Finite Group Databasebeta

← C83×#19499 #35247323

Subgroups — C83×#19499 #35247323

Order 21248.

574 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×#3231C211yesmaximal, characteristic, complemented
2C83×#3116C211yesmaximal, characteristic
3C83×#3076C211yesmaximal, characteristic
4C83×#2991C211yesmaximal, characteristic
5C83×#1703C211yesmaximal, characteristic, complemented
6C83×#1699C211yesmaximal, characteristic, complemented
7C83×#1695C211yesmaximal, characteristic, complemented
8C83×#1691C211yesmaximal, characteristic, complemented
9C83×#1684C211yesmaximal, characteristic, complemented
10C83×#1680C211yesmaximal, characteristic, complemented
11C83×#1676C211yesmaximal, characteristic, complemented
12C83×#1672C211yesmaximal, characteristic, complemented
13C83×#1573C211yesmaximal, characteristic, complemented
14C83×#1559C211yesmaximal, characteristic, complemented
15C83×#1550C211yesmaximal, characteristic, complemented
16#533×C83C2211yescharacteristic
17#533×C83C2211yescharacteristic
18C4×#41×C83C2211yescharacteristic
19#500×C83C2211yescharacteristic
20#498×C83C2211yescharacteristic
21#487×C83C2211yescharacteristic
22#487×C83C2211yescharacteristic
23#485×C83—21no—
24#485×C83—21no—
25#485×C83—21no—
26#479×C83—21no—
27#479×C83—21no—
28#479×C83—21no—
29#478×C83—21no—
30#477×C83C2211yescharacteristic
31#477×C83C2211yescharacteristic
32#476×C83C2211yescharacteristic
33#476×C83C2211yescharacteristic
34#475×C83C2211yescharacteristic
35#474×C83C2211yescharacteristic
36#462×C83C2211yescharacteristic
37#461×C83C2211yescharacteristic
38#452×C83—21no—
39C8×Q8×C83C2211yescharacteristic
40C8×Q8×C83C2211yescharacteristic
41#441×C83—21no—
42#440×C83—21no—
43#436×C83—21no—
44#436×C83—21no—
45#436×C83C2211yescharacteristic
46#436×C83C2211yescharacteristic
47#432×C83C2211yescharacteristic
48#431×C83—21no—
49#431×C83C2211yescharacteristic
50#427×C83—21no—
51#423×C83—21no—
52#423×C83C2211yescharacteristic
53C2×C4⋊C8×C83C2211yescharacteristic
54#416×C83—21no—
55#335×C83C2211yescharacteristic
56#335×C83C2211yescharacteristic
57#334×C83C2211yescharacteristic
58#334×C83C2211yescharacteristic
59#333×C83C2211yescharacteristic
60#333×C83C2211yescharacteristic
61#333×C83C2211yescharacteristic
62#333×C83C2211yescharacteristic
63#332×C83C2211yescharacteristic
64#332×C83C2211yescharacteristic
65#332×C83C2211yescharacteristic
66#332×C83C2211yescharacteristic
67C2×#41×C83D411yescharacteristic
68C2×Q16×C83—21no—
69C2×SD16×C83—21no—
70C2×M16×C83—21no—
71C2×M16×C83—21no—
72C2×M16×C83—21no—
73C22×C8×C83—21no—
74C4⋊Q8×C83C2311yescharacteristic
75C4⋊Q8×C83C2311yescharacteristic
76C4⋊Q8×C83C2311yescharacteristic
77C4⋊Q8×C83C2311yescharacteristic
78#125×C83—21no—
79#125×C83—21no—
80C22⋊Q8×C83—21no—
81C22⋊Q8×C83—21no—
82C22⋊Q8×C83—21no—
83C22⋊Q8×C83—21no—
84C4×Q8×C83—21no—
85C4×Q8×C83—21no—
86C4×Q8×C83—21no—
87C4×Q8×C83—21no—
88C4×Q8×C83D411yescharacteristic
89C4×Q8×C83C2311yescharacteristic
90C4×D4×C83—21no—
91C4×D4×C83—21no—
92C4×D4×C83D411yescharacteristic
93C4×D4×C83C2311yescharacteristic
94#117×C83—21no—
95#117×C83—21no—
96#117×C83—21no—
97#117×C83D411yescharacteristic
98C2×C42×C83—21no—
99C2×C42×C83C2311yescharacteristic
100#107×C83—21no—
101#107×C83—21no—
102#107×C83—21no—
103#107×C83—21no—
104#107×C83—21no—
105#106×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×C83—21no—
113C4⋊C8×C83—21no—
114C4⋊C8×C83D411yescharacteristic
115C4⋊C8×C83D411yescharacteristic
116C4⋊C8×C83C2311yescharacteristic
117C4⋊C8×C83C2311yescharacteristic
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—21no—
131#102×C83—21no—
132#102×C83—21no—
133#102×C83—21no—
134C22⋊C8×C83—21no—
135C22⋊C8×C83—21no—
136C22⋊C8×C83—21no—
137C22⋊C8×C83D411yescharacteristic
138C22⋊C8×C83D411yescharacteristic
139#97×C83—21no—
140C4×C8×C83—21no—
141C4×C8×C83—21no—
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#41×C83—22no—
145#41×C83—41no—
146C2×Q8×C83—21no—
147C2×Q8×C83—21no—
148C2×Q8×C83—21no—
149C2×Q8×C83—21no—
150C2×Q8×C83C2×D411yescharacteristic
151C2×D4×C83—21no—
152C2×D4×C83C2×D411yescharacteristic
153C22×C4×C83—21no—
154C22×C4×C83—21no—
155C22×C4×C83—21no—
156C22×C4×C83C2×D411yescharacteristic
157C22×C4×C83C2×D411yescharacteristic
158C22×C4×C83#4111yescharacteristic
159Q16×C83—42no—
160SD16×C83—42no—
161M16×C83—81no—
162M16×C83—81no—
163M16×C83—81no—
164C2×C8×C83—21no—
165C2×C8×C83—21no—
166C2×C8×C83—21no—
167C2×C8×C83—21no—
168C2×C8×C83—21no—
169C2×C8×C83—21no—
170C2×C8×C83—42no—
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×C83C2×D411yescharacteristic
190C4⋊C4×C83C2×D411yescharacteristic
191C22⋊C4×C83—21no—
192C22⋊C4×C83—21no—
193C22⋊C4×C83—21no—
194C22⋊C4×C83—41no—
195C22⋊C4×C83—41no—
196C42×C83—21no—
197C42×C83—21no—
198C42×C83—21no—
199C42×C83—41no—
200C42×C83—41no—
201C42×C83C2×D411yescharacteristic
202C42×C83C2×D411yescharacteristic
203C42×C83#4111yescharacteristic
204C42×C83C2411yescharacteristic
205C23×C83—21no—
206C23×C83#12111yescharacteristic
207Q8×C83—21no—
208Q8×C83—41no—
209Q8×C83—41no—
210Q8×C83—41no—
211Q8×C83—41no—
212Q8×C83—81no—
213Q8×C83—81no—
214Q8×C83#13712yes—
215D4×C83—21no—
216D4×C83—21no—
217D4×C83—42no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83—21no—
222C2×C4×C83—21no—
223C2×C4×C83—21no—
224C2×C4×C83—21no—
225C2×C4×C83—41no—
226C2×C4×C83—42no—
227C2×C4×C83—42no—
228C2×C4×C83—41no—
229C2×C4×C83—41no—
230C2×C4×C83—41no—
231C2×C4×C83—41no—
232C2×C4×C83—41no—
233C2×C4×C83—41no—
234C2×C4×C83#12111yescharacteristic
235C2×C4×C83#12111yescharacteristic
236C2×C4×C83#12111yescharacteristic
237C2×C4×C83C22×D411yescharacteristic
238C2×C4×C83C22×D411yescharacteristic
239C2×C4×C83C2×#4111yescharacteristic
240C8×C83—21no—
241C8×C83—21no—
242C8×C83—21no—
243C8×C83—21no—
244C8×C83—41no—
245C8×C83—41no—
246C8×C83—41no—
247C8×C83—41no—
248C8×C83—41no—
249C8×C83—41no—
250C22×C83—21no—
251C22×C83—21no—
252C22×C83—21no—
253C22×C83—41no—
254C22×C83—41no—
255C22×C83—41no—
256C22×C83C2×#12111yescharacteristic
257C4×C83—21no—
258C4×C83—21no—
259C4×C83—22no—
260C4×C83—21no—
261C4×C83—21no—
262C4×C83—41no—
263C4×C83—41no—
264C4×C83—81no—
265C4×C83—81no—
266C4×C83—81no—
267C4×C83—81no—
268C4×C83C2×#13711yescharacteristic
269C4×C83#57511yescharacteristic
270C4×C83#57711yescharacteristic
271C4×C83#57811yescharacteristic
272#19499C8311yesmaximal, characteristic, direct product factor, Sylow
273C2×C83—41no—
274C2×C83—81no—
275C2×C83#304611yescharacteristic
276C2×C83#305611yescharacteristic
277C2×C83#306711yescharacteristic
278#3231C2×C8311yescharacteristic, complemented
279#3116C2×C8311yescharacteristic
280#3076C2×C8311yescharacteristic
281#2991C2×C8311yescharacteristic
282#1703C2×C8311yescharacteristic, complemented
283#1699C2×C8311yescharacteristic, complemented
284#1695C2×C8311yescharacteristic, complemented
285#1691C2×C8311yescharacteristic, complemented
286#1684C2×C8311yescharacteristic, complemented
287#1680C2×C8311yescharacteristic, complemented
288#1676C2×C8311yescharacteristic, complemented
289#1672C2×C8311yescharacteristic, complemented
290#1573C2×C8311yescharacteristic, complemented
291#1559C2×C8311yescharacteristic, complemented
292#1550C2×C8311yescharacteristic, complemented
293C83#1949911yescharacteristic, direct product factor, Sylow
294#533C22×C8311yescharacteristic
295#533C22×C8311yescharacteristic
296C4×#41C22×C8311yescharacteristic
297#500C22×C8311yescharacteristic
298#498C22×C8311yescharacteristic
299#487C22×C8311yescharacteristic
300#487C22×C8311yescharacteristic
301#485—21no—
302#485—21no—
303#485—21no—
304#479—21no—
305#479—21no—
306#479—21no—
307#478—21no—
308#477C22×C8311yescharacteristic
309#477C22×C8311yescharacteristic
310#476C22×C8311yescharacteristic
311#476C22×C8311yescharacteristic
312#475C22×C8311yescharacteristic
313#474C22×C8311yescharacteristic
314#462C22×C8311yescharacteristic
315#461C22×C8311yescharacteristic
316#452—21no—
317C8×Q8C22×C8311yescharacteristic
318C8×Q8C22×C8311yescharacteristic
319#441—21no—
320#440—21no—
321#436—21no—
322#436—21no—
323#436C22×C8311yescharacteristic
324#436C22×C8311yescharacteristic
325#432C22×C8311yescharacteristic
326#431—21no—
327#431C22×C8311yescharacteristic
328#427—21no—
329#423—21no—
330#423C22×C8311yescharacteristic
331C2×C4⋊C8C22×C8311yescharacteristic
332#416—21no—
333#335C22×C8311yescharacteristic
334#335C22×C8311yescharacteristic
335#334C22×C8311yescharacteristic
336#334C22×C8311yescharacteristic
337#333C22×C8311yescharacteristic
338#333C22×C8311yescharacteristic
339#333C22×C8311yescharacteristic
340#333C22×C8311yescharacteristic
341#332C22×C8311yescharacteristic
342#332C22×C8311yescharacteristic
343#332C22×C8311yescharacteristic
344#332C22×C8311yescharacteristic
345C2×#41D4×C8311yescharacteristic
346C2×Q16—21no—
347C2×SD16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C22×C8—21no—
352C4⋊Q8C23×C8311yescharacteristic
353C4⋊Q8C23×C8311yescharacteristic
354C4⋊Q8C23×C8311yescharacteristic
355C4⋊Q8C23×C8311yescharacteristic
356#125—21no—
357#125—21no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8D4×C8311yescharacteristic
367C4×Q8C23×C8311yescharacteristic
368C4×D4—21no—
369C4×D4—21no—
370C4×D4D4×C8311yescharacteristic
371C4×D4C23×C8311yescharacteristic
372#117—21no—
373#117—21no—
374#117—21no—
375#117D4×C8311yescharacteristic
376C2×C42—21no—
377C2×C42C23×C8311yescharacteristic
378#107—21no—
379#107—21no—
380#107—21no—
381#107—21no—
382#107—21no—
383#106—21no—
384#106—21no—
385#106—21no—
386#106—21no—
387#106—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8D4×C8311yescharacteristic
393C4⋊C8D4×C8311yescharacteristic
394C4⋊C8C23×C8311yescharacteristic
395C4⋊C8C23×C8311yescharacteristic
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#103—21no—
407#103—21no—
408#103—21no—
409#102—21no—
410#102—21no—
411#102—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8D4×C8311yescharacteristic
416C22⋊C8D4×C8311yescharacteristic
417#97—21no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8C23×C8311yescharacteristic
421C4×C8C23×C8311yescharacteristic
422#41—22no—
423#41—41no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8C2×D4×C8311yescharacteristic
429C2×D4—21no—
430C2×D4C2×D4×C8311yescharacteristic
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4C2×D4×C8311yescharacteristic
435C22×C4C2×D4×C8311yescharacteristic
436C22×C4#41×C8311yescharacteristic
437Q16—42no—
438SD16—42no—
439M16—81no—
440M16—81no—
441M16—81no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—42no—
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⋊C4C2×D4×C8311yescharacteristic
468C4⋊C4C2×D4×C8311yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—41no—
478C42—41no—
479C42C2×D4×C8311yescharacteristic
480C42C2×D4×C8311yescharacteristic
481C42#41×C8311yescharacteristic
482C42C24×C8311yescharacteristic
483C23—21no—
484C23#121×C8311yescharacteristic
485Q8—21no—
486Q8—41no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—81no—
491Q8—81no—
492Q8#137×C8312yes—
493D4—21no—
494D4—21no—
495D4—42no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4#121×C8311yescharacteristic
513C2×C4#121×C8311yescharacteristic
514C2×C4#121×C8311yescharacteristic
515C2×C4C22×D4×C8311yescharacteristic
516C2×C4C22×D4×C8311yescharacteristic
517C2×C4C2×#41×C8311yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—21no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22C2×#121×C8311yescharacteristic
535C4—21no—
536C4—21no—
537C4—22no—
538C4—21no—
539C4—21no—
540C4—41no—
541C4—41no—
542C4—81no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4C2×#137×C8311yescharacteristic
547C4#575×C8311yescharacteristic
548C4#577×C8311yescharacteristic
549C4#578×C8311yescharacteristic
550C2—41no—
551C2—81no—
552C2C83×#304611yescharacteristic
553C2C83×#305611yescharacteristic
554C2C83×#306711yescharacteristic
subgroupG/H
center, socleC22×C83C2×#121
commutator, Frattini, cosocleC42C24×C83
prime radicalC2×#41×C83D4
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
1. C83×#3231C2semidirect
5. C83×#1703C2semidirect
6. C83×#1699C2semidirect
7. C83×#1695C2semidirect
8. C83×#1691C2semidirect
9. C83×#1684C2semidirect
10. C83×#1680C2semidirect
11. C83×#1676C2semidirect
12. C83×#1672C2semidirect
13. C83×#1573C2semidirect
14. C83×#1559C2semidirect
15. C83×#1550C2semidirect
272. #19499C83direct (N × H)
278. #3231C2×C83semidirect
282. #1703C2×C83semidirect
283. #1699C2×C83semidirect
284. #1695C2×C83semidirect
285. #1691C2×C83semidirect
286. #1684C2×C83semidirect
287. #1680C2×C83semidirect
288. #1676C2×C83semidirect
289. #1672C2×C83semidirect
290. #1573C2×C83semidirect
291. #1559C2×C83semidirect
292. #1550C2×C83semidirect
293. C83#19499direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#32312
C83×#31162
C83×#30762
C83×#29912
C83×#17032
C83×#16992
C83×#16952
C83×#16912
C83×#16842
C83×#16802
C83×#16762
C83×#16722
C83×#15732
C83×#15592
C83×#15502
#1949983