Finite Group Databasebeta

← #25087956

Subgroups — #25087956

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147492C211yesmaximal, characteristic, complemented
2#19146454C211yesmaximal, characteristic, complemented
3#19146419C211yesmaximal, characteristic, complemented
4#19134194C211yesmaximal, characteristic, complemented
5#19134094C211yesmaximal, characteristic, complemented
6#19134064C211yesmaximal, characteristic, complemented
7#19134020C211yesmaximal, characteristic, complemented
8#19134002C211yesmaximal, characteristic, complemented
9#19133800C211yesmaximal, characteristic, complemented
10#19133774C211yesmaximal, characteristic, complemented
11#19133746C211yesmaximal, characteristic, complemented
12#19133697C211yesmaximal, characteristic, complemented
13#19133483C211yesmaximal, characteristic, complemented
14D8×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3272C211yesmaximal, characteristic
16#14583606C2211yescharacteristic
17D4×Dic86C2211yescharacteristic, complemented
18#14583307—21no—
19#14583297C2211yescharacteristic, complemented
20#14583251C2211yescharacteristic, complemented
21#14583251C2211yescharacteristic, complemented
22#14583245C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583229—21no—
25#14583215—21no—
26#14583201—21no—
27#14583189C2211yescharacteristic
28#14583189C2211yescharacteristic, complemented
29#14583187—21no—
30#14583181C2211yescharacteristic, complemented
31#14583179C2211yescharacteristic
32#14583126—21no—
33#14583126—21no—
34#14583104C2211yescharacteristic
35#14583096C2211yescharacteristic
36#14583050—21no—
37#14583037—21no—
38#14583029C2211yescharacteristic, complemented
39#14583011—21no—
40C4×#10621883C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic, complemented
43C2×#13063248—21no—
44C2×#13063246—21no—
45#14582652C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, 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
55C8×C43⋊C8C2211yescharacteristic, complemented
56C2×AGL(1,ℤ/8)×C43—21no—
57C43×#547C2211yescharacteristic
58D42×C43C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#468—21no—
61C43×#461C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#450—21no—
64C43×#449—21no—
65C4×D8×C43C2211yescharacteristic
66C43×#436C2211yescharacteristic
67C22×Dic86—21no—
68C2×#10621883—21no—
69C2×#10621883—21no—
70C2×#10621883D411yescharacteristic
71C22×C43⋊C8—21no—
72C22×C43⋊C8—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063324—21no—
76#13063316—21no—
77#13063304—21no—
78#13063304—21no—
79#13063302—41no—
80#13063302—41no—
81C4×Dic86C2311yescharacteristic
82D4×Dic43—21no—
83D4×Dic43—21no—
84C2×C4⋊Dic43—21no—
85#13063258—21no—
86#13063257—21no—
87#13063257—21no—
88#13063256—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#13063248—21no—
98#13063248—21no—
99#13063248—21no—
100#13063248—41no—
101#13063248D411yescharacteristic
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246—41no—
109#13063246D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112#13063235—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×#41×C43—21no—
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118AGL(1,ℤ/8)×C43—44no—
119C2×SD16×C43—21no—
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×D8×C43—21no—
123C2×D8×C43D411yescharacteristic
124C2×M16×C43—21no—
125C4⋊Q8×C43C2311yescharacteristic
126#127×C43C2311yescharacteristic
127#123×C43—41no—
128C22⋊Q8×C43—21no—
129#121×C43—21no—
130#121×C43—21no—
131#121×C43—21no—
132#120×C43—41no—
133C4×D4×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136C2×C4⋊C4×C43—21no—
137#107×C43D411yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×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—
167C22×Dic43—41no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—42no—
171C2×Dic86—41no—
172C2×Dic86—81no—
173C2×Dic86C2×D411yescharacteristic
174SD16×C43—42no—
175SD16×C43—42no—
176SD16×C43—81no—
177D8×C43—42no—
178D8×C43SD1614yescomplemented
179M16×C43—42no—
180C2×C8×C43—21no—
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43C2×D411yescharacteristic
187C4⋊C4×C43C2×D411yescharacteristic
188C4⋊C4×C43C2×D411yescharacteristic
189C22⋊C4×C43—21no—
190C22⋊C4×C43—21no—
191C22⋊C4×C43—21no—
192C22⋊C4×C43—41no—
193C22⋊C4×C43—41no—
194C42×C43C2411yescharacteristic
195C22⋊Dic43—41no—
196C22⋊Dic43—41no—
197#10621883—41no—
198#10621883—81no—
199#10621883—81no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—41no—
205C4⋊Dic43C2×D411yescharacteristic
206Dic43⋊C4—21no—
207Dic43⋊C4—41no—
208Dic43⋊C4—41no—
209C4×Dic43—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—81no—
215C2×C43⋊C8—81no—
216C2×C43⋊C8C2×D411yescharacteristic
217C2×C43⋊C8C2×D411yescharacteristic
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—41no—
222C23×C43—82no—
223C23×C43—82no—
224C23×C43—161no—
225Q8×C43—41no—
226Q8×C43—41no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—81no—
236D4×C43—82no—
237D4×C43—82no—
238D4×C43—82no—
239D4×C43C2×SD1612yes—
240D4×C43C2×SD1612yes—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—41no—
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—82no—
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—82no—
260C2×Dic43—161no—
261Dic86—21no—
262Dic86—21no—
263Dic86—41no—
264Dic86—41no—
265Dic86—82no—
266Dic86—81no—
267C8×C43—21no—
268C8×C43—41no—
269C8×C43C2×SD1612yes—
270C43⋊C8—21no—
271C43⋊C8—21no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276#19891—431nomaximal, Sylow
277C22×C43—22no—
278C22×C43—22no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—164no—
290C22×C43D4211yescharacteristic
291C4×C43—21no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—81no—
296C4×C43C22×SD1611yescharacteristic
297C4×C43#57511yescharacteristic
298C4×C43#57611yescharacteristic
299C4×C43#57711yescharacteristic
300Dic43—41no—
301Dic43—41no—
302Dic43—81no—
303Dic43—81no—
304#3384—431no—
305#3298—431no—
306#3295—431no—
307#3272D4311yescharacteristic
308#1708—431no—
309#1691—431no—
310#1686—431no—
311#1679—431no—
312#1677—431no—
313#1643—431no—
314#1639—431no—
315#1635—431no—
316#1627—431no—
317#1590—431no—
318C8×D8—431no—
319C2×C43—42no—
320C2×C43—42no—
321C2×C43—81no—
322C2×C43—161no—
323C2×C43#327311yescharacteristic
324C2×C43D4×SD1611yescharacteristic
325C2×C43#329011yescharacteristic
326C2×AGL(1,ℤ/8)—21no—
327#554—431no—
328D4×Q8—431no—
329#547C2×D4311yescharacteristic
330D42C2×D4311yescharacteristic
331#501—861no—
332#498—431no—
333#492C2×D4311yescharacteristic
334#487—431no—
335#487—431no—
336#486—431no—
337#486—431no—
338#483—861no—
339#481—861no—
340#478—861no—
341#476—431no—
342#476—431no—
343#476—861no—
344#475—431no—
345#474—431no—
346#468—21no—
347#465—861no—
348#465—861no—
349#461—431no—
350#461C2×D4311yescharacteristic
351#460—431no—
352#459C2×D4311yescharacteristic
353#450—21no—
354#450—861no—
355#449—21no—
356#448—861no—
357#446—431no—
358#442—861no—
359C4×SD16—431no—
360C4×D8C2×D4311yescharacteristic
361#436C2×D4311yescharacteristic
362C8×D4—431no—
363C8×D4—431no—
364C2×#103—861no—
365C2×#102—861no—
366#335—431no—
367#334—431no—
368#333—431no—
369#332—431no—
370#332—431no—
371#331—431no—
372Q8⋊C8—431no—
373D4⋊C8—431no—
374D4⋊C8—431no—
375D4⋊C8—431no—
376C82—431no—
377C43#1989111yescharacteristic, complemented, Sylow
378C2×#41—21no—
379C22×Q8—861no—
380C22×D4—21no—
381C22×D4—21no—
382AGL(1,ℤ/8)—44no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16—431no—
387C2×SD16—861no—
388C2×SD16—861no—
389C2×D8—21no—
390C2×D8C22⋊D4311yescharacteristic
391C2×M16—21no—
392C22×C8—861no—
393C22×C8—861no—
394C4⋊Q8—431no—
395C4⋊Q8—431no—
396C4⋊Q8—861no—
397C4⋊Q8C22×D4311yescharacteristic
398#127C22×D4311yescharacteristic
399#125—861no—
400#123—41no—
401C22⋊Q8—21no—
402C22⋊Q8—861no—
403C22⋊Q8—861no—
404C22⋊Q8—1721no—
405C22⋊Q8—1721no—
406#121—21no—
407#121—21no—
408#121—21no—
409#120—41no—
410C4×Q8—431no—
411C4×D4—861no—
412C4×D4—861no—
413C4×D4C22×D4311yescharacteristic
414C4×D4C22×D4311yescharacteristic
415C4×D4C22×D4311yescharacteristic
416C2×C4⋊C4—21no—
417C2×C4⋊C4—861no—
418#107—861no—
419#107C22⋊D4311yescharacteristic
420#106—431no—
421#106—861no—
422#106—861no—
423#106—861no—
424#106—861no—
425#106—861no—
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8—861no—
430C4⋊C8C22×D4311yescharacteristic
431#103—21no—
432#103—431no—
433#103—861no—
434#103—861no—
435#103—861no—
436#103—861no—
437#103—1721no—
438#102—21no—
439#102—431no—
440#102—861no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102—861no—
446#102—1721no—
447#102C22⋊D4311yescharacteristic
448#102C22⋊D4311yescharacteristic
449C22⋊C8—21no—
450C22⋊C8—861no—
451C22⋊C8—861no—
452#97—861no—
453C4×C8—431no—
454C4×C8—431no—
455C4×C8C22×D4311yescharacteristic
456C24—41no—
457#41—42no—
458#41—81no—
459C2×Q8—21no—
460C2×Q8—431no—
461C2×Q8—861no—
462C2×Q8—861no—
463C2×Q8—3441no—
464C2×Q8—1721no—
465C2×Q8—1722no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—41no—
474C2×D4—81no—
475C2×D4—81no—
476C2×D4D4×D4311yescharacteristic
477C2×D4C2×C22⋊D4311yescharacteristic
478C2×D4C2×C22⋊D4311yescharacteristic
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4—1721no—
484C22×C4—1721no—
485SD16—42no—
486SD16—42no—
487SD16—81no—
488SD16—3441no—
489SD16—3441no—
490SD16—1721no—
491D8—42no—
492D8#1062188314yescomplemented
493M16—42no—
494C2×C8—21no—
495C2×C8—431no—
496C2×C8—431no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—3441no—
502C2×C8—3441no—
503C2×C8C2×C22⋊D4311yescharacteristic
504C2×C8C2×C22⋊D4311yescharacteristic
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—41no—
508C4⋊C4—431no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—1721no—
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—
527C42—861no—
528C42C23×D4311yescharacteristic
529C23—21no—
530C23—21no—
531C23—21no—
532C23—41no—
533C23—82no—
534C23—82no—
535C23—161no—
536Q8—41no—
537Q8—41no—
538Q8—861no—
539Q8—861no—
540Q8—3441no—
541Q8—3442no—
542Q8—1721no—
543Q8—1721no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—81no—
553D4—82no—
554D4—82no—
555D4—82no—
556D4C2×#1062188312yes—
557D4C2×#1062188312yes—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—82no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—3442no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—6881no—
575C2×C4C2×D4×D4311yescharacteristic
576C2×C4C22×C22⋊D4311yescharacteristic
577C2×C4#1306337011yescharacteristic
578C8—21no—
579C8—41no—
580C8—861no—
581C8—861no—
582C8—1721no—
583C8—1721no—
584C8—1721no—
585C8—1721no—
586C8C2×#1062188312yes—
587C22—22no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—164no—
600C22D4×C22⋊D4311yescharacteristic
601C4—21no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—81no—
606C4—3441no—
607C4—3441no—
608C4—1721no—
609C4—1721no—
610C4C22×#1062188311yescharacteristic
611C4#1458369511yescharacteristic
612C4#1458370311yescharacteristic
613C4#1458371011yescharacteristic
614C2—42no—
615C2—42no—
616C2—81no—
617C2—161no—
618C2#1914620011yescharacteristic
619C2D4×#1062188311yescharacteristic
620C2#1914637511yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3272C2
socleC22×C43D42
hypercenter#3272D43
hypocenterC43#19891
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3272

Complements

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

NH ≅ G/Ntype
1. #19147492C2semidirect
2. #19146454C2semidirect
3. #19146419C2semidirect
4. #19134194C2semidirect
5. #19134094C2semidirect
6. #19134064C2semidirect
7. #19134020C2semidirect
8. #19134002C2semidirect
9. #19133800C2semidirect
10. #19133774C2semidirect
11. #19133746C2semidirect
12. #19133697C2semidirect
13. #19133483C2semidirect
14. D8×C43⋊C8C2semidirect
17. D4×Dic86C22semidirect
19. #14583297C22semidirect
20. #14583251C22semidirect
21. #14583251C22semidirect
28. #14583189C22semidirect
30. #14583181C22semidirect
38. #14583029C22semidirect
42. D4×C43⋊C8C22semidirect
45. #14582652C22semidirect
46. #14582649C22semidirect
47. #14582647C22semidirect
48. #14582645C22semidirect
49. #14582644C22semidirect
51. #14582629C22semidirect
54. D4⋊(C43⋊C8)C22semidirect
55. C8×C43⋊C8C22semidirect
178. D8×C43SD16semidirect
377. C43#19891semidirect
492. D8#10621883semidirect

Maximal subgroups

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

subgroupindex
#191474922
#191464542
#191464192
#191341942
#191340942
#191340642
#191340202
#191340022
#191338002
#191337742
#191337462
#191336972
#191334832
D8×C43⋊C82
C43×#32722
#1989143