Finite Group Databasebeta

← #35375831

Subgroups — #35375831

Order 21248.

656 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24916476C211yesmaximal, characteristic, complemented
2#24916471C211yesmaximal, characteristic, complemented
3C4×#14581813C211yesmaximal, characteristic
4#24906358C211yesmaximal, characteristic, complemented
5#24906357C211yesmaximal, characteristic, complemented
6#24906301C211yesmaximal, characteristic, complemented
7#24906300C211yesmaximal, characteristic, complemented
8#24906298C211yesmaximal, characteristic, complemented
9C8×#13050575C211yesmaximal, characteristic, complemented
10#24906255C211yesmaximal, characteristic, complemented
11#24906223C211yesmaximal, characteristic, complemented
12#24905896C211yesmaximal, characteristic, complemented
13#24905894C211yesmaximal, characteristic, complemented
14#24905742C211yesmaximal, characteristic, complemented
15C83×#1582C211yesmaximal, characteristic, complemented
16C2×#14581813C411yescharacteristic
17C4×#13050591C2211yescharacteristic
18C4×#13050589C2211yescharacteristic
19#19127832C2211yescharacteristic
20#19127831C2211yescharacteristic
21#19127828C2211yescharacteristic
22C4×#13050580C2211yescharacteristic
23#19127793C411yescharacteristic
24C4×#13050579C2211yescharacteristic
25SD16×Dic83C411yescharacteristic
26#19127788C411yescharacteristic
27C4×#13050575C2211yescharacteristic
28#19127781C411yescharacteristic
29#19127774—21no—
30#19127772—21no—
31#19127771—21no—
32#19127769—21no—
33C8×D332C2211yescharacteristic
34D4×C83⋊C8C2211yescharacteristic
35#19127766C2211yescharacteristic
36#19127757—21no—
37#19127757C2211yescharacteristic
38#19127757C2211yescharacteristic
39#19127755—21no—
40#19127752C2211yescharacteristic
41#19127736C411yescharacteristic
42#19127696C411yescharacteristic
43#19127694C411yescharacteristic
44C4×#13050573C2211yescharacteristic
45C2×#14581702—21no—
46#97×D83—21no—
47C4×C8×D83C2211yescharacteristic
48#19127453C2211yescharacteristic
49#19127453C2211yescharacteristic
50#19127452C2211yescharacteristic
51#19127433C2211yescharacteristic
52Q8⋊(C83⋊C8)C2211yescharacteristic
53#19127431C2211yescharacteristic
54#19127430C2211yescharacteristic
55D4⋊(C83⋊C8)C2211yescharacteristic
56#19127428C2211yescharacteristic
57#19127423C2211yescharacteristic
58C8×C83⋊C8C2211yescharacteristic
59C8×C83⋊C8C2211yescharacteristic
60#446×C83C2211yescharacteristic
61C4×SD16×C83C2211yescharacteristic
62C8×D4×C83C2211yescharacteristic
63#334×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65D4⋊C8×C83C2211yescharacteristic
66#322×C83C2211yescharacteristic
67C2×#13050591C2×C411yescharacteristic
68C2×#13050589C2×C411yescharacteristic
69#14581813—24no—
70C2×#13050580C2×C411yescharacteristic
71C2×#13050579C2×C411yescharacteristic
72C2×#13050575C2×C411yescharacteristic
73C2×#13050573D411yescharacteristic
74C2×#13050573D411yescharacteristic
75C22×C83⋊C8—21no—
76C2×C8×D83—21no—
77C2×C8×D83—21no—
78C2×C8×D83C2×C411yescharacteristic
79C2×C8×D83C2×C411yescharacteristic
80Q8×Dic83C2×C411yescharacteristic
81C4×Dic166C2311yescharacteristic
82#14581757C2×C411yescharacteristic
83C4×D332—21no—
84C4×D332C2311yescharacteristic
85D4×Dic83C2×C411yescharacteristic
86#14581754—21no—
87#14581754C2×C411yescharacteristic
88C4×C22⋊D83—21no—
89(C22⋊D83)⋊C4—21no—
90#14581750—21no—
91#14581750C2×C411yescharacteristic
92#14581750C2×C411yescharacteristic
93#14581748—21no—
94C2×C4×Dic83—21no—
95C42×D83—21no—
96C42×D83C2311yescharacteristic
97#14581725C2×C411yescharacteristic
98#14581725C2×C411yescharacteristic
99#14581724C2×C411yescharacteristic
100C4⋊(C83⋊C8)—21no—
101C4⋊(C83⋊C8)C2311yescharacteristic
102C4⋊(C83⋊C8)C2311yescharacteristic
103Dic83⋊C8—21no—
104Dic83⋊C8—21no—
105Dic83⋊C8—21no—
106#14581717C2×C411yescharacteristic
107#14581716C2×C411yescharacteristic
108#14581715C2×C411yescharacteristic
109#14581714C2×C411yescharacteristic
110#14581713C2×C411yescharacteristic
111#14581712C2×C411yescharacteristic
112C22⋊(C83⋊C8)—21no—
113(C2×D83)⋊C8—21no—
114(C2×D83)⋊C8—21no—
115(C2×D83)⋊C8—21no—
116(C2×D83)⋊C8—21no—
117(C2×D83)⋊C8—21no—
118#14581703—21no—
119#14581702—21no—
120#14581702—21no—
121#14581702—21no—
122#14581702—21no—
123#14581702D411yescharacteristic
124#14581702D411yescharacteristic
125C4×C83⋊C8C2311yescharacteristic
126C4×C83⋊C8C2311yescharacteristic
127C4×C83⋊C8C2311yescharacteristic
128C8×Dic83C2×C411yescharacteristic
129C8×Dic83C2×C411yescharacteristic
130C2×SD16×C83C2×C411yescharacteristic
131C22×C8×C83—21no—
132C4×Q8×C83C2311yescharacteristic
133C4×D4×C83C2311yescharacteristic
134#106×C83C2×C411yescharacteristic
135C4⋊C8×C83—21no—
136C4⋊C8×C83C2311yescharacteristic
137C4⋊C8×C83C2311yescharacteristic
138#103×C83C2×C411yescharacteristic
139#102×C83C2×C411yescharacteristic
140C22⋊C8×C83—21no—
141#97×C83—21no—
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C4×C8×C83C2311yescharacteristic
145#13050591—22no—
146#13050591—41no—
147#13050589—22no—
148#13050589—41no—
149C2×Dic166C22×C411yescharacteristic
150C2×D332—21no—
151C2×D332C22×C411yescharacteristic
152C2×C22⋊D83—21no—
153C22×Dic83—21no—
154C22×Dic83—21no—
155C2×C4×D83—21no—
156C2×C4×D83—21no—
157C2×C4×D83—21no—
158C2×C4×D83C22×C411yescharacteristic
159C2×C4×D83C2×D411yescharacteristic
160C2×C4×D83#4111yescharacteristic
161#13050580—22no—
162#13050579—22no—
163#13050575M1614yescomplemented
164#13050573—22no—
165#13050573—22no—
166C2×C83⋊C8—21no—
167C2×C83⋊C8—21no—
168C2×C83⋊C8—21no—
169C2×C83⋊C8—42no—
170C2×C83⋊C8C22×C411yescharacteristic
171C2×C83⋊C8C22×C411yescharacteristic
172C2×C83⋊C8C2×D411yescharacteristic
173C2×C83⋊C8C2×D411yescharacteristic
174C8×D83—22no—
175C8×D83—41no—
176C8×D83—42no—
177C8×D83—42no—
178C4⋊Dic83—21no—
179C4⋊Dic83C22×C411yescharacteristic
180C4⋊Dic83C22×C411yescharacteristic
181Dic83⋊C4—21no—
182Dic83⋊C4—21no—
183C22⋊Dic83—21no—
184(C2×D83)⋊C4—21no—
185(C2×D83)⋊C4—21no—
186(C2×D83)⋊C4—21no—
187(C2×D83)⋊C4—21no—
188C4×Dic83—21no—
189C4×Dic83—21no—
190C4×Dic83—21no—
191C4×Dic83—21no—
192C4×Dic83—21no—
193C4×Dic83C22×C411yescharacteristic
194C4×Dic83C2×D411yescharacteristic
195C4×Dic83#4111yescharacteristic
196C2×Q8×C83C22×C411yescharacteristic
197C2×D4×C83C22×C411yescharacteristic
198C22×C4×C83—21no—
199SD16×C83—22no—
200C2×C8×C83—21no—
201C2×C8×C83—21no—
202C2×C8×C83—21no—
203C2×C8×C83—42no—
204C2×C8×C83C22×C411yescharacteristic
205C2×C8×C83C22×C411yescharacteristic
206C2×C8×C83C2×D411yescharacteristic
207C2×C8×C83C2×D411yescharacteristic
208C4⋊C4×C83—21no—
209C4⋊C4×C83C22×C411yescharacteristic
210C4⋊C4×C83C22×C411yescharacteristic
211C22⋊C4×C83—21no—
212C42×C83—21no—
213C42×C83C2411yescharacteristic
214C23×C83—21no—
215C22×D83—21no—
216C22×D83C4×D411yescharacteristic
217Q8×C83—21no—
218Q8×C83—21no—
219D4×C83—21no—
220D4×C83C2×M1612yes—
221C2×C4×C83—21no—
222C2×C4×C83—21no—
223C2×C4×C83—21no—
224C2×C4×C83—41no—
225C2×C4×C83—41no—
226C2×C4×C83C23×C411yescharacteristic
227C2×C4×C83C22×D411yescharacteristic
228C2×C4×C83C2×#4111yescharacteristic
229C22⋊D83—42no—
230C2×Dic83—21no—
231C2×Dic83—21no—
232C2×Dic83—21no—
233C2×Dic83—42no—
234C2×Dic83—81no—
235C2×Dic83C4×D411yescharacteristic
236C2×Dic83C4×D411yescharacteristic
237C2×Dic83C4×D411yescharacteristic
238D332—21no—
239D332—42no—
240D332C2×M1612yes—
241C4×D83—21no—
242C4×D83—21no—
243C4×D83—21no—
244C4×D83—21no—
245C4×D83—41no—
246C4×D83—42no—
247C4×D83—41no—
248C4×D83—41no—
249C4×D83—81no—
250Dic166—21no—
251Dic166—21no—
252C8×C83—21no—
253C8×C83—21no—
254C8×C83—21no—
255C8×C83—41no—
256C8×C83—41no—
257C8×C83—41no—
258C8×C83#13512yescomplemented
259C83⋊C8—21no—
260C83⋊C8—21no—
261C83⋊C8—41no—
262C83⋊C8—41no—
263C83⋊C8—41no—
264C83⋊C8C2×M1612yes—
265C83⋊C8#13512yescomplemented
266C22×C83—22no—
267C22×C83—41no—
268C22×C83—41no—
269C22×C83C2×C4×D411yescharacteristic
270C2×D83—21no—
271C2×D83—22no—
272C2×D83—21no—
273C2×D83—21no—
274C2×D83—41no—
275C2×D83—41no—
276C4×C83—21no—
277C4×C83—41no—
278C4×C83—41no—
279C4×C83—41no—
280C4×C83C22×M1611yescharacteristic
281C4×C83#56811yescharacteristic
282C4×C83C2×#13511yescharacteristic
283C4×C83C2×#13511yescharacteristic
284Dic83—21no—
285Dic83—21no—
286Dic83—21no—
287Dic83—41no—
288Dic83—41no—
289Dic83—41no—
290#18035—831nomaximal, Sylow
291C2×C83—42no—
292C2×C83D4×M1611yescharacteristic
293C2×C83C4×#13511yescharacteristic
294C2×C83#295711yescharacteristic
295D83—41no—
296D83—42no—
297#2970—831no—
298#2970—831no—
299C4×#135—831no—
300#1591—831no—
301#1591—831no—
302#1582—831no—
303#1582—831no—
304#1582—831no—
305#1582D8311yescharacteristic, complemented
306C8×D8—831no—
307C8×D8—831no—
308#1568—831no—
309#1488—831no—
310#1488—831no—
311C8×M16—831no—
312C83#1803511yescharacteristic, complemented, Sylow
313C2×#135—831no—
314C4×#41—831no—
315C4×#41—831no—
316#446—831no—
317#446—831no—
318#446—831no—
319#446C2×D8311yescharacteristic
320C4×Q16—831no—
321C4×Q16—831no—
322C4×SD16—831no—
323C4×SD16—831no—
324C4×SD16—831no—
325C4×SD16C2×D8311yescharacteristic
326C4×D8—831no—
327C4×D8—831no—
328#435—1661no—
329#435—1661no—
330#435—1661no—
331#435—1661no—
332C8×D4—831no—
333C8×D4—831no—
334C8×D4—831no—
335C8×D4C2×D8311yescharacteristic
336#432—831no—
337#432—831no—
338#432—1661no—
339#432—1661no—
340#431—831no—
341#427—831no—
342#416—831no—
343#416—831no—
344C4×M16—831no—
345C2×#97—1661no—
346C2×#97—1661no—
347C2×C4×C8—831no—
348#335—831no—
349#335—831no—
350#334—831no—
351#334C2×D8311yescharacteristic
352Q8⋊C8—831no—
353Q8⋊C8—831no—
354Q8⋊C8—831no—
355Q8⋊C8C2×D8311yescharacteristic
356D4⋊C8—831no—
357D4⋊C8—831no—
358D4⋊C8—831no—
359D4⋊C8C2×D8311yescharacteristic
360#322—831no—
361#322C2×D8311yescharacteristic
362C82—831no—
363C82—831no—
364C2×#41—831no—
365C2×#41—831no—
366#135—1664no—
367C2×Q16—831no—
368C2×SD16—831no—
369C2×SD16C4×D8311yescharacteristic
370C2×D8—831no—
371C2×M16—831no—
372C2×M16—831no—
373C22×C8—21no—
374C22×C8—831no—
375C22×C8—831no—
376C22×C8—1661no—
377C22×C8—1661no—
378C22×C8—1661no—
379C4×Q8—831no—
380C4×Q8—831no—
381C4×Q8—831no—
382C4×Q8C22×D8311yescharacteristic
383C4×D4—831no—
384C4×D4—831no—
385C4×D4—831no—
386C4×D4—1661no—
387C4×D4—1661no—
388C4×D4—1661no—
389C4×D4—1661no—
390C4×D4C22×D8311yescharacteristic
391#117—831no—
392#117—831no—
393#117—1661no—
394#117—1661no—
395C2×C42—831no—
396C2×C42—1661no—
397C2×C42—1661no—
398#107—831no—
399#107—831no—
400#106—831no—
401#106C4×D8311yescharacteristic
402C4⋊C8—21no—
403C4⋊C8—831no—
404C4⋊C8—831no—
405C4⋊C8—1661no—
406C4⋊C8—1661no—
407C4⋊C8—1661no—
408C4⋊C8—1661no—
409C4⋊C8C22×D8311yescharacteristic
410C4⋊C8C22×D8311yescharacteristic
411#103—831no—
412#103—831no—
413#103—831no—
414#103C4×D8311yescharacteristic
415#102—831no—
416#102—831no—
417#102—831no—
418#102C4×D8311yescharacteristic
419C22⋊C8—21no—
420C22⋊C8—1661no—
421C22⋊C8—1661no—
422C22⋊C8—1661no—
423C22⋊C8—1661no—
424C22⋊C8—1661no—
425C22⋊C8—1661no—
426#97—21no—
427#97—831no—
428#97—831no—
429#97—1661no—
430#97—1661no—
431#97—1661no—
432#97—1661no—
433#97—1661no—
434C4×C8—831no—
435C4×C8—831no—
436C4×C8—831no—
437C4×C8—831no—
438C4×C8—831no—
439C4×C8C22×D8311yescharacteristic
440C4×C8C22×D8311yescharacteristic
441C4×C8C22×D8311yescharacteristic
442#41—3321no—
443#41—3321no—
444#41—1662no—
445#41—1662no—
446C2×Q8—831no—
447C2×Q8C2×C4×D8311yescharacteristic
448C2×D4—831no—
449C2×D4—1661no—
450C2×D4—1661no—
451C2×D4C2×C4×D8311yescharacteristic
452C22×C4—21no—
453C22×C4—831no—
454C22×C4—831no—
455C22×C4—831no—
456C22×C4—1661no—
457C22×C4—1661no—
458C22×C4—1661no—
459C22×C4—1661no—
460C22×C4—1661no—
461Q16—1662no—
462SD16—22no—
463SD16—1662no—
464D8—834no—
465M16—1662no—
466M16—1662no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—42no—
471C2×C8—3321no—
472C2×C8—3322no—
473C2×C8—3322no—
474C2×C8—3322no—
475C2×C8—831no—
476C2×C8—831no—
477C2×C8—831no—
478C2×C8—831no—
479C2×C8—1662no—
480C2×C8—1661no—
481C2×C8—1661no—
482C2×C8—1661no—
483C2×C8C2×C4×D8311yescharacteristic
484C2×C8C2×C4×D8311yescharacteristic
485C2×C8D4×D8311yescharacteristic
486C2×C8D4×D8311yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—831no—
489C4⋊C4—831no—
490C4⋊C4—1661no—
491C4⋊C4—1661no—
492C4⋊C4—1661no—
493C4⋊C4C2×C4×D8311yescharacteristic
494C4⋊C4C2×C4×D8311yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—1661no—
497C22⋊C4—1661no—
498C22⋊C4—1661no—
499C22⋊C4—1661no—
500C22⋊C4—1661no—
501C42—21no—
502C42—831no—
503C42—831no—
504C42—831no—
505C42—1661no—
506C42—1661no—
507C42—1661no—
508C42—1661no—
509C42—1661no—
510C42C23×D8311yescharacteristic
511C23—21no—
512C23—831no—
513C23—1661no—
514Q8—21no—
515Q8—21no—
516Q8—1661no—
517Q8—1661no—
518D4—21no—
519D4—3322no—
520D4—3322no—
521D4—832no—
522D4—1661no—
523D4M16×D8312yes—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—3321no—
530C2×C4—3322no—
531C2×C4—3322no—
532C2×C4—3321no—
533C2×C4—3321no—
534C2×C4—831no—
535C2×C4—831no—
536C2×C4—831no—
537C2×C4—6641no—
538C2×C4—6641no—
539C2×C4—1661no—
540C2×C4—1661no—
541C2×C4—1661no—
542C2×C4—1661no—
543C2×C4—1661no—
544C2×C4—1661no—
545C2×C4—1661no—
546C2×C4C22×C4×D8311yescharacteristic
547C2×C4C2×D4×D8311yescharacteristic
548C2×C4#41×D8311yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—3321no—
556C8—3321no—
557C8—3321no—
558C8—832no—
559C8—832no—
560C8—1661no—
561C8—1661no—
562C8#1458181312yescomplemented
563C22—22no—
564C22—41no—
565C22—41no—
566C22—3321no—
567C22—3321no—
568C22—1661no—
569C22—1661no—
570C22—1662no—
571C22—1661no—
572C22C4×D4×D8311yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—3321no—
578C4—3321no—
579C4—3321no—
580C4—1661no—
581C4—1661no—
582C4—1661no—
583C4C2×M16×D8311yescharacteristic
584C4#1912846611yescharacteristic
585C4#135×D8311yescharacteristic
586C4C2×#1458181311yescharacteristic
587C2—42no—
588C2—3322no—
589C2—3321no—
590C2#2491619611yescharacteristic
591C2C4×#1458181311yescharacteristic
592C2#2491637711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1582C2
socleC22×C83C2×C4×D4
prime radicalC2×#14581813C4
cosocleC42×C83C24
hypercenter#1582D83
hypocenterC83#18035
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
1. #24916476C2semidirect
2. #24916471C2semidirect
4. #24906358C2semidirect
5. #24906357C2semidirect
6. #24906301C2semidirect
7. #24906300C2semidirect
8. #24906298C2semidirect
9. C8×#13050575C2semidirect
10. #24906255C2semidirect
11. #24906223C2semidirect
12. #24905896C2semidirect
13. #24905894C2semidirect
14. #24905742C2semidirect
15. C83×#1582C2semidirect
163. #13050575M16semidirect
258. C8×C83#135semidirect
265. C83⋊C8#135semidirect
305. #1582D83semidirect
312. C83#18035semidirect
562. C8#14581813semidirect

Maximal subgroups

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

subgroupindex
#249164762
#249164712
C4×#145818132
#249063582
#249063572
#249063012
#249063002
#249062982
C8×#130505752
#249062552
#249062232
#249058962
#249058942
#249057422
C83×#15822
#1803583