Finite Group Databasebeta

← #25088224

Subgroups — #25088224

Order 11008.

666 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147300C211yesmaximal, characteristic, complemented
2#19146539C211yesmaximal, characteristic, complemented
3#19146419C211yesmaximal, characteristic, complemented
4#19134199C211yesmaximal, characteristic, complemented
5#19134132C211yesmaximal, characteristic, complemented
6#19134128C211yesmaximal, characteristic, complemented
7#19134006C211yesmaximal, characteristic, complemented
8#19134002C211yesmaximal, characteristic, complemented
9#19133740C211yesmaximal, characteristic, complemented
10#19133727C211yesmaximal, characteristic, complemented
11#19133659C211yesmaximal, characteristic, complemented
12#19133649C211yesmaximal, characteristic, complemented
13#19133483C211yesmaximal, characteristic, complemented
14D8×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3325C211yesmaximal, characteristic, complemented
16#14583606C2211yescharacteristic
17#14583570C2211yescharacteristic, complemented
18#14583278C2211yescharacteristic, complemented
19#14583275C2211yescharacteristic
20#14583262—21no—
21#14583247C2211yescharacteristic, complemented
22#14583246C2211yescharacteristic, complemented
23#14583245C2211yescharacteristic
24#14583223—21no—
25#14583215—21no—
26#14583202—21no—
27#14583191C2211yescharacteristic, complemented
28#14583189C2211yescharacteristic
29#14583189C2211yescharacteristic, complemented
30#14583133—21no—
31#14583126—21no—
32#14583096C2211yescharacteristic
33#14583094C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583092—21no—
36#14583050—21no—
37#14583042—21no—
38#14583029C2211yescharacteristic, complemented
39#14583008—21no—
40C4×#10621883C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic, complemented
43#14582893—21no—
44C2×#13063246—21no—
45#14582652C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582647C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic
50#14582642C2211yescharacteristic, complemented
51#14582629C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic, complemented
55C8×C43⋊C8C2211yescharacteristic, complemented
56C43×#555C2211yescharacteristic
57D42×C43C2211yescharacteristic
58C43×#486C2211yescharacteristic
59C43×#482—21no—
60C43×#476C2211yescharacteristic
61C43×#469—21no—
62C43×#459C2211yescharacteristic
63C43×#447—21no—
64C4×D8×C43C2211yescharacteristic
65C43×#436C2211yescharacteristic
66C43×#418—21no—
67C2×#10621898—21no—
68C2×#10621885—41no—
69C2×#10621883—21no—
70C2×#10621883D411yescharacteristic
71C2×#10621882—21no—
72C2×#10621882—21no—
73C2×#10621882—41no—
74C22×C43⋊C8—21no—
75C22×C43⋊C8—21no—
76#13063325C2311yescharacteristic
77#13063322C2311yescharacteristic
78#13063321—21no—
79#13063316—21no—
80#13063304—21no—
81#13063302—41no—
82#13063299—21no—
83#13063298—41no—
84C4×Dic86C2311yescharacteristic
85D4×Dic43—21no—
86#13063287—21no—
87C2×C4⋊Dic43—21no—
88#13063258—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256D411yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95Dic43⋊C8—21no—
96#13063248—21no—
97#13063248D411yescharacteristic
98#13063247—21no—
99#13063247—21no—
100#13063246—21no—
101#13063246—21no—
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246D411yescharacteristic
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245—21no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112#13063235—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C22×D4×C43—21no—
116C22×D4×C43—21no—
117C2×D8×C43—21no—
118C2×D8×C43D411yescharacteristic
119C2×M16×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121#127×C43C2311yescharacteristic
122#124×C43—41no—
123#121×C43—21no—
124#121×C43—21no—
125#121×C43—21no—
126#121×C43—21no—
127#120×C43—41no—
128C4×D4×C43C2311yescharacteristic
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131#117×C43—21no—
132#117×C43—21no—
133#107×C43D411yescharacteristic
134#106×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#102×C43—21no—
137#102×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C24×C43—41no—
145C2×Q8×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—41no—
150C2×D4×C43—41no—
151C2×D4×C43—41no—
152C2×D4×C43—42no—
153C2×D4×C43—42no—
154C2×D4×C43—81no—
155C2×D4×C43—81no—
156C2×D4×C43C2×D411yescharacteristic
157C2×D4×C43C2×D411yescharacteristic
158C2×D4×C43C2×D411yescharacteristic
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C2×C22⋊D43—41no—
163C2×C22⋊D43—41no—
164C22×Dic43—41no—
165#10621898—42no—
166#10621898—81no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×C4×D43—41no—
171C2×Dic86—21no—
172C2×Dic86C2×D411yescharacteristic
173D8×C43—22no—
174D8×C43—81no—
175M16×C43—81no—
176C2×C8×C43—21no—
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43C2×D411yescharacteristic
182C4⋊C4×C43C2×D411yescharacteristic
183C4⋊C4×C43C2×D411yescharacteristic
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C22⋊C4×C43—41no—
188C22⋊C4×C43—41no—
189C22⋊C4×C43—41no—
190C42×C43—41no—
191C42×C43C2411yescharacteristic
192C22⋊Dic43—41no—
193#10621885—82no—
194#10621883—41no—
195#10621883—81no—
196#10621882—42no—
197#10621882—82no—
198#10621882—81no—
199(C2×D43)⋊C4—41no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—41no—
203C4⋊Dic43C2×D411yescharacteristic
204Dic43⋊C4—21no—
205Dic43⋊C4—41no—
206C4×Dic43—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—81no—
212C2×C43⋊C8—81no—
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—41no—
219C23×C43—82no—
220C23×C43—82no—
221C23×C43—161no—
222C22×D43—41no—
223Q8×C43—81no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—81no—
234D4×C43—82no—
235D4×C43—82no—
236D4×C43—161no—
237D4×C43#13512yes—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C22⋊D43—82no—
252C22⋊D43—161no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—41no—
256C2×Dic43—161no—
257D172—41no—
258D172—41no—
259D172—41no—
260D172—41no—
261D172—81no—
262C4×D43—82no—
263Dic86—21no—
264Dic86—21no—
265Dic86—81no—
266C8×C43—21no—
267C8×C43—21no—
268C8×C43—41no—
269C43⋊C8—22no—
270C43⋊C8—21no—
271C43⋊C8—21no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275#19911—431nomaximal, Sylow
276C22×C43—22no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—164no—
289C22×C43D4211yescharacteristic
290C2×D43—81no—
291C2×D43—81no—
292C2×D43—81no—
293C4×C43—21no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—81no—
298C4×C43C2×#13511yescharacteristic
299C4×C43#57511yescharacteristic
300C4×C43#57611yescharacteristic
301C4×C43#57711yescharacteristic
302Dic43—41no—
303Dic43—41no—
304Dic43—81no—
305#3366—431no—
306#3325D4311yescharacteristic, complemented
307#3305—431no—
308#3295—431no—
309#1709—431no—
310#1698—431no—
311#1697—431no—
312#1677—431no—
313#1677—431no—
314#1634—431no—
315#1632—431no—
316#1621—431no—
317#1619—431no—
318#1590—431no—
319C8×D8—431no—
320C2×C43—42no—
321C2×C43—81no—
322C2×C43—81no—
323C2×C43—161no—
324C2×C43#327311yescharacteristic
325C2×C43#328211yescharacteristic
326C2×C43#329211yescharacteristic
327D43—161no—
328#555C2×D4311yescharacteristic
329#554—431no—
330#550—431no—
331D42C2×D4311yescharacteristic
332#494—431no—
333#493—431no—
334#490—861no—
335#486—431no—
336#486—431no—
337#486—431no—
338#486C2×D4311yescharacteristic
339#482—21no—
340#482—861no—
341#481—861no—
342#478—861no—
343#477—431no—
344#476—431no—
345#476—431no—
346#476C2×D4311yescharacteristic
347#469—21no—
348#466—861no—
349#465—861no—
350#460—431no—
351#459—431no—
352#459—431no—
353#459—861no—
354#459C2×D4311yescharacteristic
355#450—861no—
356#449—861no—
357#447—21no—
358#446—431no—
359#442—861no—
360C4×SD16—431no—
361C4×D8C2×D4311yescharacteristic
362#436C2×D4311yescharacteristic
363C8×D4—431no—
364C8×D4—431no—
365#418—21no—
366#416—861no—
367C2×#102—861no—
368#335—431no—
369#334—431no—
370#333—431no—
371#333—431no—
372#331—431no—
373#331—431no—
374Q8⋊C8—431no—
375D4⋊C8—431no—
376D4⋊C8—431no—
377D4⋊C8—431no—
378C82—431no—
379C43#1991111yescharacteristic, complemented, Sylow
380C2×#41—861no—
381C22×D4—21no—
382C22×D4—21no—
383C2×Q16—1721no—
384C2×SD16—431no—
385C2×SD16—861no—
386C2×D8—21no—
387C2×D8—861no—
388C2×D8—861no—
389C2×D8—1721no—
390C2×D8C22⋊D4311yescharacteristic
391C2×M16—21no—
392C22×C8—861no—
393C22×C8—861no—
394C4⋊Q8—431no—
395C4⋊Q8C22×D4311yescharacteristic
396#127—431no—
397#127—861no—
398#127C22×D4311yescharacteristic
399#125—861no—
400#124—41no—
401C22⋊Q8—861no—
402C22⋊Q8—1721no—
403#121—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—861no—
408#121—1721no—
409#120—41no—
410C4×Q8—431no—
411C4×D4—861no—
412C4×D4—861no—
413C4×D4C22×D4311yescharacteristic
414C4×D4C22×D4311yescharacteristic
415C4×D4C22×D4311yescharacteristic
416#117—21no—
417#117—21no—
418C2×C4⋊C4—861no—
419#107—861no—
420#107C22⋊D4311yescharacteristic
421#106—21no—
422#106—431no—
423#106—861no—
424#106—861no—
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8—861no—
429C4⋊C8C22×D4311yescharacteristic
430#103—431no—
431#103—861no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—431no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102—861no—
446#102—861no—
447#102—861no—
448#102C22⋊D4311yescharacteristic
449#102C22⋊D4311yescharacteristic
450C22⋊C8—21no—
451C22⋊C8—861no—
452C22⋊C8—861no—
453#97—861no—
454C4×C8—431no—
455C4×C8—431no—
456C4×C8C22×D4311yescharacteristic
457C24—41no—
458#41—3441no—
459#41—1722no—
460C2×Q8—21no—
461C2×Q8—431no—
462C2×Q8—861no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—41no—
471C2×D4—81no—
472C2×D4—81no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—1721no—
477C2×D4—1721no—
478C2×D4D4×D4311yescharacteristic
479C2×D4C2×C22⋊D4311yescharacteristic
480C2×D4C2×C22⋊D4311yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—1721no—
485C22×C4—1721no—
486Q16—3442no—
487SD16—3441no—
488SD16—1721no—
489D8—22no—
490D8—81no—
491D8—3442no—
492D8—3441no—
493D8—1722no—
494M16—81no—
495C2×C8—21no—
496C2×C8—431no—
497C2×C8—431no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—3441no—
503C2×C8—3441no—
504C2×C8C2×C22⋊D4311yescharacteristic
505C2×C8C2×C22⋊D4311yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—431no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—1721no—
513C4⋊C4—1721no—
514C4⋊C4D4×D4311yescharacteristic
515C4⋊C4C2×C22⋊D4311yescharacteristic
516C4⋊C4C2×C22⋊D4311yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—1721no—
524C22⋊C4—1721no—
525C42—41no—
526C42—861no—
527C42C23×D4311yescharacteristic
528C23—21no—
529C23—21no—
530C23—21no—
531C23—41no—
532C23—82no—
533C23—82no—
534C23—161no—
535C23—1721no—
536Q8—81no—
537Q8—861no—
538Q8—861no—
539Q8—3441no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—81no—
550D4—82no—
551D4—82no—
552D4—161no—
553D4—3441no—
554D4—3442no—
555D4—1721no—
556D4—1721no—
557D4—1721no—
558D4—1721no—
559D4—6881no—
560D4#1306334512yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—3442no—
574C2×C4—1721no—
575C2×C4—6881no—
576C2×C4C2×D4×D4311yescharacteristic
577C2×C4C22×C22⋊D4311yescharacteristic
578C2×C4#1306337011yescharacteristic
579C8—21no—
580C8—21no—
581C8—41no—
582C8—862no—
583C8—861no—
584C8—861no—
585C8—1721no—
586C8—1721no—
587C8—1721no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—164no—
601C22—3441no—
602C22—3441no—
603C22—3441no—
604C22D4×C22⋊D4311yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—81no—
610C4—3441no—
611C4—1721no—
612C4—1721no—
613C4C2×#1306334511yescharacteristic
614C4#1458369511yescharacteristic
615C4#1458370311yescharacteristic
616C4#1458371011yescharacteristic
617C2—42no—
618C2—81no—
619C2—81no—
620C2—161no—
621C2—6881no—
622C2#1914620011yescharacteristic
623C2#1914629811yescharacteristic
624C2#1914639211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3325C2
socleC22×C43D42
hypercenter#3325D43
hypocenterC43#19911
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3325

Complements

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

NH ≅ G/Ntype
1. #19147300C2semidirect
2. #19146539C2semidirect
3. #19146419C2semidirect
4. #19134199C2semidirect
5. #19134132C2semidirect
6. #19134128C2semidirect
7. #19134006C2semidirect
8. #19134002C2semidirect
9. #19133740C2semidirect
10. #19133727C2semidirect
11. #19133659C2semidirect
12. #19133649C2semidirect
13. #19133483C2semidirect
14. D8×C43⋊C8C2semidirect
15. C43×#3325C2semidirect
17. #14583570C22semidirect
18. #14583278C22semidirect
21. #14583247C22semidirect
22. #14583246C22semidirect
27. #14583191C22semidirect
29. #14583189C22semidirect
38. #14583029C22semidirect
42. D4×C43⋊C8C22semidirect
45. #14582652C22semidirect
46. #14582649C22semidirect
47. #14582648C22semidirect
48. #14582647C22semidirect
50. #14582642C22semidirect
51. #14582629C22semidirect
54. D4⋊(C43⋊C8)C22semidirect
55. C8×C43⋊C8C22semidirect
306. #3325D43semidirect
379. C43#19911semidirect

Maximal subgroups

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

subgroupindex
#191473002
#191465392
#191464192
#191341992
#191341322
#191341282
#191340062
#191340022
#191337402
#191337272
#191336592
#191336492
#191334832
D8×C43⋊C82
C43×#33252
#1991143