Finite Group Databasebeta

← #35375381

Subgroups — #35375381

Order 21248.

610 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#24917485C211yesmaximal, characteristic
2#24916471C211yesmaximal, characteristic, complemented
3#24916466C211yesmaximal, characteristic, complemented
4#24906369C211yesmaximal, characteristic, complemented
5#24906367C211yesmaximal, characteristic, complemented
6#24906334C211yesmaximal, characteristic, complemented
7#24906327C211yesmaximal, characteristic, complemented
8#24906321C211yesmaximal, characteristic, complemented
9#24906319C211yesmaximal, characteristic, complemented
10#24906284C211yesmaximal, characteristic, complemented
11#24906242C211yesmaximal, characteristic, complemented
12#24905922C211yesmaximal, characteristic, complemented
13#24905842C211yesmaximal, characteristic, complemented
14#24905751C211yesmaximal, characteristic, complemented
15C83×SD16⋊C8C211yesmaximal, characteristic, complemented
16#19128238C2211yescharacteristic
17C4×#13050589C2211yescharacteristic
18#19128040C411yescharacteristic
19#19128027C411yescharacteristic
20#19128011C411yescharacteristic
21#19128003C411yescharacteristic
22#19127926C411yescharacteristic
23#19127918C411yescharacteristic
24#19127860C411yescharacteristic
25#19127847C411yescharacteristic
26#19127832C2211yescharacteristic
27#19127831C2211yescharacteristic
28#19127828C2211yescharacteristic
29C4×#13050580C2211yescharacteristic
30C4×#13050579C2211yescharacteristic
31C4×#13050575C2211yescharacteristic
32#19127780—21no—
33#19127780C2211yescharacteristic
34#19127772—21no—
35#19127771—21no—
36#19127769—21no—
37D4×C83⋊C8C2211yescharacteristic
38#19127766C2211yescharacteristic
39#19127761—21no—
40#19127757C2211yescharacteristic
41#19127755—21no—
42#19127753C2211yescharacteristic
43#19127752C2211yescharacteristic
44#19127655—21no—
45C4×#13050573C2211yescharacteristic
46C2×#14581702—21no—
47C4×C8×D83C2211yescharacteristic
48#19127454C2211yescharacteristic
49#19127451C2211yescharacteristic
50#19127451C2211yescharacteristic
51#19127433C2211yescharacteristic
52Q8⋊(C83⋊C8)C2211yescharacteristic
53#19127431C2211yescharacteristic
54#19127430C2211yescharacteristic
55D4⋊(C83⋊C8)C2211yescharacteristic
56#19127428C2211yescharacteristic
57#19127423C2211yescharacteristic
58#19127423C2211yescharacteristic
59#19127423C2211yescharacteristic
60C8×Q8×C83C2211yescharacteristic
61C4×SD16×C83C2211yescharacteristic
62C8×D4×C83C2211yescharacteristic
63#335×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65D4⋊C8×C83C2211yescharacteristic
66#322×C83C2211yescharacteristic
67C2×#13050589C2×C411yescharacteristic
68C2×#13050580C2×C411yescharacteristic
69C2×#13050579C2×C411yescharacteristic
70C2×#13050575C2×C411yescharacteristic
71C2×#13050573—21no—
72C2×#13050573D411yescharacteristic
73C2×#13050573D411yescharacteristic
74C22×C83⋊C8—21no—
75C2×C8×D83—21no—
76C2×C8×D83—21no—
77#14581787—21no—
78#14581783C2×C411yescharacteristic
79#14581781C2×C411yescharacteristic
80#14581777—21no—
81#14581768C2×C411yescharacteristic
82#14581767C2×C411yescharacteristic
83C4×Dic166C2311yescharacteristic
84#14581757C2×C411yescharacteristic
85C4×D332—21no—
86C4×D332C2311yescharacteristic
87D4×Dic83C2×C411yescharacteristic
88C4×C22⋊D83—21no—
89(C22⋊D83)⋊C4—21no—
90#14581750C2×C411yescharacteristic
91#14581749—21no—
92#14581748—21no—
93C2×C4×Dic83—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#14581702—21no—
122#14581702D411yescharacteristic
123#14581702D411yescharacteristic
124C4×C83⋊C8C2311yescharacteristic
125C4×C83⋊C8C2311yescharacteristic
126C4×C83⋊C8C2311yescharacteristic
127C8×Dic83—21no—
128C8×Dic83—21no—
129C2×SD16×C83C2×C411yescharacteristic
130C22×C8×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—
140C4×C8×C83—21no—
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#13050589—22no—
145#13050589—41no—
146C2×Dic166C22×C411yescharacteristic
147C2×D332—21no—
148C2×D332C22×C411yescharacteristic
149C2×C22⋊D83—21no—
150C22×Dic83—21no—
151C22×Dic83—21no—
152C2×C4×D83—21no—
153C2×C4×D83C22×C411yescharacteristic
154C2×C4×D83C2×D411yescharacteristic
155C2×C4×D83#4111yescharacteristic
156#13050580—41no—
157#13050579—41no—
158#13050575—22no—
159#13050573—41no—
160#13050573—41no—
161#13050573—42no—
162C2×C83⋊C8—21no—
163C2×C83⋊C8—21no—
164C2×C83⋊C8—21no—
165C2×C83⋊C8—42no—
166C2×C83⋊C8C22×C411yescharacteristic
167C2×C83⋊C8C22×C411yescharacteristic
168C2×C83⋊C8C2×D411yescharacteristic
169C2×C83⋊C8C2×D411yescharacteristic
170C8×D83—42no—
171C8×D83—42no—
172C4⋊Dic83—21no—
173C4⋊Dic83C22×C411yescharacteristic
174C4⋊Dic83C22×C411yescharacteristic
175Dic83⋊C4—21no—
176Dic83⋊C4—21no—
177Dic83⋊C4—21no—
178Dic83⋊C4—21no—
179C22⋊Dic83—21no—
180(C2×D83)⋊C4—21no—
181(C2×D83)⋊C4—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—22no—
196C2×C8×C83—21no—
197C2×C8×C83—21no—
198C2×C8×C83—21no—
199C2×C8×C83—42no—
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#13112yes—
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—42no—
226C2×Dic83—21no—
227C2×Dic83—21no—
228C2×Dic83—21no—
229C2×Dic83—42no—
230C2×Dic83—81no—
231C2×Dic83C4×D411yescharacteristic
232C2×Dic83C4×D411yescharacteristic
233C2×Dic83C4×D411yescharacteristic
234D332—21no—
235D332—21no—
236D332—81no—
237C4×D83—21no—
238C4×D83—21no—
239C4×D83—21no—
240C4×D83—21no—
241C4×D83—41no—
242C4×D83—41no—
243C4×D83—41no—
244Dic166—21no—
245Dic166—21no—
246C8×C83—21no—
247C8×C83—21no—
248C8×C83—21no—
249C8×C83—21no—
250C8×C83—41no—
251C8×C83—41no—
252C8×C83—41no—
253C83⋊C8—22no—
254C83⋊C8—21no—
255C83⋊C8—21no—
256C83⋊C8—21no—
257C83⋊C8—21no—
258C83⋊C8—41no—
259C83⋊C8—41no—
260C22×C83—22no—
261C22×C83—41no—
262C22×C83—41no—
263C22×C83C2×C4×D411yescharacteristic
264C2×D83—21no—
265C2×D83—21no—
266C2×D83—21no—
267C2×D83—41no—
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×C83#57511yescharacteristic
277C4×C83#57511yescharacteristic
278Dic83—21no—
279Dic83—21no—
280Dic83—21no—
281Dic83—41no—
282Dic83—41no—
283Dic83—41no—
284#18002—831nomaximal, Sylow
285C2×C83—42no—
286C2×C83#293311yescharacteristic
287C2×C83#294311yescharacteristic
288C2×C83#295611yescharacteristic
289D83—41no—
290D83—81no—
291#3102—831no—
292#2970—831no—
293#2969—831no—
294#1593—831no—
295#1592—831no—
296#1587—831no—
297#1586—831no—
298#1585—831no—
299#1585—831no—
300#1580—831no—
301SD16⋊C8D8311yescharacteristic, complemented
302#1572—831no—
303#1494—831no—
304#1476—831no—
305#1451—831no—
306C83#1800211yescharacteristic, 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#446—831no—
320C8×Q8C2×D8311yescharacteristic
321C4×Q16—831no—
322C4×SD16—831no—
323C4×SD16C2×D8311yescharacteristic
324C4×D8—831no—
325#436—831no—
326#436—1661no—
327#435—1661no—
328#435—1661no—
329#435—1661no—
330C8×D4—831no—
331C8×D4—831no—
332C8×D4C2×D8311yescharacteristic
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#335C2×D8311yescharacteristic
344#334—831no—
345#334—831no—
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—
356#322—831no—
357#322C2×D8311yescharacteristic
358C2×#41—831no—
359C2×Q16—831no—
360C2×SD16—831no—
361C2×SD16C4×D8311yescharacteristic
362C2×D8—831no—
363C2×M16—831no—
364C2×M16—831no—
365C2×M16—1661no—
366C22×C8—21no—
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—831no—
421#97—831no—
422#97—1661no—
423#97—1661no—
424#97—1661no—
425#97—1661no—
426C4×C8—21no—
427C4×C8—831no—
428C4×C8—831no—
429C4×C8—831no—
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—22no—
452SD16—3321no—
453D8—1662no—
454M16—3322no—
455M16—3321no—
456M16—3321no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—42no—
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—3322no—
510D4—6641no—
511D4—1661no—
512D4—1661no—
513D4#1458179812yes—
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—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—3321no—
545C8—3321no—
546C8—1662no—
547C8—1661no—
548C8—1661no—
549C8—1661no—
550C8—1661no—
551C22—22no—
552C22—41no—
553C22—41no—
554C22—3321no—
555C22—3321no—
556C22—3321no—
557C22—1661no—
558C22—1661no—
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—
571C4C2×#1458179811yescharacteristic
572C4#1912846611yescharacteristic
573C4#1912849711yescharacteristic
574C4#1912850011yescharacteristic
575C2—42no—
576C2—3321no—
577C2—6641no—
578C2#2491618311yescharacteristic
579C2#2491625811yescharacteristic
580C2#2491637111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×SD16⋊C8C2
socleC22×C83C2×C4×D4
prime radical#19127847C4
cosocleC42×C83C24
hypercenterSD16⋊C8D83
hypocenterC83#18002
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
2. #24916471C2semidirect
3. #24916466C2semidirect
4. #24906369C2semidirect
5. #24906367C2semidirect
6. #24906334C2semidirect
7. #24906327C2semidirect
8. #24906321C2semidirect
9. #24906319C2semidirect
10. #24906284C2semidirect
11. #24906242C2semidirect
12. #24905922C2semidirect
13. #24905842C2semidirect
14. #24905751C2semidirect
15. C83×SD16⋊C8C2semidirect
301. SD16⋊C8D83semidirect
306. C83#18002semidirect

Maximal subgroups

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

subgroupindex
#249174852
#249164712
#249164662
#249063692
#249063672
#249063342
#249063272
#249063212
#249063192
#249062842
#249062422
#249059222
#249058422
#249057512
C83×SD16⋊C82
#1800283