Finite Group Databasebeta

← C83×#19159 #35246983

Subgroups — C83×#19159 #35246983

Order 21248.

620 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3167C211yesmaximal, characteristic, complemented
2C83×#3107C211yesmaximal, characteristic, complemented
3C83×#3106C211yesmaximal, characteristic
4C83×#2965C211yesmaximal, characteristic, complemented
5C83×#1704C211yesmaximal, characteristic, complemented
6C83×#1703C211yesmaximal, characteristic, complemented
7C83×#1702C211yesmaximal, characteristic, complemented
8C83×#1701C211yesmaximal, characteristic, complemented
9C83×#1692C211yesmaximal, characteristic, complemented
10C83×#1691C211yesmaximal, characteristic, complemented
11C83×#1686C211yesmaximal, characteristic, complemented
12C83×#1685C211yesmaximal, characteristic, complemented
13C83×#1564C211yesmaximal, characteristic, complemented
14C83×#1544C211yesmaximal, characteristic, complemented
15C83×#1543C211yesmaximal, characteristic, complemented
16#533×C83C2211yescharacteristic
17#532×C83C2211yescharacteristic
18C4×#41×C83C2211yescharacteristic
19#498×C83C2211yescharacteristic
20#492×C83C2211yescharacteristic
21#487×C83C2211yescharacteristic
22#486×C83C2211yescharacteristic
23#485×C83—21no—
24#482×C83—21no—
25#477×C83C2211yescharacteristic
26#476×C83C2211yescharacteristic
27#475×C83C2211yescharacteristic
28#474×C83C2211yescharacteristic
29#465×C83—21no—
30#465×C83—21no—
31#462×C83C2211yescharacteristic
32#461×C83C2211yescharacteristic
33#460×C83C2211yescharacteristic
34#459×C83C2211yescharacteristic
35#452×C83—21no—
36#449×C83—21no—
37#446×C83C2211yescharacteristic
38#446×C83C2211yescharacteristic
39C4×Q16×C83—21no—
40C4×SD16×C83—21no—
41C4×SD16×C83—21no—
42C4×SD16×C83—21no—
43C4×SD16×C83—21no—
44C4×D8×C83—21no—
45#436×C83C2211yescharacteristic
46#436×C83C2211yescharacteristic
47#435×C83—21no—
48#435×C83—21no—
49#431×C83—21no—
50#431×C83C2211yescharacteristic
51#431×C83C2211yescharacteristic
52#431×C83C2211yescharacteristic
53C4×M16×C83—21no—
54C2×C4×C8×C83C2211yescharacteristic
55#335×C83C2211yescharacteristic
56#335×C83C2211yescharacteristic
57#334×C83C2211yescharacteristic
58#334×C83C2211yescharacteristic
59#333×C83C2211yescharacteristic
60#333×C83C2211yescharacteristic
61#332×C83C2211yescharacteristic
62#332×C83C2211yescharacteristic
63#332×C83C2211yescharacteristic
64#332×C83C2211yescharacteristic
65#331×C83C2211yescharacteristic
66#331×C83C2211yescharacteristic
67C2×#41×C83—21no—
68C2×#41×C83D411yescharacteristic
69C2×Q16×C83—21no—
70C2×SD16×C83—21no—
71C2×SD16×C83—21no—
72C2×SD16×C83—21no—
73C2×SD16×C83—21no—
74C2×D8×C83—21no—
75C2×M16×C83—21no—
76C2×M16×C83—21no—
77C22×C8×C83D411yescharacteristic
78C22×C8×C83D411yescharacteristic
79C4⋊Q8×C83C2311yescharacteristic
80C4⋊Q8×C83C2311yescharacteristic
81C4⋊Q8×C83C2311yescharacteristic
82#127×C83C2311yescharacteristic
83#125×C83—21no—
84#124×C83—21no—
85C22⋊Q8×C83—21no—
86C22⋊Q8×C83—21no—
87#121×C83—21no—
88#121×C83—21no—
89C4×Q8×C83—21no—
90C4×Q8×C83—21no—
91C4×Q8×C83D411yescharacteristic
92C4×Q8×C83C2311yescharacteristic
93C4×D4×C83—21no—
94C4×D4×C83—21no—
95C4×D4×C83—21no—
96C4×D4×C83—21no—
97C4×D4×C83D411yescharacteristic
98C4×D4×C83C2311yescharacteristic
99#117×C83—21no—
100#117×C83—21no—
101#117×C83D411yescharacteristic
102C2×C42×C83—21no—
103C2×C42×C83C2311yescharacteristic
104#107×C83—21no—
105#107×C83—21no—
106#106×C83—21no—
107#106×C83—21no—
108#106×C83—21no—
109#106×C83—21no—
110C4⋊C8×C83—21no—
111C4⋊C8×C83—21no—
112C4⋊C8×C83C2311yescharacteristic
113C4⋊C8×C83C2311yescharacteristic
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#102×C83—21no—
125#102×C83—21no—
126#102×C83—21no—
127#102×C83—21no—
128#102×C83—21no—
129#102×C83—21no—
130C22⋊C8×C83—21no—
131C22⋊C8×C83—21no—
132C22⋊C8×C83—21no—
133C22⋊C8×C83—21no—
134C22⋊C8×C83—21no—
135#97×C83—21no—
136#97×C83—21no—
137C4×C8×C83—21no—
138C4×C8×C83—21no—
139C4×C8×C83—21no—
140C4×C8×C83D411yescharacteristic
141C4×C8×C83D411yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#41×C83—41no—
145#41×C83—41no—
146#41×C83—82no—
147C2×Q8×C83—21no—
148C2×Q8×C83—21no—
149C2×Q8×C83—21no—
150C2×Q8×C83C2×D411yescharacteristic
151C2×D4×C83—21no—
152C2×D4×C83—21no—
153C2×D4×C83—21no—
154C2×D4×C83—21no—
155C2×D4×C83—41no—
156C2×D4×C83C2×D411yescharacteristic
157C22×C4×C83—21no—
158C22×C4×C83—21no—
159C22×C4×C83—21no—
160C22×C4×C83—41no—
161C22×C4×C83C2×D411yescharacteristic
162C22×C4×C83C2×D411yescharacteristic
163C22×C4×C83#4111yescharacteristic
164Q16×C83—42no—
165SD16×C83—42no—
166SD16×C83—42no—
167SD16×C83—42no—
168SD16×C83—42no—
169D8×C83—42no—
170M16×C83—42no—
171M16×C83—42no—
172C2×C8×C83—22no—
173C2×C8×C83—21no—
174C2×C8×C83—21no—
175C2×C8×C83—21no—
176C2×C8×C83—21no—
177C2×C8×C83—21no—
178C2×C8×C83—21no—
179C2×C8×C83—41no—
180C2×C8×C83C2×D411yescharacteristic
181C2×C8×C83C2×D411yescharacteristic
182C2×C8×C83C2×D411yescharacteristic
183C2×C8×C83C2×D411yescharacteristic
184C4⋊C4×C83—21no—
185C4⋊C4×C83—21no—
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×C83C2×D411yescharacteristic
195C4⋊C4×C83C2×D411yescharacteristic
196C22⋊C4×C83—21no—
197C22⋊C4×C83—21no—
198C22⋊C4×C83—21no—
199C22⋊C4×C83—41no—
200C22⋊C4×C83—41no—
201C22⋊C4×C83—41no—
202C42×C83—21no—
203C42×C83—21no—
204C42×C83—21no—
205C42×C83—41no—
206C42×C83C2×D411yescharacteristic
207C42×C83C2×D411yescharacteristic
208C42×C83#4111yescharacteristic
209C42×C83C2411yescharacteristic
210C23×C83—21no—
211C23×C83—41no—
212C23×C83#12111yescharacteristic
213Q8×C83—21no—
214Q8×C83—21no—
215Q8×C83—41no—
216Q8×C83—41no—
217Q8×C83—41no—
218Q8×C83—41no—
219Q8×C83—81no—
220D4×C83—21no—
221D4×C83—21no—
222D4×C83—42no—
223D4×C83—41no—
224D4×C83—41no—
225D4×C83—41no—
226D4×C83—41no—
227D4×C83—81no—
228D4×C83—82no—
229C2×C4×C83—21no—
230C2×C4×C83—21no—
231C2×C4×C83—21no—
232C2×C4×C83—21no—
233C2×C4×C83—22no—
234C2×C4×C83—21no—
235C2×C4×C83—21no—
236C2×C4×C83—21no—
237C2×C4×C83—42no—
238C2×C4×C83—41no—
239C2×C4×C83—41no—
240C2×C4×C83—42no—
241C2×C4×C83—41no—
242C2×C4×C83—41no—
243C2×C4×C83—41no—
244C2×C4×C83—82no—
245C2×C4×C83#12111yescharacteristic
246C2×C4×C83#12111yescharacteristic
247C2×C4×C83#12111yescharacteristic
248C2×C4×C83C22×D411yescharacteristic
249C2×C4×C83C22×D411yescharacteristic
250C2×C4×C83C2×#4111yescharacteristic
251C8×C83—21no—
252C8×C83—21no—
253C8×C83—21no—
254C8×C83—41no—
255C8×C83—41no—
256C8×C83—41no—
257C8×C83—41no—
258C8×C83—41no—
259C8×C83—41no—
260C8×C83#13512yes—
261C22×C83—21no—
262C22×C83—21no—
263C22×C83—21no—
264C22×C83—41no—
265C22×C83—41no—
266C22×C83—41no—
267C22×C83—81no—
268C22×C83—81no—
269C22×C83—81no—
270C22×C83C2×#12111yescharacteristic
271C4×C83—21no—
272C4×C83—21no—
273C4×C83—21no—
274C4×C83—41no—
275C4×C83—41no—
276C4×C83—41no—
277C4×C83—81no—
278C4×C83—81no—
279C4×C83—81no—
280C4×C83#47112yes—
281C4×C83C2×#13511yescharacteristic
282C4×C83#57511yescharacteristic
283C4×C83#57511yescharacteristic
284C4×C83#57511yescharacteristic
285#19159C8311yesmaximal, characteristic, direct product factor, Sylow
286C2×C83—41no—
287C2×C83—81no—
288C2×C83—161no—
289C2×C83#303511yescharacteristic
290C2×C83#305411yescharacteristic
291C2×C83C2×#47111yescharacteristic
292#3167C2×C8311yescharacteristic, complemented
293#3107C2×C8311yescharacteristic, complemented
294#3106C2×C8311yescharacteristic
295#2965C2×C8311yescharacteristic, complemented
296#1704C2×C8311yescharacteristic, complemented
297#1703C2×C8311yescharacteristic, complemented
298#1702C2×C8311yescharacteristic, complemented
299#1701C2×C8311yescharacteristic, complemented
300#1692C2×C8311yescharacteristic, complemented
301#1691C2×C8311yescharacteristic, complemented
302#1686C2×C8311yescharacteristic, complemented
303#1685C2×C8311yescharacteristic, complemented
304#1564C2×C8311yescharacteristic, complemented
305#1544C2×C8311yescharacteristic, complemented
306#1543C2×C8311yescharacteristic, complemented
307C83#1915911yescharacteristic, direct product factor, Sylow
308#533C22×C8311yescharacteristic
309#532C22×C8311yescharacteristic
310C4×#41C22×C8311yescharacteristic
311#498C22×C8311yescharacteristic
312#492C22×C8311yescharacteristic
313#487C22×C8311yescharacteristic
314#486C22×C8311yescharacteristic
315#485—21no—
316#482—21no—
317#477C22×C8311yescharacteristic
318#476C22×C8311yescharacteristic
319#475C22×C8311yescharacteristic
320#474C22×C8311yescharacteristic
321#465—21no—
322#465—21no—
323#462C22×C8311yescharacteristic
324#461C22×C8311yescharacteristic
325#460C22×C8311yescharacteristic
326#459C22×C8311yescharacteristic
327#452—21no—
328#449—21no—
329#446C22×C8311yescharacteristic
330#446C22×C8311yescharacteristic
331C4×Q16—21no—
332C4×SD16—21no—
333C4×SD16—21no—
334C4×SD16—21no—
335C4×SD16—21no—
336C4×D8—21no—
337#436C22×C8311yescharacteristic
338#436C22×C8311yescharacteristic
339#435—21no—
340#435—21no—
341#431—21no—
342#431C22×C8311yescharacteristic
343#431C22×C8311yescharacteristic
344#431C22×C8311yescharacteristic
345C4×M16—21no—
346C2×C4×C8C22×C8311yescharacteristic
347#335C22×C8311yescharacteristic
348#335C22×C8311yescharacteristic
349#334C22×C8311yescharacteristic
350#334C22×C8311yescharacteristic
351#333C22×C8311yescharacteristic
352#333C22×C8311yescharacteristic
353#332C22×C8311yescharacteristic
354#332C22×C8311yescharacteristic
355#332C22×C8311yescharacteristic
356#332C22×C8311yescharacteristic
357#331C22×C8311yescharacteristic
358#331C22×C8311yescharacteristic
359C2×#41—21no—
360C2×#41D4×C8311yescharacteristic
361C2×Q16—21no—
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×D8—21no—
367C2×M16—21no—
368C2×M16—21no—
369C22×C8D4×C8311yescharacteristic
370C22×C8D4×C8311yescharacteristic
371C4⋊Q8C23×C8311yescharacteristic
372C4⋊Q8C23×C8311yescharacteristic
373C4⋊Q8C23×C8311yescharacteristic
374#127C23×C8311yescharacteristic
375#125—21no—
376#124—21no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379#121—21no—
380#121—21no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8D4×C8311yescharacteristic
384C4×Q8C23×C8311yescharacteristic
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4D4×C8311yescharacteristic
390C4×D4C23×C8311yescharacteristic
391#117—21no—
392#117—21no—
393#117D4×C8311yescharacteristic
394C2×C42—21no—
395C2×C42C23×C8311yescharacteristic
396#107—21no—
397#107—21no—
398#106—21no—
399#106—21no—
400#106—21no—
401#106—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8C23×C8311yescharacteristic
405C4⋊C8C23×C8311yescharacteristic
406C4⋊C8C23×C8311yescharacteristic
407C4⋊C8C23×C8311yescharacteristic
408C4⋊C8C23×C8311yescharacteristic
409C4⋊C8C23×C8311yescharacteristic
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427#97—21no—
428#97—21no—
429C4×C8—21no—
430C4×C8—21no—
431C4×C8—21no—
432C4×C8D4×C8311yescharacteristic
433C4×C8D4×C8311yescharacteristic
434C4×C8C23×C8311yescharacteristic
435C4×C8C23×C8311yescharacteristic
436#41—41no—
437#41—41no—
438#41—82no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×D4×C8311yescharacteristic
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4C2×D4×C8311yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—41no—
453C22×C4C2×D4×C8311yescharacteristic
454C22×C4C2×D4×C8311yescharacteristic
455C22×C4#41×C8311yescharacteristic
456Q16—42no—
457SD16—42no—
458SD16—42no—
459SD16—42no—
460SD16—42no—
461D8—42no—
462M16—42no—
463M16—42no—
464C2×C8—22no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—41no—
472C2×C8C2×D4×C8311yescharacteristic
473C2×C8C2×D4×C8311yescharacteristic
474C2×C8C2×D4×C8311yescharacteristic
475C2×C8C2×D4×C8311yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4C2×D4×C8311yescharacteristic
487C4⋊C4C2×D4×C8311yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—41no—
498C42C2×D4×C8311yescharacteristic
499C42C2×D4×C8311yescharacteristic
500C42#41×C8311yescharacteristic
501C42C24×C8311yescharacteristic
502C23—21no—
503C23—41no—
504C23#121×C8311yescharacteristic
505Q8—21no—
506Q8—21no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—81no—
512D4—21no—
513D4—21no—
514D4—42no—
515D4—41no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—81no—
520D4—82no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4#121×C8311yescharacteristic
538C2×C4#121×C8311yescharacteristic
539C2×C4#121×C8311yescharacteristic
540C2×C4C22×D4×C8311yescharacteristic
541C2×C4C22×D4×C8311yescharacteristic
542C2×C4C2×#41×C8311yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8#135×C8312yes—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22C2×#121×C8311yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4#471×C8312yes—
573C4C2×#135×C8311yescharacteristic
574C4#575×C8311yescharacteristic
575C4#575×C8311yescharacteristic
576C4#575×C8311yescharacteristic
577C2—41no—
578C2—81no—
579C2—161no—
580C2C83×#303511yescharacteristic
581C2C83×#305411yescharacteristic
582C2C2×#471×C8311yescharacteristic
subgroupG/H
centerC2×C4×C83#121
commutator, Frattini, cosocleC42C24×C83
socleC22×C83C2×#121
prime radicalC83×#3106C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C83 ◁ C2×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#3167C2semidirect
2. C83×#3107C2semidirect
4. C83×#2965C2semidirect
5. C83×#1704C2semidirect
6. C83×#1703C2semidirect
7. C83×#1702C2semidirect
8. C83×#1701C2semidirect
9. C83×#1692C2semidirect
10. C83×#1691C2semidirect
11. C83×#1686C2semidirect
12. C83×#1685C2semidirect
13. C83×#1564C2semidirect
14. C83×#1544C2semidirect
15. C83×#1543C2semidirect
285. #19159C83direct (N × H)
292. #3167C2×C83semidirect
293. #3107C2×C83semidirect
295. #2965C2×C83semidirect
296. #1704C2×C83semidirect
297. #1703C2×C83semidirect
298. #1702C2×C83semidirect
299. #1701C2×C83semidirect
300. #1692C2×C83semidirect
301. #1691C2×C83semidirect
302. #1686C2×C83semidirect
303. #1685C2×C83semidirect
304. #1564C2×C83semidirect
305. #1544C2×C83semidirect
306. #1543C2×C83semidirect
307. C83#19159direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#31672
C83×#31072
C83×#31062
C83×#29652
C83×#17042
C83×#17032
C83×#17022
C83×#17012
C83×#16922
C83×#16912
C83×#16862
C83×#16852
C83×#15642
C83×#15442
C83×#15432
#1915983