Finite Group Databasebeta

← #35433331

Subgroups — #35433331

Order 21248.

892 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127719C211yesmaximal, characteristic
2#24915983C211yesmaximal, characteristic
3C2×#19127683C211yesmaximal, characteristic
4#24908914C218yesmaximal, complemented
5C2×#19127473C211yesmaximal, characteristic, complemented
6#24907190C211yesmaximal, characteristic, complemented
7C2×#19127457C211yesmaximal, characteristic, complemented
8C83×#2905C211yesmaximal, characteristic, complemented
9C22×#13050590C2211yescharacteristic
10C22×#13050574C2211yescharacteristic
11C22×#13050574C2211yescharacteristic
12C2×#14581751C2211yescharacteristic
13#19127719—22no—
14#19127719C2214yes—
15C2×#14581720—22no—
16#19127711—21no—
17#19127707—21no—
18#19127703—22no—
19#19127698C2214yes—
20#19127683—22no—
21#19127683C2214yes—
22C2×#14581710—21no—
23C2×#14581708—21no—
24#19127473C2214yescomplemented
25#19127466C2214yescomplemented
26#19127457C2214yescomplemented
27C22×M16×C83C2211yescharacteristic
28C22×M16×C83C2211yescharacteristic
29C2×#117×C83C2211yescharacteristic
30#424×C83—22no—
31#424×C83C2214yescomplemented
32#423×C83—22no—
33C2×#13050590—21no—
34C2×#13050590—21no—
35C2×#13050590—21no—
36C2×#13050590—21no—
37C2×#13050590—21no—
38C2×#13050590—21no—
39C2×#13050590—21no—
40C2×#13050590—21no—
41C2×#13050590—21no—
42C2×#13050590—21no—
43C2×#13050590D412yes—
44C2×#13050590C2312yes—
45C22×Dic166D411yescharacteristic
46C22×D332D411yescharacteristic
47C22×C22⋊D83—21no—
48C22×C4×D83—21no—
49C2×#13050574—21no—
50C2×#13050574—21no—
51C2×#13050574—21no—
52C2×#13050574—21no—
53C2×#13050574—21no—
54C2×#13050574—21no—
55C2×#13050574—21no—
56C2×#13050574—21no—
57C2×#13050574—21no—
58C2×#13050574—21no—
59C2×#13050574C2312yes—
60C2×#13050574C2312yes—
61C22×C83⋊C8—21no—
62C22×C83⋊C8—21no—
63#14581751—21no—
64#14581751—21no—
65#14581751—21no—
66#14581751C2312yes—
67C2×C4⋊Dic83—21no—
68C2×C22⋊Dic83—21no—
69C2×C4×Dic83—21no—
70#14581720—28no—
71#14581717—24no—
72#14581714—24no—
73#14581710—24no—
74#14581708—24no—
75C23×C4×C83C2311yescharacteristic
76C2×M16×C83—21no—
77C2×M16×C83—21no—
78C2×M16×C83—21no—
79C2×M16×C83—21no—
80C2×M16×C83—21no—
81C2×M16×C83—21no—
82C2×M16×C83—21no—
83C2×M16×C83—21no—
84C2×M16×C83—21no—
85C2×M16×C83—21no—
86C2×M16×C83—21no—
87C2×M16×C83C2312yes—
88C22×C8×C83—21no—
89C22×C8×C83C2312yes—
90#117×C83—21no—
91#117×C83—21no—
92#117×C83D412yes—
93#117×C83C2312yes—
94C2×C4⋊C4×C83—21no—
95C2×C22⋊C4×C83—21no—
96C2×C42×C83D412yes—
97C4⋊C8×C83—28no—
98C23×D83—21no—
99#13050590—22no—
100#13050590—22no—
101#13050590—22no—
102#13050590—22no—
103#13050590—22no—
104#13050590—22no—
105#13050590—22no—
106#13050590—22no—
107#13050590—41no—
108#13050590—41no—
109#13050590—41no—
110#13050590—41no—
111#13050590—41no—
112#13050590—41no—
113#13050590—41no—
114#13050590—41no—
115C2×Dic166—21no—
116C2×Dic166—21no—
117C2×Dic166—21no—
118C2×Dic166—21no—
119C2×Dic166—21no—
120C2×Dic166C2×D412yes—
121C2×D332—21no—
122C2×D332—21no—
123C2×D332—21no—
124C2×D332—21no—
125C2×D332—21no—
126C2×D332C2×D412yes—
127C2×C22⋊D83—22no—
128C2×C22⋊D83—22no—
129C2×C22⋊D83—41no—
130C2×C22⋊D83—41no—
131C2×C22⋊D83—41no—
132C2×C22⋊D83—41no—
133C22×Dic83—21no—
134C22×Dic83—41no—
135C2×C4×D83—22no—
136C2×C4×D83—22no—
137C2×C4×D83—41no—
138C2×C4×D83—41no—
139C2×C4×D83—41no—
140C2×C4×D83—41no—
141#13050574—22no—
142#13050574—22no—
143#13050574—22no—
144#13050574—22no—
145#13050574—41no—
146#13050574—41no—
147#13050574—41no—
148#13050574—41no—
149C2×C83⋊C8—22no—
150C2×C83⋊C8—22no—
151C2×C83⋊C8—41no—
152C2×C83⋊C8—41no—
153C2×C83⋊C8—41no—
154C2×C83⋊C8—41no—
155C4⋊Dic83—22no—
156C4⋊Dic83—41no—
157C22⋊Dic83—22no—
158C22⋊Dic83—41no—
159C4×Dic83—22no—
160C4×Dic83—41no—
161C24×C83#4111yescharacteristic
162C22×C4×C83—22no—
163C22×C4×C83C2×D411yescharacteristic
164C22×C4×C83C2×D411yescharacteristic
165C22×C4×C83C2×D411yescharacteristic
166C22×C4×C83C2×D411yescharacteristic
167C22×C4×C83#4111yescharacteristic
168C22×C4×C83#4111yescharacteristic
169C22×C4×C83#4111yescharacteristic
170C22×C4×C83#4111yescharacteristic
171C22×C4×C83#4111yescharacteristic
172C22×C4×C83#4111yescharacteristic
173C22×C4×C83#4111yescharacteristic
174C22×C4×C83#4111yescharacteristic
175C22×C4×C83#4111yescharacteristic
176C22×C4×C83C2411yescharacteristic
177M16×C83—22no—
178M16×C83—22no—
179M16×C83—41no—
180M16×C83—41no—
181M16×C83—41no—
182M16×C83—41no—
183M16×C83—41no—
184M16×C83—41no—
185C2×C8×C83—22no—
186C2×C8×C83—22no—
187C2×C8×C83—22no—
188C2×C8×C83—22no—
189C2×C8×C83—41no—
190C2×C8×C83—41no—
191C4⋊C4×C83—22no—
192C4⋊C4×C83—22no—
193C22⋊C4×C83—22no—
194C22⋊C4×C83—22no—
195C42×C83—22no—
196C42×C83C2×D414yes—
197C23×C83—81no—
198C23×C83#12311yescharacteristic
199C23×C83#12311yescharacteristic
200C23×C83#12311yescharacteristic
201C23×C83#12311yescharacteristic
202C23×C83#12611yescharacteristic
203C23×C83#12611yescharacteristic
204C23×C83C2×#4111yescharacteristic
205C22×D83—22no—
206C22×D83—41no—
207C22×D83—41no—
208C22×D83—82no—
209C2×C4×C83—24no—
210C2×C4×C83—82no—
211C2×C4×C83#12111yescharacteristic
212C2×C4×C83#12111yescharacteristic
213C2×C4×C83#12111yescharacteristic
214C2×C4×C83#12111yescharacteristic
215C2×C4×C83#12311yescharacteristic
216C2×C4×C83#12311yescharacteristic
217C2×C4×C83#12311yescharacteristic
218C2×C4×C83#12311yescharacteristic
219C2×C4×C83#12311yescharacteristic
220C2×C4×C83#12311yescharacteristic
221C2×C4×C83#12311yescharacteristic
222C2×C4×C83#12311yescharacteristic
223C2×C4×C83#12411yescharacteristic
224C2×C4×C83#12411yescharacteristic
225C2×C4×C83#12411yescharacteristic
226C2×C4×C83#12411yescharacteristic
227C2×C4×C83#12611yescharacteristic
228C2×C4×C83#12611yescharacteristic
229C2×C4×C83#12611yescharacteristic
230C2×C4×C83#12611yescharacteristic
231C2×C4×C83#12611yescharacteristic
232C2×C4×C83#12611yescharacteristic
233C2×C4×C83C22×D411yescharacteristic
234C2×C4×C83C22×D411yescharacteristic
235C2×C4×C83C2×#4111yescharacteristic
236C2×C4×C83C2×#4111yescharacteristic
237C2×C4×C83C2×#4111yescharacteristic
238C2×C4×C83C2×#4111yescharacteristic
239C22⋊D83—42no—
240C22⋊D83—42no—
241C22⋊D83—42no—
242C22⋊D83—42no—
243C2×Dic83—22no—
244C2×Dic83—41no—
245C2×Dic83—41no—
246C2×Dic83—42no—
247C2×Dic83—82no—
248D332—22no—
249D332—22no—
250D332—41no—
251D332—41no—
252C4×D83—42no—
253C4×D83—42no—
254C4×D83—42no—
255C4×D83—42no—
256Dic166—22no—
257Dic166—22no—
258Dic166—41no—
259Dic166—41no—
260C8×C83—42no—
261C8×C83—42no—
262C83⋊C8—42no—
263C83⋊C8—42no—
264C22×C83—41no—
265C22×C83—41no—
266C22×C83—41no—
267C22×C83—41no—
268C22×C83—41no—
269C22×C83—41no—
270C22×C83—41no—
271C22×C83#39711yescharacteristic
272C22×C83#39711yescharacteristic
273C22×C83#39711yescharacteristic
274C22×C83#39711yescharacteristic
275C22×C83C2×#12311yescharacteristic
276C22×C83C2×#12311yescharacteristic
277C22×C83C2×#12611yescharacteristic
278C2×D83—42no—
279C2×D83—82no—
280C2×D83—82no—
281C2×D83—82no—
282C4×C83—44no—
283C4×C83#39711yescharacteristic
284C4×C83#39711yescharacteristic
285C4×C83#39711yescharacteristic
286C4×C83#39711yescharacteristic
287C4×C83C2×#12111yescharacteristic
288C4×C83C2×#12311yescharacteristic
289C4×C83C2×#12411yescharacteristic
290C4×C83C2×#12611yescharacteristic
291Dic83—42no—
292Dic83—82no—
293#23649—831nomaximal, Sylow
294C2×C83—21no—
295C2×C83—21no—
296C2×C83—21no—
297C2×C83—21no—
298C2×C83—21no—
299C2×C83—21no—
300C2×C83—21no—
301C2×C83C2×#39711yescharacteristic
302D83—82no—
303#2905D8311yescharacteristic, complemented
304C2×#421—831no—
305#2896—831no—
306C2×#413—831no—
307#2080—838no—
308C2×#344—831no—
309#1738—831no—
310C2×H(3,ℤ/4)—831no—
311C83#2364911yescharacteristic, complemented, Sylow
312C22×#41—831no—
313C22×M16—831no—
314C22×M16—831no—
315C22×M16C2×D8311yescharacteristic
316C22×M16C2×D8311yescharacteristic
317C2×#117—831no—
318C2×#117C2×D8311yescharacteristic
319#424—22no—
320#424C2×D8314yescomplemented
321#423—22no—
322#421—834no—
323#421—1662no—
324C2×#104—1662no—
325#419—1661no—
326#418—1661no—
327#417—1662no—
328#416—834no—
329#413—834no—
330#413—1662no—
331C2×#101—1661no—
332C2×#100—1661no—
333#344—834no—
334#341—834no—
335H(3,ℤ/4)—834no—
336C2×#41—832no—
337C2×#41—832no—
338C2×#41—1661no—
339C2×#41—1661no—
340C2×#41—1661no—
341C2×#41—1661no—
342C2×#41—1661no—
343C2×#41—1661no—
344C2×#41—1661no—
345C2×#41—1661no—
346C2×#41—1661no—
347C2×#41—1661no—
348C22×Q8—831no—
349C22×D4—831no—
350C22×D4—1661no—
351C23×C4—1661no—
352C23×C4C22×D8311yescharacteristic
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—832no—
365C2×M16—832no—
366C2×M16—1661no—
367C2×M16—1661no—
368C2×M16—1661no—
369C2×M16—1661no—
370C2×M16—1661no—
371C2×M16—1661no—
372C2×M16—1661no—
373C2×M16—1661no—
374C2×M16—1661no—
375C2×M16—1661no—
376C2×M16C22×D8312yes—
377C22×C8—21no—
378C22×C8—1661no—
379C22×C8—1661no—
380C22×C8C22×D8312yes—
381#117—21no—
382#117—21no—
383#117—832no—
384#117—1661no—
385#117—1661no—
386#117—1661no—
387#117C22⋊D8312yes—
388#117C22×D8312yes—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—1661no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—1661no—
393C2×C42—1661no—
394C2×C42C22⋊D8312yes—
395C4⋊C8—28no—
396#104—1668no—
397#103—1664no—
398#102—1664no—
399#101—1664no—
400#100—1664no—
401C24—1661no—
402C24#1305059011yescharacteristic
403#41—3321no—
404#41—3321no—
405#41—3321no—
406#41—3321no—
407#41—3321no—
408#41—3321no—
409#41—3321no—
410#41—3321no—
411#41—1662no—
412#41—1662no—
413#41—1662no—
414#41—1662no—
415#41—1662no—
416#41—1662no—
417#41—1662no—
418#41—1662no—
419C2×Q8—832no—
420C2×Q8—1661no—
421C2×Q8—1661no—
422C2×Q8—1661no—
423C2×Q8—1661no—
424C2×Q8—1661no—
425C2×D4—3321no—
426C2×D4—3321no—
427C2×D4—3321no—
428C2×D4—3321no—
429C2×D4—832no—
430C2×D4—1662no—
431C2×D4—1662no—
432C2×D4—1661no—
433C2×D4—1661no—
434C2×D4—1661no—
435C2×D4—1661no—
436C2×D4—1661no—
437C22×C4—22no—
438C22×C4—3321no—
439C22×C4—3321no—
440C22×C4—3321no—
441C22×C4—3321no—
442C22×C4—3321no—
443C22×C4—1661no—
444C22×C4—1662no—
445C22×C4—1662no—
446C22×C4D4×D8311yescharacteristic
447C22×C4D4×D8311yescharacteristic
448C22×C4C2×C22⋊D8311yescharacteristic
449C22×C4C2×C22⋊D8311yescharacteristic
450C22×C4#1305058911yescharacteristic
451C22×C4#1305058911yescharacteristic
452C22×C4#1305059011yescharacteristic
453C22×C4#1305059011yescharacteristic
454C22×C4#1305059011yescharacteristic
455C22×C4#1305059111yescharacteristic
456C22×C4#1305059111yescharacteristic
457C22×C4#1305059111yescharacteristic
458C22×C4#1305059111yescharacteristic
459C22×C4C23×D8311yescharacteristic
460M16—22no—
461M16—22no—
462M16—41no—
463M16—41no—
464M16—41no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—3321no—
469M16—3321no—
470M16—3321no—
471M16—3321no—
472M16—1662no—
473M16—1662no—
474M16—1662no—
475M16—1662no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—3321no—
483C2×C8—3321no—
484C2×C8—3321no—
485C2×C8—3321no—
486C2×C8—1662no—
487C2×C8—1662no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—3321no—
491C4⋊C4—1662no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—3321no—
495C22⋊C4—1662no—
496C42—22no—
497C42—3321no—
498C42—1662no—
499C42C2×C22⋊D8314yes—
500C23—81no—
501C23—3321no—
502C23—3321no—
503C23—6642no—
504C23—1662no—
505C23#1458177511yescharacteristic
506C23#1458177511yescharacteristic
507C23#1458177711yescharacteristic
508C23#1458177711yescharacteristic
509C23#1458178711yescharacteristic
510C23#1458178711yescharacteristic
511C23C2×#1305059011yescharacteristic
512Q8—3321no—
513Q8—3321no—
514Q8—1662no—
515Q8—1662no—
516D4—3322no—
517D4—3322no—
518D4—3322no—
519D4—3322no—
520D4—3321no—
521D4—3321no—
522D4—1662no—
523D4—1662no—
524C2×C4—24no—
525C2×C4—82no—
526C2×C4—3321no—
527C2×C4—3321no—
528C2×C4—3322no—
529C2×C4—3322no—
530C2×C4—3322no—
531C2×C4—3322no—
532C2×C4—3322no—
533C2×C4—6642no—
534C2×C4—1662no—
535C2×C4#1458176311yescharacteristic
536C2×C4#1458176311yescharacteristic
537C2×C4#1458176311yescharacteristic
538C2×C4#1458176311yescharacteristic
539C2×C4#1458177511yescharacteristic
540C2×C4#1458177511yescharacteristic
541C2×C4#1458177711yescharacteristic
542C2×C4#1458177711yescharacteristic
543C2×C4#1458177711yescharacteristic
544C2×C4#1458177711yescharacteristic
545C2×C4#1458177711yescharacteristic
546C2×C4#1458177711yescharacteristic
547C2×C4#1458178111yescharacteristic
548C2×C4#1458178111yescharacteristic
549C2×C4#1458178111yescharacteristic
550C2×C4#1458178111yescharacteristic
551C2×C4#1458178711yescharacteristic
552C2×C4#1458178711yescharacteristic
553C2×C4#1458178711yescharacteristic
554C2×C4#1458178711yescharacteristic
555C2×C4#1458178711yescharacteristic
556C2×C4#1458178711yescharacteristic
557C2×C4C2×D4×D8311yescharacteristic
558C2×C4C22×C22⋊D8311yescharacteristic
559C2×C4C2×#1305058911yescharacteristic
560C2×C4C2×#1305059011yescharacteristic
561C2×C4C2×#1305059111yescharacteristic
562C2×C4C2×#1305059111yescharacteristic
563C8—42no—
564C8—42no—
565C8—3322no—
566C8—3322no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—3322no—
575C22—6642no—
576C22—6642no—
577C22—6642no—
578C22#1912762711yescharacteristic
579C22#1912762711yescharacteristic
580C22#1912762711yescharacteristic
581C22#1912762711yescharacteristic
582C22C2×#1458177511yescharacteristic
583C22C2×#1458177711yescharacteristic
584C22C2×#1458178711yescharacteristic
585C4—44no—
586C4—3322no—
587C4—6642no—
588C4#1912762711yescharacteristic
589C4#1912762711yescharacteristic
590C4#1912762711yescharacteristic
591C4#1912762711yescharacteristic
592C4C2×#1458176311yescharacteristic
593C4C2×#1458177711yescharacteristic
594C4C2×#1458178111yescharacteristic
595C4C2×#1458178711yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—21no—
603C2—6642no—
604C2C2×#1912762711yescharacteristic
subgroupG/H
centerC4C2×#14581781
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#2905C2
socleC2×C83C2×#397
prime radicalC22×#13050590C22
hypercenter#2905D83
hypocenterC83#23649
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C4 ◁ C23×C4 ◁ #2905

Complements

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

NH ≅ G/Ntype
4. #24908914C2semidirect
5. C2×#19127473C2semidirect
6. #24907190C2semidirect
7. C2×#19127457C2semidirect
8. C83×#2905C2semidirect
24. #19127473C22semidirect
25. #19127466C22semidirect
26. #19127457C22semidirect
31. #424×C83C22semidirect
303. #2905D83semidirect
311. C83#23649semidirect
320. #424C2×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191277192
#249159832
C2×#191276832
#249089142
C2×#191274732
#249071902
C2×#191274572
C83×#29052
#2364983