Finite Group Databasebeta

← C83×#19881 #35247705

Subgroups — C83×#19881 #35247705

Order 21248.

562 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3395C211yesmaximal, characteristic, complemented
2C83×#3381C211yesmaximal, characteristic
3C83×#3364C211yesmaximal, characteristic
4C83×#3356C211yesmaximal, characteristic
5C83×#1716C211yesmaximal, characteristic, complemented
6C83×#1689C211yesmaximal, characteristic
7C83×#1680C211yesmaximal, characteristic, complemented
8C83×#1672C211yesmaximal, characteristic, complemented
9C83×#1672C211yesmaximal, characteristic, complemented
10C83×#1653C211yesmaximal, characteristic, complemented
11C83×#1652C211yesmaximal, characteristic
12C83×#1644C211yesmaximal, characteristic
13C83×#1636C211yesmaximal, characteristic, complemented
14C83×#1583C211yesmaximal, characteristic
15C83×#1579C211yesmaximal, characteristic, complemented
16#557×C83C2211yescharacteristic
17#557×C83C2211yescharacteristic
18#556×C83C2211yescharacteristic
19#554×C83C2211yescharacteristic
20#499×C83—21no—
21#498×C83C2211yescharacteristic
22#498×C83C2211yescharacteristic
23#498×C83C2211yescharacteristic
24#494×C83—21no—
25#494×C83C2211yescharacteristic
26#488×C83—21no—
27#487×C83C2211yescharacteristic
28#487×C83C2211yescharacteristic
29#485×C83—21no—
30#483×C83—21no—
31#479×C83—21no—
32#479×C83—21no—
33#478×C83—21no—
34#477×C83C2211yescharacteristic
35#477×C83C2211yescharacteristic
36#475×C83C2211yescharacteristic
37#474×C83C2211yescharacteristic
38#474×C83C2211yescharacteristic
39#470×C83—21no—
40#464×C83—21no—
41#462×C83—21no—
42#462×C83—21no—
43#462×C83C2211yescharacteristic
44#462×C83C2211yescharacteristic
45#462×C83C2211yescharacteristic
46C8×Q8×C83C2211yescharacteristic
47C8×Q8×C83C2211yescharacteristic
48C8×Q8×C83C2211yescharacteristic
49C4×Q16×C83—21no—
50C4×Q16×C83—21no—
51C4×Q16×C83C2211yescharacteristic
52C4×SD16×C83—21no—
53C4×SD16×C83C2211yescharacteristic
54#436×C83C2211yescharacteristic
55#428×C83—21no—
56#334×C83C2211yescharacteristic
57#334×C83C2211yescharacteristic
58#333×C83C2211yescharacteristic
59#332×C83C2211yescharacteristic
60#332×C83C2211yescharacteristic
61#332×C83C2211yescharacteristic
62Q8⋊C8×C83C2211yescharacteristic
63Q8⋊C8×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65D4⋊C8×C83C2211yescharacteristic
66#322×C83C2211yescharacteristic
67C2×Q16×C83—21no—
68C2×Q16×C83—21no—
69C2×Q16×C83—21no—
70C2×Q16×C83—21no—
71C2×Q16×C83—21no—
72C2×Q16×C83D411yescharacteristic
73C2×SD16×C83D411yescharacteristic
74C2×M16×C83—21no—
75C4⋊Q8×C83—21no—
76C4⋊Q8×C83—21no—
77C4⋊Q8×C83C2311yescharacteristic
78C4⋊Q8×C83C2311yescharacteristic
79C4⋊Q8×C83C2311yescharacteristic
80C4⋊Q8×C83C2311yescharacteristic
81#126×C83—41no—
82#125×C83—21no—
83#125×C83—21no—
84#125×C83—21no—
85#125×C83—41no—
86#125×C83—41no—
87#124×C83—21no—
88C22⋊Q8×C83—21no—
89C22⋊Q8×C83—21no—
90C22⋊Q8×C83—41no—
91C4×Q8×C83—21no—
92C4×Q8×C83—21no—
93C4×Q8×C83—21no—
94C4×Q8×C83—21no—
95C4×Q8×C83—21no—
96C4×Q8×C83C2311yescharacteristic
97C4×Q8×C83C2311yescharacteristic
98C4×Q8×C83C2311yescharacteristic
99C4×D4×C83—21no—
100C4×D4×C83C2311yescharacteristic
101#117×C83—21no—
102C2×C4⋊C4×C83—21no—
103#107×C83—21no—
104#107×C83—21no—
105#107×C83—21no—
106#107×C83—21no—
107#107×C83D411yescharacteristic
108#106×C83—21no—
109#106×C83—21no—
110#106×C83—21no—
111#106×C83—21no—
112#106×C83—21no—
113#106×C83—41no—
114#106×C83D411yescharacteristic
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×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#103×C83D411yescharacteristic
134#102×C83—21no—
135#102×C83—21no—
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
144C2×Q8×C83—21no—
145C2×Q8×C83—21no—
146C2×Q8×C83—21no—
147C2×Q8×C83—21no—
148C2×Q8×C83C2×D411yescharacteristic
149C2×Q8×C83C2×D411yescharacteristic
150C2×Q8×C83C2×D411yescharacteristic
151C2×D4×C83C2×D411yescharacteristic
152C22×C4×C83—21no—
153C22×C4×C83—41no—
154Q16×C83—22no—
155Q16×C83—42no—
156Q16×C83—42no—
157Q16×C83—81no—
158Q16×C83—81no—
159Q16×C83—81no—
160SD16×C83—22no—
161M16×C83—42no—
162C2×C8×C83—21no—
163C2×C8×C83—21no—
164C2×C8×C83—21no—
165C2×C8×C83—21no—
166C2×C8×C83—21no—
167C2×C8×C83C2×D411yescharacteristic
168C2×C8×C83C2×D411yescharacteristic
169C2×C8×C83C2×D411yescharacteristic
170C2×C8×C83C2×D411yescharacteristic
171C4⋊C4×C83—21no—
172C4⋊C4×C83—21no—
173C4⋊C4×C83—21no—
174C4⋊C4×C83—21no—
175C4⋊C4×C83—21no—
176C4⋊C4×C83—21no—
177C4⋊C4×C83—21no—
178C4⋊C4×C83—21no—
179C4⋊C4×C83—21no—
180C4⋊C4×C83—21no—
181C4⋊C4×C83—21no—
182C4⋊C4×C83—41no—
183C4⋊C4×C83—41no—
184C4⋊C4×C83—41no—
185C4⋊C4×C83—41no—
186C4⋊C4×C83—41no—
187C4⋊C4×C83—41no—
188C4⋊C4×C83—41no—
189C4⋊C4×C83—41no—
190C4⋊C4×C83—41no—
191C4⋊C4×C83C2×D411yescharacteristic
192C4⋊C4×C83C2×D411yescharacteristic
193C4⋊C4×C83C2×D411yescharacteristic
194C4⋊C4×C83C2×D411yescharacteristic
195C22⋊C4×C83—21no—
196C22⋊C4×C83—41no—
197C22⋊C4×C83—41no—
198C22⋊C4×C83—41no—
199C42×C83—21no—
200C42×C83—21no—
201C42×C83—21no—
202C42×C83—41no—
203C42×C83—41no—
204C42×C83—41no—
205C42×C83C2411yescharacteristic
206C23×C83—21no—
207Q8×C83—21no—
208Q8×C83—21no—
209Q8×C83—21no—
210Q8×C83—21no—
211Q8×C83—21no—
212Q8×C83—41no—
213Q8×C83—41no—
214Q8×C83—41no—
215Q8×C83—41no—
216Q8×C83—41no—
217Q8×C83—41no—
218Q8×C83—81no—
219Q8×C83#13712yes—
220D4×C83—21no—
221D4×C83—21no—
222C2×C4×C83—21no—
223C2×C4×C83—21no—
224C2×C4×C83—21no—
225C2×C4×C83—21no—
226C2×C4×C83—21no—
227C2×C4×C83—21no—
228C2×C4×C83—21no—
229C2×C4×C83—41no—
230C2×C4×C83—41no—
231C2×C4×C83—41no—
232C2×C4×C83—41no—
233C2×C4×C83—41no—
234C2×C4×C83—41no—
235C2×C4×C83—161no—
236C2×C4×C83C22×D411yescharacteristic
237C2×C4×C83C22×D411yescharacteristic
238C2×C4×C83H(5,𝔽2)11yescharacteristic
239C8×C83—21no—
240C8×C83—21no—
241C8×C83—21no—
242C8×C83—41no—
243C8×C83—41no—
244C8×C83—41no—
245C8×C83—41no—
246C8×C83—41no—
247C8×C83#13512yes—
248C22×C83—41no—
249C22×C83—41no—
250C22×C83—41no—
251C22×C83D4211yescharacteristic
252C4×C83—22no—
253C4×C83—21no—
254C4×C83—41no—
255C4×C83—41no—
256C4×C83—41no—
257C4×C83—41no—
258C4×C83—41no—
259C4×C83—41no—
260C4×C83—81no—
261C4×C83—81no—
262C4×C83—81no—
263C4×C83—81no—
264C4×C83C2×#13511yescharacteristic
265C4×C83C2×#13711yescharacteristic
266C4×C83#57711yescharacteristic
267C4×C83#57811yescharacteristic
268#19881C8311yesmaximal, characteristic, direct product factor, Sylow
269C2×C83—81no—
270C2×C83#327011yescharacteristic
271C2×C83#328411yescharacteristic
272C2×C83#328911yescharacteristic
273#3395C2×C8311yescharacteristic, complemented
274#3381C2×C8311yescharacteristic
275#3364C2×C8311yescharacteristic
276#3356C2×C8311yescharacteristic
277#1716C2×C8311yescharacteristic, complemented
278#1689C2×C8311yescharacteristic
279#1680C2×C8311yescharacteristic, complemented
280#1672C2×C8311yescharacteristic, complemented
281#1672C2×C8311yescharacteristic, complemented
282#1653C2×C8311yescharacteristic, complemented
283#1652C2×C8311yescharacteristic
284#1644C2×C8311yescharacteristic
285#1636C2×C8311yescharacteristic, complemented
286#1583C2×C8311yescharacteristic
287#1579C2×C8311yescharacteristic, complemented
288C83#1988111yescharacteristic, direct product factor, Sylow
289#557C22×C8311yescharacteristic
290#557C22×C8311yescharacteristic
291#556C22×C8311yescharacteristic
292#554C22×C8311yescharacteristic
293#499—21no—
294#498C22×C8311yescharacteristic
295#498C22×C8311yescharacteristic
296#498C22×C8311yescharacteristic
297#494—21no—
298#494C22×C8311yescharacteristic
299#488—21no—
300#487C22×C8311yescharacteristic
301#487C22×C8311yescharacteristic
302#485—21no—
303#483—21no—
304#479—21no—
305#479—21no—
306#478—21no—
307#477C22×C8311yescharacteristic
308#477C22×C8311yescharacteristic
309#475C22×C8311yescharacteristic
310#474C22×C8311yescharacteristic
311#474C22×C8311yescharacteristic
312#470—21no—
313#464—21no—
314#462—21no—
315#462—21no—
316#462C22×C8311yescharacteristic
317#462C22×C8311yescharacteristic
318#462C22×C8311yescharacteristic
319C8×Q8C22×C8311yescharacteristic
320C8×Q8C22×C8311yescharacteristic
321C8×Q8C22×C8311yescharacteristic
322C4×Q16—21no—
323C4×Q16—21no—
324C4×Q16C22×C8311yescharacteristic
325C4×SD16—21no—
326C4×SD16C22×C8311yescharacteristic
327#436C22×C8311yescharacteristic
328#428—21no—
329#334C22×C8311yescharacteristic
330#334C22×C8311yescharacteristic
331#333C22×C8311yescharacteristic
332#332C22×C8311yescharacteristic
333#332C22×C8311yescharacteristic
334#332C22×C8311yescharacteristic
335Q8⋊C8C22×C8311yescharacteristic
336Q8⋊C8C22×C8311yescharacteristic
337Q8⋊C8C22×C8311yescharacteristic
338D4⋊C8C22×C8311yescharacteristic
339#322C22×C8311yescharacteristic
340C2×Q16—21no—
341C2×Q16—21no—
342C2×Q16—21no—
343C2×Q16—21no—
344C2×Q16—21no—
345C2×Q16D4×C8311yescharacteristic
346C2×SD16D4×C8311yescharacteristic
347C2×M16—21no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8C23×C8311yescharacteristic
351C4⋊Q8C23×C8311yescharacteristic
352C4⋊Q8C23×C8311yescharacteristic
353C4⋊Q8C23×C8311yescharacteristic
354#126—41no—
355#125—21no—
356#125—21no—
357#125—21no—
358#125—41no—
359#125—41no—
360#124—21no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—41no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8C23×C8311yescharacteristic
370C4×Q8C23×C8311yescharacteristic
371C4×Q8C23×C8311yescharacteristic
372C4×D4—21no—
373C4×D4C23×C8311yescharacteristic
374#117—21no—
375C2×C4⋊C4—21no—
376#107—21no—
377#107—21no—
378#107—21no—
379#107—21no—
380#107D4×C8311yescharacteristic
381#106—21no—
382#106—21no—
383#106—21no—
384#106—21no—
385#106—21no—
386#106—41no—
387#106D4×C8311yescharacteristic
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8C23×C8311yescharacteristic
392C4⋊C8C23×C8311yescharacteristic
393C4⋊C8C23×C8311yescharacteristic
394C4⋊C8C23×C8311yescharacteristic
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—41no—
404#103D4×C8311yescharacteristic
405#103D4×C8311yescharacteristic
406#103D4×C8311yescharacteristic
407#102—21no—
408#102—21no—
409#102D4×C8311yescharacteristic
410C22⋊C8—21no—
411C4×C8—21no—
412C4×C8—21no—
413C4×C8—21no—
414C4×C8C23×C8311yescharacteristic
415C4×C8C23×C8311yescharacteristic
416C4×C8C23×C8311yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8C2×D4×C8311yescharacteristic
422C2×Q8C2×D4×C8311yescharacteristic
423C2×Q8C2×D4×C8311yescharacteristic
424C2×D4C2×D4×C8311yescharacteristic
425C22×C4—21no—
426C22×C4—41no—
427Q16—22no—
428Q16—42no—
429Q16—42no—
430Q16—81no—
431Q16—81no—
432Q16—81no—
433SD16—22no—
434M16—42no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8C2×D4×C8311yescharacteristic
441C2×C8C2×D4×C8311yescharacteristic
442C2×C8C2×D4×C8311yescharacteristic
443C2×C8C2×D4×C8311yescharacteristic
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4C2×D4×C8311yescharacteristic
465C4⋊C4C2×D4×C8311yescharacteristic
466C4⋊C4C2×D4×C8311yescharacteristic
467C4⋊C4C2×D4×C8311yescharacteristic
468C22⋊C4—21no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—41no—
476C42—41no—
477C42—41no—
478C42C24×C8311yescharacteristic
479C23—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—41no—
486Q8—41no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—81no—
492Q8#137×C8312yes—
493D4—21no—
494D4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—161no—
509C2×C4C22×D4×C8311yescharacteristic
510C2×C4C22×D4×C8311yescharacteristic
511C2×C4H(5,𝔽2)×C8311yescharacteristic
512C8—21no—
513C8—21no—
514C8—21no—
515C8—41no—
516C8—41no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8#135×C8312yes—
521C22—41no—
522C22—41no—
523C22—41no—
524C22D42×C8311yescharacteristic
525C4—21no—
526C4—22no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—81no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4C2×#135×C8311yescharacteristic
538C4C2×#137×C8311yescharacteristic
539C4#577×C8311yescharacteristic
540C4#578×C8311yescharacteristic
541C2—81no—
542C2C83×#327011yescharacteristic
543C2C83×#328411yescharacteristic
544C2C83×#328911yescharacteristic
subgroupG/H
center, socleC22×C83D42
commutator, Frattini, cosocleC42C24×C83
prime radicalC2×D4×C83C2×D4
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×#3395C2semidirect
5. C83×#1716C2semidirect
7. C83×#1680C2semidirect
8. C83×#1672C2semidirect
9. C83×#1672C2semidirect
10. C83×#1653C2semidirect
13. C83×#1636C2semidirect
15. C83×#1579C2semidirect
268. #19881C83direct (N × H)
273. #3395C2×C83semidirect
277. #1716C2×C83semidirect
279. #1680C2×C83semidirect
280. #1672C2×C83semidirect
281. #1672C2×C83semidirect
282. #1653C2×C83semidirect
285. #1636C2×C83semidirect
287. #1579C2×C83semidirect
288. C83#19881direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#33952
C83×#33812
C83×#33642
C83×#33562
C83×#17162
C83×#16892
C83×#16802
C83×#16722
C83×#16532
C83×#16522
C83×#16442
C83×#16362
C83×#15832
C83×#15792
#1988183