Finite Group Databasebeta

← C83×#19873 #35247697

Subgroups — C83×#19873 #35247697

Order 21248.

572 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3400C211yesmaximal, characteristic
2C83×#3395C211yesmaximal, characteristic, complemented
3C83×#3383C211yesmaximal, characteristic, complemented
4C83×#3365C211yesmaximal, characteristic
5C83×#1722C211yesmaximal, characteristic
6C83×#1690C211yesmaximal, characteristic, complemented
7C83×#1682C211yesmaximal, characteristic
8C83×#1674C211yesmaximal, characteristic, complemented
9C83×#1666C211yesmaximal, characteristic
10C83×#1648C211yesmaximal, characteristic, complemented
11C83×#1648C211yesmaximal, characteristic, complemented
12C83×#1640C211yesmaximal, characteristic
13C83×#1626C211yesmaximal, characteristic
14C83×#1584C211yesmaximal, characteristic, complemented
15C83×#1579C211yesmaximal, characteristic, complemented
16#559×C83C2211yescharacteristic
17#557×C83C2211yescharacteristic
18#557×C83C2211yescharacteristic
19#557×C83C2211yescharacteristic
20#500×C83C2211yescharacteristic
21#500×C83C2211yescharacteristic
22#499×C83—21no—
23#497×C83—21no—
24#494×C83—21no—
25#494×C83C2211yescharacteristic
26#492×C83C2211yescharacteristic
27#488×C83—21no—
28#486×C83C2211yescharacteristic
29#486×C83C2211yescharacteristic
30#479×C83—21no—
31#479×C83—21no—
32#478×C83—21no—
33#475×C83C2211yescharacteristic
34#475×C83C2211yescharacteristic
35#475×C83C2211yescharacteristic
36#464×C83—21no—
37#464×C83—21no—
38#462×C83—21no—
39#462×C83—21no—
40#462×C83C2211yescharacteristic
41#462×C83C2211yescharacteristic
42#462×C83C2211yescharacteristic
43#461×C83—21no—
44#460×C83C2211yescharacteristic
45#460×C83C2211yescharacteristic
46#446×C83C2211yescharacteristic
47C8×Q8×C83C2211yescharacteristic
48C8×Q8×C83C2211yescharacteristic
49C8×Q8×C83C2211yescharacteristic
50#440×C83—21no—
51C4×Q16×C83—21no—
52C4×Q16×C83—21no—
53C4×Q16×C83C2211yescharacteristic
54C4×Q16×C83C2211yescharacteristic
55C4×SD16×C83—21no—
56#335×C83C2211yescharacteristic
57#334×C83C2211yescharacteristic
58#332×C83C2211yescharacteristic
59#332×C83C2211yescharacteristic
60#332×C83C2211yescharacteristic
61#331×C83C2211yescharacteristic
62Q8⋊C8×C83C2211yescharacteristic
63Q8⋊C8×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65Q8⋊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×Q16×C83D411yescharacteristic
74C2×SD16×C83—21no—
75C2×SD16×C83—21no—
76C2×SD16×C83—21no—
77C2×SD16×C83—21no—
78C4⋊Q8×C83—21no—
79C4⋊Q8×C83—21no—
80C4⋊Q8×C83—21no—
81C4⋊Q8×C83C2311yescharacteristic
82C4⋊Q8×C83C2311yescharacteristic
83C4⋊Q8×C83C2311yescharacteristic
84#127×C83C2311yescharacteristic
85#125×C83—21no—
86#125×C83—21no—
87#125×C83—21no—
88#125×C83—41no—
89#125×C83—41no—
90#125×C83—41no—
91#124×C83—21no—
92#124×C83—21no—
93#123×C83—41no—
94C4×Q8×C83—21no—
95C4×Q8×C83—21no—
96C4×Q8×C83—21no—
97C4×Q8×C83—21no—
98C4×Q8×C83—21no—
99C4×Q8×C83—21no—
100C4×Q8×C83C2311yescharacteristic
101C4×Q8×C83C2311yescharacteristic
102C4×Q8×C83C2311yescharacteristic
103C4×Q8×C83C2311yescharacteristic
104C4×D4×C83—21no—
105C4×D4×C83—21no—
106#107×C83—21no—
107#107×C83—21no—
108#107×C83—41no—
109#107×C83D411yescharacteristic
110#107×C83D411yescharacteristic
111#106×C83—21no—
112#106×C83—21no—
113#106×C83—21no—
114C4⋊C8×C83—21no—
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×C83D411yescharacteristic
129#103×C83D411yescharacteristic
130#103×C83D411yescharacteristic
131#103×C83D411yescharacteristic
132#102×C83—21no—
133#102×C83—21no—
134#102×C83—21no—
135#102×C83—21no—
136#102×C83—41no—
137#97×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×C83C2×D411yescharacteristic
148C2×Q8×C83C2×D411yescharacteristic
149C2×Q8×C83C2×D411yescharacteristic
150C2×Q8×C83C2×D411yescharacteristic
151C2×D4×C83—21no—
152C2×D4×C83—21no—
153C2×D4×C83—21no—
154C22×C4×C83—41no—
155Q16×C83—22no—
156Q16×C83—22no—
157Q16×C83—42no—
158Q16×C83—81no—
159Q16×C83—81no—
160Q16×C83—81no—
161Q16×C83—81no—
162SD16×C83—42no—
163SD16×C83—42no—
164SD16×C83—81no—
165SD16×C83—81no—
166C2×C8×C83—21no—
167C2×C8×C83—21no—
168C2×C8×C83—21no—
169C2×C8×C83—21no—
170C2×C8×C83—21no—
171C2×C8×C83C2×D411yescharacteristic
172C2×C8×C83C2×D411yescharacteristic
173C2×C8×C83C2×D411yescharacteristic
174C2×C8×C83C2×D411yescharacteristic
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—21no—
183C4⋊C4×C83—21no—
184C4⋊C4×C83—21no—
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×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—41no—
199C22⋊C4×C83—41no—
200C22⋊C4×C83—41no—
201C42×C83—21no—
202C42×C83—21no—
203C42×C83—21no—
204C42×C83—21no—
205C42×C83—41no—
206C42×C83—41no—
207C42×C83—41no—
208C42×C83C2411yescharacteristic
209C23×C83—41no—
210Q8×C83—21no—
211Q8×C83—21no—
212Q8×C83—21no—
213Q8×C83—21no—
214Q8×C83—21no—
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#13712yes—
224D4×C83—41no—
225D4×C83—41no—
226D4×C83—41no—
227D4×C83—41no—
228D4×C83—81no—
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—21no—
237C2×C4×C83—41no—
238C2×C4×C83—41no—
239C2×C4×C83—41no—
240C2×C4×C83—161no—
241C2×C4×C83C22×D411yescharacteristic
242C2×C4×C83C22×D411yescharacteristic
243C2×C4×C83H(5,𝔽2)11yescharacteristic
244C8×C83—21no—
245C8×C83—21no—
246C8×C83—21no—
247C8×C83—41no—
248C8×C83—41no—
249C8×C83—41no—
250C8×C83—41no—
251C8×C83—41no—
252C8×C83#13512yes—
253C22×C83—81no—
254C22×C83—81no—
255C22×C83—81no—
256C22×C83D4211yescharacteristic
257C4×C83—22no—
258C4×C83—21no—
259C4×C83—41no—
260C4×C83—41no—
261C4×C83—41no—
262C4×C83—41no—
263C4×C83—41no—
264C4×C83—41no—
265C4×C83—41no—
266C4×C83—81no—
267C4×C83—81no—
268C4×C83—81no—
269C4×C83C2×#13511yescharacteristic
270C4×C83C2×#13711yescharacteristic
271C4×C83#57611yescharacteristic
272C4×C83#57811yescharacteristic
273#19873C8311yesmaximal, characteristic, direct product factor, Sylow
274C2×C83—161no—
275C2×C83#327011yescharacteristic
276C2×C83#328711yescharacteristic
277C2×C83#328911yescharacteristic
278#3400C2×C8311yescharacteristic
279#3395C2×C8311yescharacteristic, complemented
280#3383C2×C8311yescharacteristic, complemented
281#3365C2×C8311yescharacteristic
282#1722C2×C8311yescharacteristic
283#1690C2×C8311yescharacteristic, complemented
284#1682C2×C8311yescharacteristic
285#1674C2×C8311yescharacteristic, complemented
286#1666C2×C8311yescharacteristic
287#1648C2×C8311yescharacteristic, complemented
288#1648C2×C8311yescharacteristic, complemented
289#1640C2×C8311yescharacteristic
290#1626C2×C8311yescharacteristic
291#1584C2×C8311yescharacteristic, complemented
292#1579C2×C8311yescharacteristic, complemented
293C83#1987311yescharacteristic, direct product factor, Sylow
294#559C22×C8311yescharacteristic
295#557C22×C8311yescharacteristic
296#557C22×C8311yescharacteristic
297#557C22×C8311yescharacteristic
298#500C22×C8311yescharacteristic
299#500C22×C8311yescharacteristic
300#499—21no—
301#497—21no—
302#494—21no—
303#494C22×C8311yescharacteristic
304#492C22×C8311yescharacteristic
305#488—21no—
306#486C22×C8311yescharacteristic
307#486C22×C8311yescharacteristic
308#479—21no—
309#479—21no—
310#478—21no—
311#475C22×C8311yescharacteristic
312#475C22×C8311yescharacteristic
313#475C22×C8311yescharacteristic
314#464—21no—
315#464—21no—
316#462—21no—
317#462—21no—
318#462C22×C8311yescharacteristic
319#462C22×C8311yescharacteristic
320#462C22×C8311yescharacteristic
321#461—21no—
322#460C22×C8311yescharacteristic
323#460C22×C8311yescharacteristic
324#446C22×C8311yescharacteristic
325C8×Q8C22×C8311yescharacteristic
326C8×Q8C22×C8311yescharacteristic
327C8×Q8C22×C8311yescharacteristic
328#440—21no—
329C4×Q16—21no—
330C4×Q16—21no—
331C4×Q16C22×C8311yescharacteristic
332C4×Q16C22×C8311yescharacteristic
333C4×SD16—21no—
334#335C22×C8311yescharacteristic
335#334C22×C8311yescharacteristic
336#332C22×C8311yescharacteristic
337#332C22×C8311yescharacteristic
338#332C22×C8311yescharacteristic
339#331C22×C8311yescharacteristic
340Q8⋊C8C22×C8311yescharacteristic
341Q8⋊C8C22×C8311yescharacteristic
342Q8⋊C8C22×C8311yescharacteristic
343Q8⋊C8C22×C8311yescharacteristic
344#322C22×C8311yescharacteristic
345C2×Q16—21no—
346C2×Q16—21no—
347C2×Q16—21no—
348C2×Q16—21no—
349C2×Q16—21no—
350C2×Q16D4×C8311yescharacteristic
351C2×Q16D4×C8311yescharacteristic
352C2×SD16—21no—
353C2×SD16—21no—
354C2×SD16—21no—
355C2×SD16—21no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8C23×C8311yescharacteristic
360C4⋊Q8C23×C8311yescharacteristic
361C4⋊Q8C23×C8311yescharacteristic
362#127C23×C8311yescharacteristic
363#125—21no—
364#125—21no—
365#125—21no—
366#125—41no—
367#125—41no—
368#125—41no—
369#124—21no—
370#124—21no—
371#123—41no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8C23×C8311yescharacteristic
379C4×Q8C23×C8311yescharacteristic
380C4×Q8C23×C8311yescharacteristic
381C4×Q8C23×C8311yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384#107—21no—
385#107—21no—
386#107—41no—
387#107D4×C8311yescharacteristic
388#107D4×C8311yescharacteristic
389#106—21no—
390#106—21no—
391#106—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8C23×C8311yescharacteristic
397C4⋊C8C23×C8311yescharacteristic
398C4⋊C8C23×C8311yescharacteristic
399C4⋊C8C23×C8311yescharacteristic
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103D4×C8311yescharacteristic
407#103D4×C8311yescharacteristic
408#103D4×C8311yescharacteristic
409#103D4×C8311yescharacteristic
410#102—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—41no—
415#97—21no—
416C4×C8—21no—
417C4×C8—21no—
418C4×C8—21no—
419C4×C8C23×C8311yescharacteristic
420C4×C8C23×C8311yescharacteristic
421C4×C8C23×C8311yescharacteristic
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8C2×D4×C8311yescharacteristic
426C2×Q8C2×D4×C8311yescharacteristic
427C2×Q8C2×D4×C8311yescharacteristic
428C2×Q8C2×D4×C8311yescharacteristic
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C22×C4—41no—
433Q16—22no—
434Q16—22no—
435Q16—42no—
436Q16—81no—
437Q16—81no—
438Q16—81no—
439Q16—81no—
440SD16—42no—
441SD16—42no—
442SD16—81no—
443SD16—81no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8C2×D4×C8311yescharacteristic
450C2×C8C2×D4×C8311yescharacteristic
451C2×C8C2×D4×C8311yescharacteristic
452C2×C8C2×D4×C8311yescharacteristic
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4C2×D4×C8311yescharacteristic
473C4⋊C4C2×D4×C8311yescharacteristic
474C4⋊C4C2×D4×C8311yescharacteristic
475C4⋊C4C2×D4×C8311yescharacteristic
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—41no—
484C42—41no—
485C42—41no—
486C42C24×C8311yescharacteristic
487C23—41no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8#137×C8312yes—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—81no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—161no—
519C2×C4C22×D4×C8311yescharacteristic
520C2×C4C22×D4×C8311yescharacteristic
521C2×C4H(5,𝔽2)×C8311yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8#135×C8312yes—
531C22—81no—
532C22—81no—
533C22—81no—
534C22D42×C8311yescharacteristic
535C4—21no—
536C4—22no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—81no—
545C4—81no—
546C4—81no—
547C4C2×#135×C8311yescharacteristic
548C4C2×#137×C8311yescharacteristic
549C4#576×C8311yescharacteristic
550C4#578×C8311yescharacteristic
551C2—161no—
552C2C83×#327011yescharacteristic
553C2C83×#328711yescharacteristic
554C2C83×#328911yescharacteristic
subgroupG/H
center, socleC22×C83D42
commutator, Frattini, cosocleC42C24×C83
prime radical#127×C83C23
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C83×#3395C2semidirect
3. C83×#3383C2semidirect
6. C83×#1690C2semidirect
8. C83×#1674C2semidirect
10. C83×#1648C2semidirect
11. C83×#1648C2semidirect
14. C83×#1584C2semidirect
15. C83×#1579C2semidirect
273. #19873C83direct (N × H)
279. #3395C2×C83semidirect
280. #3383C2×C83semidirect
283. #1690C2×C83semidirect
285. #1674C2×C83semidirect
287. #1648C2×C83semidirect
288. #1648C2×C83semidirect
291. #1584C2×C83semidirect
292. #1579C2×C83semidirect
293. C83#19873direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#34002
C83×#33952
C83×#33832
C83×#33652
C83×#17222
C83×#16902
C83×#16822
C83×#16742
C83×#16662
C83×#16482
C83×#16402
C83×#16262
C83×#15842
C83×#15792
#1987383