Finite Group Databasebeta

← C83×#19829 #35247653

Subgroups — C83×#19829 #35247653

Order 21248.

590 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3381C211yesmaximal, characteristic, complemented
2C83×#3363C211yesmaximal, characteristic, complemented
3C83×#3362C211yesmaximal, characteristic
4C83×#3333C211yesmaximal, characteristic
5C83×#1720C211yesmaximal, characteristic, complemented
6C83×#1703C211yesmaximal, characteristic, complemented
7C83×#1678C211yesmaximal, characteristic, complemented
8C83×#1678C211yesmaximal, characteristic, complemented
9C83×#1672C211yesmaximal, characteristic, complemented
10C83×#1641C211yesmaximal, characteristic
11C83×#1633C211yesmaximal, characteristic, complemented
12C83×#1632C211yesmaximal, characteristic, complemented
13C83×#1626C211yesmaximal, characteristic, complemented
14C83×#1583C211yesmaximal, characteristic, complemented
15C83×#1579C211yesmaximal, characteristic, complemented
16Q82×C83C2211yescharacteristic
17#557×C83C2211yescharacteristic
18#554×C83C2211yescharacteristic
19#550×C83C2211yescharacteristic
20#499×C83—21no—
21#498×C83C2211yescharacteristic
22#494×C83C2211yescharacteristic
23#487×C83—21no—
24#487×C83C2211yescharacteristic
25#486×C83—21no—
26#486×C83C2211yescharacteristic
27#486×C83C2211yescharacteristic
28#486×C83C2211yescharacteristic
29#480×C83—21no—
30#479×C83—21no—
31#478×C83—21no—
32#477×C83—21no—
33#477×C83C2211yescharacteristic
34#477×C83C2211yescharacteristic
35#477×C83C2211yescharacteristic
36#476×C83—21no—
37#476×C83C2211yescharacteristic
38#474×C83C2211yescharacteristic
39#468×C83—21no—
40#462×C83—21no—
41#462×C83C2211yescharacteristic
42#460×C83—21no—
43#460×C83C2211yescharacteristic
44#460×C83C2211yescharacteristic
45#452×C83—21no—
46C8×Q8×C83C2211yescharacteristic
47C8×Q8×C83C2211yescharacteristic
48C8×Q8×C83C2211yescharacteristic
49C4×Q16×C83—21no—
50C4×Q16×C83C2211yescharacteristic
51C4×SD16×C83—21no—
52C4×SD16×C83—21no—
53C4×SD16×C83C2211yescharacteristic
54#436×C83C2211yescharacteristic
55#417×C83—21no—
56#334×C83C2211yescharacteristic
57#334×C83C2211yescharacteristic
58#333×C83C2211yescharacteristic
59#333×C83C2211yescharacteristic
60#332×C83C2211yescharacteristic
61#331×C83C2211yescharacteristic
62Q8⋊C8×C83C2211yescharacteristic
63Q8⋊C8×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65D4⋊C8×C83C2211yescharacteristic
66#322×C83C2211yescharacteristic
67C2×#41×C83—21no—
68C2×Q16×C83—21no—
69C2×Q16×C83—41no—
70C2×Q16×C83D411yescharacteristic
71C2×SD16×C83—21no—
72C2×SD16×C83—21no—
73C2×SD16×C83D411yescharacteristic
74C2×M16×C83—21no—
75C4⋊Q8×C83—21no—
76C4⋊Q8×C83—21no—
77C4⋊Q8×C83—21no—
78C4⋊Q8×C83—41no—
79C4⋊Q8×C83C2311yescharacteristic
80C4⋊Q8×C83C2311yescharacteristic
81C4⋊Q8×C83C2311yescharacteristic
82#127×C83—21no—
83#127×C83C2311yescharacteristic
84#125×C83—21no—
85#125×C83—21no—
86#125×C83—41no—
87C22⋊Q8×C83—21no—
88C22⋊Q8×C83—41no—
89#121×C83—21no—
90#121×C83—41no—
91C4×Q8×C83—21no—
92C4×Q8×C83—21no—
93C4×Q8×C83—21no—
94C4×Q8×C83—21no—
95C4×Q8×C83C2311yescharacteristic
96C4×Q8×C83C2311yescharacteristic
97C4×Q8×C83C2311yescharacteristic
98C4×D4×C83—21no—
99C4×D4×C83—21no—
100C4×D4×C83C2311yescharacteristic
101C2×C4⋊C4×C83—21no—
102#107×C83—21no—
103#107×C83—21no—
104#107×C83—21no—
105#107×C83—21no—
106#107×C83D411yescharacteristic
107#106×C83—21no—
108#106×C83—21no—
109#106×C83—21no—
110#106×C83D411yescharacteristic
111C4⋊C8×C83—21no—
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×C83D411yescharacteristic
125#103×C83D411yescharacteristic
126#103×C83D411yescharacteristic
127#102×C83—21no—
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—41no—
136#102×C83D411yescharacteristic
137C22⋊C8×C83—21no—
138C4×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—41no—
150C2×Q8×C83C2×D411yescharacteristic
151C2×Q8×C83C2×D411yescharacteristic
152C2×Q8×C83C2×D411yescharacteristic
153C2×D4×C83—21no—
154C2×D4×C83—21no—
155C2×D4×C83—21no—
156C2×D4×C83—41no—
157C2×D4×C83—41no—
158C2×D4×C83C2×D411yescharacteristic
159C22×C4×C83—21no—
160C22×C4×C83—41no—
161C22×C4×C83—41no—
162Q16×C83—22no—
163Q16×C83—42no—
164Q16×C83—82no—
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×C83C2×D411yescharacteristic
175C2×C8×C83C2×D411yescharacteristic
176C2×C8×C83C2×D411yescharacteristic
177C2×C8×C83C2×D411yescharacteristic
178C4⋊C4×C83—21no—
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—41no—
188C4⋊C4×C83—41no—
189C4⋊C4×C83—41no—
190C4⋊C4×C83—41no—
191C4⋊C4×C83—41no—
192C4⋊C4×C83—41no—
193C4⋊C4×C83—41no—
194C4⋊C4×C83C2×D411yescharacteristic
195C4⋊C4×C83C2×D411yescharacteristic
196C4⋊C4×C83C2×D411yescharacteristic
197C4⋊C4×C83C2×D411yescharacteristic
198C22⋊C4×C83—21no—
199C22⋊C4×C83—41no—
200C22⋊C4×C83—41no—
201C42×C83—21no—
202C42×C83—21no—
203C42×C83—21no—
204C42×C83—41no—
205C42×C83—41no—
206C42×C83C2411yescharacteristic
207C23×C83—21no—
208C23×C83—41no—
209Q8×C83—21no—
210Q8×C83—21no—
211Q8×C83—21no—
212Q8×C83—21no—
213Q8×C83—41no—
214Q8×C83—41no—
215Q8×C83—81no—
216Q8×C83—81no—
217Q8×C83—161no—
218Q8×C83#13512yes—
219Q8×C83#13712yes—
220D4×C83—21no—
221D4×C83—21no—
222D4×C83—41no—
223D4×C83—41no—
224D4×C83—41no—
225D4×C83—41no—
226D4×C83—82no—
227D4×C83—81no—
228D4×C83—161no—
229C2×C4×C83—21no—
230C2×C4×C83—21no—
231C2×C4×C83—21no—
232C2×C4×C83—21no—
233C2×C4×C83—21no—
234C2×C4×C83—21no—
235C2×C4×C83—21no—
236C2×C4×C83—41no—
237C2×C4×C83—41no—
238C2×C4×C83—41no—
239C2×C4×C83—41no—
240C2×C4×C83—41no—
241C2×C4×C83—82no—
242C2×C4×C83—161no—
243C2×C4×C83C22×D411yescharacteristic
244C2×C4×C83C22×D411yescharacteristic
245C2×C4×C83H(5,𝔽2)11yescharacteristic
246C8×C83—21no—
247C8×C83—21no—
248C8×C83—21no—
249C8×C83—21no—
250C8×C83—41no—
251C8×C83—41no—
252C8×C83—41no—
253C8×C83—41no—
254C8×C83—41no—
255C22×C83—41no—
256C22×C83—41no—
257C22×C83—41no—
258C22×C83—81no—
259C22×C83—81no—
260C22×C83—81no—
261C22×C83D4211yescharacteristic
262C4×C83—22no—
263C4×C83—22no—
264C4×C83—21no—
265C4×C83—41no—
266C4×C83—41no—
267C4×C83—41no—
268C4×C83—41no—
269C4×C83—41no—
270C4×C83—81no—
271C4×C83—81no—
272C4×C83—81no—
273C4×C83C2×#13511yescharacteristic
274C4×C83C2×#13711yescharacteristic
275C4×C83#57711yescharacteristic
276C4×C83#57811yescharacteristic
277#19829C8311yesmaximal, characteristic, direct product factor, Sylow
278C2×C83—81no—
279C2×C83—161no—
280C2×C83#327011yescharacteristic
281C2×C83#328211yescharacteristic
282C2×C83#328811yescharacteristic
283#3381C2×C8311yescharacteristic, complemented
284#3363C2×C8311yescharacteristic, complemented
285#3362C2×C8311yescharacteristic
286#3333C2×C8311yescharacteristic
287#1720C2×C8311yescharacteristic, complemented
288#1703C2×C8311yescharacteristic, complemented
289#1678C2×C8311yescharacteristic, complemented
290#1678C2×C8311yescharacteristic, complemented
291#1672C2×C8311yescharacteristic, complemented
292#1641C2×C8311yescharacteristic
293#1633C2×C8311yescharacteristic, complemented
294#1632C2×C8311yescharacteristic, complemented
295#1626C2×C8311yescharacteristic, complemented
296#1583C2×C8311yescharacteristic, complemented
297#1579C2×C8311yescharacteristic, complemented
298C83#1982911yescharacteristic, direct product factor, Sylow
299Q82C22×C8311yescharacteristic
300#557C22×C8311yescharacteristic
301#554C22×C8311yescharacteristic
302#550C22×C8311yescharacteristic
303#499—21no—
304#498C22×C8311yescharacteristic
305#494C22×C8311yescharacteristic
306#487—21no—
307#487C22×C8311yescharacteristic
308#486—21no—
309#486C22×C8311yescharacteristic
310#486C22×C8311yescharacteristic
311#486C22×C8311yescharacteristic
312#480—21no—
313#479—21no—
314#478—21no—
315#477—21no—
316#477C22×C8311yescharacteristic
317#477C22×C8311yescharacteristic
318#477C22×C8311yescharacteristic
319#476—21no—
320#476C22×C8311yescharacteristic
321#474C22×C8311yescharacteristic
322#468—21no—
323#462—21no—
324#462C22×C8311yescharacteristic
325#460—21no—
326#460C22×C8311yescharacteristic
327#460C22×C8311yescharacteristic
328#452—21no—
329C8×Q8C22×C8311yescharacteristic
330C8×Q8C22×C8311yescharacteristic
331C8×Q8C22×C8311yescharacteristic
332C4×Q16—21no—
333C4×Q16C22×C8311yescharacteristic
334C4×SD16—21no—
335C4×SD16—21no—
336C4×SD16C22×C8311yescharacteristic
337#436C22×C8311yescharacteristic
338#417—21no—
339#334C22×C8311yescharacteristic
340#334C22×C8311yescharacteristic
341#333C22×C8311yescharacteristic
342#333C22×C8311yescharacteristic
343#332C22×C8311yescharacteristic
344#331C22×C8311yescharacteristic
345Q8⋊C8C22×C8311yescharacteristic
346Q8⋊C8C22×C8311yescharacteristic
347Q8⋊C8C22×C8311yescharacteristic
348D4⋊C8C22×C8311yescharacteristic
349#322C22×C8311yescharacteristic
350C2×#41—21no—
351C2×Q16—21no—
352C2×Q16—41no—
353C2×Q16D4×C8311yescharacteristic
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16D4×C8311yescharacteristic
357C2×M16—21no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—41no—
362C4⋊Q8C23×C8311yescharacteristic
363C4⋊Q8C23×C8311yescharacteristic
364C4⋊Q8C23×C8311yescharacteristic
365#127—21no—
366#127C23×C8311yescharacteristic
367#125—21no—
368#125—21no—
369#125—41no—
370C22⋊Q8—21no—
371C22⋊Q8—41no—
372#121—21no—
373#121—41no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8C23×C8311yescharacteristic
379C4×Q8C23×C8311yescharacteristic
380C4×Q8C23×C8311yescharacteristic
381C4×D4—21no—
382C4×D4—21no—
383C4×D4C23×C8311yescharacteristic
384C2×C4⋊C4—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#107—21no—
389#107D4×C8311yescharacteristic
390#106—21no—
391#106—21no—
392#106—21no—
393#106D4×C8311yescharacteristic
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8C23×C8311yescharacteristic
398C4⋊C8C23×C8311yescharacteristic
399C4⋊C8C23×C8311yescharacteristic
400C4⋊C8C23×C8311yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103D4×C8311yescharacteristic
408#103D4×C8311yescharacteristic
409#103D4×C8311yescharacteristic
410#102—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—41no—
419#102D4×C8311yescharacteristic
420C22⋊C8—21no—
421C4×C8—21no—
422C4×C8—21no—
423C4×C8—21no—
424C4×C8C23×C8311yescharacteristic
425C4×C8C23×C8311yescharacteristic
426C4×C8C23×C8311yescharacteristic
427#41—42no—
428#41—81no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—41no—
433C2×Q8C2×D4×C8311yescharacteristic
434C2×Q8C2×D4×C8311yescharacteristic
435C2×Q8C2×D4×C8311yescharacteristic
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4C2×D4×C8311yescharacteristic
442C22×C4—21no—
443C22×C4—41no—
444C22×C4—41no—
445Q16—22no—
446Q16—42no—
447Q16—82no—
448SD16—22no—
449SD16—42no—
450SD16—81no—
451M16—81no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8C2×D4×C8311yescharacteristic
458C2×C8C2×D4×C8311yescharacteristic
459C2×C8C2×D4×C8311yescharacteristic
460C2×C8C2×D4×C8311yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4C2×D4×C8311yescharacteristic
478C4⋊C4C2×D4×C8311yescharacteristic
479C4⋊C4C2×D4×C8311yescharacteristic
480C4⋊C4C2×D4×C8311yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—41no—
488C42—41no—
489C42C24×C8311yescharacteristic
490C23—21no—
491C23—41no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—81no—
500Q8—161no—
501Q8#135×C8312yes—
502Q8#137×C8312yes—
503D4—21no—
504D4—21no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—82no—
510D4—81no—
511D4—161no—
512C2×C4—21no—
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—82no—
525C2×C4—161no—
526C2×C4C22×D4×C8311yescharacteristic
527C2×C4C22×D4×C8311yescharacteristic
528C2×C4H(5,𝔽2)×C8311yescharacteristic
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22D42×C8311yescharacteristic
545C4—22no—
546C4—21no—
547C4—22no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4C2×#135×C8311yescharacteristic
557C4C2×#137×C8311yescharacteristic
558C4#577×C8311yescharacteristic
559C4#578×C8311yescharacteristic
560C2—81no—
561C2—161no—
562C2C83×#327011yescharacteristic
563C2C83×#328211yescharacteristic
564C2C83×#328811yescharacteristic
subgroupG/H
center, socleC22×C83D42
commutator, Frattini, cosocleC42C24×C83
prime radical#550×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×#3363C2semidirect
5. C83×#1720C2semidirect
6. C83×#1703C2semidirect
7. C83×#1678C2semidirect
8. C83×#1678C2semidirect
9. C83×#1672C2semidirect
11. C83×#1633C2semidirect
12. C83×#1632C2semidirect
13. C83×#1626C2semidirect
14. C83×#1583C2semidirect
15. C83×#1579C2semidirect
277. #19829C83direct (N × H)
283. #3381C2×C83semidirect
284. #3363C2×C83semidirect
287. #1720C2×C83semidirect
288. #1703C2×C83semidirect
289. #1678C2×C83semidirect
290. #1678C2×C83semidirect
291. #1672C2×C83semidirect
293. #1633C2×C83semidirect
294. #1632C2×C83semidirect
295. #1626C2×C83semidirect
296. #1583C2×C83semidirect
297. #1579C2×C83semidirect
298. C83#19829direct (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×#33632
C83×#33622
C83×#33332
C83×#17202
C83×#17032
C83×#16782
C83×#16722
C83×#16412
C83×#16332
C83×#16322
C83×#16262
C83×#15832
C83×#15792
#1982983