Finite Group Databasebeta

← #35375040

Subgroups — #35375040

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#24918059C211yesmaximal, characteristic
2#24916612C211yesmaximal, characteristic, complemented
3#24916541C211yesmaximal, characteristic, complemented
4#24906374C211yesmaximal, characteristic, complemented
5#24906368C211yesmaximal, characteristic, complemented
6#24906350C211yesmaximal, characteristic, complemented
7#24906345C211yesmaximal, characteristic, complemented
8#24906284C211yesmaximal, characteristic, complemented
9#24906278C211yesmaximal, characteristic, complemented
10#24906260C211yesmaximal, characteristic, complemented
11#24906255C211yesmaximal, characteristic, complemented
12#24906231C211yesmaximal, characteristic, complemented
13#24905915C211yesmaximal, characteristic, complemented
14C8×#13050574C211yesmaximal, characteristic, complemented
15C83×#1494C211yesmaximal, characteristic, complemented
16#19128251C2211yescharacteristic
17#19128111C411yescharacteristic
18#19128091C411yescharacteristic
19#19128067C411yescharacteristic
20#19128060C411yescharacteristic
21#19127952C411yescharacteristic
22#19127952C411yescharacteristic
23#19127949C411yescharacteristic
24#19127949C411yescharacteristic
25#19127832C2211yescharacteristic
26Q8×C83⋊C8C2211yescharacteristic
27C4×#13050577C2211yescharacteristic
28C4×#13050577C2211yescharacteristic
29C4×#13050575C2211yescharacteristic
30C4×#13050575C2211yescharacteristic
31#19127779—21no—
32#19127779C2211yescharacteristic
33#19127778C2211yescharacteristic
34#19127778C2211yescharacteristic
35#19127774—21no—
36#19127774—21no—
37#19127773—21no—
38D4×C83⋊C8C2211yescharacteristic
39#19127766C2211yescharacteristic
40#19127766C2211yescharacteristic
41#19127762—21no—
42#19127754C2211yescharacteristic
43#19127728—21no—
44#19127725C2211yescharacteristic
45#19127666—21no—
46#19127666—21no—
47C4×#13050574C2211yescharacteristic
48#19127453C2211yescharacteristic
49#19127453C2211yescharacteristic
50#19127451C2211yescharacteristic
51#19127451C2211yescharacteristic
52#19127430C2211yescharacteristic
53#19127430C2211yescharacteristic
54#19127430C2211yescharacteristic
55#19127430C2211yescharacteristic
56#19127423C2211yescharacteristic
57#19127423C2211yescharacteristic
58C8×C83⋊C8C2211yescharacteristic
59C8×C83⋊C8C2211yescharacteristic
60#529×C83C2211yescharacteristic
61#432×C83C2211yescharacteristic
62C2×C4×C8×C83C2211yescharacteristic
63Q8⋊C8×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65D4⋊C8×C83C2211yescharacteristic
66D4⋊C8×C83C2211yescharacteristic
67C2×#13050590—21no—
68C2×#13050577C2×C411yescharacteristic
69C2×#13050577C2×C411yescharacteristic
70C2×#13050575C2×C411yescharacteristic
71C2×#13050575C2×C411yescharacteristic
72C2×#13050574—21no—
73C2×#13050574—21no—
74C2×#13050574C2×C411yescharacteristic
75C2×#13050574C2×C411yescharacteristic
76C2×#13050573—21no—
77C2×#13050573—21no—
78C22×C83⋊C8—21no—
79C2×C8×D83—21no—
80C2×C8×D83—21no—
81#14581792C2×C411yescharacteristic
82#14581789C2×C411yescharacteristic
83#14581780—21no—
84#14581766—21no—
85#14581766C2×C411yescharacteristic
86#14581766C2×C411yescharacteristic
87C4×D332—21no—
88C4×D332C2311yescharacteristic
89C4×D332C2311yescharacteristic
90#14581725C2×C411yescharacteristic
91#14581725C2×C411yescharacteristic
92#14581723C2×C411yescharacteristic
93#14581723C2×C411yescharacteristic
94C4⋊(C83⋊C8)—21no—
95C4⋊(C83⋊C8)—21no—
96C4⋊(C83⋊C8)—21no—
97C4⋊(C83⋊C8)D411yescharacteristic
98C4⋊(C83⋊C8)D411yescharacteristic
99C4⋊(C83⋊C8)C2311yescharacteristic
100C4⋊(C83⋊C8)C2311yescharacteristic
101#14581716C2×C411yescharacteristic
102#14581716C2×C411yescharacteristic
103#14581713C2×C411yescharacteristic
104#14581713C2×C411yescharacteristic
105#14581712C2×C411yescharacteristic
106#14581712C2×C411yescharacteristic
107#14581712C2×C411yescharacteristic
108#14581712C2×C411yescharacteristic
109C22⋊(C83⋊C8)—21no—
110C22⋊(C83⋊C8)—21no—
111C22⋊(C83⋊C8)D411yescharacteristic
112C22⋊(C83⋊C8)D411yescharacteristic
113(C2×D83)⋊C8—21no—
114(C2×D83)⋊C8—21no—
115(C2×D83)⋊C8—21no—
116(C2×D83)⋊C8—21no—
117#14581703—21no—
118#14581703C2×C411yescharacteristic
119#14581703C2×C411yescharacteristic
120C4×C83⋊C8—21no—
121C4×C83⋊C8C2311yescharacteristic
122C4×C83⋊C8C2311yescharacteristic
123C4×C83⋊C8C2311yescharacteristic
124C4×C83⋊C8C2311yescharacteristic
125C22×C8×C83—21no—
126#126×C83—21no—
127#125×C83C2×C411yescharacteristic
128#124×C83C2×C411yescharacteristic
129#123×C83—21no—
130C22⋊Q8×C83C2×C411yescharacteristic
131#121×C83C2×C411yescharacteristic
132C4×Q8×C83C2311yescharacteristic
133C4×D4×C83—21no—
134C4×D4×C83C2311yescharacteristic
135#117×C83—21no—
136C2×C42×C83C2311yescharacteristic
137C4⋊C8×C83C2311yescharacteristic
138C4⋊C8×C83C2311yescharacteristic
139C22⋊C8×C83—21no—
140#97×C83—21no—
141C4×C8×C83—21no—
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#13050590—81no—
145#13050590—81no—
146C2×Dic166—21no—
147C2×D332—21no—
148C2×D332—21no—
149C2×D332C22×C411yescharacteristic
150C2×D332C22×C411yescharacteristic
151C2×C22⋊D83—21no—
152C2×C22⋊D83—21no—
153C2×C4×D83—21no—
154C2×C4×D83—21no—
155#13050577—22no—
156#13050577—22no—
157#13050575—22no—
158#13050575—22no—
159#13050574—22no—
160#13050574—22no—
161#13050574—81no—
162#13050574—81no—
163#13050573—81no—
164#13050573—81no—
165C2×C83⋊C8—21no—
166C2×C83⋊C8—21no—
167C2×C83⋊C8—81no—
168C2×C83⋊C8C22×C411yescharacteristic
169C2×C83⋊C8C22×C411yescharacteristic
170C2×C83⋊C8C22×C411yescharacteristic
171C2×C83⋊C8C22×C411yescharacteristic
172C2×C83⋊C8C2×D411yescharacteristic
173C2×C83⋊C8C2×D411yescharacteristic
174C2×C83⋊C8C2×D411yescharacteristic
175C2×C83⋊C8C2×D411yescharacteristic
176C8×D83—81no—
177C8×D83—81no—
178C4⋊Dic83—21no—
179C4⋊Dic83C22×C411yescharacteristic
180C4⋊Dic83C22×C411yescharacteristic
181(C2×D83)⋊C4—21no—
182(C2×D83)⋊C4—21no—
183(C2×D83)⋊C4—21no—
184(C2×D83)⋊C4—21no—
185C2×Q8×C83C22×C411yescharacteristic
186C2×D4×C83—21no—
187C2×D4×C83C22×C411yescharacteristic
188C22×C4×C83—21no—
189C22×C4×C83C22×C411yescharacteristic
190C22×C4×C83C2×D411yescharacteristic
191C22×C4×C83#4111yescharacteristic
192C2×C8×C83—21no—
193C2×C8×C83—21no—
194C2×C8×C83—21no—
195C2×C8×C83—21no—
196C2×C8×C83—42no—
197C4⋊C4×C83—21no—
198C4⋊C4×C83—21no—
199C4⋊C4×C83—21no—
200C4⋊C4×C83—21no—
201C4⋊C4×C83C22×C411yescharacteristic
202C4⋊C4×C83C22×C411yescharacteristic
203C22⋊C4×C83—21no—
204C22⋊C4×C83—21no—
205C22⋊C4×C83—21no—
206C22⋊C4×C83—21no—
207C22⋊C4×C83—21no—
208C42×C83—21no—
209C42×C83C22×C411yescharacteristic
210C42×C83C2×D411yescharacteristic
211C42×C83#4111yescharacteristic
212C42×C83C2411yescharacteristic
213C23×C83—21no—
214C23×C83C4×D411yescharacteristic
215C22×D83—21no—
216C22×D83—21no—
217Q8×C83—21no—
218Q8×C83—21no—
219D4×C83—21no—
220D4×C83—21no—
221D4×C83—81no—
222C2×C4×C83—21no—
223C2×C4×C83—21no—
224C2×C4×C83—21no—
225C2×C4×C83—21no—
226C2×C4×C83—21no—
227C2×C4×C83—21no—
228C2×C4×C83—21no—
229C2×C4×C83—41no—
230C2×C4×C83—41no—
231C2×C4×C83—41no—
232C2×C4×C83C4×D411yescharacteristic
233C2×C4×C83C4×D411yescharacteristic
234C2×C4×C83C4×D411yescharacteristic
235C2×C4×C83C23×C411yescharacteristic
236C2×C4×C83C22×D411yescharacteristic
237C2×C4×C83C2×#4111yescharacteristic
238C22⋊D83—81no—
239C22⋊D83—81no—
240C2×Dic83—21no—
241C2×Dic83—21no—
242D332—21no—
243D332—21no—
244D332—21no—
245D332—21no—
246D332—81no—
247D332—81no—
248C4×D83—41no—
249C4×D83—41no—
250C4×D83—41no—
251C4×D83—41no—
252Dic166—81no—
253C8×C83—22no—
254C8×C83—41no—
255C8×C83—41no—
256C8×C83—41no—
257C83⋊C8—21no—
258C83⋊C8—21no—
259C83⋊C8—21no—
260C83⋊C8—21no—
261C83⋊C8—21no—
262C83⋊C8—21no—
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×C83C2×C4×D411yescharacteristic
274C2×D83—41no—
275C2×D83—41no—
276C2×D83—41no—
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×C83—41no—
287C4×C83C2×#13111yescharacteristic
288C4×C83C2×#13111yescharacteristic
289C4×C83#57611yescharacteristic
290C4×C83#57711yescharacteristic
291Dic83—41no—
292Dic83—41no—
293#17968—831nomaximal, Sylow
294C2×C83—41no—
295C2×C83—81no—
296C2×C83#293111yescharacteristic
297C2×C83#294611yescharacteristic
298C2×C83#295611yescharacteristic
299D83—81no—
300D83—81no—
301#3171—831no—
302#2993—831no—
303#2981—831no—
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#1494D8311yescharacteristic, complemented
314#1492—831no—
315C8×M16—831no—
316C83#1796811yescharacteristic, complemented, Sylow
317#532—831no—
318#529C2×D8311yescharacteristic
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—831no—
335#436—831no—
336#436—1661no—
337#435—1661no—
338#435—1661no—
339#435—1661no—
340C8×D4—831no—
341C8×D4—831no—
342C8×D4—831no—
343#433—1661no—
344#432C2×D8311yescharacteristic
345#431—831no—
346#424—1661no—
347#423—831no—
348#408—1661no—
349#408—1661no—
350C4×M16—831no—
351C2×C4×C8C2×D8311yescharacteristic
352#335—831no—
353#335—831no—
354#334—831no—
355#334—831no—
356Q8⋊C8C2×D8311yescharacteristic
357Q8⋊C8C2×D8311yescharacteristic
358D4⋊C8—831no—
359D4⋊C8—831no—
360D4⋊C8—831no—
361D4⋊C8—831no—
362D4⋊C8C2×D8311yescharacteristic
363D4⋊C8C2×D8311yescharacteristic
364#322—831no—
365#322—831no—
366C82—831no—
367C82—831no—
368C2×#41—1661no—
369C2×SD16—831no—
370C2×SD16—831no—
371C2×D8—831no—
372C2×D8—831no—
373C2×M16—831no—
374C2×M16—831no—
375C2×M16—1661no—
376C2×M16—1661no—
377C2×M16—1661no—
378C2×M16—1661no—
379C22×C8—21no—
380C22×C8—1661no—
381C22×C8—1661no—
382C22×C8—1661no—
383C4⋊Q8—831no—
384#127—831no—
385#126—21no—
386#125C4×D8311yescharacteristic
387#124—1661no—
388#124C4×D8311yescharacteristic
389#123—21no—
390C22⋊Q8C4×D8311yescharacteristic
391#121—831no—
392#121—831no—
393#121—1661no—
394#121C4×D8311yescharacteristic
395C4×Q8C22×D8311yescharacteristic
396C4×D4—21no—
397C4×D4—831no—
398C4×D4—831no—
399C4×D4—1661no—
400C4×D4C22×D8311yescharacteristic
401#117—21no—
402C2×C42C22×D8311yescharacteristic
403#107—831no—
404#107—831no—
405#106—831no—
406#106—831no—
407C4⋊C8—831no—
408C4⋊C8—831no—
409C4⋊C8—831no—
410C4⋊C8—831no—
411C4⋊C8—1661no—
412C4⋊C8—1661no—
413C4⋊C8—1661no—
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—831no—
426C22⋊C8—831no—
427C22⋊C8—1661no—
428C22⋊C8—1661no—
429C22⋊C8—1661no—
430C22⋊C8—1661no—
431C22⋊C8—1661no—
432C22⋊C8—1661no—
433#97—21no—
434#97—831no—
435#97—831no—
436#97—1661no—
437C4×C8—21no—
438C4×C8—831no—
439C4×C8—831no—
440C4×C8—831no—
441C4×C8—831no—
442C4×C8—1661no—
443C4×C8C22×D8311yescharacteristic
444C4×C8C22×D8311yescharacteristic
445#41—6641no—
446#41—6641no—
447C2×Q8—1661no—
448C2×Q8C2×C4×D8311yescharacteristic
449C2×D4—21no—
450C2×D4—831no—
451C2×D4—831no—
452C2×D4—1661no—
453C2×D4—1661no—
454C2×D4—1661no—
455C2×D4—1661no—
456C2×D4C2×C4×D8311yescharacteristic
457C22×C4—21no—
458C22×C4—1661no—
459C22×C4—1661no—
460C22×C4C2×C4×D8311yescharacteristic
461C22×C4D4×D8311yescharacteristic
462C22×C4#1305058911yescharacteristic
463SD16—1662no—
464SD16—1662no—
465D8—1662no—
466D8—1662no—
467M16—6641no—
468M16—6641no—
469M16—6641no—
470M16—6641no—
471M16—1662no—
472M16—1662no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—42no—
478C2×C8—831no—
479C2×C8—831no—
480C2×C8—831no—
481C2×C8—831no—
482C2×C8—831no—
483C2×C8—831no—
484C2×C8—831no—
485C2×C8—831no—
486C2×C8—6641no—
487C2×C8—6641no—
488C2×C8—6641no—
489C2×C8—1661no—
490C2×C8—1661no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—831no—
496C4⋊C4—831no—
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—21no—
505C22⋊C4—1661no—
506C22⋊C4—1661no—
507C22⋊C4—1661no—
508C22⋊C4—1661no—
509C42—21no—
510C42C2×C4×D8311yescharacteristic
511C42D4×D8311yescharacteristic
512C42#1305058911yescharacteristic
513C42C23×D8311yescharacteristic
514C23—21no—
515C23—1661no—
516C23—1661no—
517C23(C22⋊D83)⋊C411yescharacteristic
518Q8—21no—
519Q8—21no—
520Q8—6641no—
521D4—21no—
522D4—21no—
523D4—81no—
524D4—6641no—
525D4—6641no—
526D4—6641no—
527D4—6641no—
528D4—1661no—
529D4—1661no—
530D4—1661no—
531D4—1661no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—3321no—
543C2×C4—3321no—
544C2×C4—3321no—
545C2×C4—3321no—
546C2×C4—1661no—
547C2×C4—1661no—
548C2×C4(C22⋊D83)⋊C411yescharacteristic
549C2×C4(C22⋊D83)⋊C411yescharacteristic
550C2×C4(C22⋊D83)⋊C411yescharacteristic
551C2×C4C22×C4×D8311yescharacteristic
552C2×C4C2×D4×D8311yescharacteristic
553C2×C4C2×#1305058911yescharacteristic
554C8—22no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—3321no—
559C8—3321no—
560C8—832no—
561C8—832no—
562C8—1661no—
563C8—1661no—
564C8—1661no—
565C8—1661no—
566C8—1661no—
567C8—1661no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—3321no—
575C22—3321no—
576C22—3321no—
577C22—3321no—
578C22—3321no—
579C22—3321no—
580C22C2×(C22⋊D83)⋊C411yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—3321no—
589C4—3321no—
590C4#131×D8311yescharacteristic
591C4#131×D8311yescharacteristic
592C4#1912850311yescharacteristic
593C4#1912850811yescharacteristic
594C2—41no—
595C2—81no—
596C2—6641no—
597C2—6641no—
598C2#2491617111yescharacteristic
599C2#2491629811yescharacteristic
600C2#2491636911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1494C2
socleC22×C83C2×C4×D4
prime radical#24918059C2
cosocleC42×C83C24
hypercenter#1494D83
hypocenterC83#17968
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #24916612C2semidirect
3. #24916541C2semidirect
4. #24906374C2semidirect
5. #24906368C2semidirect
6. #24906350C2semidirect
7. #24906345C2semidirect
8. #24906284C2semidirect
9. #24906278C2semidirect
10. #24906260C2semidirect
11. #24906255C2semidirect
12. #24906231C2semidirect
13. #24905915C2semidirect
14. C8×#13050574C2semidirect
15. C83×#1494C2semidirect
313. #1494D83semidirect
316. C83#17968semidirect

Maximal subgroups

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

subgroupindex
#249180592
#249166122
#249165412
#249063742
#249063682
#249063502
#249063452
#249062842
#249062782
#249062602
#249062552
#249062312
#249059152
C8×#130505742
C83×#14942
#1796883