Finite Group Databasebeta

← #25086268

Subgroups — #25086268

Order 11008.

648 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147579C211yesmaximal, characteristic, complemented
2#19146514C211yesmaximal, characteristic, complemented
3#19146408C211yesmaximal, characteristic
4#19134256C211yesmaximal, characteristic, complemented
5#19134142C211yesmaximal, characteristic, complemented
6#19134037C211yesmaximal, characteristic, complemented
7#19134029C211yesmaximal, characteristic, complemented
8#19133958C211yesmaximal, characteristic, complemented
9#19133878C211yesmaximal, characteristic, complemented
10#19133865C211yesmaximal, characteristic, complemented
11#19133774C211yesmaximal, characteristic, complemented
12#19133704C211yesmaximal, characteristic, complemented
13#19133422C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C43×#3324C211yesmaximal, characteristic, complemented
16#14583622C2211yescharacteristic, complemented
17#14583553C2211yescharacteristic
18#14583295C2211yescharacteristic, complemented
19#14583281—21no—
20#14583278C2211yescharacteristic, complemented
21#14583250C2211yescharacteristic, complemented
22#14583245C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583243—21no—
25#14583210—21no—
26#14583179C2211yescharacteristic
27#14583179C2211yescharacteristic
28#14583139—21no—
29#14583133—21no—
30#14583121—21no—
31#14583118—21no—
32#14583109C2211yescharacteristic, complemented
33#14583104C2211yescharacteristic
34#14583101C2211yescharacteristic, complemented
35#14583091C2211yescharacteristic
36#14583058—21no—
37#14583033—21no—
38Q8×C43⋊C8C2211yescharacteristic, complemented
39C4×#10621885—21no—
40C4×#10621882C2211yescharacteristic
41C8×D172C2211yescharacteristic, complemented
42D4×C43⋊C8C2211yescharacteristic
43#14582892—21no—
44C2×#13063246—21no—
45#14582652C2211yescharacteristic, complemented
46#14582651C2211yescharacteristic, complemented
47#14582646C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582644C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic, complemented
55#14582620C2211yescharacteristic, complemented
56C43×#556C2211yescharacteristic
57D42×C43C2211yescharacteristic
58C43×#486C2211yescharacteristic
59C43×#482—21no—
60C43×#474C2211yescharacteristic
61C43×#468—21no—
62C43×#460C2211yescharacteristic
63C43×#450—21no—
64C4×SD16×C43C2211yescharacteristic
65C43×#436C2211yescharacteristic
66C43×#418—21no—
67C2×#10621900—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621883—21no—
72C2×#10621884—21no—
73C2×#10621882—21no—
74C2×#10621882D411yescharacteristic
75C22×C43⋊C8—21no—
76C2×C8×D43—21no—
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063320—41no—
80#13063313—21no—
81#13063309—41no—
82#13063305—21no—
83#13063301—21no—
84#13063299—21no—
85C4×Dic86—21no—
86C4×D172C2311yescharacteristic
87#13063283—21no—
88C2×C4⋊Dic43—21no—
89#13063258—21no—
90#13063258—21no—
91#13063258D411yescharacteristic
92#13063256—41no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063250—21no—
98#13063250—21no—
99#13063249—21no—
100#13063248—21no—
101#13063248—21no—
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—41no—
108#13063246D411yescharacteristic
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111(C2×D43)⋊C8—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C22×D4×C43—21no—
116C22×D4×C43—21no—
117C2×SD16×C43—21no—
118C2×SD16×C43D411yescharacteristic
119C2×M16×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121#127×C43C2311yescharacteristic
122#126×C43—41no—
123#124×C43—21no—
124C22⋊Q8×C43—21no—
125#121×C43—21no—
126#121×C43—21no—
127#120×C43—41no—
128C4×Q8×C43—21no—
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131C4×D4×C43C2311yescharacteristic
132#117×C43—21no—
133#107×C43—21no—
134#106×C43D411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136#103×C43D411yescharacteristic
137#102×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C24×C43—41no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
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
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C2×C22⋊D43—41no—
161C22×Dic43—41no—
162#10621900—42no—
163#10621900—81no—
164C2×D172C2×D411yescharacteristic
165C2×C4×D43—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168SD16×C43—22no—
169SD16×C43—81no—
170M16×C43—81no—
171C2×C8×C43—21no—
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43C2×D411yescharacteristic
179C4⋊C4×C43C2×D411yescharacteristic
180C4⋊C4×C43C2×D411yescharacteristic
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—41no—
184C22⋊C4×C43—41no—
185C22⋊C4×C43—41no—
186C42×C43—21no—
187C42×C43—41no—
188C42×C43C2411yescharacteristic
189#10621885—42no—
190#10621885—81no—
191#10621885—81no—
192#10621884—81no—
193#10621883—81no—
194#10621882—41no—
195#10621882—81no—
196(C2×D43)⋊C4—21no—
197(C2×D43)⋊C4—41no—
198(C2×D43)⋊C4—41no—
199(C2×D43)⋊C4—41no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—41no—
205C4⋊Dic43C2×D411yescharacteristic
206Dic43⋊C4—41no—
207C4×Dic43—41no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—81no—
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215C8×D43—81no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—41no—
219C23×C43—82no—
220C23×C43—82no—
221C23×C43—161no—
222C22×D43—21no—
223Q8×C43—21no—
224Q8×C43—21no—
225Q8×C43—41no—
226Q8×C43—41no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—81no—
235D4×C43—82no—
236D4×C43—82no—
237D4×C43#13512yes—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C22⋊D43—82no—
251C2×Dic43—21no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—82no—
255D172—21no—
256D172—21no—
257C4×D43—41no—
258C4×D43—41no—
259Dic86—41no—
260Dic86—41no—
261Dic86—41no—
262Dic86—41no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—41no—
266C43⋊C8—21no—
267C43⋊C8—21no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272#19777—431nomaximal, Sylow
273C22×C43—22no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—164no—
283C22×C43D4211yescharacteristic
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—41no—
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—81no—
293C4×C43C2×#13511yescharacteristic
294C4×C43#57511yescharacteristic
295C4×C43#57611yescharacteristic
296C4×C43#57611yescharacteristic
297Dic43—41no—
298Dic43—81no—
299Dic43—81no—
300#3393—431no—
301#3324D4311yescharacteristic, complemented
302#3302—431no—
303#3294—431no—
304#1720—431no—
305#1699—431no—
306#1682—431no—
307#1681—431no—
308#1669—431no—
309#1654—431no—
310#1652—431no—
311#1639—431no—
312#1628—431no—
313#1581—431no—
314SD16⋊C8—431no—
315C2×C43—42no—
316C2×C43—81no—
317C2×C43—161no—
318C2×C43#326811yescharacteristic
319C2×C43#328011yescharacteristic
320C2×C43#328911yescharacteristic
321D43—81no—
322#556—431no—
323#556C2×D4311yescharacteristic
324#547—431no—
325D42C2×D4311yescharacteristic
326#498—431no—
327#495—861no—
328#494—431no—
329#487—431no—
330#486—431no—
331#486—431no—
332#486C2×D4311yescharacteristic
333#485—861no—
334#482—21no—
335#480—861no—
336#474—431no—
337#474—431no—
338#474C2×D4311yescharacteristic
339#468—21no—
340#467—861no—
341#466—861no—
342#464—861no—
343#464—861no—
344#462—431no—
345#461—431no—
346#461—431no—
347#460C2×D4311yescharacteristic
348#459—431no—
349#452—861no—
350#450—21no—
351#447—861no—
352C8×Q8—431no—
353C4×Q16—861no—
354C4×SD16C2×D4311yescharacteristic
355C4×D8—431no—
356#436C2×D4311yescharacteristic
357C8×D4—431no—
358C8×D4—431no—
359#418—21no—
360#416—861no—
361C2×#102—861no—
362#335—431no—
363#335—431no—
364#332—431no—
365#332—431no—
366#332—431no—
367#331—431no—
368Q8⋊C8—431no—
369D4⋊C8—431no—
370D4⋊C8—431no—
371D4⋊C8—431no—
372#322—431no—
373C43#1977711yescharacteristic, complemented, Sylow
374C2×#41—861no—
375C22×D4—21no—
376C22×D4—21no—
377C2×Q16—861no—
378C2×Q16—861no—
379C2×Q16—861no—
380C2×SD16—21no—
381C2×SD16—861no—
382C2×SD16—861no—
383C2×SD16C22⋊D4311yescharacteristic
384C2×D8—431no—
385C2×D8—861no—
386C2×M16—21no—
387C22×C8—861no—
388C22×C8—861no—
389C4⋊Q8—431no—
390C4⋊Q8—431no—
391C4⋊Q8C22×D4311yescharacteristic
392#127C22×D4311yescharacteristic
393#126—41no—
394#126—1721no—
395#124—21no—
396#124—861no—
397#123—1721no—
398C22⋊Q8—21no—
399C22⋊Q8—861no—
400C22⋊Q8—861no—
401#121—21no—
402#121—21no—
403#121—861no—
404#120—41no—
405C4×Q8—21no—
406C4×Q8—861no—
407C4×Q8C22×D4311yescharacteristic
408C4×D4—431no—
409C4×D4C22×D4311yescharacteristic
410C4×D4C22×D4311yescharacteristic
411#117—21no—
412#117—861no—
413C2×C4⋊C4—861no—
414#107—21no—
415#107—431no—
416#107—861no—
417#107—861no—
418#106—1721no—
419#106C22⋊D4311yescharacteristic
420C4⋊C8—431no—
421C4⋊C8—431no—
422C4⋊C8—431no—
423C4⋊C8—861no—
424C4⋊C8C22×D4311yescharacteristic
425#103—861no—
426#103—861no—
427#103—861no—
428#103—861no—
429#103—861no—
430#103C22⋊D4311yescharacteristic
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—431no—
436#102—431no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441#102—861no—
442#102—1721no—
443#102C22⋊D4311yescharacteristic
444C22⋊C8—21no—
445C22⋊C8—861no—
446C22⋊C8—861no—
447C4×C8—431no—
448C4×C8—431no—
449C4×C8—861no—
450C4×C8C22×D4311yescharacteristic
451C24—41no—
452#41—3441no—
453#41—1722no—
454C2×Q8—21no—
455C2×Q8—861no—
456C2×Q8—861no—
457C2×Q8C2×C22⋊D4311yescharacteristic
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—81no—
466C2×D4—81no—
467C2×D4—431no—
468C2×D4—1721no—
469C2×D4D4×D4311yescharacteristic
470C2×D4C2×C22⋊D4311yescharacteristic
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—861no—
474C22×C4—1721no—
475Q16—3441no—
476Q16—3441no—
477Q16—1722no—
478SD16—22no—
479SD16—81no—
480SD16—3441no—
481SD16—3441no—
482D8—3441no—
483D8—1721no—
484M16—81no—
485C2×C8—21no—
486C2×C8—431no—
487C2×C8—431no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—3441no—
493C2×C8—3441no—
494C2×C8C2×C22⋊D4311yescharacteristic
495C2×C8C2×C22⋊D4311yescharacteristic
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—41no—
500C4⋊C4—431no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—1721no—
506C4⋊C4—1721no—
507C4⋊C4D4×D4311yescharacteristic
508C4⋊C4C2×C22⋊D4311yescharacteristic
509C4⋊C4C2×C22⋊D4311yescharacteristic
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—861no—
516C22⋊C4—1721no—
517C22⋊C4—1721no—
518C22⋊C4—1721no—
519C42—21no—
520C42—41no—
521C42—1721no—
522C42C23×D4311yescharacteristic
523C23—21no—
524C23—21no—
525C23—41no—
526C23—82no—
527C23—82no—
528C23—161no—
529C23—861no—
530Q8—21no—
531Q8—21no—
532Q8—41no—
533Q8—41no—
534Q8—1721no—
535Q8—1721no—
536Q8—1721no—
537Q8—1721no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—81no—
546D4—82no—
547D4—82no—
548D4—861no—
549D4—861no—
550D4—3442no—
551D4#1306334512yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—861no—
562C2×C4—3442no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4C2×D4×D4311yescharacteristic
568C2×C4C22×C22⋊D4311yescharacteristic
569C2×C4#1306337011yescharacteristic
570C8—21no—
571C8—21no—
572C8—41no—
573C8—861no—
574C8—861no—
575C8—1721no—
576C8—1721no—
577C8—1721no—
578C8—1721no—
579C22—22no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—164no—
589C22—1721no—
590C22—1721no—
591C22—1721no—
592C22D4×C22⋊D4311yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—3441no—
600C4—3441no—
601C4—1721no—
602C4C2×#1306334511yescharacteristic
603C4#1458369511yescharacteristic
604C4#1458370211yescharacteristic
605C4#1458370311yescharacteristic
606C2—42no—
607C2—81no—
608C2—161no—
609C2—3441no—
610C2#1914612911yescharacteristic
611C2#1914627611yescharacteristic
612C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3324C2
socleC22×C43D42
prime radical#19146408C2
hypercenter#3324D43
hypocenterC43#19777
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3324

Complements

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

NH ≅ G/Ntype
1. #19147579C2semidirect
2. #19146514C2semidirect
4. #19134256C2semidirect
5. #19134142C2semidirect
6. #19134037C2semidirect
7. #19134029C2semidirect
8. #19133958C2semidirect
9. #19133878C2semidirect
10. #19133865C2semidirect
11. #19133774C2semidirect
12. #19133704C2semidirect
13. #19133422C2semidirect
14. SD16⋊(C43⋊C8)C2semidirect
15. C43×#3324C2semidirect
16. #14583622C22semidirect
18. #14583295C22semidirect
20. #14583278C22semidirect
21. #14583250C22semidirect
32. #14583109C22semidirect
34. #14583101C22semidirect
38. Q8×C43⋊C8C22semidirect
41. C8×D172C22semidirect
45. #14582652C22semidirect
46. #14582651C22semidirect
47. #14582646C22semidirect
48. #14582645C22semidirect
49. #14582644C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. #14582620C22semidirect
301. #3324D43semidirect
373. C43#19777semidirect

Maximal subgroups

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

subgroupindex
#191475792
#191465142
#191464082
#191342562
#191341422
#191340372
#191340292
#191339582
#191338782
#191338652
#191337742
#191337042
#191334222
SD16⋊(C43⋊C8)2
C43×#33242
#1977743