Finite Group Databasebeta

← C83×#19383 #35247207

Subgroups — C83×#19383 #35247207

Order 21248.

606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3251C211yesmaximal, characteristic
2C83×#3218C211yesmaximal, characteristic, complemented
3C83×#3141C211yesmaximal, characteristic, complemented
4C83×#2969C211yesmaximal, characteristic, complemented
5C83×#1702C211yesmaximal, characteristic, complemented
6C83×#1701C211yesmaximal, characteristic, complemented
7C83×#1700C211yesmaximal, characteristic, complemented
8C83×#1699C211yesmaximal, characteristic, complemented
9C83×#1682C211yesmaximal, characteristic, complemented
10C83×#1681C211yesmaximal, characteristic, complemented
11C83×#1680C211yesmaximal, characteristic, complemented
12C83×#1679C211yesmaximal, characteristic, complemented
13C83×#1569C211yesmaximal, characteristic, complemented
14C83×#1553C211yesmaximal, characteristic, complemented
15C83×#1546C211yesmaximal, characteristic, complemented
16#532×C83C2211yescharacteristic
17C2×C4⋊Q8×C83C2211yescharacteristic
18#529×C83C2211yescharacteristic
19#497×C83—21no—
20#491×C83—21no—
21#489×C83—21no—
22#489×C83—21no—
23#487×C83C2211yescharacteristic
24#487×C83C2211yescharacteristic
25#486×C83C2211yescharacteristic
26#486×C83C2211yescharacteristic
27#478×C83—21no—
28#475×C83C2211yescharacteristic
29#474×C83C2211yescharacteristic
30#469×C83—21no—
31#468×C83—21no—
32#463×C83—21no—
33#462×C83C2211yescharacteristic
34#462×C83C2211yescharacteristic
35#461×C83C2211yescharacteristic
36#461×C83C2211yescharacteristic
37#460×C83C2211yescharacteristic
38#459×C83C2211yescharacteristic
39#451×C83—21no—
40#448×C83—21no—
41#446×C83C2211yescharacteristic
42C8×Q8×C83C2211yescharacteristic
43#436×C83—21no—
44#436×C83C2211yescharacteristic
45#435×C83—21no—
46C8×D4×C83C2211yescharacteristic
47#433×C83—21no—
48#432×C83C2211yescharacteristic
49#431×C83C2211yescharacteristic
50#423×C83C2211yescharacteristic
51#417×C83—21no—
52#417×C83—21no—
53#405×C83—21no—
54C4×M16×C83C2211yescharacteristic
55#335×C83C2211yescharacteristic
56#335×C83C2211yescharacteristic
57#334×C83C2211yescharacteristic
58#334×C83C2211yescharacteristic
59#332×C83C2211yescharacteristic
60#332×C83C2211yescharacteristic
61#332×C83C2211yescharacteristic
62#332×C83C2211yescharacteristic
63#332×C83C2211yescharacteristic
64#332×C83C2211yescharacteristic
65#331×C83C2211yescharacteristic
66#331×C83C2211yescharacteristic
67C2×#41×C83—21no—
68C22×Q8×C83—21no—
69C2×Q16×C83—21no—
70C2×Q16×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—
77C2×M16×C83D411yescharacteristic
78C2×M16×C83D411yescharacteristic
79C22×C8×C83—21no—
80C4⋊Q8×C83—21no—
81C4⋊Q8×C83—21no—
82C4⋊Q8×C83—21no—
83C4⋊Q8×C83C2311yescharacteristic
84C4⋊Q8×C83C2311yescharacteristic
85C4⋊Q8×C83C2311yescharacteristic
86#127×C83C2311yescharacteristic
87#126×C83—21no—
88#125×C83D411yescharacteristic
89#124×C83—21no—
90#124×C83D411yescharacteristic
91#123×C83—21no—
92C22⋊Q8×C83D411yescharacteristic
93#121×C83—21no—
94#121×C83—21no—
95#121×C83D411yescharacteristic
96C4×Q8×C83C2311yescharacteristic
97C4×D4×C83—21no—
98C4×D4×C83—21no—
99C4×D4×C83—21no—
100C4×D4×C83C2311yescharacteristic
101#117×C83—21no—
102C2×C4⋊C4×C83—21no—
103C2×C4⋊C4×C83—21no—
104C2×C42×C83C2311yescharacteristic
105#107×C83—21no—
106#106×C83—21no—
107C4⋊C8×C83—21no—
108C4⋊C8×C83—21no—
109C4⋊C8×C83—21no—
110C4⋊C8×C83C2311yescharacteristic
111C4⋊C8×C83C2311yescharacteristic
112C4⋊C8×C83C2311yescharacteristic
113C4⋊C8×C83C2311yescharacteristic
114C4⋊C8×C83C2311yescharacteristic
115C4⋊C8×C83C2311yescharacteristic
116#103×C83—21no—
117#103×C83—21no—
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#102×C83—21no—
126#102×C83—21no—
127#102×C83—21no—
128#102×C83—21no—
129#102×C83—21no—
130#102×C83—21no—
131#102×C83—21no—
132C22⋊C8×C83—21no—
133C22⋊C8×C83—21no—
134C22⋊C8×C83—21no—
135C22⋊C8×C83—21no—
136#97×C83—21no—
137#97×C83—21no—
138#97×C83D411yescharacteristic
139#97×C83D411yescharacteristic
140C4×C8×C83—21no—
141C4×C8×C83—21no—
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#41×C83—42no—
145#41×C83—42no—
146C2×Q8×C83—21no—
147C2×Q8×C83—21no—
148C2×Q8×C83—21no—
149C2×Q8×C83—41no—
150C2×Q8×C83—81no—
151C2×Q8×C83—81no—
152C2×Q8×C83C2×D411yescharacteristic
153C2×D4×C83—21no—
154C2×D4×C83—21no—
155C2×D4×C83—21no—
156C2×D4×C83—21no—
157C2×D4×C83—41no—
158C2×D4×C83C2×D411yescharacteristic
159C22×C4×C83—21no—
160C22×C4×C83—41no—
161C22×C4×C83—41no—
162C22×C4×C83C2×D411yescharacteristic
163C22×C4×C83C2×D411yescharacteristic
164C22×C4×C83#4111yescharacteristic
165Q16×C83—81no—
166Q16×C83—81no—
167SD16×C83—81no—
168SD16×C83—81no—
169SD16×C83—81no—
170D8×C83—81no—
171M16×C83—41no—
172M16×C83—41no—
173M16×C83—42no—
174M16×C83—81no—
175C2×C8×C83—21no—
176C2×C8×C83—21no—
177C2×C8×C83—21no—
178C2×C8×C83—21no—
179C2×C8×C83—21no—
180C2×C8×C83—21no—
181C2×C8×C83—42no—
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—21no—
193C4⋊C4×C83—21no—
194C4⋊C4×C83—21no—
195C4⋊C4×C83—21no—
196C4⋊C4×C83—41no—
197C4⋊C4×C83—41no—
198C4⋊C4×C83C2×D411yescharacteristic
199C4⋊C4×C83C2×D411yescharacteristic
200C22⋊C4×C83—21no—
201C22⋊C4×C83—21no—
202C22⋊C4×C83—21no—
203C22⋊C4×C83—21no—
204C22⋊C4×C83—21no—
205C22⋊C4×C83—41no—
206C22⋊C4×C83—41no—
207C42×C83—21no—
208C42×C83C2×D411yescharacteristic
209C42×C83C2×D411yescharacteristic
210C42×C83#4111yescharacteristic
211C42×C83C2411yescharacteristic
212C23×C83—21no—
213C23×C83—41no—
214C23×C83#12111yescharacteristic
215Q8×C83—21no—
216Q8×C83—21no—
217Q8×C83—41no—
218Q8×C83—41no—
219Q8×C83—41no—
220Q8×C83—41no—
221Q8×C83—41no—
222Q8×C83—41no—
223Q8×C83—82no—
224D4×C83—21no—
225D4×C83—21no—
226D4×C83—41no—
227D4×C83—41no—
228D4×C83—41no—
229D4×C83—41no—
230D4×C83—81no—
231D4×C83—81no—
232D4×C83—82no—
233C2×C4×C83—21no—
234C2×C4×C83—21no—
235C2×C4×C83—21no—
236C2×C4×C83—21no—
237C2×C4×C83—21no—
238C2×C4×C83—21no—
239C2×C4×C83—21no—
240C2×C4×C83—41no—
241C2×C4×C83—41no—
242C2×C4×C83—41no—
243C2×C4×C83—41no—
244C2×C4×C83—41no—
245C2×C4×C83—41no—
246C2×C4×C83—82no—
247C2×C4×C83—82no—
248C2×C4×C83#12111yescharacteristic
249C2×C4×C83#12111yescharacteristic
250C2×C4×C83#12111yescharacteristic
251C2×C4×C83C22×D411yescharacteristic
252C2×C4×C83C22×D411yescharacteristic
253C2×C4×C83C2×#4111yescharacteristic
254C8×C83—21no—
255C8×C83—21no—
256C8×C83—21no—
257C8×C83—21no—
258C8×C83—41no—
259C8×C83—41no—
260C8×C83—41no—
261C8×C83—41no—
262C8×C83—41no—
263C8×C83—41no—
264C22×C83—21no—
265C22×C83—21no—
266C22×C83—21no—
267C22×C83—41no—
268C22×C83—41no—
269C22×C83—41no—
270C22×C83—81no—
271C22×C83—81no—
272C22×C83—81no—
273C22×C83C2×#12111yescharacteristic
274C4×C83—21no—
275C4×C83—21no—
276C4×C83—21no—
277C4×C83—21no—
278C4×C83—41no—
279C4×C83—41no—
280C4×C83—41no—
281C4×C83—81no—
282C4×C83—81no—
283C4×C83—81no—
284C4×C83#57511yescharacteristic
285C4×C83#57511yescharacteristic
286C4×C83#57611yescharacteristic
287C4×C83#57711yescharacteristic
288#19383C8311yesmaximal, characteristic, direct product factor, Sylow
289C2×C83—41no—
290C2×C83—81no—
291C2×C83—161no—
292C2×C83#304011yescharacteristic
293C2×C83#306211yescharacteristic
294C2×C83#306911yescharacteristic
295#3251C2×C8311yescharacteristic
296#3218C2×C8311yescharacteristic, complemented
297#3141C2×C8311yescharacteristic, complemented
298#2969C2×C8311yescharacteristic, complemented
299#1702C2×C8311yescharacteristic, complemented
300#1701C2×C8311yescharacteristic, complemented
301#1700C2×C8311yescharacteristic, complemented
302#1699C2×C8311yescharacteristic, complemented
303#1682C2×C8311yescharacteristic, complemented
304#1681C2×C8311yescharacteristic, complemented
305#1680C2×C8311yescharacteristic, complemented
306#1679C2×C8311yescharacteristic, complemented
307#1569C2×C8311yescharacteristic, complemented
308#1553C2×C8311yescharacteristic, complemented
309#1546C2×C8311yescharacteristic, complemented
310C83#1938311yescharacteristic, direct product factor, Sylow
311#532C22×C8311yescharacteristic
312C2×C4⋊Q8C22×C8311yescharacteristic
313#529C22×C8311yescharacteristic
314#497—21no—
315#491—21no—
316#489—21no—
317#489—21no—
318#487C22×C8311yescharacteristic
319#487C22×C8311yescharacteristic
320#486C22×C8311yescharacteristic
321#486C22×C8311yescharacteristic
322#478—21no—
323#475C22×C8311yescharacteristic
324#474C22×C8311yescharacteristic
325#469—21no—
326#468—21no—
327#463—21no—
328#462C22×C8311yescharacteristic
329#462C22×C8311yescharacteristic
330#461C22×C8311yescharacteristic
331#461C22×C8311yescharacteristic
332#460C22×C8311yescharacteristic
333#459C22×C8311yescharacteristic
334#451—21no—
335#448—21no—
336#446C22×C8311yescharacteristic
337C8×Q8C22×C8311yescharacteristic
338#436—21no—
339#436C22×C8311yescharacteristic
340#435—21no—
341C8×D4C22×C8311yescharacteristic
342#433—21no—
343#432C22×C8311yescharacteristic
344#431C22×C8311yescharacteristic
345#423C22×C8311yescharacteristic
346#417—21no—
347#417—21no—
348#405—21no—
349C4×M16C22×C8311yescharacteristic
350#335C22×C8311yescharacteristic
351#335C22×C8311yescharacteristic
352#334C22×C8311yescharacteristic
353#334C22×C8311yescharacteristic
354#332C22×C8311yescharacteristic
355#332C22×C8311yescharacteristic
356#332C22×C8311yescharacteristic
357#332C22×C8311yescharacteristic
358#332C22×C8311yescharacteristic
359#332C22×C8311yescharacteristic
360#331C22×C8311yescharacteristic
361#331C22×C8311yescharacteristic
362C2×#41—21no—
363C22×Q8—21no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×D8—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16D4×C8311yescharacteristic
373C2×M16D4×C8311yescharacteristic
374C22×C8—21no—
375C4⋊Q8—21no—
376C4⋊Q8—21no—
377C4⋊Q8—21no—
378C4⋊Q8C23×C8311yescharacteristic
379C4⋊Q8C23×C8311yescharacteristic
380C4⋊Q8C23×C8311yescharacteristic
381#127C23×C8311yescharacteristic
382#126—21no—
383#125D4×C8311yescharacteristic
384#124—21no—
385#124D4×C8311yescharacteristic
386#123—21no—
387C22⋊Q8D4×C8311yescharacteristic
388#121—21no—
389#121—21no—
390#121D4×C8311yescharacteristic
391C4×Q8C23×C8311yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4C23×C8311yescharacteristic
396#117—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C42C23×C8311yescharacteristic
400#107—21no—
401#106—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8C23×C8311yescharacteristic
406C4⋊C8C23×C8311yescharacteristic
407C4⋊C8C23×C8311yescharacteristic
408C4⋊C8C23×C8311yescharacteristic
409C4⋊C8C23×C8311yescharacteristic
410C4⋊C8C23×C8311yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431#97—21no—
432#97—21no—
433#97D4×C8311yescharacteristic
434#97D4×C8311yescharacteristic
435C4×C8—21no—
436C4×C8—21no—
437C4×C8C23×C8311yescharacteristic
438C4×C8C23×C8311yescharacteristic
439#41—42no—
440#41—42no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—41no—
445C2×Q8—81no—
446C2×Q8—81no—
447C2×Q8C2×D4×C8311yescharacteristic
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4C2×D4×C8311yescharacteristic
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4C2×D4×C8311yescharacteristic
458C22×C4C2×D4×C8311yescharacteristic
459C22×C4#41×C8311yescharacteristic
460Q16—81no—
461Q16—81no—
462SD16—81no—
463SD16—81no—
464SD16—81no—
465D8—81no—
466M16—41no—
467M16—41no—
468M16—42no—
469M16—81no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—42no—
477C2×C8C2×D4×C8311yescharacteristic
478C2×C8C2×D4×C8311yescharacteristic
479C2×C8C2×D4×C8311yescharacteristic
480C2×C8C2×D4×C8311yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4C2×D4×C8311yescharacteristic
494C4⋊C4C2×D4×C8311yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C42—21no—
503C42C2×D4×C8311yescharacteristic
504C42C2×D4×C8311yescharacteristic
505C42#41×C8311yescharacteristic
506C42C24×C8311yescharacteristic
507C23—21no—
508C23—41no—
509C23#121×C8311yescharacteristic
510Q8—21no—
511Q8—21no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—82no—
519D4—21no—
520D4—21no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—81no—
526D4—81no—
527D4—82no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4#121×C8311yescharacteristic
544C2×C4#121×C8311yescharacteristic
545C2×C4#121×C8311yescharacteristic
546C2×C4C22×D4×C8311yescharacteristic
547C2×C4C22×D4×C8311yescharacteristic
548C2×C4C2×#41×C8311yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22C2×#121×C8311yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4#575×C8311yescharacteristic
580C4#575×C8311yescharacteristic
581C4#576×C8311yescharacteristic
582C4#577×C8311yescharacteristic
583C2—41no—
584C2—81no—
585C2—161no—
586C2C83×#304011yescharacteristic
587C2C83×#306211yescharacteristic
588C2C83×#306911yescharacteristic
subgroupG/H
center, socleC22×C83C2×#121
commutator, Frattini, cosocleC42C24×C83
prime radicalC83×#3251C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C2×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C83×#3218C2semidirect
3. C83×#3141C2semidirect
4. C83×#2969C2semidirect
5. C83×#1702C2semidirect
6. C83×#1701C2semidirect
7. C83×#1700C2semidirect
8. C83×#1699C2semidirect
9. C83×#1682C2semidirect
10. C83×#1681C2semidirect
11. C83×#1680C2semidirect
12. C83×#1679C2semidirect
13. C83×#1569C2semidirect
14. C83×#1553C2semidirect
15. C83×#1546C2semidirect
288. #19383C83direct (N × H)
296. #3218C2×C83semidirect
297. #3141C2×C83semidirect
298. #2969C2×C83semidirect
299. #1702C2×C83semidirect
300. #1701C2×C83semidirect
301. #1700C2×C83semidirect
302. #1699C2×C83semidirect
303. #1682C2×C83semidirect
304. #1681C2×C83semidirect
305. #1680C2×C83semidirect
306. #1679C2×C83semidirect
307. #1569C2×C83semidirect
308. #1553C2×C83semidirect
309. #1546C2×C83semidirect
310. C83#19383direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#32512
C83×#32182
C83×#31412
C83×#29692
C83×#17022
C83×#17012
C83×#17002
C83×#16992
C83×#16822
C83×#16812
C83×#16802
C83×#16792
C83×#15692
C83×#15532
C83×#15462
#1938383