Finite Group Databasebeta

← C83×#19822 #35247646

Subgroups — C83×#19822 #35247646

Order 21248.

598 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3381C211yesmaximal, characteristic, complemented
2C83×#3359C211yesmaximal, characteristic, complemented
3C83×#3331C211yesmaximal, characteristic
4C83×#3298C211yesmaximal, characteristic
5C83×#1718C211yesmaximal, characteristic, complemented
6C83×#1699C211yesmaximal, characteristic, complemented
7C83×#1684C211yesmaximal, characteristic, complemented
8C83×#1680C211yesmaximal, characteristic, complemented
9C83×#1671C211yesmaximal, characteristic, complemented
10C83×#1648C211yesmaximal, characteristic, complemented
11C83×#1647C211yesmaximal, characteristic
12C83×#1643C211yesmaximal, characteristic, complemented
13C83×#1637C211yesmaximal, characteristic, complemented
14C83×#1583C211yesmaximal, characteristic, complemented
15C83×SD16⋊C8C211yesmaximal, characteristic, complemented
16#557×C83C2211yescharacteristic
17#554×C83C2211yescharacteristic
18D4×Q8×C83C2211yescharacteristic
19#547×C83C2211yescharacteristic
20#500×C83C2211yescharacteristic
21#499×C83—21no—
22#498×C83C2211yescharacteristic
23#487×C83—21no—
24#487×C83C2211yescharacteristic
25#487×C83C2211yescharacteristic
26#487×C83C2211yescharacteristic
27#487×C83C2211yescharacteristic
28#483×C83—21no—
29#483×C83—21no—
30#479×C83—21no—
31#478×C83—21no—
32#477×C83C2211yescharacteristic
33#476×C83C2211yescharacteristic
34#475×C83—21no—
35#475×C83C2211yescharacteristic
36#475×C83C2211yescharacteristic
37#474×C83C2211yescharacteristic
38#470×C83—21no—
39#465×C83—21no—
40#462×C83C2211yescharacteristic
41#461×C83—21no—
42#461×C83C2211yescharacteristic
43#461×C83C2211yescharacteristic
44#452×C83—21no—
45#448×C83—21no—
46C8×Q8×C83C2211yescharacteristic
47C8×Q8×C83C2211yescharacteristic
48C4×SD16×C83—21no—
49C4×SD16×C83—21no—
50C4×SD16×C83C2211yescharacteristic
51C4×SD16×C83C2211yescharacteristic
52#436×C83C2211yescharacteristic
53C8×D4×C83C2211yescharacteristic
54#417×C83—21no—
55C2×#103×C83—21no—
56#335×C83C2211yescharacteristic
57#334×C83C2211yescharacteristic
58#333×C83C2211yescharacteristic
59#332×C83C2211yescharacteristic
60#332×C83C2211yescharacteristic
61#332×C83C2211yescharacteristic
62Q8⋊C8×C83C2211yescharacteristic
63Q8⋊C8×C83C2211yescharacteristic
64D4⋊C8×C83C2211yescharacteristic
65D4⋊C8×C83C2211yescharacteristic
66#322×C83C2211yescharacteristic
67C2×#41×C83—21no—
68C22×Q8×C83—21no—
69C2×Q16×C83—21no—
70C2×SD16×C83—21no—
71C2×SD16×C83—21no—
72C2×SD16×C83D411yescharacteristic
73C2×SD16×C83D411yescharacteristic
74C2×M16×C83—21no—
75C22×C8×C83—21no—
76C4⋊Q8×C83—21no—
77C4⋊Q8×C83—21no—
78C4⋊Q8×C83C2311yescharacteristic
79C4⋊Q8×C83C2311yescharacteristic
80C4⋊Q8×C83C2311yescharacteristic
81C4⋊Q8×C83C2311yescharacteristic
82#125×C83—21no—
83#125×C83—21no—
84#125×C83—41no—
85#123×C83—41no—
86C22⋊Q8×C83—21no—
87C22⋊Q8×C83—21no—
88C22⋊Q8×C83—21no—
89C22⋊Q8×C83—41no—
90C22⋊Q8×C83—41no—
91#121×C83—21no—
92C4×Q8×C83—21no—
93C4×Q8×C83—21no—
94C4×Q8×C83C2311yescharacteristic
95C4×Q8×C83C2311yescharacteristic
96C4×D4×C83—21no—
97C4×D4×C83—21no—
98C4×D4×C83C2311yescharacteristic
99C4×D4×C83C2311yescharacteristic
100C2×C4⋊C4×C83—21no—
101C2×C4⋊C4×C83—21no—
102#107×C83—21no—
103#107×C83—21no—
104#107×C83—41no—
105#106×C83—21no—
106#106×C83—21no—
107#106×C83—21no—
108#106×C83—21no—
109#106×C83—21no—
110#106×C83D411yescharacteristic
111#106×C83D411yescharacteristic
112C4⋊C8×C83—21no—
113C4⋊C8×C83—21no—
114C4⋊C8×C83C2311yescharacteristic
115C4⋊C8×C83C2311yescharacteristic
116C4⋊C8×C83C2311yescharacteristic
117C4⋊C8×C83C2311yescharacteristic
118#103×C83—21no—
119#103×C83—21no—
120#103×C83—21no—
121#103×C83—21no—
122#103×C83—21no—
123#103×C83—21no—
124#103×C83—21no—
125#103×C83—21no—
126#103×C83—21no—
127#103×C83—21no—
128#103×C83—21no—
129#103×C83—21no—
130#103×C83—41no—
131#103×C83D411yescharacteristic
132#103×C83D411yescharacteristic
133#102×C83—21no—
134#102×C83—21no—
135#102×C83D411yescharacteristic
136#102×C83D411yescharacteristic
137C22⋊C8×C83—21no—
138C22⋊C8×C83—21no—
139C4×C8×C83—21no—
140C4×C8×C83—21no—
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#41×C83—42no—
145#41×C83—81no—
146C2×Q8×C83—21no—
147C2×Q8×C83—21no—
148C2×Q8×C83—21no—
149C2×Q8×C83—21no—
150C2×Q8×C83—41no—
151C2×Q8×C83—42no—
152C2×Q8×C83—81no—
153C2×Q8×C83C2×D411yescharacteristic
154C2×Q8×C83C2×D411yescharacteristic
155C2×D4×C83—41no—
156C2×D4×C83C2×D411yescharacteristic
157C2×D4×C83C2×D411yescharacteristic
158C22×C4×C83—21no—
159C22×C4×C83—21no—
160C22×C4×C83—41no—
161C22×C4×C83—41no—
162C22×C4×C83—41no—
163Q16×C83—81no—
164SD16×C83—22no—
165SD16×C83—22no—
166SD16×C83—42no—
167SD16×C83—81no—
168M16×C83—81no—
169C2×C8×C83—21no—
170C2×C8×C83—21no—
171C2×C8×C83—21no—
172C2×C8×C83—21no—
173C2×C8×C83—21no—
174C2×C8×C83—81no—
175C2×C8×C83C2×D411yescharacteristic
176C2×C8×C83C2×D411yescharacteristic
177C2×C8×C83C2×D411yescharacteristic
178C2×C8×C83C2×D411yescharacteristic
179C4⋊C4×C83—21no—
180C4⋊C4×C83—21no—
181C4⋊C4×C83—21no—
182C4⋊C4×C83—21no—
183C4⋊C4×C83—21no—
184C4⋊C4×C83—21no—
185C4⋊C4×C83—21no—
186C4⋊C4×C83—21no—
187C4⋊C4×C83—21no—
188C4⋊C4×C83—21no—
189C4⋊C4×C83—41no—
190C4⋊C4×C83—41no—
191C4⋊C4×C83—41no—
192C4⋊C4×C83—41no—
193C4⋊C4×C83—41no—
194C4⋊C4×C83—41no—
195C4⋊C4×C83—41no—
196C4⋊C4×C83C2×D411yescharacteristic
197C4⋊C4×C83C2×D411yescharacteristic
198C4⋊C4×C83C2×D411yescharacteristic
199C4⋊C4×C83C2×D411yescharacteristic
200C22⋊C4×C83—21no—
201C22⋊C4×C83—21no—
202C22⋊C4×C83—41no—
203C22⋊C4×C83—41no—
204C22⋊C4×C83—41no—
205C42×C83—21no—
206C42×C83—21no—
207C42×C83—41no—
208C42×C83C2411yescharacteristic
209C23×C83—21no—
210C23×C83—21no—
211Q8×C83—21no—
212Q8×C83—21no—
213Q8×C83—21no—
214Q8×C83—41no—
215Q8×C83—41no—
216Q8×C83—41no—
217Q8×C83—41no—
218Q8×C83—41no—
219Q8×C83—41no—
220Q8×C83—82no—
221Q8×C83—81no—
222Q8×C83#13712yes—
223D4×C83—21no—
224D4×C83—21no—
225D4×C83—21no—
226D4×C83—82no—
227D4×C83#13512yes—
228C2×C4×C83—21no—
229C2×C4×C83—21no—
230C2×C4×C83—21no—
231C2×C4×C83—21no—
232C2×C4×C83—21no—
233C2×C4×C83—21no—
234C2×C4×C83—41no—
235C2×C4×C83—41no—
236C2×C4×C83—41no—
237C2×C4×C83—41no—
238C2×C4×C83—41no—
239C2×C4×C83—41no—
240C2×C4×C83—41no—
241C2×C4×C83—41no—
242C2×C4×C83—82no—
243C2×C4×C83—82no—
244C2×C4×C83—161no—
245C2×C4×C83C22×D411yescharacteristic
246C2×C4×C83C22×D411yescharacteristic
247C2×C4×C83H(5,𝔽2)11yescharacteristic
248C8×C83—21no—
249C8×C83—21no—
250C8×C83—21no—
251C8×C83—21no—
252C8×C83—41no—
253C8×C83—41no—
254C8×C83—41no—
255C8×C83—41no—
256C8×C83—41no—
257C22×C83—22no—
258C22×C83—41no—
259C22×C83—41no—
260C22×C83—41no—
261C22×C83—41no—
262C22×C83—41no—
263C22×C83D4211yescharacteristic
264C4×C83—22no—
265C4×C83—21no—
266C4×C83—41no—
267C4×C83—41no—
268C4×C83—41no—
269C4×C83—41no—
270C4×C83—41no—
271C4×C83—81no—
272C4×C83—81no—
273C4×C83—81no—
274C4×C83—81no—
275C4×C83C2×#13511yescharacteristic
276C4×C83C2×#13711yescharacteristic
277C4×C83#57711yescharacteristic
278C4×C83#57711yescharacteristic
279#19822C8311yesmaximal, characteristic, direct product factor, Sylow
280C2×C83—42no—
281C2×C83—81no—
282C2×C83#326611yescharacteristic
283C2×C83#328211yescharacteristic
284C2×C83#328911yescharacteristic
285#3381C2×C8311yescharacteristic, complemented
286#3359C2×C8311yescharacteristic, complemented
287#3331C2×C8311yescharacteristic
288#3298C2×C8311yescharacteristic
289#1718C2×C8311yescharacteristic, complemented
290#1699C2×C8311yescharacteristic, complemented
291#1684C2×C8311yescharacteristic, complemented
292#1680C2×C8311yescharacteristic, complemented
293#1671C2×C8311yescharacteristic, complemented
294#1648C2×C8311yescharacteristic, complemented
295#1647C2×C8311yescharacteristic
296#1643C2×C8311yescharacteristic, complemented
297#1637C2×C8311yescharacteristic, complemented
298#1583C2×C8311yescharacteristic, complemented
299SD16⋊C8C2×C8311yescharacteristic, complemented
300C83#1982211yescharacteristic, direct product factor, Sylow
301#557C22×C8311yescharacteristic
302#554C22×C8311yescharacteristic
303D4×Q8C22×C8311yescharacteristic
304#547C22×C8311yescharacteristic
305#500C22×C8311yescharacteristic
306#499—21no—
307#498C22×C8311yescharacteristic
308#487—21no—
309#487C22×C8311yescharacteristic
310#487C22×C8311yescharacteristic
311#487C22×C8311yescharacteristic
312#487C22×C8311yescharacteristic
313#483—21no—
314#483—21no—
315#479—21no—
316#478—21no—
317#477C22×C8311yescharacteristic
318#476C22×C8311yescharacteristic
319#475—21no—
320#475C22×C8311yescharacteristic
321#475C22×C8311yescharacteristic
322#474C22×C8311yescharacteristic
323#470—21no—
324#465—21no—
325#462C22×C8311yescharacteristic
326#461—21no—
327#461C22×C8311yescharacteristic
328#461C22×C8311yescharacteristic
329#452—21no—
330#448—21no—
331C8×Q8C22×C8311yescharacteristic
332C8×Q8C22×C8311yescharacteristic
333C4×SD16—21no—
334C4×SD16—21no—
335C4×SD16C22×C8311yescharacteristic
336C4×SD16C22×C8311yescharacteristic
337#436C22×C8311yescharacteristic
338C8×D4C22×C8311yescharacteristic
339#417—21no—
340C2×#103—21no—
341#335C22×C8311yescharacteristic
342#334C22×C8311yescharacteristic
343#333C22×C8311yescharacteristic
344#332C22×C8311yescharacteristic
345#332C22×C8311yescharacteristic
346#332C22×C8311yescharacteristic
347Q8⋊C8C22×C8311yescharacteristic
348Q8⋊C8C22×C8311yescharacteristic
349D4⋊C8C22×C8311yescharacteristic
350D4⋊C8C22×C8311yescharacteristic
351#322C22×C8311yescharacteristic
352C2×#41—21no—
353C22×Q8—21no—
354C2×Q16—21no—
355C2×SD16—21no—
356C2×SD16—21no—
357C2×SD16D4×C8311yescharacteristic
358C2×SD16D4×C8311yescharacteristic
359C2×M16—21no—
360C22×C8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8C23×C8311yescharacteristic
364C4⋊Q8C23×C8311yescharacteristic
365C4⋊Q8C23×C8311yescharacteristic
366C4⋊Q8C23×C8311yescharacteristic
367#125—21no—
368#125—21no—
369#125—41no—
370#123—41no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—41no—
375C22⋊Q8—41no—
376#121—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8C23×C8311yescharacteristic
380C4×Q8C23×C8311yescharacteristic
381C4×D4—21no—
382C4×D4—21no—
383C4×D4C23×C8311yescharacteristic
384C4×D4C23×C8311yescharacteristic
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387#107—21no—
388#107—21no—
389#107—41no—
390#106—21no—
391#106—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395#106D4×C8311yescharacteristic
396#106D4×C8311yescharacteristic
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8C23×C8311yescharacteristic
400C4⋊C8C23×C8311yescharacteristic
401C4⋊C8C23×C8311yescharacteristic
402C4⋊C8C23×C8311yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—41no—
416#103D4×C8311yescharacteristic
417#103D4×C8311yescharacteristic
418#102—21no—
419#102—21no—
420#102D4×C8311yescharacteristic
421#102D4×C8311yescharacteristic
422C22⋊C8—21no—
423C22⋊C8—21no—
424C4×C8—21no—
425C4×C8—21no—
426C4×C8C23×C8311yescharacteristic
427C4×C8C23×C8311yescharacteristic
428C4×C8C23×C8311yescharacteristic
429#41—42no—
430#41—81no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—41no—
436C2×Q8—42no—
437C2×Q8—81no—
438C2×Q8C2×D4×C8311yescharacteristic
439C2×Q8C2×D4×C8311yescharacteristic
440C2×D4—41no—
441C2×D4C2×D4×C8311yescharacteristic
442C2×D4C2×D4×C8311yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448Q16—81no—
449SD16—22no—
450SD16—22no—
451SD16—42no—
452SD16—81no—
453M16—81no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—81no—
460C2×C8C2×D4×C8311yescharacteristic
461C2×C8C2×D4×C8311yescharacteristic
462C2×C8C2×D4×C8311yescharacteristic
463C2×C8C2×D4×C8311yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4C2×D4×C8311yescharacteristic
482C4⋊C4C2×D4×C8311yescharacteristic
483C4⋊C4C2×D4×C8311yescharacteristic
484C4⋊C4C2×D4×C8311yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C42—21no—
491C42—21no—
492C42—41no—
493C42C24×C8311yescharacteristic
494C23—21no—
495C23—21no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—82no—
506Q8—81no—
507Q8#137×C8312yes—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—82no—
512D4#135×C8312yes—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—161no—
530C2×C4C22×D4×C8311yescharacteristic
531C2×C4C22×D4×C8311yescharacteristic
532C2×C4H(5,𝔽2)×C8311yescharacteristic
533C8—21no—
534C8—21no—
535C8—21no—
536C8—21no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—41no—
542C22—22no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22D42×C8311yescharacteristic
549C4—21no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4C2×#135×C8311yescharacteristic
561C4C2×#137×C8311yescharacteristic
562C4#577×C8311yescharacteristic
563C4#577×C8311yescharacteristic
564C2—42no—
565C2—81no—
566C2C83×#326611yescharacteristic
567C2C83×#328211yescharacteristic
568C2C83×#328911yescharacteristic
subgroupG/H
center, socleC22×C83D42
commutator, Frattini, cosocleC42C24×C83
prime radical#547×C83C22
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×#3381C2semidirect
2. C83×#3359C2semidirect
5. C83×#1718C2semidirect
6. C83×#1699C2semidirect
7. C83×#1684C2semidirect
8. C83×#1680C2semidirect
9. C83×#1671C2semidirect
10. C83×#1648C2semidirect
12. C83×#1643C2semidirect
13. C83×#1637C2semidirect
14. C83×#1583C2semidirect
15. C83×SD16⋊C8C2semidirect
279. #19822C83direct (N × H)
285. #3381C2×C83semidirect
286. #3359C2×C83semidirect
289. #1718C2×C83semidirect
290. #1699C2×C83semidirect
291. #1684C2×C83semidirect
292. #1680C2×C83semidirect
293. #1671C2×C83semidirect
294. #1648C2×C83semidirect
296. #1643C2×C83semidirect
297. #1637C2×C83semidirect
298. #1583C2×C83semidirect
299. SD16⋊C8C2×C83semidirect
300. C83#19822direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#33812
C83×#33592
C83×#33312
C83×#32982
C83×#17182
C83×#16992
C83×#16842
C83×#16802
C83×#16712
C83×#16482
C83×#16472
C83×#16432
C83×#16372
C83×#15832
C83×SD16⋊C82
#1982283