Finite Group Databasebeta

← #35375347

Subgroups — #35375347

Order 21248.

616 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#24917475C211yesmaximal, characteristic
2#24916481C211yesmaximal, characteristic, complemented
3#24906353C211yesmaximal, characteristic, complemented
4#24906346C211yesmaximal, characteristic, complemented
5#24906311C211yesmaximal, characteristic, complemented
6#24906306C211yesmaximal, characteristic, complemented
7#24906304C211yesmaximal, characteristic, complemented
8#24906292C211yesmaximal, characteristic, complemented
9C8×#13050580C211yesmaximal, characteristic, complemented
10C8×#13050578C211yesmaximal, characteristic, complemented
11#24906241C211yesmaximal, characteristic, complemented
12#24905923C211yesmaximal, characteristic, complemented
13#24905843C211yesmaximal, characteristic, complemented
14M16×C83⋊C8C211yesmaximal, characteristic, complemented
15C83×#2969C211yesmaximal, characteristic, complemented
16C4×#13050590C2211yescharacteristic
17#19128039C411yescharacteristic
18#19128022C411yescharacteristic
19#19128005C411yescharacteristic
20#19127998C411yescharacteristic
21#19127920C411yescharacteristic
22#19127913C411yescharacteristic
23#19127861C411yescharacteristic
24#19127844C411yescharacteristic
25C8×Dic166C2211yescharacteristic
26C8×Dic166C2211yescharacteristic
27C4×#13050580C2211yescharacteristic
28C4×#13050577C2211yescharacteristic
29C4×#13050578C2211yescharacteristic
30C4×#13050575C2211yescharacteristic
31#19127780C2211yescharacteristic
32#19127780C2211yescharacteristic
33#19127777—21no—
34#19127777—21no—
35#19127758C2211yescharacteristic
36#19127756—21no—
37#19127754C2211yescharacteristic
38#19127653—21no—
39C2×C4×C83⋊C8C2211yescharacteristic
40#19127453C2211yescharacteristic
41#19127453C2211yescharacteristic
42#19127451C2211yescharacteristic
43#19127451C2211yescharacteristic
44Q8⋊(C83⋊C8)C2211yescharacteristic
45Q8⋊(C83⋊C8)C2211yescharacteristic
46#19127431C2211yescharacteristic
47#19127431C2211yescharacteristic
48D4⋊(C83⋊C8)C2211yescharacteristic
49D4⋊(C83⋊C8)C2211yescharacteristic
50#19127428C2211yescharacteristic
51#19127428C2211yescharacteristic
52#19127422C2211yescharacteristic
53#19127422C2211yescharacteristic
54C8×C83⋊C8C2211yescharacteristic
55C8×C83⋊C8C2211yescharacteristic
56#529×C83C2211yescharacteristic
57#446×C83C2211yescharacteristic
58C8×Q8×C83C2211yescharacteristic
59#436×C83—21no—
60#436×C83C2211yescharacteristic
61#435×C83—21no—
62C8×D4×C83C2211yescharacteristic
63#433×C83—21no—
64#431×C83C2211yescharacteristic
65#405×C83—21no—
66C4×M16×C83C2211yescharacteristic
67C2×#13050590C2×C411yescharacteristic
68C2×#13050580C2×C411yescharacteristic
69C2×#13050578C2×C411yescharacteristic
70C2×#13050577C2×C411yescharacteristic
71C2×#13050575C2×C411yescharacteristic
72C2×#13050573—21no—
73C2×#13050573—21no—
74C22×C83⋊C8—21no—
75C4×Dic166C2×C411yescharacteristic
76C4×Dic166C2311yescharacteristic
77C4×D332C2×C411yescharacteristic
78C4×D332C2311yescharacteristic
79C4×C22⋊D83—21no—
80C4×C22⋊D83—21no—
81#14581751C2×C411yescharacteristic
82#14581749—21no—
83C42×D83—21no—
84#14581725C2×C411yescharacteristic
85#14581725C2×C411yescharacteristic
86#14581723C2×C411yescharacteristic
87#14581723C2×C411yescharacteristic
88C4⋊(C83⋊C8)C2×C411yescharacteristic
89C4⋊(C83⋊C8)C2×C411yescharacteristic
90C4⋊(C83⋊C8)C2311yescharacteristic
91C4⋊(C83⋊C8)C2311yescharacteristic
92Dic83⋊C8—21no—
93Dic83⋊C8—21no—
94#14581716C2×C411yescharacteristic
95#14581716C2×C411yescharacteristic
96#14581715C2×C411yescharacteristic
97#14581715C2×C411yescharacteristic
98#14581713C2×C411yescharacteristic
99#14581713C2×C411yescharacteristic
100#14581712C2×C411yescharacteristic
101#14581712C2×C411yescharacteristic
102C22⋊(C83⋊C8)—21no—
103C22⋊(C83⋊C8)C2×C411yescharacteristic
104C22⋊(C83⋊C8)C2×C411yescharacteristic
105(C2×D83)⋊C8—21no—
106(C2×D83)⋊C8—21no—
107#14581703—21no—
108C4×C83⋊C8—21no—
109C4×C83⋊C8C2311yescharacteristic
110C4×C83⋊C8C2311yescharacteristic
111C4×C83⋊C8C2311yescharacteristic
112C4×C83⋊C8C2311yescharacteristic
113C8×Dic83—21no—
114C8×Dic83—21no—
115C2×M16×C83—21no—
116C2×M16×C83D411yescharacteristic
117C2×M16×C83D411yescharacteristic
118C22×C8×C83—21no—
119#126×C83—21no—
120#125×C83C2×C411yescharacteristic
121#124×C83C2×C411yescharacteristic
122#123×C83—21no—
123C22⋊Q8×C83C2×C411yescharacteristic
124#121×C83C2×C411yescharacteristic
125C4×Q8×C83C2311yescharacteristic
126C4×D4×C83—21no—
127C4×D4×C83C2311yescharacteristic
128#117×C83—21no—
129C2×C42×C83C2311yescharacteristic
130C4⋊C8×C83—21no—
131C4⋊C8×C83—21no—
132C4⋊C8×C83C2311yescharacteristic
133C4⋊C8×C83C2311yescharacteristic
134C22⋊C8×C83—21no—
135C22⋊C8×C83—21no—
136C22⋊C8×C83—21no—
137#97×C83—21no—
138#97×C83D411yescharacteristic
139#97×C83D411yescharacteristic
140C4×C8×C83—21no—
141C4×C8×C83—21no—
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#13050590—22no—
145#13050590—41no—
146C2×Dic166C22×C411yescharacteristic
147C2×D332C22×C411yescharacteristic
148C2×C22⋊D83—21no—
149C2×C4×D83—21no—
150C2×C4×D83—21no—
151C2×C4×D83—21no—
152#13050580—22no—
153#13050578—22no—
154#13050577—41no—
155#13050575—41no—
156#13050573—42no—
157#13050573—42no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8—21no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8—42no—
163C2×C83⋊C8C22×C411yescharacteristic
164C2×C83⋊C8C22×C411yescharacteristic
165C2×C83⋊C8C22×C411yescharacteristic
166C2×C83⋊C8C22×C411yescharacteristic
167C4⋊Dic83C22×C411yescharacteristic
168C4⋊Dic83C22×C411yescharacteristic
169Dic83⋊C4—21no—
170Dic83⋊C4—21no—
171C22⋊Dic83—21no—
172(C2×D83)⋊C4—21no—
173(C2×D83)⋊C4—21no—
174C4×Dic83—21no—
175C4×Dic83—21no—
176C4×Dic83—21no—
177C2×Q8×C83C22×C411yescharacteristic
178C2×D4×C83—21no—
179C2×D4×C83C22×C411yescharacteristic
180C22×C4×C83—21no—
181C22×C4×C83C22×C411yescharacteristic
182C22×C4×C83C2×D411yescharacteristic
183C22×C4×C83#4111yescharacteristic
184M16×C83—22no—
185M16×C83—22no—
186M16×C83—42no—
187C2×C8×C83—21no—
188C2×C8×C83—21no—
189C2×C8×C83—42no—
190C2×C8×C83C2×D411yescharacteristic
191C2×C8×C83C2×D411yescharacteristic
192C2×C8×C83C2×D411yescharacteristic
193C2×C8×C83C2×D411yescharacteristic
194C4⋊C4×C83—21no—
195C4⋊C4×C83—21no—
196C4⋊C4×C83—21no—
197C4⋊C4×C83—21no—
198C4⋊C4×C83C22×C411yescharacteristic
199C4⋊C4×C83C22×C411yescharacteristic
200C22⋊C4×C83—21no—
201C22⋊C4×C83—21no—
202C22⋊C4×C83—21no—
203C22⋊C4×C83—21no—
204C22⋊C4×C83—21no—
205C42×C83—21no—
206C42×C83C22×C411yescharacteristic
207C42×C83C2×D411yescharacteristic
208C42×C83#4111yescharacteristic
209C42×C83C2411yescharacteristic
210C23×C83—21no—
211C23×C83C4×D411yescharacteristic
212C22×D83—21no—
213Q8×C83—21no—
214Q8×C83—21no—
215D4×C83—21no—
216D4×C83—21no—
217D4×C83—81no—
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—41no—
227C2×C4×C83—41no—
228C2×C4×C83C4×D411yescharacteristic
229C2×C4×C83C4×D411yescharacteristic
230C2×C4×C83C4×D411yescharacteristic
231C2×C4×C83C23×C411yescharacteristic
232C2×C4×C83C22×D411yescharacteristic
233C2×C4×C83C2×#4111yescharacteristic
234C22⋊D83—42no—
235C2×Dic83—21no—
236C2×Dic83—21no—
237C2×Dic83—21no—
238D332—21no—
239D332—21no—
240C4×D83—42no—
241C4×D83—41no—
242C4×D83—41no—
243C4×D83—81no—
244Dic166—21no—
245Dic166#13112yes—
246C8×C83—21no—
247C8×C83—21no—
248C8×C83—41no—
249C8×C83—41no—
250C8×C83#13512yes—
251C8×C83#13512yes—
252C83⋊C8—22no—
253C83⋊C8—21no—
254C83⋊C8—21no—
255C83⋊C8—21no—
256C83⋊C8—21no—
257C83⋊C8—41no—
258C83⋊C8—41no—
259C83⋊C8—41no—
260C22×C83—21no—
261C22×C83—21no—
262C22×C83—21no—
263C22×C83—41no—
264C22×C83—41no—
265C22×C83—41no—
266C22×C83C2×C4×D411yescharacteristic
267C2×D83—41no—
268C2×D83—41no—
269C2×D83—41no—
270C4×C83—21no—
271C4×C83—21no—
272C4×C83—21no—
273C4×C83—21no—
274C4×C83—41no—
275C4×C83—41no—
276C4×C83—41no—
277C4×C83C2×#13111yescharacteristic
278C4×C83#56811yescharacteristic
279C4×C83C2×#13511yescharacteristic
280C4×C83C2×#13511yescharacteristic
281Dic83—22no—
282Dic83—41no—
283Dic83—41no—
284#17999—831nomaximal, Sylow
285C2×C83—41no—
286C2×C83—81no—
287C2×C83#293311yescharacteristic
288C2×C83C4×#13511yescharacteristic
289C2×C83#295611yescharacteristic
290D83—81no—
291#3102—831no—
292#2971—831no—
293#2969D8311yescharacteristic, complemented
294#1590—831no—
295#1589—831no—
296#1584—831no—
297#1583—831no—
298#1583—831no—
299#1581—831no—
300C8×Q16—831no—
301C8×SD16—831no—
302#1572—831no—
303#1494—831no—
304#1476—831no—
305C8×M16—831no—
306C83#1799911yescharacteristic, complemented, Sylow
307#529C2×D8311yescharacteristic
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#446C2×D8311yescharacteristic
318C8×Q8—831no—
319C8×Q8—831no—
320C8×Q8C2×D8311yescharacteristic
321C4×Q16—831no—
322C4×SD16—831no—
323C4×SD16—831no—
324C4×D8—831no—
325#436—21no—
326#436—831no—
327#436—831no—
328#436—1661no—
329#436—1661no—
330#436C2×D8311yescharacteristic
331#435—21no—
332C8×D4C2×D8311yescharacteristic
333#433—21no—
334#432—831no—
335#432—1661no—
336#431—831no—
337#431C2×D8311yescharacteristic
338#405—21no—
339C4×M16—1661no—
340C4×M16C2×D8311yescharacteristic
341C2×C4×C8—831no—
342#335—831no—
343#335—831no—
344#334—831no—
345#334—831no—
346Q8⋊C8—831no—
347Q8⋊C8—831no—
348Q8⋊C8—831no—
349Q8⋊C8—831no—
350D4⋊C8—831no—
351D4⋊C8—831no—
352D4⋊C8—831no—
353D4⋊C8—831no—
354#322—831no—
355#322—831no—
356C82—831no—
357C82—831no—
358C2×#41—831no—
359C2×Q16—831no—
360C2×SD16—831no—
361C2×SD16—831no—
362C2×D8—831no—
363C2×M16—21no—
364C2×M16—1661no—
365C2×M16—1661no—
366C2×M16C22⋊D8311yescharacteristic
367C2×M16C22⋊D8311yescharacteristic
368C22×C8—21no—
369C22×C8—1661no—
370#126—21no—
371#125C4×D8311yescharacteristic
372#124C4×D8311yescharacteristic
373#123—21no—
374C22⋊Q8C4×D8311yescharacteristic
375#121C4×D8311yescharacteristic
376C4×Q8—831no—
377C4×Q8—831no—
378C4×Q8C22×D8311yescharacteristic
379C4×D4—21no—
380C4×D4—831no—
381C4×D4—831no—
382C4×D4—1661no—
383C4×D4—1661no—
384C4×D4C22×D8311yescharacteristic
385#117—21no—
386#117—831no—
387#117—1661no—
388C2×C42—1661no—
389C2×C42C22×D8311yescharacteristic
390#107—831no—
391#107—831no—
392#106—831no—
393#106—831no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—831no—
397C4⋊C8—831no—
398C4⋊C8—831no—
399C4⋊C8—831no—
400C4⋊C8—1661no—
401C4⋊C8—1661no—
402C4⋊C8C22×D8311yescharacteristic
403C4⋊C8C22×D8311yescharacteristic
404#103—831no—
405#103—831no—
406#103—831no—
407#103—831no—
408#102—831no—
409#102—831no—
410#102—831no—
411#102—831no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—831no—
416C22⋊C8—831no—
417C22⋊C8—1661no—
418C22⋊C8—1661no—
419C22⋊C8—1661no—
420#97—21no—
421#97—1661no—
422#97C22⋊D8311yescharacteristic
423#97C22⋊D8311yescharacteristic
424C4×C8—21no—
425C4×C8—21no—
426C4×C8—831no—
427C4×C8—831no—
428C4×C8—831no—
429C4×C8—831no—
430C4×C8—1661no—
431C4×C8—1661no—
432C4×C8—1661no—
433C4×C8C22×D8311yescharacteristic
434C4×C8C22×D8311yescharacteristic
435#41—3321no—
436#41—1662no—
437C2×Q8—831no—
438C2×Q8C2×C4×D8311yescharacteristic
439C2×D4—21no—
440C2×D4—831no—
441C2×D4—1661no—
442C2×D4C2×C4×D8311yescharacteristic
443C22×C4—21no—
444C22×C4—1661no—
445C22×C4—1661no—
446C22×C4—1661no—
447C22×C4C2×C4×D8311yescharacteristic
448C22×C4C2×C22⋊D8311yescharacteristic
449C22×C4#1305059011yescharacteristic
450Q16—1662no—
451SD16—3321no—
452SD16—1662no—
453D8—3321no—
454M16—22no—
455M16—22no—
456M16—42no—
457M16—3322no—
458M16—3322no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—42no—
462C2×C8—3322no—
463C2×C8—831no—
464C2×C8—831no—
465C2×C8—831no—
466C2×C8—831no—
467C2×C8—1661no—
468C2×C8—1661no—
469C2×C8—1661no—
470C2×C8—1661no—
471C2×C8C2×C22⋊D8311yescharacteristic
472C2×C8C2×C22⋊D8311yescharacteristic
473C2×C8C2×C22⋊D8311yescharacteristic
474C2×C8C2×C22⋊D8311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—831no—
480C4⋊C4—831no—
481C4⋊C4—1661no—
482C4⋊C4—1661no—
483C4⋊C4C2×C4×D8311yescharacteristic
484C4⋊C4C2×C4×D8311yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—1661no—
491C22⋊C4—1661no—
492C22⋊C4—1661no—
493C42—21no—
494C42—1661no—
495C42—1661no—
496C42—1661no—
497C42C2×C4×D8311yescharacteristic
498C42C2×C22⋊D8311yescharacteristic
499C42#1305059011yescharacteristic
500C42C23×D8311yescharacteristic
501C23—21no—
502C23—1661no—
503C23C4×C22⋊D8311yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—832no—
507Q8—1661no—
508D4—21no—
509D4—21no—
510D4—81no—
511D4—3322no—
512D4—1661no—
513D4—1661no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—3322no—
525C2×C4—3321no—
526C2×C4—3321no—
527C2×C4—6641no—
528C2×C4—1661no—
529C2×C4—1661no—
530C2×C4—1661no—
531C2×C4C4×C22⋊D8311yescharacteristic
532C2×C4C4×C22⋊D8311yescharacteristic
533C2×C4C4×C22⋊D8311yescharacteristic
534C2×C4C22×C4×D8311yescharacteristic
535C2×C4C22×C22⋊D8311yescharacteristic
536C2×C4C2×#1305059011yescharacteristic
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—3321no—
542C8—3321no—
543C8—3321no—
544C8—1662no—
545C8—1661no—
546C8—1661no—
547C8—1661no—
548C8—1661no—
549C8#1458181212yes—
550C8#1458181212yes—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—3321no—
558C22—3321no—
559C22—3321no—
560C22C2×C4×C22⋊D8311yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—3321no—
569C4—3321no—
570C4—1662no—
571C4#131×D8311yescharacteristic
572C4#1912846611yescharacteristic
573C4C2×#1458181211yescharacteristic
574C4C2×#1458181211yescharacteristic
575C2—41no—
576C2—81no—
577C2—6641no—
578C2#2491618511yescharacteristic
579C2C4×#1458181211yescharacteristic
580C2#2491637011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#2969C2
socleC22×C83C2×C4×D4
prime radical#19127844C4
cosocleC42×C83C24
hypercenter#2969D83
hypocenterC83#17999
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. #24916481C2semidirect
3. #24906353C2semidirect
4. #24906346C2semidirect
5. #24906311C2semidirect
6. #24906306C2semidirect
7. #24906304C2semidirect
8. #24906292C2semidirect
9. C8×#13050580C2semidirect
10. C8×#13050578C2semidirect
11. #24906241C2semidirect
12. #24905923C2semidirect
13. #24905843C2semidirect
14. M16×C83⋊C8C2semidirect
15. C83×#2969C2semidirect
293. #2969D83semidirect
306. C83#17999semidirect

Maximal subgroups

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

subgroupindex
#249174752
#249164812
#249063532
#249063462
#249063112
#249063062
#249063042
#249062922
C8×#130505802
C8×#130505782
#249062412
#249059232
#249058432
M16×C83⋊C82
C83×#29692
#1799983