Finite Group Databasebeta

← #35376258

Subgroups — #35376258

Order 21248.

656 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918052C211yesmaximal, characteristic
2#24916467C211yesmaximal, characteristic, complemented
3#24906375C211yesmaximal, characteristic, complemented
4#24906351C211yesmaximal, characteristic, complemented
5#24906339C211yesmaximal, characteristic, complemented
6#24906327C211yesmaximal, characteristic, complemented
7#24906299C211yesmaximal, characteristic, complemented
8#24906290C211yesmaximal, characteristic, complemented
9#24906275C211yesmaximal, characteristic, complemented
10C8×#13050575C211yesmaximal, characteristic, complemented
11#24906213C211yesmaximal, characteristic, complemented
12#24905880C211yesmaximal, characteristic, complemented
13#24905874C211yesmaximal, characteristic, complemented
14#24905766C211yesmaximal, characteristic, complemented
15C83×#2935C211yesmaximal, characteristic, complemented
16#19128235C2211yescharacteristic
17#19128107C411yescharacteristic
18#19128088C411yescharacteristic
19#19128065C411yescharacteristic
20#19128063C411yescharacteristic
21#19127952C411yescharacteristic
22#19127952C411yescharacteristic
23#19127945C411yescharacteristic
24#19127945C411yescharacteristic
25#19127831C2211yescharacteristic
26C8×Dic166C2211yescharacteristic
27C4×#13050578C2211yescharacteristic
28C4×#13050578C2211yescharacteristic
29C4×#13050575C2211yescharacteristic
30C4×#13050575C2211yescharacteristic
31#19127780C2211yescharacteristic
32#19127777—21no—
33#19127770—21no—
34C8×D332C2211yescharacteristic
35#19127763—21no—
36#19127754C2211yescharacteristic
37#19127658—21no—
38C4×#13050574C2211yescharacteristic
39C4×#13050574C2211yescharacteristic
40#19127453C2211yescharacteristic
41#19127453C2211yescharacteristic
42#19127451C2211yescharacteristic
43#19127451C2211yescharacteristic
44#19127431C2211yescharacteristic
45#19127431C2211yescharacteristic
46D4⋊(C83⋊C8)C2211yescharacteristic
47D4⋊(C83⋊C8)C2211yescharacteristic
48D4⋊(C83⋊C8)C2211yescharacteristic
49D4⋊(C83⋊C8)C2211yescharacteristic
50#19127428C2211yescharacteristic
51#19127428C2211yescharacteristic
52#19127423C2211yescharacteristic
53#19127423C2211yescharacteristic
54#19127422C2211yescharacteristic
55C8×C83⋊C8C2211yescharacteristic
56C2×#131×C83—21no—
57#532×C83C2211yescharacteristic
58#436×C83C2211yescharacteristic
59#436×C83C2211yescharacteristic
60#435×C83—21no—
61#435×C83—21no—
62C8×D4×C83C2211yescharacteristic
63C8×D4×C83C2211yescharacteristic
64C2×C4⋊C8×C83C2211yescharacteristic
65#408×C83—21no—
66C4×M16×C83C2211yescharacteristic
67C2×#13050578C2×C411yescharacteristic
68C2×#13050578C2×C411yescharacteristic
69C2×#13050575C2×C411yescharacteristic
70C2×#13050575C2×C411yescharacteristic
71C2×#13050574—21no—
72C2×#13050574C2×C411yescharacteristic
73C2×#13050574C2×C411yescharacteristic
74C2×#13050573—21no—
75C2×C8×D83—21no—
76#14581786—21no—
77#14581784C2×C411yescharacteristic
78#14581780C2×C411yescharacteristic
79#14581775—21no—
80#14581771C2×C411yescharacteristic
81#14581766C2×C411yescharacteristic
82C4×Dic166C2311yescharacteristic
83C4×D332C2311yescharacteristic
84C4×C22⋊D83—21no—
85#14581749—21no—
86#14581725C2×C411yescharacteristic
87#14581725C2×C411yescharacteristic
88#14581723C2×C411yescharacteristic
89#14581723C2×C411yescharacteristic
90C4⋊(C83⋊C8)C2311yescharacteristic
91C4⋊(C83⋊C8)C2311yescharacteristic
92Dic83⋊C8—21no—
93Dic83⋊C8—21no—
94#14581715C2×C411yescharacteristic
95#14581715C2×C411yescharacteristic
96#14581713C2×C411yescharacteristic
97#14581713C2×C411yescharacteristic
98#14581713C2×C411yescharacteristic
99#14581713C2×C411yescharacteristic
100#14581712C2×C411yescharacteristic
101#14581712C2×C411yescharacteristic
102C22⋊(C83⋊C8)—21no—
103(C2×D83)⋊C8—21no—
104(C2×D83)⋊C8—21no—
105#14581703—21no—
106#14581703C2×C411yescharacteristic
107#14581703C2×C411yescharacteristic
108#14581702—21no—
109C4×C83⋊C8—21no—
110C4×C83⋊C8C2311yescharacteristic
111C4×C83⋊C8C2311yescharacteristic
112C4×C83⋊C8C2311yescharacteristic
113C4×C83⋊C8C2311yescharacteristic
114C8×Dic83—21no—
115C2×#41×C83—21no—
116#131×C83—44no—
117C2×M16×C83—21no—
118C2×M16×C83—21no—
119C2×M16×C83D411yescharacteristic
120C2×M16×C83D411yescharacteristic
121C22×C8×C83—21no—
122C22×C8×C83—21no—
123C22×C8×C83—21no—
124C4⋊Q8×C83C2×C411yescharacteristic
125#127×C83C2×C411yescharacteristic
126#124×C83—21no—
127#121×C83—21no—
128#121×C83C2×C411yescharacteristic
129#121×C83C2×C411yescharacteristic
130C4×D4×C83—21no—
131C4×D4×C83C2311yescharacteristic
132C4×D4×C83C2311yescharacteristic
133C2×C42×C83C2311yescharacteristic
134C4⋊C8×C83—21no—
135C4⋊C8×C83C2311yescharacteristic
136C4⋊C8×C83C2311yescharacteristic
137C22⋊C8×C83—21no—
138C22⋊C8×C83—21no—
139C22⋊C8×C83—21no—
140C22⋊C8×C83—21no—
141#97×C83D411yescharacteristic
142#97×C83D411yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C4×C8×C83C2311yescharacteristic
145C2×Dic166C22×C411yescharacteristic
146C2×D332C22×C411yescharacteristic
147C2×C22⋊D83—21no—
148C2×C4×D83—21no—
149#13050578—22no—
150#13050578—41no—
151#13050575—22no—
152#13050575—41no—
153#13050574—22no—
154#13050574—41no—
155#13050574—42no—
156#13050573—42no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8—21no—
161C2×C83⋊C8C22×C411yescharacteristic
162C2×C83⋊C8C22×C411yescharacteristic
163C2×C83⋊C8C22×C411yescharacteristic
164C2×C83⋊C8C22×C411yescharacteristic
165C8×D83—42no—
166C4⋊Dic83C22×C411yescharacteristic
167C4⋊Dic83C22×C411yescharacteristic
168Dic83⋊C4—21no—
169Dic83⋊C4—21no—
170Dic83⋊C4—21no—
171Dic83⋊C4—21no—
172C22⋊Dic83—21no—
173(C2×D83)⋊C4—21no—
174(C2×D83)⋊C4—21no—
175(C2×D83)⋊C4—21no—
176(C2×D83)⋊C4—21no—
177C4×Dic83—21no—
178#41×C83—42no—
179#41×C83—42no—
180C2×Q8×C83—21no—
181C2×D4×C83—21no—
182C2×D4×C83—21no—
183C2×D4×C83—21no—
184C2×D4×C83—21no—
185C2×D4×C83C22×C411yescharacteristic
186C2×D4×C83C22×C411yescharacteristic
187C22×C4×C83—21no—
188C22×C4×C83—21no—
189C22×C4×C83C22×C411yescharacteristic
190C22×C4×C83C2×D411yescharacteristic
191C22×C4×C83#4111yescharacteristic
192M16×C83—22no—
193M16×C83—41no—
194M16×C83—42no—
195M16×C83—42no—
196C2×C8×C83—21no—
197C2×C8×C83—21no—
198C2×C8×C83—42no—
199C2×C8×C83—42no—
200C2×C8×C83—42no—
201C2×C8×C83C2×D411yescharacteristic
202C2×C8×C83C2×D411yescharacteristic
203C2×C8×C83C2×D411yescharacteristic
204C2×C8×C83C2×D411yescharacteristic
205C4⋊C4×C83—21no—
206C4⋊C4×C83C22×C411yescharacteristic
207C4⋊C4×C83C22×C411yescharacteristic
208C22⋊C4×C83—21no—
209C22⋊C4×C83—21no—
210C22⋊C4×C83—21no—
211C22⋊C4×C83—21no—
212C42×C83C22×C411yescharacteristic
213C42×C83C2×D411yescharacteristic
214C42×C83#4111yescharacteristic
215C42×C83C2411yescharacteristic
216C23×C83—21no—
217C23×C83—21no—
218C23×C83C4×D411yescharacteristic
219C22×D83—21no—
220Q8×C83—42no—
221D4×C83—21no—
222D4×C83—21no—
223D4×C83—21no—
224D4×C83—21no—
225D4×C83—42no—
226D4×C83—42no—
227D4×C83—42no—
228D4×C83—81no—
229C2×C4×C83—21no—
230C2×C4×C83—21no—
231C2×C4×C83—21no—
232C2×C4×C83—21no—
233C2×C4×C83—21no—
234C2×C4×C83—21no—
235C2×C4×C83—41no—
236C2×C4×C83—41no—
237C2×C4×C83—41no—
238C2×C4×C83—41no—
239C2×C4×C83—41no—
240C2×C4×C83C4×D411yescharacteristic
241C2×C4×C83C4×D411yescharacteristic
242C2×C4×C83C4×D411yescharacteristic
243C2×C4×C83C23×C411yescharacteristic
244C2×C4×C83C22×D411yescharacteristic
245C2×C4×C83C2×#4111yescharacteristic
246C22⋊D83—81no—
247C2×Dic83—21no—
248C2×Dic83—21no—
249C2×Dic83—21no—
250D332—21no—
251D332—21no—
252C4×D83—41no—
253C4×D83—41no—
254Dic166—21no—
255Dic166—21no—
256C8×C83—21no—
257C8×C83—21no—
258C8×C83—21no—
259C8×C83—41no—
260C8×C83—41no—
261C8×C83AGL(1,ℤ/8)12yes—
262C83⋊C8—22no—
263C83⋊C8—21no—
264C83⋊C8—21no—
265C83⋊C8—21no—
266C83⋊C8—41no—
267C83⋊C8—41no—
268C83⋊C8—41no—
269C83⋊C8#13112yescomplemented
270C22×C83—21no—
271C22×C83—21no—
272C22×C83—21no—
273C22×C83—41no—
274C22×C83—41no—
275C22×C83—41no—
276C22×C83—41no—
277C22×C83—41no—
278C22×C83—41no—
279C22×C83C2×C4×D411yescharacteristic
280C2×D83—41no—
281C2×D83—41no—
282C2×D83—41no—
283C4×C83—21no—
284C4×C83—21no—
285C4×C83—21no—
286C4×C83—21no—
287C4×C83—41no—
288C4×C83—41no—
289C4×C83C2×#13111yescharacteristic
290C4×C83#56811yescharacteristic
291C4×C83C2×AGL(1,ℤ/8)11yescharacteristic
292C4×C83#57511yescharacteristic
293Dic83—41no—
294Dic83—41no—
295Dic83—41no—
296#18076—831nomaximal, Sylow
297C2×C83—41no—
298C2×C83—81no—
299C2×C83—81no—
300C2×C83#293511yescharacteristic
301C2×C83C4×AGL(1,ℤ/8)11yescharacteristic
302C2×C83#295611yescharacteristic
303D83—81no—
304#3171—831no—
305#2969—831no—
306#2935D8311yescharacteristic, complemented
307#1594—831no—
308#1590—831no—
309#1588—831no—
310#1586—831no—
311#1582—831no—
312#1581—831no—
313SD16⋊C8—831no—
314C8×D8—831no—
315#1565—831no—
316#1484—831no—
317#1483—831no—
318#1455—831no—
319C83#1807611yescharacteristic, complemented, Sylow
320C2×#131—21no—
321#532C2×D8311yescharacteristic
322#529—831no—
323#501—831no—
324#496—831no—
325#490—831no—
326#489—831no—
327#469—831no—
328#469—831no—
329#468—831no—
330#468—831no—
331#446—831no—
332C8×Q8—831no—
333C4×SD16—831no—
334C4×SD16—831no—
335C4×D8—831no—
336C4×D8—831no—
337#436—831no—
338#436—1661no—
339#436C2×D8311yescharacteristic
340#436C2×D8311yescharacteristic
341#435—21no—
342#435—21no—
343#435—1661no—
344C8×D4—831no—
345C8×D4C2×D8311yescharacteristic
346C8×D4C2×D8311yescharacteristic
347#433—1661no—
348#431—831no—
349C2×C4⋊C8C2×D8311yescharacteristic
350#408—21no—
351#405—1661no—
352C4×M16—831no—
353C4×M16—831no—
354C4×M16C2×D8311yescharacteristic
355#335—831no—
356#335—831no—
357#334—831no—
358#334—831no—
359Q8⋊C8—831no—
360Q8⋊C8—831no—
361D4⋊C8—831no—
362D4⋊C8—831no—
363D4⋊C8—831no—
364D4⋊C8—831no—
365D4⋊C8—831no—
366D4⋊C8—831no—
367#322—831no—
368#322—831no—
369#322—831no—
370C82—831no—
371C2×#41—21no—
372C2×SD16—831no—
373C2×SD16—831no—
374C2×D8—831no—
375C2×D8—831no—
376#131—44no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—831no—
380C2×M16—831no—
381C2×M16—1661no—
382C2×M16—1661no—
383C2×M16C22⋊D8311yescharacteristic
384C2×M16C22⋊D8311yescharacteristic
385C22×C8—21no—
386C22×C8—21no—
387C22×C8—21no—
388C22×C8—1661no—
389C4⋊Q8C4×D8311yescharacteristic
390#127C4×D8311yescharacteristic
391#126—1661no—
392#125—831no—
393#124—21no—
394#124—831no—
395#123—1661no—
396C22⋊Q8—831no—
397#121—21no—
398#121—831no—
399#121C4×D8311yescharacteristic
400#121C4×D8311yescharacteristic
401C4×Q8—831no—
402C4×D4—21no—
403C4×D4—831no—
404C4×D4—1661no—
405C4×D4C22×D8311yescharacteristic
406C4×D4C22×D8311yescharacteristic
407#117—1661no—
408C2×C42C22×D8311yescharacteristic
409#107—831no—
410#107—831no—
411#106—831no—
412#106—831no—
413C4⋊C8—21no—
414C4⋊C8—831no—
415C4⋊C8—831no—
416C4⋊C8—1661no—
417C4⋊C8—1661no—
418C4⋊C8C22×D8311yescharacteristic
419C4⋊C8C22×D8311yescharacteristic
420#103—831no—
421#103—831no—
422#102—831no—
423#102—831no—
424#102—831no—
425#102—831no—
426#102—831no—
427#102—831no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8—1661no—
433C22⋊C8—1661no—
434C22⋊C8—1661no—
435#97—831no—
436#97—831no—
437#97—1661no—
438#97—1661no—
439#97C22⋊D8311yescharacteristic
440#97C22⋊D8311yescharacteristic
441C4×C8—831no—
442C4×C8—831no—
443C4×C8—831no—
444C4×C8—831no—
445C4×C8—1661no—
446C4×C8—1661no—
447C4×C8C22×D8311yescharacteristic
448C4×C8C22×D8311yescharacteristic
449#41—42no—
450#41—42no—
451C2×Q8—21no—
452C2×Q8—831no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—831no—
458C2×D4—1661no—
459C2×D4C2×C4×D8311yescharacteristic
460C2×D4C2×C4×D8311yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—1661no—
464C22×C4C2×C4×D8311yescharacteristic
465C22×C4C2×C22⋊D8311yescharacteristic
466C22×C4#1305059011yescharacteristic
467SD16—3321no—
468SD16—1662no—
469D8—3321no—
470D8—1662no—
471M16—22no—
472M16—41no—
473M16—42no—
474M16—42no—
475M16—3322no—
476M16—3322no—
477M16—3321no—
478M16—1662no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—42no—
482C2×C8—42no—
483C2×C8—42no—
484C2×C8—3322no—
485C2×C8—831no—
486C2×C8—831no—
487C2×C8—831no—
488C2×C8—831no—
489C2×C8—1661no—
490C2×C8—1661no—
491C2×C8—1661no—
492C2×C8—1661no—
493C2×C8C2×C22⋊D8311yescharacteristic
494C2×C8C2×C22⋊D8311yescharacteristic
495C2×C8C2×C22⋊D8311yescharacteristic
496C2×C8C2×C22⋊D8311yescharacteristic
497C4⋊C4—21no—
498C4⋊C4—831no—
499C4⋊C4—831no—
500C4⋊C4—1661no—
501C4⋊C4—1661no—
502C4⋊C4—1661no—
503C4⋊C4—1661no—
504C4⋊C4C2×C4×D8311yescharacteristic
505C4⋊C4C2×C4×D8311yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—1661no—
511C22⋊C4—1661no—
512C22⋊C4—1661no—
513C22⋊C4—1661no—
514C22⋊C4—1661no—
515C42—1661no—
516C42C2×C4×D8311yescharacteristic
517C42C2×C22⋊D8311yescharacteristic
518C42#1305059011yescharacteristic
519C42C23×D8311yescharacteristic
520C23—21no—
521C23—21no—
522C23—1661no—
523C23C4×C22⋊D8311yescharacteristic
524Q8—42no—
525Q8—1661no—
526Q8—1661no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—42no—
532D4—42no—
533D4—42no—
534D4—81no—
535D4—6641no—
536D4—1661no—
537D4—1661no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—3321no—
550C2×C4—3321no—
551C2×C4—1661no—
552C2×C4—1661no—
553C2×C4—1661no—
554C2×C4C4×C22⋊D8311yescharacteristic
555C2×C4C4×C22⋊D8311yescharacteristic
556C2×C4C4×C22⋊D8311yescharacteristic
557C2×C4C22×C4×D8311yescharacteristic
558C2×C4C22×C22⋊D8311yescharacteristic
559C2×C4C2×#1305059011yescharacteristic
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—3321no—
566C8—3321no—
567C8—3321no—
568C8—832no—
569C8—1662no—
570C8—1661no—
571C8—1661no—
572C8—1661no—
573C8#1458181812yes—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—3321no—
584C22—3321no—
585C22—3321no—
586C22C2×C4×C22⋊D8311yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—3321no—
594C4—3321no—
595C4—3321no—
596C4#131×D8311yescharacteristic
597C4#1912846611yescharacteristic
598C4C2×#1458181811yescharacteristic
599C4#1912849911yescharacteristic
600C2—41no—
601C2—81no—
602C2—81no—
603C2—6641no—
604C2#2491620511yescharacteristic
605C2C4×#1458181811yescharacteristic
606C2#2491637011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#2935C2
socleC22×C83C2×C4×D4
prime radical#24918052C2
cosocleC42×C83C24
hypercenter#2935D83
hypocenterC83#18076
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2935

Complements

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

NH ≅ G/Ntype
2. #24916467C2semidirect
3. #24906375C2semidirect
4. #24906351C2semidirect
5. #24906339C2semidirect
6. #24906327C2semidirect
7. #24906299C2semidirect
8. #24906290C2semidirect
9. #24906275C2semidirect
10. C8×#13050575C2semidirect
11. #24906213C2semidirect
12. #24905880C2semidirect
13. #24905874C2semidirect
14. #24905766C2semidirect
15. C83×#2935C2semidirect
269. C83⋊C8#131semidirect
306. #2935D83semidirect
319. C83#18076semidirect

Maximal subgroups

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

subgroupindex
#249180522
#249164672
#249063752
#249063512
#249063392
#249063272
#249062992
#249062902
#249062752
C8×#130505752
#249062132
#249058802
#249058742
#249057662
C83×#29352
#1807683