Finite Group Databasebeta

← #35375321

Subgroups — #35375321

Order 21248.

618 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917479C211yesmaximal, characteristic
2#24916476C211yesmaximal, characteristic, complemented
3#24916470C211yesmaximal, characteristic, complemented
4#24906357C211yesmaximal, characteristic, complemented
5#24906311C211yesmaximal, characteristic, complemented
6#24906300C211yesmaximal, characteristic, complemented
7#24906298C211yesmaximal, characteristic, complemented
8#24906290C211yesmaximal, characteristic, complemented
9C8×#13050579C211yesmaximal, characteristic, complemented
10#24906255C211yesmaximal, characteristic, complemented
11#24906240C211yesmaximal, characteristic, complemented
12#24905920C211yesmaximal, characteristic, complemented
13#24905844C211yesmaximal, characteristic, complemented
14C8×#13050573C211yesmaximal, characteristic, complemented
15C83×#1590C211yesmaximal, characteristic, complemented
16#19128233C2211yescharacteristic
17C4×#13050591C2211yescharacteristic
18#19128045C411yescharacteristic
19#19128024C411yescharacteristic
20#19128006C411yescharacteristic
21#19128000C411yescharacteristic
22#19127921C411yescharacteristic
23#19127915C411yescharacteristic
24#19127866C411yescharacteristic
25#19127845C411yescharacteristic
26#19127832C2211yescharacteristic
27#19127828C2211yescharacteristic
28C8×Dic166C2211yescharacteristic
29C4×#13050580C2211yescharacteristic
30C4×#13050579C2211yescharacteristic
31C4×#13050575C2211yescharacteristic
32#19127777—21no—
33#19127774—21no—
34#19127771—21no—
35#19127769—21no—
36C8×D332C2211yescharacteristic
37D4×C83⋊C8C2211yescharacteristic
38#19127766C2211yescharacteristic
39#19127759—21no—
40#19127757—21no—
41#19127757C2211yescharacteristic
42#19127753C2211yescharacteristic
43#19127752C2211yescharacteristic
44#19127659—21no—
45C4×#13050573C2211yescharacteristic
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
58#19127422C2211yescharacteristic
59C8×C83⋊C8C2211yescharacteristic
60#446×C83C2211yescharacteristic
61C4×SD16×C83C2211yescharacteristic
62#436×C83C2211yescharacteristic
63#334×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65D4⋊C8×C83C2211yescharacteristic
66C82×C83C2211yescharacteristic
67C2×#13050591C2×C411yescharacteristic
68C2×#13050580C2×C411yescharacteristic
69C2×#13050579C2×C411yescharacteristic
70C2×#13050575C2×C411yescharacteristic
71C2×#13050573D411yescharacteristic
72C2×#13050573D411yescharacteristic
73C22×C83⋊C8—21no—
74C2×C8×D83—21no—
75C2×C8×D83—21no—
76C2×C8×D83—21no—
77#14581785—21no—
78#14581783C2×C411yescharacteristic
79#14581779C2×C411yescharacteristic
80#14581774—21no—
81#14581772C2×C411yescharacteristic
82#14581763C2×C411yescharacteristic
83Q8×Dic83C2×C411yescharacteristic
84C4×Dic166C2311yescharacteristic
85C4×D332—21no—
86C4×D332C2311yescharacteristic
87#14581754—21no—
88#14581754C2×C411yescharacteristic
89C4×C22⋊D83—21no—
90#14581751—21no—
91#14581750—21no—
92#14581750C2×C411yescharacteristic
93C42×D83—21no—
94C42×D83C2311yescharacteristic
95#14581725C2×C411yescharacteristic
96#14581725C2×C411yescharacteristic
97#14581724C2×C411yescharacteristic
98C4⋊(C83⋊C8)—21no—
99C4⋊(C83⋊C8)C2311yescharacteristic
100C4⋊(C83⋊C8)C2311yescharacteristic
101Dic83⋊C8—21no—
102Dic83⋊C8—21no—
103Dic83⋊C8C2×C411yescharacteristic
104Dic83⋊C8C2×C411yescharacteristic
105#14581717C2×C411yescharacteristic
106#14581716C2×C411yescharacteristic
107#14581715C2×C411yescharacteristic
108#14581714C2×C411yescharacteristic
109#14581713C2×C411yescharacteristic
110#14581712C2×C411yescharacteristic
111C22⋊(C83⋊C8)—21no—
112(C2×D83)⋊C8—21no—
113(C2×D83)⋊C8—21no—
114(C2×D83)⋊C8—21no—
115(C2×D83)⋊C8—21no—
116(C2×D83)⋊C8C2×C411yescharacteristic
117(C2×D83)⋊C8C2×C411yescharacteristic
118#14581703—21no—
119#14581702—21no—
120#14581702—21no—
121#14581702D411yescharacteristic
122#14581702D411yescharacteristic
123C4×C83⋊C8C2311yescharacteristic
124C4×C83⋊C8C2311yescharacteristic
125C4×C83⋊C8C2311yescharacteristic
126C8×Dic83—21no—
127C8×Dic83—21no—
128C8×Dic83—21no—
129C2×SD16×C83C2×C411yescharacteristic
130C2×M16×C83—21no—
131C4×Q8×C83C2311yescharacteristic
132C4×D4×C83C2311yescharacteristic
133#106×C83C2×C411yescharacteristic
134C4⋊C8×C83—21no—
135C4⋊C8×C83C2311yescharacteristic
136C4⋊C8×C83C2311yescharacteristic
137#103×C83C2×C411yescharacteristic
138#102×C83C2×C411yescharacteristic
139C22⋊C8×C83—21no—
140#97×C83—21no—
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#13050591—22no—
145#13050591—41no—
146C2×Dic166C22×C411yescharacteristic
147C2×D332—21no—
148C2×D332C22×C411yescharacteristic
149C2×C22⋊D83—21no—
150C2×C4×D83—21no—
151C2×C4×D83—21no—
152C2×C4×D83—21no—
153C2×C4×D83C22×C411yescharacteristic
154C2×C4×D83C2×D411yescharacteristic
155C2×C4×D83#4111yescharacteristic
156#13050580—41no—
157#13050579—22no—
158#13050575—22no—
159#13050573—22no—
160#13050573—22no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8—21no—
163C2×C83⋊C8—21no—
164C2×C83⋊C8—42no—
165C2×C83⋊C8C22×C411yescharacteristic
166C2×C83⋊C8C22×C411yescharacteristic
167C2×C83⋊C8C2×D411yescharacteristic
168C2×C83⋊C8C2×D411yescharacteristic
169C8×D83—42no—
170C8×D83—42no—
171C8×D83—42no—
172C4⋊Dic83—21no—
173C4⋊Dic83—21no—
174C4⋊Dic83—21no—
175C4⋊Dic83C22×C411yescharacteristic
176C4⋊Dic83C22×C411yescharacteristic
177Dic83⋊C4—21no—
178Dic83⋊C4—21no—
179C22⋊Dic83—21no—
180C22⋊Dic83—21no—
181C22⋊Dic83—21no—
182(C2×D83)⋊C4—21no—
183(C2×D83)⋊C4—21no—
184(C2×D83)⋊C4—21no—
185(C2×D83)⋊C4—21no—
186C4×Dic83—21no—
187C4×Dic83—21no—
188C4×Dic83—21no—
189C4×Dic83C22×C411yescharacteristic
190C4×Dic83C2×D411yescharacteristic
191C4×Dic83#4111yescharacteristic
192C2×Q8×C83C22×C411yescharacteristic
193C2×D4×C83C22×C411yescharacteristic
194C22×C4×C83—21no—
195SD16×C83—41no—
196M16×C83—42no—
197C2×C8×C83—21no—
198C2×C8×C83—21no—
199C2×C8×C83—21no—
200C2×C8×C83C22×C411yescharacteristic
201C2×C8×C83C22×C411yescharacteristic
202C2×C8×C83C2×D411yescharacteristic
203C2×C8×C83C2×D411yescharacteristic
204C4⋊C4×C83—21no—
205C4⋊C4×C83C22×C411yescharacteristic
206C4⋊C4×C83C22×C411yescharacteristic
207C22⋊C4×C83—21no—
208C42×C83—21no—
209C42×C83C2411yescharacteristic
210C23×C83—21no—
211C22×D83—21no—
212C22×D83C4×D411yescharacteristic
213Q8×C83—21no—
214Q8×C83—21no—
215D4×C83—21no—
216D4×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—41no—
221C2×C4×C83—41no—
222C2×C4×C83C23×C411yescharacteristic
223C2×C4×C83C22×D411yescharacteristic
224C2×C4×C83C2×#4111yescharacteristic
225C22⋊D83—81no—
226C2×Dic83—21no—
227C2×Dic83—21no—
228C2×Dic83—21no—
229C2×Dic83C4×D411yescharacteristic
230C2×Dic83C4×D411yescharacteristic
231C2×Dic83C4×D411yescharacteristic
232D332—21no—
233D332—42no—
234D332#13112yes—
235C4×D83—21no—
236C4×D83—21no—
237C4×D83—21no—
238C4×D83—21no—
239C4×D83—41no—
240C4×D83—42no—
241C4×D83—41no—
242C4×D83—41no—
243C4×D83—81no—
244Dic166—21no—
245Dic166—21no—
246C8×C83—22no—
247C8×C83—21no—
248C8×C83—21no—
249C8×C83—21no—
250C8×C83—41no—
251C8×C83—41no—
252C8×C83#13512yes—
253C83⋊C8—21no—
254C83⋊C8—21no—
255C83⋊C8—21no—
256C83⋊C8—41no—
257C83⋊C8—41no—
258C83⋊C8—41no—
259C83⋊C8#13512yes—
260C22×C83—41no—
261C22×C83—41no—
262C22×C83—41no—
263C22×C83C2×C4×D411yescharacteristic
264C2×D83—21no—
265C2×D83—22no—
266C2×D83—21no—
267C2×D83—21no—
268C2×D83—41no—
269C2×D83—41no—
270C4×C83—21no—
271C4×C83—41no—
272C4×C83—41no—
273C4×C83—41no—
274C4×C83C2×#13111yescharacteristic
275C4×C83#56811yescharacteristic
276C4×C83C2×#13511yescharacteristic
277C4×C83C2×#13511yescharacteristic
278Dic83—21no—
279Dic83—21no—
280Dic83—21no—
281Dic83—41no—
282Dic83—41no—
283Dic83—41no—
284#17996—831nomaximal, Sylow
285C2×C83—81no—
286C2×C83#293311yescharacteristic
287C2×C83C4×#13511yescharacteristic
288C2×C83#295611yescharacteristic
289D83—41no—
290D83—42no—
291#3102—831no—
292#2970—831no—
293#2969—831no—
294#1591—831no—
295#1590D8311yescharacteristic, complemented
296#1584—831no—
297#1582—831no—
298#1582—831no—
299#1581—831no—
300C8×SD16—831no—
301C8×D8—831no—
302#1572—831no—
303#1494—831no—
304#1476—831no—
305C8×M16—831no—
306C83#1799611yescharacteristic, complemented, Sylow
307#529—831no—
308C4×#41—831no—
309#485—831no—
310#482—831no—
311#479—831no—
312#478—831no—
313#464—831no—
314#463—831no—
315#452—831no—
316#449—831no—
317#446—831no—
318#446—831no—
319#446C2×D8311yescharacteristic
320C8×Q8—831no—
321C4×Q16—831no—
322C4×SD16—831no—
323C4×SD16C2×D8311yescharacteristic
324C4×D8—831no—
325#436—1661no—
326#436C2×D8311yescharacteristic
327#435—1661no—
328#435—1661no—
329#435—1661no—
330C8×D4—831no—
331C8×D4—831no—
332C8×D4—831no—
333#433—1661no—
334#432—831no—
335#432—1661no—
336#431—831no—
337#431—831no—
338#405—1661no—
339C4×M16—831no—
340C2×#97—1661no—
341C2×C4×C8—831no—
342#335—831no—
343#335—831no—
344#334—831no—
345#334C2×D8311yescharacteristic
346Q8⋊C8—831no—
347Q8⋊C8—831no—
348Q8⋊C8—831no—
349Q8⋊C8C2×D8311yescharacteristic
350D4⋊C8—831no—
351D4⋊C8—831no—
352D4⋊C8—831no—
353D4⋊C8C2×D8311yescharacteristic
354#322—831no—
355#322—831no—
356C82—831no—
357C82C2×D8311yescharacteristic
358C2×#41—831no—
359C2×Q16—831no—
360C2×SD16—831no—
361C2×SD16C4×D8311yescharacteristic
362C2×D8—831no—
363C2×M16—21no—
364C2×M16—831no—
365C2×M16—831no—
366C22×C8—1661no—
367C22×C8—1661no—
368C22×C8—1661no—
369C22×C8—1661no—
370#126—1661no—
371#125—831no—
372#124—831no—
373#123—1661no—
374C22⋊Q8—831no—
375#121—831no—
376C4×Q8—831no—
377C4×Q8—831no—
378C4×Q8C22×D8311yescharacteristic
379C4×D4—831no—
380C4×D4—831no—
381C4×D4—1661no—
382C4×D4—1661no—
383C4×D4—1661no—
384C4×D4C22×D8311yescharacteristic
385#117—831no—
386#117—1661no—
387#117—1661no—
388C2×C42—831no—
389C2×C42—1661no—
390#107—831no—
391#107—831no—
392#106—831no—
393#106C4×D8311yescharacteristic
394C4⋊C8—21no—
395C4⋊C8—831no—
396C4⋊C8—831no—
397C4⋊C8—831no—
398C4⋊C8—831no—
399C4⋊C8—1661no—
400C4⋊C8—1661no—
401C4⋊C8—1661no—
402C4⋊C8C22×D8311yescharacteristic
403C4⋊C8C22×D8311yescharacteristic
404#103—831no—
405#103—831no—
406#103—831no—
407#103C4×D8311yescharacteristic
408#102—831no—
409#102—831no—
410#102—831no—
411#102C4×D8311yescharacteristic
412C22⋊C8—21no—
413C22⋊C8—831no—
414C22⋊C8—831no—
415C22⋊C8—1661no—
416C22⋊C8—1661no—
417C22⋊C8—1661no—
418C22⋊C8—1661no—
419C22⋊C8—1661no—
420#97—21no—
421#97—831no—
422#97—831no—
423#97—1661no—
424#97—1661no—
425#97—1661no—
426C4×C8—831no—
427C4×C8—831no—
428C4×C8—831no—
429C4×C8—1661no—
430C4×C8—1661no—
431C4×C8—1661no—
432C4×C8C22×D8311yescharacteristic
433C4×C8C22×D8311yescharacteristic
434C4×C8C22×D8311yescharacteristic
435#41—3321no—
436#41—1662no—
437C2×Q8—831no—
438C2×Q8C2×C4×D8311yescharacteristic
439C2×D4—831no—
440C2×D4—1661no—
441C2×D4—1661no—
442C2×D4C2×C4×D8311yescharacteristic
443C22×C4—21no—
444C22×C4—831no—
445C22×C4—831no—
446C22×C4—831no—
447C22×C4—1661no—
448C22×C4—1661no—
449C22×C4—1661no—
450Q16—3321no—
451SD16—41no—
452SD16—1662no—
453D8—1662no—
454M16—42no—
455M16—1662no—
456M16—1662no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—3322no—
461C2×C8—3322no—
462C2×C8—3322no—
463C2×C8—3322no—
464C2×C8—831no—
465C2×C8—831no—
466C2×C8—831no—
467C2×C8—831no—
468C2×C8—1661no—
469C2×C8—1661no—
470C2×C8—1661no—
471C2×C8C2×C4×D8311yescharacteristic
472C2×C8C2×C4×D8311yescharacteristic
473C2×C8D4×D8311yescharacteristic
474C2×C8D4×D8311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—831no—
477C4⋊C4—831no—
478C4⋊C4—1661no—
479C4⋊C4—1661no—
480C4⋊C4—1661no—
481C4⋊C4—1661no—
482C4⋊C4—1661no—
483C4⋊C4C2×C4×D8311yescharacteristic
484C4⋊C4C2×C4×D8311yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—1661no—
487C22⋊C4—1661no—
488C22⋊C4—1661no—
489C22⋊C4—1661no—
490C22⋊C4—1661no—
491C22⋊C4—1661no—
492C22⋊C4—1661no—
493C42—21no—
494C42—831no—
495C42—831no—
496C42—831no—
497C42—1661no—
498C42—1661no—
499C42—1661no—
500C42C23×D8311yescharacteristic
501C23—21no—
502C23—831no—
503C23—1661no—
504Q8—21no—
505Q8—21no—
506Q8—1661no—
507Q8—1661no—
508D4—21no—
509D4—21no—
510D4—3322no—
511D4—832no—
512D4—6641no—
513D4—1661no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—3321no—
520C2×C4—3322no—
521C2×C4—3321no—
522C2×C4—3321no—
523C2×C4—831no—
524C2×C4—831no—
525C2×C4—831no—
526C2×C4—6641no—
527C2×C4—1661no—
528C2×C4—1661no—
529C2×C4—1661no—
530C2×C4—1661no—
531C2×C4—1661no—
532C2×C4—1661no—
533C2×C4—1661no—
534C2×C4C22×C4×D8311yescharacteristic
535C2×C4C2×D4×D8311yescharacteristic
536C2×C4#41×D8311yescharacteristic
537C8—22no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—3321no—
544C8—3321no—
545C8—3321no—
546C8—832no—
547C8—1661no—
548C8—1661no—
549C8—1661no—
550C8#1458181312yes—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—3321no—
555C22—3321no—
556C22—1661no—
557C22—1661no—
558C22—1662no—
559C22—1661no—
560C22C4×D4×D8311yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—3321no—
566C4—3321no—
567C4—3321no—
568C4—1661no—
569C4—1661no—
570C4—1661no—
571C4#131×D8311yescharacteristic
572C4#1912846711yescharacteristic
573C4#135×D8311yescharacteristic
574C4C2×#1458181311yescharacteristic
575C2—81no—
576C2—3322no—
577C2—3321no—
578C2#2491619211yescharacteristic
579C2C4×#1458181311yescharacteristic
580C2#2491636811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1590C2
socleC22×C83C2×C4×D4
prime radical#19127845C4
cosocleC42×C83C24
hypercenter#1590D83
hypocenterC83#17996
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
2. #24916476C2semidirect
3. #24916470C2semidirect
4. #24906357C2semidirect
5. #24906311C2semidirect
6. #24906300C2semidirect
7. #24906298C2semidirect
8. #24906290C2semidirect
9. C8×#13050579C2semidirect
10. #24906255C2semidirect
11. #24906240C2semidirect
12. #24905920C2semidirect
13. #24905844C2semidirect
14. C8×#13050573C2semidirect
15. C83×#1590C2semidirect
295. #1590D83semidirect
306. C83#17996semidirect

Maximal subgroups

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

subgroupindex
#249174792
#249164762
#249164702
#249063572
#249063112
#249063002
#249062982
#249062902
C8×#130505792
#249062552
#249062402
#249059202
#249058442
C8×#130505732
C83×#15902
#1799683