Finite Group Databasebeta

← #25086424

Subgroups — #25086424

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147311C211yesmaximal, characteristic, complemented
2#19146512C211yesmaximal, characteristic, complemented
3D4×#10621883C211yesmaximal, characteristic, complemented
4#19134245C211yesmaximal, characteristic, complemented
5#19134160C211yesmaximal, characteristic, complemented
6#19134018C211yesmaximal, characteristic, complemented
7#19134016C211yesmaximal, characteristic, complemented
8#19133934C211yesmaximal, characteristic, complemented
9#19133843C211yesmaximal, characteristic, complemented
10#19133830C211yesmaximal, characteristic, complemented
11#19133774C211yesmaximal, characteristic, complemented
12#19133703C211yesmaximal, characteristic, complemented
13#19133431C211yesmaximal, characteristic, complemented
14#19133419C211yesmaximal, characteristic, complemented
15C43×#3294C211yesmaximal, characteristic
16C22×#10621883—21no—
17#14583619C2211yescharacteristic, complemented
18D4×Dic86C2211yescharacteristic
19#14583302C2211yescharacteristic, complemented
20#14583271C2211yescharacteristic
21#14583257—21no—
22#14583250C2211yescharacteristic, complemented
23#14583249C2211yescharacteristic, complemented
24#14583245C2211yescharacteristic
25#14583237—21no—
26#14583193—21no—
27#14583179C2211yescharacteristic
28#14583179C2211yescharacteristic, complemented
29#14583138—21no—
30#14583126—21no—
31#14583112—21no—
32#14583106C2211yescharacteristic, complemented
33#14583104C2211yescharacteristic
34#14583104C2211yescharacteristic
35#14583096C2211yescharacteristic
36#14583061—21no—
37#14583050—21no—
38#14583037—21no—
39#14583029C2211yescharacteristic, complemented
40#14582996—21no—
41C4×#10621883C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic, complemented
44#14582895—21no—
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582646C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582644C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic
51#14582629C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic, complemented
55#14582620C2211yescharacteristic, complemented
56C43×#547C2211yescharacteristic
57D42×C43C2211yescharacteristic
58C43×#486C2211yescharacteristic
59C43×#480—21no—
60C43×#474C2211yescharacteristic
61C43×#466—21no—
62C43×#459C2211yescharacteristic
63C43×#447—21no—
64C4×D8×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C2×#102×C43—21no—
67C22×Dic86—21no—
68C2×#10621885—21no—
69C2×#10621883—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621883—21no—
74C2×#10621883—44no—
75C2×#10621883D411yescharacteristic
76C22×C43⋊C8—21no—
77C22×C43⋊C8—21no—
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063324—21no—
81#13063318—41no—
82#13063312—21no—
83#13063304—21no—
84#13063304—21no—
85#13063302—41no—
86C4×Dic86C2311yescharacteristic
87#13063290—21no—
88D4×Dic43—21no—
89#13063284—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258—41no—
93#13063256D411yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97Dic43⋊C8—21no—
98#13063250—21no—
99#13063250—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248D411yescharacteristic
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246—41no—
110#13063246D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113#13063235—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C2×#41×C43—21no—
117C22×D4×C43—21no—
118C22×D4×C43—21no—
119C2×D8×C43—21no—
120C2×D8×C43D411yescharacteristic
121C22×C8×C43—21no—
122C4⋊Q8×C43C2311yescharacteristic
123#127×C43C2311yescharacteristic
124#123×C43—41no—
125C22⋊Q8×C43—21no—
126#121×C43—21no—
127#121×C43—21no—
128#121×C43—21no—
129#120×C43—41no—
130C4×D4×C43C2311yescharacteristic
131C4×D4×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133C2×C4⋊C4×C43—21no—
134#107×C43—21no—
135#107×C43D411yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#102×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43D411yescharacteristic
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146#41×C43—42no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—41no—
153C2×D4×C43—41no—
154C2×D4×C43—41no—
155C2×D4×C43—42no—
156C2×D4×C43—42no—
157C2×D4×C43—81no—
158C2×D4×C43—81no—
159C2×D4×C43C2×D411yescharacteristic
160C2×D4×C43C2×D411yescharacteristic
161C2×D4×C43C2×D411yescharacteristic
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—41no—
166C22×Dic43—41no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—42no—
170C2×Dic86—41no—
171C2×Dic86—81no—
172C2×Dic86C2×D411yescharacteristic
173D8×C43—22no—
174D8×C43—81no—
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×C43—41no—
182C4⋊C4×C43C2×D411yescharacteristic
183C4⋊C4×C43C2×D411yescharacteristic
184C4⋊C4×C43C2×D411yescharacteristic
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C22⋊C4×C43—21no—
188C22⋊C4×C43—41no—
189C22⋊C4×C43—41no—
190C42×C43C2411yescharacteristic
191C22⋊Dic43—41no—
192C22⋊Dic43—41no—
193C22⋊Dic43—41no—
194#10621885—81no—
195#10621883—22no—
196#10621883—42no—
197#10621883—42no—
198#10621883—42no—
199#10621883—42no—
200#10621883—81no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43C2×D411yescharacteristic
206Dic43⋊C4—21no—
207Dic43⋊C4—41no—
208Dic43⋊C4—41no—
209C4×Dic43—21no—
210C4×Dic43—41no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—42no—
216C2×C43⋊C8—81no—
217C2×C43⋊C8C2×D411yescharacteristic
218C2×C43⋊C8C2×D411yescharacteristic
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—41no—
223C23×C43—82no—
224C23×C43—82no—
225C23×C43—161no—
226Q8×C43—41no—
227Q8×C43—41no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—21no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—81no—
237D4×C43—82no—
238D4×C43—82no—
239D4×C43—82no—
240D4×C43#13512yes—
241D4×C43AGL(1,ℤ/8)12yes—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—82no—
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—82no—
261Dic86—21no—
262Dic86—21no—
263Dic86—41no—
264Dic86—41no—
265Dic86—41no—
266Dic86—41no—
267Dic86—82no—
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—41no—
271C43⋊C8—21no—
272C43⋊C8—21no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277#19787—431nomaximal, Sylow
278C22×C43—22no—
279C22×C43—22no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—164no—
291C22×C43D4211yescharacteristic
292C4×C43—21no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—81no—
297C4×C43C2×#13511yescharacteristic
298C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C43#57611yescharacteristic
300C4×C43#57711yescharacteristic
301Dic43—41no—
302Dic43—41no—
303Dic43—81no—
304Dic43—81no—
305#3367—431no—
306#3302—431no—
307#3294D4311yescharacteristic
308D4×SD16—431no—
309#1719—431no—
310#1702—431no—
311#1679—431no—
312#1679—431no—
313#1665—431no—
314#1649—431no—
315#1647—431no—
316#1639—431no—
317#1628—431no—
318#1582—431no—
319#1580—431no—
320C2×C43—42no—
321C2×C43—42no—
322C2×C43—81no—
323C2×C43—161no—
324C2×C43#326411yescharacteristic
325C2×C43#328211yescharacteristic
326C2×C43#328911yescharacteristic
327C22×SD16—861no—
328#556—431no—
329D4×Q8—431no—
330#547C2×D4311yescharacteristic
331D42C2×D4311yescharacteristic
332#500—431no—
333#492—431no—
334#489—861no—
335#487—431no—
336#487—431no—
337#486—431no—
338#486C2×D4311yescharacteristic
339#485—861no—
340#480—21no—
341#477—861no—
342#474—431no—
343#474—431no—
344#474C2×D4311yescharacteristic
345#467—861no—
346#466—21no—
347#465—861no—
348#463—861no—
349#462—431no—
350#461—431no—
351#461—431no—
352#460—431no—
353#459C2×D4311yescharacteristic
354#452—861no—
355#450—861no—
356#448—861no—
357#447—21no—
358#446—431no—
359#440—861no—
360C4×SD16—431no—
361C4×D8C2×D4311yescharacteristic
362C8×D4—431no—
363C8×D4—431no—
364C8×D4C2×D4311yescharacteristic
365#416—861no—
366C2×#102—21no—
367#334—431no—
368#334—431no—
369#332—431no—
370#332—431no—
371#332—431no—
372#331—431no—
373Q8⋊C8—431no—
374D4⋊C8—431no—
375D4⋊C8—431no—
376D4⋊C8—431no—
377#322—431no—
378C43#1978711yescharacteristic, complemented, Sylow
379C2×#41—21no—
380C22×Q8—861no—
381C22×D4—21no—
382C22×D4—21no—
383C2×Q16—861no—
384C2×SD16—431no—
385C2×SD16—861no—
386C2×SD16—861no—
387C2×SD16—861no—
388C2×SD16—861no—
389C2×SD16—861no—
390C2×SD16—1724no—
391C2×D8—21no—
392C2×D8C22⋊D4311yescharacteristic
393C22×C8—21no—
394C22×C8—861no—
395C22×C8—861no—
396C4⋊Q8—431no—
397C4⋊Q8—431no—
398C4⋊Q8—861no—
399C4⋊Q8C22×D4311yescharacteristic
400#127C22×D4311yescharacteristic
401#126—1721no—
402#124—861no—
403#123—41no—
404C22⋊Q8—21no—
405C22⋊Q8—861no—
406C22⋊Q8—861no—
407C22⋊Q8—1721no—
408#121—21no—
409#121—21no—
410#121—21no—
411#120—41no—
412C4×Q8—431no—
413C4×Q8—861no—
414C4×D4—861no—
415C4×D4C22×D4311yescharacteristic
416C4×D4C22×D4311yescharacteristic
417C4×D4C22×D4311yescharacteristic
418#117—861no—
419C2×C4⋊C4—21no—
420#107—21no—
421#107—861no—
422#107—861no—
423#107—1721no—
424#107C22⋊D4311yescharacteristic
425#106—431no—
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8—861no—
430C4⋊C8C22×D4311yescharacteristic
431#103—431no—
432#103—861no—
433#103—861no—
434#103—861no—
435#103—861no—
436#103—861no—
437#103—861no—
438#103—861no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—431no—
444#102—861no—
445#102—861no—
446#102—861no—
447#102—1721no—
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—42no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—431no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×Q8—3441no—
465C2×Q8—1721no—
466C2×Q8—1722no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—41no—
475C2×D4—81no—
476C2×D4—81no—
477C2×D4D4×D4311yescharacteristic
478C2×D4C2×C22⋊D4311yescharacteristic
479C2×D4C2×C22⋊D4311yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—41no—
484C22×C4—1721no—
485Q16—3441no—
486SD16—862no—
487SD16—3441no—
488SD16—1722no—
489SD16—1722no—
490SD16—1722no—
491SD16—1722no—
492D8—22no—
493D8—81no—
494C2×C8—21no—
495C2×C8—81no—
496C2×C8—431no—
497C2×C8—431no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—3441no—
503C2×C8—1722no—
504C2×C8C2×C22⋊D4311yescharacteristic
505C2×C8C2×C22⋊D4311yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—41no—
509C4⋊C4—431no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—1721no—
516C4⋊C4—1721no—
517C4⋊C4D4×D4311yescharacteristic
518C4⋊C4C2×C22⋊D4311yescharacteristic
519C4⋊C4C2×C22⋊D4311yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—1721no—
526C22⋊C4—1721no—
527C22⋊C4—1721no—
528C42—861no—
529C42—1721no—
530C42C23×D4311yescharacteristic
531C23—21no—
532C23—21no—
533C23—21no—
534C23—41no—
535C23—82no—
536C23—82no—
537C23—161no—
538Q8—41no—
539Q8—41no—
540Q8—861no—
541Q8—861no—
542Q8—3442no—
543Q8—1721no—
544Q8—1721no—
545Q8—1721no—
546Q8—1721no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—21no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—81no—
556D4—82no—
557D4—82no—
558D4—82no—
559D4#1306334512yes—
560D4#1306334912yes—
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—82no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—3442no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4C2×D4×D4311yescharacteristic
578C2×C4C22×C22⋊D4311yescharacteristic
579C2×C4#1306337011yescharacteristic
580C8—21no—
581C8—21no—
582C8—41no—
583C8—861no—
584C8—861no—
585C8—1721no—
586C8—1721no—
587C8—1721no—
588C8—1721no—
589C22—22no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—164no—
602C22D4×C22⋊D4311yescharacteristic
603C4—21no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—81no—
608C4—3441no—
609C4—3441no—
610C4—1721no—
611C4—1721no—
612C4C2×#1306334511yescharacteristic
613C4C2×#1306334911yescharacteristic
614C4#1458370011yescharacteristic
615C4#1458371011yescharacteristic
616C2—42no—
617C2—42no—
618C2—81no—
619C2—161no—
620C2#1914607511yescharacteristic
621C2#1914629811yescharacteristic
622C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3294C2
socleC22×C43D42
hypercenter#3294D43
hypocenterC43#19787
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3294

Complements

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

NH ≅ G/Ntype
1. #19147311C2semidirect
2. #19146512C2semidirect
3. D4×#10621883C2semidirect
4. #19134245C2semidirect
5. #19134160C2semidirect
6. #19134018C2semidirect
7. #19134016C2semidirect
8. #19133934C2semidirect
9. #19133843C2semidirect
10. #19133830C2semidirect
11. #19133774C2semidirect
12. #19133703C2semidirect
13. #19133431C2semidirect
14. #19133419C2semidirect
17. #14583619C22semidirect
19. #14583302C22semidirect
22. #14583250C22semidirect
23. #14583249C22semidirect
28. #14583179C22semidirect
32. #14583106C22semidirect
39. #14583029C22semidirect
43. D4×C43⋊C8C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582646C22semidirect
48. #14582645C22semidirect
49. #14582644C22semidirect
51. #14582629C22semidirect
54. D4⋊(C43⋊C8)C22semidirect
55. #14582620C22semidirect
378. C43#19787semidirect

Maximal subgroups

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

subgroupindex
#191473112
#191465122
D4×#106218832
#191342452
#191341602
#191340182
#191340162
#191339342
#191338432
#191338302
#191337742
#191337032
#191334312
#191334192
C43×#32942
#1978743