Finite Group Databasebeta

← #25081788

Subgroups — #25081788

Order 11008.

662 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145546C211yesmaximal, characteristic, complemented
2#19144696C211yesmaximal, characteristic, complemented
3#19144594C211yesmaximal, characteristic
4#19143616C211yesmaximal, characteristic, complemented
5#19134031C211yesmaximal, characteristic, complemented
6#19134030C211yesmaximal, characteristic, complemented
7#19134019C211yesmaximal, characteristic, complemented
8#19134018C211yesmaximal, characteristic, complemented
9#19133959C211yesmaximal, characteristic, complemented
10#19133958C211yesmaximal, characteristic, complemented
11#19133933C211yesmaximal, characteristic, complemented
12#19133372C211yesmaximal, characteristic, complemented
13#19133297C211yesmaximal, characteristic, complemented
14#19133258C211yesmaximal, characteristic, complemented
15C43×#1665C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583447C2211yescharacteristic
18C4×D4×D43C2211yescharacteristic
19#14583278C2211yescharacteristic, complemented
20#14583250C2211yescharacteristic, complemented
21#14583245C2211yescharacteristic, complemented
22#14583236—21no—
23#14583211—21no—
24#14583180C2211yescharacteristic
25#14583179C2211yescharacteristic
26#14583176C2211yescharacteristic
27#14583119—21no—
28#14583119—21no—
29#14583105C2211yescharacteristic
30#14583104C2211yescharacteristic
31#14583091C2211yescharacteristic
32#14583058—21no—
33#14583058—21no—
34#14583051—21no—
35#14583031—21no—
36#14582998—21no—
37#14582996—21no—
38D8×Dic43—21no—
39#14582979—21no—
40C8×D172C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42#14582964C2211yescharacteristic
43C8×C22⋊D43—21no—
44(C22⋊D43)⋊C8—21no—
45#14582955C2211yescharacteristic
46#14582951C2211yescharacteristic
47#14582951C2211yescharacteristic
48#14582950C2211yescharacteristic
49C2×(C2×D43)⋊C8—21no—
50C22⋊C8×D43—21no—
51#14582651C2211yescharacteristic, complemented
52#14582651C2211yescharacteristic, complemented
53#14582650C2211yescharacteristic, complemented
54#14582646C2211yescharacteristic, complemented
55#14582646C2211yescharacteristic, complemented
56#14582645C2211yescharacteristic, complemented
57#14582644C2211yescharacteristic, complemented
58#14582644C2211yescharacteristic, complemented
59#14582643C2211yescharacteristic, complemented
60C43×#492C2211yescharacteristic, complemented
61C43×#474C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic, complemented
65C43×#332C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic, complemented
67C2×#10621900—21no—
68C2×D4×D43D411yescharacteristic
69C22×C4×D43—21no—
70C2×#10621885—21no—
71C2×#10621885—21no—
72C2×#10621873—21no—
73C2×#10621883—21no—
74C2×#10621882—21no—
75C22×C43⋊C8—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063316—21no—
81#13063312—21no—
82#13063305—21no—
83#13063301—21no—
84#13063296—21no—
85#13063296—21no—
86Q8×Dic43—21no—
87#13063290—21no—
88C4×D172C2311yescharacteristic
89D4×Dic43—21no—
90D4×Dic43—21no—
91D4×Dic43D411yescharacteristic
92#13063287D411yescharacteristic
93C4×C22⋊D43—21no—
94(C22⋊D43)⋊C4—21no—
95#13063283—21no—
96C4⋊C4×D43D411yescharacteristic
97C22⋊C4×D43—21no—
98C42×D43C2311yescharacteristic
99#13063259—21no—
100#13063258—21no—
101#13063258—21no—
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8D411yescharacteristic
106Dic43⋊C8D411yescharacteristic
107#13063250—21no—
108#13063250—21no—
109#13063250—21no—
110#13063248—21no—
111#13063247—21no—
112#13063246—21no—
113#13063246—21no—
114#13063246—21no—
115#13063246—21no—
116#13063245—21no—
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8D411yescharacteristic
124(C2×D43)⋊C8D411yescharacteristic
125#13063235—21no—
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×SD16×C43—21no—
130C2×SD16×C43—21no—
131C2×D8×C43—21no—
132C22×C8×C43—21no—
133C4⋊Q8×C43C2311yescharacteristic
134#127×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136#107×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C23×D43—21no—
145C2×Q8×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43C2×D411yescharacteristic
150C22×C4×C43—21no—
151C2×C22⋊D43—21no—
152C2×C22⋊D43—41no—
153C22×Dic43—21no—
154C22×Dic43—41no—
155#10621900—81no—
156#10621900—81no—
157D4×D43—22no—
158D4×D43—22no—
159C2×D172C2×D411yescharacteristic
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—81no—
164C2×C4×D43—81no—
165C2×C4×D43C2×D411yescharacteristic
166C2×C4×D43C2×D411yescharacteristic
167C2×C4×D43#4111yescharacteristic
168C2×Dic86—21no—
169C2×Dic86—21no—
170SD16×C43—81no—
171SD16×C43—81no—
172D8×C43—42no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—81no—
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43C2×D411yescharacteristic
182C22⋊C4×C43—21no—
183C42×C43C2411yescharacteristic
184C22⋊Dic43—21no—
185C22⋊Dic43—41no—
186C22⋊Dic43—41no—
187#10621885—81no—
188#10621885—81no—
189#10621883—42no—
190#10621882—42no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—41no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—41no—
199C4⋊Dic43C2×D411yescharacteristic
200Dic43⋊C4—21no—
201Dic43⋊C4—41no—
202C4×Dic43—41no—
203C4×Dic43C2×D411yescharacteristic
204C4×Dic43C2×D411yescharacteristic
205C4×Dic43#4111yescharacteristic
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—81no—
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212#10621873—42no—
213C8×D43—81no—
214C8×D43—81no—
215C23×C43—21no—
216C23×C43—41no—
217C22×D43—21no—
218C22×D43—24no—
219C22×D43—81no—
220C22×D43—81no—
221C22×D43#12111yescharacteristic
222Q8×C43—41no—
223Q8×C43—41no—
224D4×C43—21no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—81no—
230D4×C43#13512yes—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C22⋊D43—24no—
239C22⋊D43—82no—
240C2×Dic43—21no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—81no—
244C2×Dic43—82no—
245C2×Dic43#12111yescharacteristic
246C2×Dic43#12111yescharacteristic
247C2×Dic43#12111yescharacteristic
248D172—21no—
249D172#13512yes—
250C4×D43—21no—
251C4×D43—21no—
252C4×D43—21no—
253C4×D43—21no—
254C4×D43—41no—
255C4×D43—41no—
256C4×D43—41no—
257C4×D43—81no—
258C4×D43—81no—
259Dic86—41no—
260Dic86—41no—
261Dic86—41no—
262Dic86—41no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43—41no—
268C43⋊C8—21no—
269C43⋊C8—21no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273#19388—431nomaximal, Sylow
274C22×C43—22no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43C2×#12111yescharacteristic
281C2×D43—21no—
282C2×D43—21no—
283C2×D43—22no—
284C2×D43—21no—
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—84no—
288C4×C43—21no—
289C4×C43—41no—
290C4×C43—81no—
291C4×C43C2×#13511yescharacteristic
292C4×C43C2×#13511yescharacteristic
293C4×C43#57611yescharacteristic
294C4×C43#57611yescharacteristic
295Dic43—21no—
296Dic43—21no—
297Dic43—21no—
298Dic43—41no—
299Dic43—81no—
300Dic43—81no—
301#3210—431no—
302#3110—431no—
303#3100—431no—
304#2972—431no—
305#1681—431no—
306#1681—431no—
307#1679—431no—
308#1679—431no—
309#1669—431no—
310#1669—431no—
311#1665—431no—
312#1665D4311yescharacteristic, complemented
313#1572—431no—
314#1553—431no—
315#1544—431no—
316C2×C43—42no—
317C2×C43—161no—
318C2×C43#304111yescharacteristic
319C2×C43#305011yescharacteristic
320C2×C43#306911yescharacteristic
321D43—41no—
322D43—42no—
323#533—431no—
324#532—431no—
325C2×C4×D4—431no—
326#494—431no—
327#492C2×D4311yescharacteristic, complemented
328#487—431no—
329#486—431no—
330#484—861no—
331#480—861no—
332#474—431no—
333#474—431no—
334#474—431no—
335#474C2×D4311yescharacteristic
336#464—861no—
337#464—861no—
338#461—431no—
339#461—431no—
340#459—431no—
341#459C2×D4311yescharacteristic
342#452—861no—
343#452—861no—
344#450—861no—
345#447—861no—
346#440—861no—
347#440—861no—
348C4×D8—861no—
349C4×D8—861no—
350C8×D4—431no—
351C8×D4—431no—
352C8×D4—431no—
353C8×D4—861no—
354C8×D4—861no—
355C8×D4C2×D4311yescharacteristic
356#432—431no—
357#431—431no—
358#431—431no—
359#431—431no—
360C2×C22⋊C8—861no—
361C2×C22⋊C8—861no—
362#335—431no—
363#335—431no—
364#334—431no—
365#334C2×D4311yescharacteristic, complemented
366#332—431no—
367#332—431no—
368#332—431no—
369#332—431no—
370#332—431no—
371#332C2×D4311yescharacteristic, complemented
372#331—431no—
373#331C2×D4311yescharacteristic, complemented
374C43#1938811yescharacteristic, complemented, Sylow
375C2×#41—861no—
376C22×D4—431no—
377C23×C4—861no—
378C2×Q16—861no—
379C2×Q16—861no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—861no—
383C2×SD16—861no—
384C2×D8—21no—
385C2×D8—861no—
386C22×C8—21no—
387C22×C8—861no—
388C22×C8—861no—
389C22×C8—861no—
390C4⋊Q8—431no—
391C4⋊Q8—431no—
392C4⋊Q8C22×D4311yescharacteristic
393#127C22×D4311yescharacteristic
394#125—861no—
395#124—861no—
396C22⋊Q8—861no—
397C22⋊Q8—861no—
398#121—861no—
399#121—861no—
400C4×Q8—861no—
401C4×Q8—861no—
402C4×D4—431no—
403C4×D4—431no—
404C4×D4—431no—
405C4×D4—861no—
406C4×D4—861no—
407C4×D4—861no—
408C4×D4—861no—
409C4×D4C22×D4311yescharacteristic
410#117—861no—
411C2×C4⋊C4—431no—
412C2×C22⋊C4—861no—
413C2×C42—431no—
414#107—21no—
415#107—861no—
416#107—861no—
417#107—861no—
418C4⋊C8—431no—
419C4⋊C8—431no—
420C4⋊C8—431no—
421C4⋊C8—431no—
422C4⋊C8—431no—
423C4⋊C8C22×D4311yescharacteristic
424C4⋊C8C22×D4311yescharacteristic
425C4⋊C8C22×D4311yescharacteristic
426#103—861no—
427#103—861no—
428#103—861no—
429#103—861no—
430#102—21no—
431#102—21no—
432#102—861no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438C22⋊C8—21no—
439C22⋊C8—431no—
440C22⋊C8—431no—
441C22⋊C8—861no—
442C22⋊C8—861no—
443C22⋊C8—861no—
444C22⋊C8—861no—
445C22⋊C8—861no—
446C22⋊C8—861no—
447#97—861no—
448C4×C8—431no—
449C4×C8—861no—
450C4×C8—861no—
451C4×C8C22×D4311yescharacteristic
452C24—861no—
453#41—3441no—
454#41—3441no—
455C2×Q8—21no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—431no—
462C2×D4—861no—
463C2×D4—862no—
464C2×D4—862no—
465C2×D4—1721no—
466C2×D4D4×D4311yescharacteristic
467C22×C4—21no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—3441no—
476C22×C4—3441no—
477C22×C4—1721no—
478Q16—3441no—
479Q16—3441no—
480SD16—81no—
481SD16—81no—
482SD16—1722no—
483SD16—1722no—
484D8—42no—
485D8—1722no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—81no—
490C2×C8—431no—
491C2×C8—431no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—3441no—
496C2×C8—3441no—
497C2×C8—3441no—
498C2×C8D4×D4311yescharacteristic
499C2×C8D4×D4311yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—431no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—1721no—
509C4⋊C4—1721no—
510C4⋊C4D4×D4311yescharacteristic
511C22⋊C4—21no—
512C22⋊C4—861no—
513C22⋊C4—861no—
514C22⋊C4—861no—
515C22⋊C4—1721no—
516C22⋊C4—1721no—
517C22⋊C4—1721no—
518C42—431no—
519C42—431no—
520C42—431no—
521C42—1721no—
522C42C23×D4311yescharacteristic
523C23—21no—
524C23—41no—
525C23—431no—
526C23—864no—
527C23—861no—
528C23—3441no—
529C23—3441no—
530Q8—41no—
531Q8—41no—
532Q8—1721no—
533Q8—1721no—
534Q8—1721no—
535Q8—1721no—
536D4—21no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—81no—
542D4—432no—
543D4—864no—
544D4—861no—
545D4—3442no—
546D4#1306334612yes—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—431no—
552C2×C4—431no—
553C2×C4—431no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—3441no—
560C2×C4—3441no—
561C2×C4—3442no—
562C2×C4—3441no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4C2×D4×D4311yescharacteristic
569C2×C4C2×D4×D4311yescharacteristic
570C2×C4#41×D4311yescharacteristic
571C8—21no—
572C8—21no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—861no—
577C8—861no—
578C8—1721no—
579C8—1721no—
580C8—1721no—
581C22—22no—
582C22—41no—
583C22—41no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—861no—
588C22—861no—
589C22—861no—
590C22—862no—
591C22—3444no—
592C22—1721no—
593C22—1721no—
594C22#121×D4311yescharacteristic
595C4—21no—
596C4—41no—
597C4—81no—
598C4—861no—
599C4—861no—
600C4—861no—
601C4—3441no—
602C4—3441no—
603C4—1721no—
604C4#135×D4311yescharacteristic
605C4C2×#1306334611yescharacteristic
606C4#1458370011yescharacteristic
607C4#1458370311yescharacteristic
608C2—42no—
609C2—161no—
610C2—1721no—
611C2—1722no—
612C2#1914409311yescharacteristic
613C2#1914417111yescharacteristic
614C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1665C2
socleC22×C43C2×#121
prime radical#19144594C2
hypercenter#1665D43
hypocenterC43#19388
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1665

Complements

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

NH ≅ G/Ntype
1. #19145546C2semidirect
2. #19144696C2semidirect
4. #19143616C2semidirect
5. #19134031C2semidirect
6. #19134030C2semidirect
7. #19134019C2semidirect
8. #19134018C2semidirect
9. #19133959C2semidirect
10. #19133958C2semidirect
11. #19133933C2semidirect
12. #19133372C2semidirect
13. #19133297C2semidirect
14. #19133258C2semidirect
15. C43×#1665C2semidirect
19. #14583278C22semidirect
20. #14583250C22semidirect
21. #14583245C22semidirect
51. #14582651C22semidirect
52. #14582651C22semidirect
53. #14582650C22semidirect
54. #14582646C22semidirect
55. #14582646C22semidirect
56. #14582645C22semidirect
57. #14582644C22semidirect
58. #14582644C22semidirect
59. #14582643C22semidirect
60. C43×#492C22semidirect
64. C43×#334C22semidirect
65. C43×#332C22semidirect
66. C43×#331C22semidirect
312. #1665D43semidirect
327. #492C2×D43semidirect
365. #334C2×D43semidirect
371. #332C2×D43semidirect
373. #331C2×D43semidirect
374. C43#19388semidirect

Maximal subgroups

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

subgroupindex
#191455462
#191446962
#191445942
#191436162
#191340312
#191340302
#191340192
#191340182
#191339592
#191339582
#191339332
#191333722
#191332972
#191332582
C43×#16652
#1938843