Finite Group Databasebeta

← #35375034

Subgroups — #35375034

Order 21248.

622 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918052C211yesmaximal, characteristic
2#24916614C211yesmaximal, characteristic, complemented
3#24906375C211yesmaximal, characteristic, complemented
4#24906365C211yesmaximal, characteristic, complemented
5#24906351C211yesmaximal, characteristic, complemented
6#24906346C211yesmaximal, characteristic, complemented
7#24906285C211yesmaximal, characteristic, complemented
8#24906275C211yesmaximal, characteristic, complemented
9C8×#13050578C211yesmaximal, characteristic, complemented
10C8×#13050575C211yesmaximal, characteristic, complemented
11#24906231C211yesmaximal, characteristic, complemented
12#24905921C211yesmaximal, characteristic, complemented
13#24905914C211yesmaximal, characteristic, complemented
14#24905744C211yesmaximal, characteristic, complemented
15C83×#2981C211yesmaximal, 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#19127776—21no—
33#19127775—21no—
34C8×D332C2211yescharacteristic
35#19127761—21no—
36#19127726—21no—
37#19127725C2211yescharacteristic
38C4×#13050574C2211yescharacteristic
39C2×C4×C83⋊C8C2211yescharacteristic
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
54C8×C83⋊C8C2211yescharacteristic
55C8×C83⋊C8C2211yescharacteristic
56#532×C83C2211yescharacteristic
57#436×C83C2211yescharacteristic
58#436×C83C2211yescharacteristic
59#435×C83—21no—
60#435×C83—21no—
61C8×D4×C83C2211yescharacteristic
62C8×D4×C83C2211yescharacteristic
63#432×C83C2211yescharacteristic
64#431×C83C2211yescharacteristic
65#408×C83—21no—
66#408×C83—21no—
67C2×#13050578C2×C411yescharacteristic
68C2×#13050578C2×C411yescharacteristic
69C2×#13050575C2×C411yescharacteristic
70C2×#13050575C2×C411yescharacteristic
71C2×#13050574—21no—
72C2×#13050574C2×C411yescharacteristic
73C2×#13050574C2×C411yescharacteristic
74C2×#13050573—21no—
75C22×C83⋊C8—21no—
76C2×C8×D83—21no—
77#14581786—21no—
78#14581784C2×C411yescharacteristic
79#14581780C2×C411yescharacteristic
80#14581775—21no—
81#14581771C2×C411yescharacteristic
82#14581766C2×C411yescharacteristic
83C4×Dic166C2311yescharacteristic
84C4×D332C2311yescharacteristic
85C4×C22⋊D83—21no—
86#14581749—21no—
87#14581725C2×C411yescharacteristic
88#14581725C2×C411yescharacteristic
89#14581723C2×C411yescharacteristic
90#14581723C2×C411yescharacteristic
91C4⋊(C83⋊C8)—21no—
92C4⋊(C83⋊C8)C2311yescharacteristic
93C4⋊(C83⋊C8)C2311yescharacteristic
94Dic83⋊C8—21no—
95Dic83⋊C8—21no—
96#14581715C2×C411yescharacteristic
97#14581715C2×C411yescharacteristic
98#14581713C2×C411yescharacteristic
99#14581713C2×C411yescharacteristic
100#14581713C2×C411yescharacteristic
101#14581713C2×C411yescharacteristic
102#14581712C2×C411yescharacteristic
103#14581712C2×C411yescharacteristic
104(C2×D83)⋊C8—21no—
105(C2×D83)⋊C8—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—
116C2×M16×C83—21no—
117C2×M16×C83—21no—
118C22×C8×C83—21no—
119C22×C8×C83—21no—
120C4⋊Q8×C83C2×C411yescharacteristic
121#127×C83C2×C411yescharacteristic
122#124×C83—21no—
123#121×C83—21no—
124#121×C83C2×C411yescharacteristic
125#121×C83C2×C411yescharacteristic
126C4×D4×C83—21no—
127C4×D4×C83C2311yescharacteristic
128C4×D4×C83C2311yescharacteristic
129C2×C42×C83C2311yescharacteristic
130C4⋊C8×C83D411yescharacteristic
131C4⋊C8×C83D411yescharacteristic
132C4⋊C8×C83C2311yescharacteristic
133C4⋊C8×C83C2311yescharacteristic
134C22⋊C8×C83—21no—
135C22⋊C8×C83—21no—
136C22⋊C8×C83—21no—
137C22⋊C8×C83—21no—
138C22⋊C8×C83—21no—
139C22⋊C8×C83D411yescharacteristic
140C22⋊C8×C83D411yescharacteristic
141#97×C83—21no—
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C2×Dic166C22×C411yescharacteristic
145C2×D332C22×C411yescharacteristic
146C2×C22⋊D83—21no—
147C2×C4×D83—21no—
148#13050578—22no—
149#13050578—22no—
150#13050575—22no—
151#13050575—22no—
152#13050574—22no—
153#13050574—22no—
154#13050574—81no—
155#13050573—81no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8—42no—
161C2×C83⋊C8C22×C411yescharacteristic
162C2×C83⋊C8C22×C411yescharacteristic
163C2×C83⋊C8C22×C411yescharacteristic
164C2×C83⋊C8C22×C411yescharacteristic
165C8×D83—81no—
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—81no—
179#41×C83—81no—
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—81no—
193M16×C83—81no—
194C2×C8×C83—21no—
195C2×C8×C83—21no—
196C2×C8×C83—81no—
197C2×C8×C83—81no—
198C2×C8×C83C2×D411yescharacteristic
199C2×C8×C83C2×D411yescharacteristic
200C2×C8×C83C2×D411yescharacteristic
201C2×C8×C83C2×D411yescharacteristic
202C4⋊C4×C83—21no—
203C4⋊C4×C83C22×C411yescharacteristic
204C4⋊C4×C83C22×C411yescharacteristic
205C22⋊C4×C83—21no—
206C22⋊C4×C83—21no—
207C22⋊C4×C83—21no—
208C22⋊C4×C83—21no—
209C42×C83C22×C411yescharacteristic
210C42×C83C2×D411yescharacteristic
211C42×C83#4111yescharacteristic
212C42×C83C2411yescharacteristic
213C23×C83—21no—
214C23×C83—21no—
215C23×C83C4×D411yescharacteristic
216C22×D83—21no—
217Q8×C83—81no—
218D4×C83—21no—
219D4×C83—21no—
220D4×C83—21no—
221D4×C83—21no—
222D4×C83—81no—
223D4×C83—81no—
224D4×C83—81no—
225D4×C83—81no—
226C2×C4×C83—21no—
227C2×C4×C83—21no—
228C2×C4×C83—21no—
229C2×C4×C83—21no—
230C2×C4×C83—21no—
231C2×C4×C83—21no—
232C2×C4×C83—41no—
233C2×C4×C83—41no—
234C2×C4×C83—41no—
235C2×C4×C83—41no—
236C2×C4×C83—41no—
237C2×C4×C83C4×D411yescharacteristic
238C2×C4×C83C4×D411yescharacteristic
239C2×C4×C83C4×D411yescharacteristic
240C2×C4×C83C23×C411yescharacteristic
241C2×C4×C83C22×D411yescharacteristic
242C2×C4×C83C2×#4111yescharacteristic
243C22⋊D83—81no—
244C2×Dic83—21no—
245C2×Dic83—21no—
246C2×Dic83—21no—
247D332—21no—
248D332—21no—
249C4×D83—41no—
250C4×D83—41no—
251Dic166—21no—
252Dic166—21no—
253C8×C83—21no—
254C8×C83—21no—
255C8×C83—21no—
256C8×C83—21no—
257C8×C83—41no—
258C8×C83—41no—
259C83⋊C8—22no—
260C83⋊C8—21no—
261C83⋊C8—21no—
262C83⋊C8—41no—
263C83⋊C8—41no—
264C83⋊C8—41no—
265C83⋊C8#13112yes—
266C83⋊C8#13112yes—
267C22×C83—21no—
268C22×C83—21no—
269C22×C83—21no—
270C22×C83—41no—
271C22×C83—41no—
272C22×C83—41no—
273C22×C83—41no—
274C22×C83—41no—
275C22×C83—41no—
276C22×C83C2×C4×D411yescharacteristic
277C2×D83—41no—
278C2×D83—41no—
279C2×D83—41no—
280C4×C83—21no—
281C4×C83—21no—
282C4×C83—21no—
283C4×C83—21no—
284C4×C83—41no—
285C4×C83—41no—
286C4×C83C2×#13111yescharacteristic
287C4×C83C2×#13111yescharacteristic
288C4×C83#57611yescharacteristic
289C4×C83#57711yescharacteristic
290Dic83—41no—
291Dic83—41no—
292Dic83—41no—
293#17968—831nomaximal, Sylow
294C2×C83—41no—
295C2×C83—81no—
296C2×C83—81no—
297C2×C83#293111yescharacteristic
298C2×C83#294611yescharacteristic
299C2×C83#295611yescharacteristic
300D83—81no—
301#3171—831no—
302#2993—831no—
303#2981D8311yescharacteristic, complemented
304#1594—831no—
305#1592—831no—
306#1590—831no—
307#1589—831no—
308#1580—831no—
309SD16⋊C8—831no—
310C8×SD16—831no—
311C8×D8—831no—
312#1569—831no—
313#1494—831no—
314#1492—831no—
315C8×M16—831no—
316C83#1796811yescharacteristic, complemented, Sylow
317#532C2×D8311yescharacteristic
318#529—831no—
319#501—831no—
320#496—831no—
321#490—831no—
322#489—831no—
323#469—831no—
324#469—831no—
325#468—831no—
326#468—831no—
327#446—831no—
328C8×Q8—831no—
329C4×SD16—831no—
330C4×SD16—831no—
331C4×D8—831no—
332C4×D8—831no—
333#436—831no—
334#436—1661no—
335#436C2×D8311yescharacteristic
336#436C2×D8311yescharacteristic
337#435—21no—
338#435—21no—
339#435—1661no—
340C8×D4—831no—
341C8×D4C2×D8311yescharacteristic
342C8×D4C2×D8311yescharacteristic
343#433—1661no—
344#432C2×D8311yescharacteristic
345#431C2×D8311yescharacteristic
346#424—1661no—
347#423—831no—
348#408—21no—
349#408—21no—
350C4×M16—831no—
351C2×C4×C8—831no—
352#335—831no—
353#335—831no—
354#334—831no—
355#334—831no—
356Q8⋊C8—831no—
357Q8⋊C8—831no—
358D4⋊C8—831no—
359D4⋊C8—831no—
360D4⋊C8—831no—
361D4⋊C8—831no—
362D4⋊C8—831no—
363D4⋊C8—831no—
364#322—831no—
365#322—831no—
366C82—831no—
367C82—831no—
368C2×#41—21no—
369C2×SD16—831no—
370C2×SD16—831no—
371C2×D8—831no—
372C2×D8—831no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—831no—
376C2×M16—831no—
377C2×M16—1661no—
378C2×M16—1661no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—1661no—
382C22×C8—1661no—
383C4⋊Q8C4×D8311yescharacteristic
384#127C4×D8311yescharacteristic
385#126—1661no—
386#125—831no—
387#124—21no—
388#124—831no—
389#123—1661no—
390C22⋊Q8—831no—
391#121—21no—
392#121—831no—
393#121C4×D8311yescharacteristic
394#121C4×D8311yescharacteristic
395C4×Q8—831no—
396C4×D4—21no—
397C4×D4—831no—
398C4×D4—1661no—
399C4×D4C22×D8311yescharacteristic
400C4×D4C22×D8311yescharacteristic
401#117—1661no—
402C2×C42C22×D8311yescharacteristic
403#107—831no—
404#107—831no—
405#106—831no—
406#106—831no—
407C4⋊C8—831no—
408C4⋊C8—831no—
409C4⋊C8—1661no—
410C4⋊C8—1661no—
411C4⋊C8—1661no—
412C4⋊C8C22⋊D8311yescharacteristic
413C4⋊C8C22⋊D8311yescharacteristic
414C4⋊C8C22×D8311yescharacteristic
415C4⋊C8C22×D8311yescharacteristic
416#103—831no—
417#103—831no—
418#102—831no—
419#102—831no—
420#102—831no—
421#102—831no—
422#102—831no—
423#102—831no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—1661no—
430C22⋊C8—1661no—
431C22⋊C8C22⋊D8311yescharacteristic
432C22⋊C8C22⋊D8311yescharacteristic
433#97—21no—
434#97—831no—
435#97—831no—
436#97—1661no—
437C4×C8—831no—
438C4×C8—831no—
439C4×C8—831no—
440C4×C8—831no—
441C4×C8—1661no—
442C4×C8—1661no—
443C4×C8C22×D8311yescharacteristic
444C4×C8C22×D8311yescharacteristic
445#41—81no—
446#41—81no—
447C2×Q8—21no—
448C2×Q8—831no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—831no—
454C2×D4—1661no—
455C2×D4C2×C4×D8311yescharacteristic
456C2×D4C2×C4×D8311yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—1661no—
460C22×C4C2×C4×D8311yescharacteristic
461C22×C4C2×C22⋊D8311yescharacteristic
462C22×C4#1305059011yescharacteristic
463SD16—1662no—
464SD16—1662no—
465D8—1662no—
466D8—1662no—
467M16—81no—
468M16—81no—
469M16—6641no—
470M16—6641no—
471M16—1662no—
472M16—1662no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—81no—
477C2×C8—3322no—
478C2×C8—831no—
479C2×C8—831no—
480C2×C8—831no—
481C2×C8—831no—
482C2×C8—6641no—
483C2×C8—1661no—
484C2×C8—1661no—
485C2×C8—1661no—
486C2×C8—1661no—
487C2×C8C2×C22⋊D8311yescharacteristic
488C2×C8C2×C22⋊D8311yescharacteristic
489C2×C8C2×C22⋊D8311yescharacteristic
490C2×C8C2×C22⋊D8311yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—831no—
493C4⋊C4—831no—
494C4⋊C4—1661no—
495C4⋊C4—1661no—
496C4⋊C4—1661no—
497C4⋊C4—1661no—
498C4⋊C4C2×C4×D8311yescharacteristic
499C4⋊C4C2×C4×D8311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—1661no—
505C22⋊C4—1661no—
506C22⋊C4—1661no—
507C22⋊C4—1661no—
508C22⋊C4—1661no—
509C42—1661no—
510C42C2×C4×D8311yescharacteristic
511C42C2×C22⋊D8311yescharacteristic
512C42#1305059011yescharacteristic
513C42C23×D8311yescharacteristic
514C23—21no—
515C23—21no—
516C23—1661no—
517C23C4×C22⋊D8311yescharacteristic
518Q8—81no—
519Q8—1661no—
520Q8—1661no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—81no—
526D4—81no—
527D4—81no—
528D4—81no—
529D4—6641no—
530D4—1661no—
531D4—1661no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—3321no—
544C2×C4—3321no—
545C2×C4—1661no—
546C2×C4—1661no—
547C2×C4—1661no—
548C2×C4C4×C22⋊D8311yescharacteristic
549C2×C4C4×C22⋊D8311yescharacteristic
550C2×C4C4×C22⋊D8311yescharacteristic
551C2×C4C22×C4×D8311yescharacteristic
552C2×C4C22×C22⋊D8311yescharacteristic
553C2×C4C2×#1305059011yescharacteristic
554C8—21no—
555C8—21no—
556C8—21no—
557C8—21no—
558C8—41no—
559C8—41no—
560C8—3321no—
561C8—3321no—
562C8—3321no—
563C8—832no—
564C8—832no—
565C8—1662no—
566C8—1661no—
567C8—1661no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—3321no—
578C22—3321no—
579C22—3321no—
580C22C2×C4×C22⋊D8311yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—3321no—
588C4—3321no—
589C4—3321no—
590C4#131×D8311yescharacteristic
591C4#131×D8311yescharacteristic
592C4#1912850411yescharacteristic
593C4#1912851211yescharacteristic
594C2—41no—
595C2—81no—
596C2—81no—
597C2—6641no—
598C2#2491617311yescharacteristic
599C2#2491629511yescharacteristic
600C2#2491637011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#2981C2
socleC22×C83C2×C4×D4
prime radical#24918052C2
cosocleC42×C83C24
hypercenter#2981D83
hypocenterC83#17968
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2981

Complements

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

NH ≅ G/Ntype
2. #24916614C2semidirect
3. #24906375C2semidirect
4. #24906365C2semidirect
5. #24906351C2semidirect
6. #24906346C2semidirect
7. #24906285C2semidirect
8. #24906275C2semidirect
9. C8×#13050578C2semidirect
10. C8×#13050575C2semidirect
11. #24906231C2semidirect
12. #24905921C2semidirect
13. #24905914C2semidirect
14. #24905744C2semidirect
15. C83×#2981C2semidirect
303. #2981D83semidirect
316. C83#17968semidirect

Maximal subgroups

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

subgroupindex
#249180522
#249166142
#249063752
#249063652
#249063512
#249063462
#249062852
#249062752
C8×#130505782
C8×#130505752
#249062312
#249059212
#249059142
#249057442
C83×#29812
#1796883