Finite Group Databasebeta

← C83×#61798 #35289622

Subgroups — C83×#61798 #35289622

Order 21248.

1674 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3550C211yesmaximal, characteristic, complemented
2C83×#3512C211yesmaximal, characteristic
3C83×#3350C214yesmaximal, complemented
4C83×#3349C214yesmaximal, complemented
5C83×#3320C214yesmaximal, complemented
6C83×#3312C214yesmaximal, complemented
7C83×#3236C212yesmaximal, complemented
8C83×#3201C214yesmaximal, complemented
9C83×#3116C212yesmaximal, complemented
10C83×#3097C214yesmaximal, complemented
11C83×#2980C211yesmaximal, characteristic, complemented
12#563×C83—22no—
13#559×C83—21no—
14Q82×C83—21no—
15#556×C83C2214yes—
16#553×C83—24no—
17#553×C83C2214yes—
18#552×C83C2214yes—
19D4×Q8×C83C2214yes—
20#542×C83—24no—
21#541×C83—21no—
22#540×C83—21no—
23#537×C83C2212yes—
24#536×C83C2214yes—
25#533×C83C2212yes—
26#532×C83C2211yescharacteristic
27#529×C83—22no—
28C2×#125×C83C2211yescharacteristic
29#520×C83C2212yes—
30C4×#41×C83C2211yescharacteristic
31#501×C83C2214yes—
32#491×C83C2214yes—
33#485×C83C2214yes—
34#485×C83C2214yes—
35#485×C83C2214yes—
36#485×C83C2214yes—
37#484×C83C2214yes—
38#484×C83C2214yes—
39#483×C83C2214yes—
40#483×C83C2214yes—
41#482×C83C2214yes—
42#479×C83C2214yes—
43#479×C83C2214yes—
44#477×C83C2212yes—
45#476×C83C2212yes—
46#470×C83C2214yes—
47#468×C83C2214yes—
48#467×C83C2214yes—
49#465×C83C2214yes—
50#462×C83C2212yes—
51#461×C83C2212yes—
52#452×C83C2214yes—
53#451×C83C2214yes—
54#448×C83C2214yes—
55#441×C83C2214yes—
56#440×C83C2214yes—
57#435×C83C2214yes—
58#435×C83C2214yes—
59#432×C83C2212yes—
60#428×C83C2214yes—
61#427×C83C2214yes—
62#419×C83C2214yes—
63C2×#103×C83C2214yes—
64#408×C83C2214yes—
65C2×#41×C83C2311yescharacteristic
66C2×#41×C83C2312yes—
67C22×Q8×C83C2314yes—
68C2×Q16×C83C2314yes—
69C2×SD16×C83C2314yes—
70C2×M16×C83C2314yes—
71C22×C8×C83C2314yes—
72C4⋊Q8×C83—24no—
73C4⋊Q8×C83—24no—
74C4⋊Q8×C83D411yescharacteristic
75C4⋊Q8×C83C2312yes—
76C4⋊Q8×C83C2312yes—
77#127×C83D411yescharacteristic
78#126×C83—24no—
79#126×C83—24no—
80#126×C83—24no—
81#126×C83—24no—
82#125×C83—24no—
83#125×C83—21no—
84#125×C83—21no—
85#125×C83—22no—
86#125×C83C2314yes—
87#124×C83—24no—
88#124×C83—24no—
89#124×C83D412yes—
90#123×C83—24no—
91#123×C83—24no—
92#123×C83—24no—
93#123×C83—24no—
94C22⋊Q8×C83—22no—
95C22⋊Q8×C83—22no—
96C22⋊Q8×C83—24no—
97C22⋊Q8×C83—24no—
98C22⋊Q8×C83C2314yes—
99C22⋊Q8×C83C2314yes—
100C22⋊Q8×C83C2314yes—
101C22⋊Q8×C83C2314yes—
102#121×C83—22no—
103#121×C83—24no—
104#121×C83—24no—
105#121×C83D414yes—
106#121×C83C2314yes—
107C4×Q8×C83—22no—
108C4×Q8×C83—24no—
109C4×Q8×C83—22no—
110C4×Q8×C83C2312yes—
111C4×Q8×C83C2314yes—
112C4×D4×C83—22no—
113C4×D4×C83—24no—
114C4×D4×C83—24no—
115C4×D4×C83—22no—
116C4×D4×C83—24no—
117C4×D4×C83C2312yes—
118C4×D4×C83C2314yes—
119#117×C83—22no—
120#117×C83—24no—
121#117×C83—21no—
122#117×C83C2314yes—
123#117×C83C2311yescharacteristic
124#117×C83C2314yes—
125C2×C4⋊C4×C83—22no—
126C2×C4⋊C4×C83C2312yes—
127C2×C4⋊C4×C83C2314yes—
128C2×C42×C83—21no—
129C2×C42×C83C2311yescharacteristic
130#107×C83C2314yes—
131#107×C83C2314yes—
132#107×C83C2314yes—
133#106×C83C2314yes—
134#106×C83C2314yes—
135#106×C83C2314yes—
136C4⋊C8×C83C2312yes—
137C4⋊C8×C83C2312yes—
138#103×C83C2314yes—
139#103×C83C2314yes—
140#103×C83C2314yes—
141#103×C83C2314yes—
142#103×C83C2314yes—
143#103×C83C2314yes—
144#103×C83C2314yes—
145#102×C83C2314yes—
146C22⋊C8×C83C2314yes—
147C22⋊C8×C83C2314yes—
148C22⋊C8×C83C2314yes—
149#97×C83C2314yes—
150#41×C83—42no—
151#41×C83—42no—
152#41×C83—42no—
153C2×Q8×C83—22no—
154C2×Q8×C83—24no—
155C2×Q8×C83—44no—
156C2×Q8×C83—44no—
157C2×Q8×C83C2×D412yes—
158C2×Q8×C83C2414yes—
159C2×Q8×C83C2411yescharacteristic
160C2×D4×C83—21no—
161C2×D4×C83—24no—
162C2×D4×C83C2×D414yes—
163C2×D4×C83C2×D414yes—
164C2×D4×C83C2×D412yes—
165C2×D4×C83C2411yescharacteristic
166C22×C4×C83—22no—
167C22×C4×C83—24no—
168C22×C4×C83—24no—
169C22×C4×C83—21no—
170C22×C4×C83—22no—
171C22×C4×C83C2×D412yes—
172C22×C4×C83C2411yescharacteristic
173C22×C4×C83C2414yes—
174Q16×C83—44no—
175SD16×C83—44no—
176M16×C83—44no—
177C2×C8×C83—44no—
178C2×C8×C83C2414yes—
179C2×C8×C83C2414yes—
180C4⋊C4×C83—24no—
181C4⋊C4×C83—24no—
182C4⋊C4×C83—22no—
183C4⋊C4×C83—24no—
184C4⋊C4×C83—22no—
185C4⋊C4×C83—24no—
186C4⋊C4×C83—22no—
187C4⋊C4×C83—22no—
188C4⋊C4×C83—22no—
189C4⋊C4×C83—24no—
190C4⋊C4×C83—24no—
191C4⋊C4×C83—24no—
192C4⋊C4×C83—24no—
193C4⋊C4×C83C2×D414yes—
194C4⋊C4×C83C2414yes—
195C4⋊C4×C83C2412yes—
196C4⋊C4×C83C2414yes—
197C22⋊C4×C83—24no—
198C22⋊C4×C83—24no—
199C22⋊C4×C83—21no—
200C22⋊C4×C83—24no—
201C22⋊C4×C83—24no—
202C22⋊C4×C83—24no—
203C22⋊C4×C83—24no—
204C22⋊C4×C83—22no—
205C22⋊C4×C83—24no—
206C22⋊C4×C83C2×D414yes—
207C22⋊C4×C83C2×D414yes—
208C42×C83—22no—
209C42×C83—21no—
210C42×C83—24no—
211C42×C83—24no—
212C42×C83—24no—
213C42×C83C2×D411yescharacteristic
214C42×C83C2×D411yescharacteristic
215C42×C83C2412yes—
216C23×C83—21no—
217C23×C83C22×D414yes—
218C23×C83C22×D411yescharacteristic
219Q8×C83—24no—
220Q8×C83—22no—
221Q8×C83—24no—
222Q8×C83—42no—
223Q8×C83—44no—
224Q8×C83—84no—
225D4×C83—22no—
226D4×C83—44no—
227D4×C83—42no—
228D4×C83—44no—
229D4×C83—42no—
230D4×C83—84no—
231C2×C4×C83—24no—
232C2×C4×C83—24no—
233C2×C4×C83—22no—
234C2×C4×C83—22no—
235C2×C4×C83—24no—
236C2×C4×C83—21no—
237C2×C4×C83—24no—
238C2×C4×C83—24no—
239C2×C4×C83—42no—
240C2×C4×C83—42no—
241C2×C4×C83—82no—
242C2×C4×C83—84no—
243C2×C4×C83—82no—
244C2×C4×C83—84no—
245C2×C4×C83C22×D412yes—
246C2×C4×C83C22×D414yes—
247C2×C4×C83C22×D411yescharacteristic
248C2×C4×C83C22×D412yes—
249C2×C4×C83C2511yescharacteristic
250C8×C83—24no—
251C8×C83—24no—
252C22×C83—22no—
253C22×C83—24no—
254C22×C83—24no—
255C22×C83—24no—
256C22×C83—21no—
257C22×C83—42no—
258C22×C83—41no—
259C22×C83C23×D411yescharacteristic
260C4×C83—22no—
261C4×C83—22no—
262C4×C83—21no—
263C4×C83—24no—
264C4×C83—42no—
265C4×C83—44no—
266C4×C83—44no—
267C4×C83—41no—
268C4×C83—44no—
269C4×C83#58512yes—
270#61798C8311yesmaximal, characteristic, direct product factor, Sylow
271C2×C83—41no—
272C2×C83—44no—
273C2×C83—81no—
274C2×C83#348511yescharacteristic
275C2×C83#358612yes—
276#3550C2×C8311yescharacteristic, complemented
277#3512C2×C8311yescharacteristic
278#3350C2×C8314yescomplemented
279#3349C2×C8314yescomplemented
280#3320C2×C8314yescomplemented
281#3312C2×C8314yescomplemented
282#3236C2×C8312yescomplemented
283#3201C2×C8314yescomplemented
284#3116C2×C8312yescomplemented
285#3097C2×C8314yescomplemented
286#2980C2×C8311yescharacteristic, complemented
287C83#6179811yescharacteristic, direct product factor, Sylow
288#563—22no—
289#559—21no—
290Q82—21no—
291#556C22×C8314yes—
292#553—24no—
293#553C22×C8314yes—
294#552C22×C8314yes—
295D4×Q8C22×C8314yes—
296#542—24no—
297#541—21no—
298#540—21no—
299#537C22×C8312yes—
300#536C22×C8314yes—
301#533C22×C8312yes—
302#532C22×C8311yescharacteristic
303#529—22no—
304C2×#125C22×C8311yescharacteristic
305#520C22×C8312yes—
306C4×#41C22×C8311yescharacteristic
307#501C22×C8314yes—
308#491C22×C8314yes—
309#485C22×C8314yes—
310#485C22×C8314yes—
311#485C22×C8314yes—
312#485C22×C8314yes—
313#484C22×C8314yes—
314#484C22×C8314yes—
315#483C22×C8314yes—
316#483C22×C8314yes—
317#482C22×C8314yes—
318#479C22×C8314yes—
319#479C22×C8314yes—
320#477C22×C8312yes—
321#476C22×C8312yes—
322#470C22×C8314yes—
323#468C22×C8314yes—
324#467C22×C8314yes—
325#465C22×C8314yes—
326#462C22×C8312yes—
327#461C22×C8312yes—
328#452C22×C8314yes—
329#451C22×C8314yes—
330#448C22×C8314yes—
331#441C22×C8314yes—
332#440C22×C8314yes—
333#435C22×C8314yes—
334#435C22×C8314yes—
335#432C22×C8312yes—
336#428C22×C8314yes—
337#427C22×C8314yes—
338#419C22×C8314yes—
339C2×#103C22×C8314yes—
340#408C22×C8314yes—
341C2×#41C23×C8311yescharacteristic
342C2×#41C23×C8312yes—
343C22×Q8C23×C8314yes—
344C2×Q16C23×C8314yes—
345C2×SD16C23×C8314yes—
346C2×M16C23×C8314yes—
347C22×C8C23×C8314yes—
348C4⋊Q8—24no—
349C4⋊Q8—24no—
350C4⋊Q8D4×C8311yescharacteristic
351C4⋊Q8C23×C8312yes—
352C4⋊Q8C23×C8312yes—
353#127D4×C8311yescharacteristic
354#126—24no—
355#126—24no—
356#126—24no—
357#126—24no—
358#125—24no—
359#125—21no—
360#125—21no—
361#125—22no—
362#125C23×C8314yes—
363#124—24no—
364#124—24no—
365#124D4×C8312yes—
366#123—24no—
367#123—24no—
368#123—24no—
369#123—24no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8—24no—
373C22⋊Q8—24no—
374C22⋊Q8C23×C8314yes—
375C22⋊Q8C23×C8314yes—
376C22⋊Q8C23×C8314yes—
377C22⋊Q8C23×C8314yes—
378#121—22no—
379#121—24no—
380#121—24no—
381#121D4×C8314yes—
382#121C23×C8314yes—
383C4×Q8—22no—
384C4×Q8—24no—
385C4×Q8—22no—
386C4×Q8C23×C8312yes—
387C4×Q8C23×C8314yes—
388C4×D4—22no—
389C4×D4—24no—
390C4×D4—24no—
391C4×D4—22no—
392C4×D4—24no—
393C4×D4C23×C8312yes—
394C4×D4C23×C8314yes—
395#117—22no—
396#117—24no—
397#117—21no—
398#117C23×C8311yescharacteristic
399#117C23×C8314yes—
400#117C23×C8314yes—
401C2×C4⋊C4—22no—
402C2×C4⋊C4C23×C8312yes—
403C2×C4⋊C4C23×C8314yes—
404C2×C42—21no—
405C2×C42C23×C8311yescharacteristic
406#107C23×C8314yes—
407#107C23×C8314yes—
408#107C23×C8314yes—
409#106C23×C8314yes—
410#106C23×C8314yes—
411#106C23×C8314yes—
412C4⋊C8C23×C8312yes—
413C4⋊C8C23×C8312yes—
414#103C23×C8314yes—
415#103C23×C8314yes—
416#103C23×C8314yes—
417#103C23×C8314yes—
418#103C23×C8314yes—
419#103C23×C8314yes—
420#103C23×C8314yes—
421#102C23×C8314yes—
422C22⋊C8C23×C8314yes—
423C22⋊C8C23×C8314yes—
424C22⋊C8C23×C8314yes—
425#97C23×C8314yes—
426#41—42no—
427#41—42no—
428#41—42no—
429C2×Q8—22no—
430C2×Q8—24no—
431C2×Q8—44no—
432C2×Q8—44no—
433C2×Q8C2×D4×C8312yes—
434C2×Q8C24×C8314yes—
435C2×Q8C24×C8311yescharacteristic
436C2×D4—21no—
437C2×D4—24no—
438C2×D4C2×D4×C8314yes—
439C2×D4C2×D4×C8314yes—
440C2×D4C2×D4×C8312yes—
441C2×D4C24×C8311yescharacteristic
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4C2×D4×C8312yes—
448C22×C4C24×C8311yescharacteristic
449C22×C4C24×C8314yes—
450Q16—44no—
451SD16—44no—
452M16—44no—
453C2×C8—44no—
454C2×C8C24×C8314yes—
455C2×C8C24×C8314yes—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—22no—
459C4⋊C4—24no—
460C4⋊C4—22no—
461C4⋊C4—24no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—24no—
466C4⋊C4—24no—
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4C2×D4×C8314yes—
470C4⋊C4C24×C8314yes—
471C4⋊C4C24×C8312yes—
472C4⋊C4C24×C8314yes—
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—21no—
476C22⋊C4—24no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—22no—
481C22⋊C4—24no—
482C22⋊C4C2×D4×C8314yes—
483C22⋊C4C2×D4×C8314yes—
484C42—22no—
485C42—21no—
486C42—24no—
487C42—24no—
488C42—24no—
489C42C2×D4×C8311yescharacteristic
490C42C2×D4×C8311yescharacteristic
491C42C24×C8312yes—
492C23—21no—
493C23C22×D4×C8314yes—
494C23C22×D4×C8311yescharacteristic
495Q8—24no—
496Q8—22no—
497Q8—24no—
498Q8—42no—
499Q8—44no—
500Q8—84no—
501D4—22no—
502D4—42no—
503D4—44no—
504D4—44no—
505D4—42no—
506D4—84no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—21no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—82no—
518C2×C4—84no—
519C2×C4—84no—
520C2×C4—82no—
521C2×C4C22×D4×C8312yes—
522C2×C4C22×D4×C8314yes—
523C2×C4C22×D4×C8311yescharacteristic
524C2×C4C22×D4×C8312yes—
525C2×C4C25×C8311yescharacteristic
526C8—24no—
527C8—24no—
528C22—22no—
529C22—24no—
530C22—24no—
531C22—24no—
532C22—21no—
533C22—42no—
534C22—41no—
535C22C23×D4×C8311yescharacteristic
536C4—22no—
537C4—22no—
538C4—21no—
539C4—24no—
540C4—42no—
541C4—44no—
542C4—44no—
543C4—41no—
544C4—44no—
545C4#585×C8312yes—
546C2—41no—
547C2—44no—
548C2—81no—
549C2C83×#348511yescharacteristic
550C2C83×#358612yes—
subgroupG/H
center, socleC22×C83C23×D4
commutator, Frattini, cosocleC2×C4C25×C83
prime radicalC83×#3512C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C83 ◁ #532×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#3550C2semidirect
3. C83×#3350C2semidirect
4. C83×#3349C2semidirect
5. C83×#3320C2semidirect
6. C83×#3312C2semidirect
7. C83×#3236C2semidirect
8. C83×#3201C2semidirect
9. C83×#3116C2semidirect
10. C83×#3097C2semidirect
11. C83×#2980C2semidirect
270. #61798C83direct (N × H)
276. #3550C2×C83semidirect
278. #3350C2×C83semidirect
279. #3349C2×C83semidirect
280. #3320C2×C83semidirect
281. #3312C2×C83semidirect
282. #3236C2×C83semidirect
283. #3201C2×C83semidirect
284. #3116C2×C83semidirect
285. #3097C2×C83semidirect
286. #2980C2×C83semidirect
287. C83#61798direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#35502
C83×#35122
C83×#33502
C83×#33492
C83×#33202
C83×#33122
C83×#32362
C83×#32012
C83×#31162
C83×#30972
C83×#29802
#6179883