#13512yes—
266C22×C83—81no—
267C22×C83—81no—
268C22×C83—81no—
269C22×C83—81no—
270C22×C83—81no—
271C22×C83—81no—
272C22×C83—81no—
273C22×C83—81no—
274C22×C83—81no—
275C22×C83D4211yescharacteristic
276C4×C83—21no—
277C4×C83—41no—
278C4×C83—41no—
279C4×C83—41no—
280C4×C83—41no—
281C4×C83—41no—
282C4×C83—41no—
283C4×C83—41no—
284C4×C83—41no—
285C4×C83—81no—
286C4×C83C2×#13511yescharacteristic
287C4×C83#57511yescharacteristic
288C4×C83#57611yescharacteristic
289C4×C83#57711yescharacteristic
290#19874C8311yesmaximal, characteristic, direct product factor, Sylow
291C2×C83—161no—
292C2×C83—161no—
293C2×C83—161no—
294C2×C83#327111yescharacteristic
295C2×C83#328711yescharacteristic
296C2×C83#328811yescharacteristic
297#3400C2×C8311yescharacteristic, complemented
298#3396C2×C8311yescharacteristic, complemented
299#3396C2×C8311yescharacteristic, complemented
300#3365C2×C8311yescharacteristic, complemented
301#1721C2×C8311yescharacteristic
302#1688C2×C8311yescharacteristic, complemented
303#1682C2×C8311yescharacteristic, complemented
304#1668C2×C8311yescharacteristic, complemented
305#1666C2×C8311yescharacteristic, complemented
306#1640C2×C8311yescharacteristic, complemented
307#1626C2×C8311yescharacteristic, complemented
308#1620C2×C8311yescharacteristic, complemented
309#1620C2×C8311yescharacteristic, complemented
310#1584C2×C8311yescharacteristic, complemented
311#1579C2×C8311yescharacteristic, complemented
312C83#1987411yescharacteristic, direct product factor, Sylow
313#559C22×C8311yescharacteristic
314#559C22×C8311yescharacteristic
315#559C22×C8311yescharacteristic
316#557C22×C8311yescharacteristic
317#497—21no—
318#495—21no—
319#495—21no—
320#493C22×C8311yescharacteristic
321#493C22×C8311yescharacteristic
322#493C22×C8311yescharacteristic
323#492C22×C8311yescharacteristic
324#488—21no—
325#486C22×C8311yescharacteristic
326#486C22×C8311yescharacteristic
327#478—21no—
328#475C22×C8311yescharacteristic
329#464—21no—
330#464—21no—
331#463—21no—
332#463—21no—
333#463—21no—
334#463—21no—
335#462C22×C8311yescharacteristic
336#461—21no—
337#460C22×C8311yescharacteristic
338#460C22×C8311yescharacteristic
339#460C22×C8311yescharacteristic
340#460C22×C8311yescharacteristic
341#460C22×C8311yescharacteristic
342#460C22×C8311yescharacteristic
343#446C22×C8311yescharacteristic
344C8×Q8C22×C8311yescharacteristic
345C8×Q8C22×C8311yescharacteristic
346C8×Q8C22×C8311yescharacteristic
347#440—21no—
348C4×Q16C22×C8311yescharacteristic
349C4×Q16C22×C8311yescharacteristic
350C4×SD16—21no—
351C4×D8—21no—
352C4×D8—21no—
353#335C22×C8311yescharacteristic
354#334C22×C8311yescharacteristic
355#332C22×C8311yescharacteristic
356#331C22×C8311yescharacteristic
357#331C22×C8311yescharacteristic
358#331C22×C8311yescharacteristic
359Q8⋊C8C22×C8311yescharacteristic
360Q8⋊C8C22×C8311yescharacteristic
361Q8⋊C8C22×C8311yescharacteristic
362Q8⋊C8C22×C8311yescharacteristic
363#322C22×C8311yescharacteristic
364C2×Q16—21no—
365C2×Q16D4×C8311yescharacteristic
366C2×Q16D4×C8311yescharacteristic
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×D8—21no—
376C2×D8—21no—
377C2×D8—21no—
378C2×D8—21no—
379C2×D8—41no—
380C4⋊Q8—21no—
381C4⋊Q8C23×C8311yescharacteristic
382#127C23×C8311yescharacteristic
383#127C23×C8311yescharacteristic
384#127C23×C8311yescharacteristic
385#125—21no—
386#125—41no—
387#124—21no—
388#124—21no—
389#124—21no—
390#124—21no—
391#124—21no—
392#124—21no—
393#123—41no—
394#123—41no—
395#123—41no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8C23×C8311yescharacteristic
399C4×Q8C23×C8311yescharacteristic
400C4×Q8C23×C8311yescharacteristic
401C4×Q8C23×C8311yescharacteristic
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408#107D4×C8311yescharacteristic
409#107D4×C8311yescharacteristic
410#106—21no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8C23×C8311yescharacteristic
416C4⋊C8C23×C8311yescharacteristic
417C4⋊C8C23×C8311yescharacteristic
418C4⋊C8C23×C8311yescharacteristic
419#103—21no—
420#103—21no—
421#103D4×C8311yescharacteristic
422#103D4×C8311yescharacteristic
423#103D4×C8311yescharacteristic
424#103D4×C8311yescharacteristic
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—41no—
434#97—21no—
435C4×C8—21no—
436C4×C8—21no—
437C4×C8—21no—
438C4×C8C23×C8311yescharacteristic
439C4×C8C23×C8311yescharacteristic
440C4×C8C23×C8311yescharacteristic
441C2×Q8—21no—
442C2×Q8C2×D4×C8311yescharacteristic
443C2×Q8C2×D4×C8311yescharacteristic
444C2×Q8C2×D4×C8311yescharacteristic
445C2×Q8C2×D4×C8311yescharacteristic
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458Q16—22no—
459Q16—41no—
460Q16—81no—
461SD16—42no—
462SD16—42no—
463SD16—81no—
464SD16—81no—
465SD16—81no—
466SD16—81no—
467SD16—81no—
468SD16—81no—
469D8—42no—
470D8—42no—
471D8—81no—
472D8—81no—
473D8—82no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8C2×D4×C8311yescharacteristic
480C2×C8C2×D4×C8311yescharacteristic
481C2×C8C2×D4×C8311yescharacteristic
482C2×C8C2×D4×C8311yescharacteristic
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4C2×D4×C8311yescharacteristic
493C4⋊C4C2×D4×C8311yescharacteristic
494C4⋊C4C2×D4×C8311yescharacteristic
495C4⋊C4C2×D4×C8311yescharacteristic
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—41no—
510C42C24×C8311yescharacteristic
511C23—41no—
512C23—41no—
513C23—41no—
514Q8—21no—
515Q8—21no—
516Q8—21no—
517Q8—21no—
518Q8—21no—
519Q8—21no—
520Q8—21no—
521Q8—21no—
522Q8—41no—
523Q8—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—81no—
537D4—81no—
538D4—81no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—161no—
549C2×C4—161no—
550C2×C4—161no—
551C2×C4C22×D4×C8311yescharacteristic
552C2×C4C22×D4×C8311yescharacteristic
553C2×C4H(5,𝔽2)×C8311yescharacteristic
554C8—21no—
555C8—21no—
556C8—21no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8#135×C8312yes—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22D42×C8311yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4C2×#135×C8311yescharacteristic
584C4#575×C8311yescharacteristic
585C4#576×C8311yescharacteristic
586C4#577×C8311yescharacteristic
587C2—161no—
588C2—161no—
589C2—161no—
590C2C83×#327111yescharacteristic
591C2C83×#328711yescharacteristic
592C2C83×#328811yescharacteristic
subgroupG/H
center, socleC22×C83D42
commutator, Frattini, cosocleC42C24×C83
prime radicalC83×#1721C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C42×C83 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C83×#3400C2semidirect
2. C83×#3396C2semidirect
3. C83×#3396C2semidirect
4. C83×#3365C2semidirect
6. C83×#1688C2semidirect
7. C83×#1682C2semidirect
8. C83×#1668C2semidirect
9. C83×#1666C2semidirect
10. C83×#1640C2semidirect
11. C83×#1626C2semidirect
12. C83×#1620C2semidirect
13. C83×#1620C2semidirect
14. C83×#1584C2semidirect
15. C83×#1579C2semidirect
290. #19874C83direct (N × H)
297. #3400C2×C83semidirect
298. #3396C2×C83semidirect
299. #3396C2×C83semidirect
300. #3365C2×C83semidirect
302. #1688C2×C83semidirect
303. #1682C2×C83semidirect
304. #1668C2×C83semidirect
305. #1666C2×C83semidirect
306. #1640C2×C83semidirect
307. #1626C2×C83semidirect
308. #1620C2×C83semidirect
309. #1620C2×C83semidirect
310. #1584C2×C83semidirect
311. #1579C2×C83semidirect
312. C83#19874direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#34002
C83×#33962
C83×#33652
C83×#17212
C83×#16882
C83×#16822
C83×#16682
C83×#16662
C83×#16402
C83×#16262
C83×#16202
C83×#15842
C83×#15792
#1987483