Finite Group Databasebeta

← #25088068

Subgroups — #25088068

Order 11008.

666 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146900C211yesmaximal, characteristic, complemented
2#19146837C211yesmaximal, characteristic, complemented
3#19146525C211yesmaximal, characteristic, complemented
4#19134206C211yesmaximal, characteristic, complemented
5#19134140C211yesmaximal, characteristic, complemented
6#19134126C211yesmaximal, characteristic, complemented
7#19134046C211yesmaximal, characteristic, complemented
8#19134029C211yesmaximal, characteristic, complemented
9#19133822C211yesmaximal, characteristic, complemented
10#19133774C211yesmaximal, characteristic, complemented
11#19133746C211yesmaximal, characteristic, complemented
12#19133682C211yesmaximal, characteristic, complemented
13#19133480C211yesmaximal, characteristic, complemented
14C8×#10621882C211yesmaximal, characteristic, complemented
15C43×#3294C211yesmaximal, characteristic, complemented
16#14583614C2211yescharacteristic
17#14583553C2211yescharacteristic, complemented
18#14583251C2211yescharacteristic, complemented
19#14583250C2211yescharacteristic, complemented
20#14583249C2211yescharacteristic, complemented
21#14583245C2211yescharacteristic
22#14583245C2211yescharacteristic
23#14583242—21no—
24#14583232—21no—
25#14583220—21no—
26#14583189C2211yescharacteristic
27#14583189C2211yescharacteristic, complemented
28#14583179C2211yescharacteristic
29#14583150—21no—
30#14583147—21no—
31#14583127—21no—
32#14583104C2211yescharacteristic
33#14583101C2211yescharacteristic, complemented
34#14583091C2211yescharacteristic
35#14583044—21no—
36#14583041—21no—
37#14583033—21no—
38C4×#10621882C2211yescharacteristic
39#14582977C2211yescharacteristic
40#14582977C2211yescharacteristic, complemented
41C8×D172C2211yescharacteristic, complemented
42#14582904—21no—
43#14582900—21no—
44#14582892—21no—
45#14582652C2211yescharacteristic, complemented
46#14582651C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, complemented
48#14582646C2211yescharacteristic, complemented
49#14582645C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic
51D4⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic, complemented
55C8×C43⋊C8C2211yescharacteristic, 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—
67C2×#10621900—21no—
68C2×#10621883—21no—
69C2×#10621884—21no—
70C2×#10621882—21no—
71C2×#10621882D411yescharacteristic
72C2×#10621877—21no—
73C2×#10621877—21no—
74C2×C8×D43—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063311—41no—
78#13063309—41no—
79#13063305—21no—
80#13063299—21no—
81#13063299—21no—
82#13063296—21no—
83C4×D172C2311yescharacteristic
84#13063284—21no—
85#13063283—21no—
86C2×C4⋊Dic43—21no—
87#13063258—21no—
88#13063258D411yescharacteristic
89#13063256—21no—
90#13063256—21no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94#13063250—21no—
95#13063250—21no—
96#13063249—21no—
97#13063249—21no—
98#13063249—21no—
99#13063248—21no—
100#13063248—41no—
101#13063246—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—
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×#41×C43—21no—
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118C2×D8×C43—21no—
119C2×D8×C43D411yescharacteristic
120C22×C8×C43—21no—
121C4⋊Q8×C43C2311yescharacteristic
122#127×C43C2311yescharacteristic
123#123×C43—41no—
124C22⋊Q8×C43—21no—
125#121×C43—21no—
126#121×C43—21no—
127#121×C43—21no—
128#120×C43—41no—
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131C4×D4×C43C2311yescharacteristic
132C2×C4⋊C4×C43—21no—
133#107×C43—21no—
134#107×C43D411yescharacteristic
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—
145#41×C43—42no—
146#41×C43—81no—
147C2×Q8×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—41no—
152C2×D4×C43—41no—
153C2×D4×C43—41no—
154C2×D4×C43—42no—
155C2×D4×C43—42no—
156C2×D4×C43—81no—
157C2×D4×C43—81no—
158C2×D4×C43C2×D411yescharacteristic
159C2×D4×C43C2×D411yescharacteristic
160C2×D4×C43C2×D411yescharacteristic
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—41no—
165C2×C22⋊D43—41no—
166C2×C22⋊D43—41no—
167C22×Dic43—41no—
168#10621900—42no—
169#10621900—81no—
170C2×D172C2×D411yescharacteristic
171C2×C4×D43—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174D8×C43—41no—
175D8×C43—81no—
176C2×C8×C43—21no—
177C2×C8×C43—81no—
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43C2×D411yescharacteristic
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C22⋊C4×C43—21no—
187C22⋊C4×C43—21no—
188C22⋊C4×C43—21no—
189C22⋊C4×C43—41no—
190C22⋊C4×C43—41no—
191C42×C43C2411yescharacteristic
192C22⋊Dic43—41no—
193#10621884—81no—
194#10621883—81no—
195#10621882—22no—
196#10621882—81no—
197(C2×D43)⋊C4—21no—
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
206C4×Dic43—41no—
207#10621877—81no—
208#10621877—81no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215C8×D43—81no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—41no—
220C23×C43—82no—
221C23×C43—82no—
222C23×C43—161no—
223C22×D43—21no—
224Q8×C43—41no—
225Q8×C43—41no—
226D4×C43—21no—
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×C43#13512yes—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—41no—
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—82no—
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C22⋊D43—82no—
255C22⋊D43—161no—
256C2×Dic43—21no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—82no—
260D172—21no—
261D172—21no—
262C4×D43—41no—
263C4×D43—41no—
264Dic86—41no—
265Dic86—41no—
266Dic86—81no—
267C8×C43—21no—
268C8×C43—21no—
269C8×C43—41no—
270C43⋊C8—21no—
271C43⋊C8—21no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276#19899—431nomaximal, Sylow
277C22×C43—22no—
278C22×C43—41no—
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
291C2×D43—41no—
292C2×D43—41no—
293C2×D43—41no—
294C4×C43—21no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—81no—
299C4×C43C2×#13511yescharacteristic
300C4×C43#57511yescharacteristic
301C4×C43#57611yescharacteristic
302C4×C43#57611yescharacteristic
303Dic43—41no—
304Dic43—81no—
305Dic43—81no—
306#3330—431no—
307#3325—431no—
308#3303—431no—
309#3294D4311yescharacteristic, complemented
310#1711—431no—
311#1699—431no—
312#1697—431no—
313#1683—431no—
314#1681—431no—
315#1646—431no—
316#1639—431no—
317#1635—431no—
318#1625—431no—
319#1589—431no—
320C8×D8—431no—
321C2×C43—42no—
322C2×C43—81no—
323C2×C43—81no—
324C2×C43—161no—
325C2×C43#327311yescharacteristic
326C2×C43#328011yescharacteristic
327C2×C43#329011yescharacteristic
328D43—81no—
329#555—431no—
330#547—431no—
331#547C2×D4311yescharacteristic
332D42C2×D4311yescharacteristic
333#487—431no—
334#487—431no—
335#487—431no—
336#486—431no—
337#486—431no—
338#486C2×D4311yescharacteristic
339#485—861no—
340#484—861no—
341#482—861no—
342#480—21no—
343#476—431no—
344#476—431no—
345#474—431no—
346#474C2×D4311yescharacteristic
347#469—861no—
348#468—861no—
349#466—21no—
350#465—861no—
351#461—431no—
352#461—431no—
353#459—431no—
354#459C2×D4311yescharacteristic
355#449—861no—
356#449—861no—
357#447—21no—
358#447—861no—
359C4×D8—431no—
360C4×D8C2×D4311yescharacteristic
361#436—431no—
362#436—431no—
363C8×D4—431no—
364C8×D4C2×D4311yescharacteristic
365#418—861no—
366#417—861no—
367#416—861no—
368C2×#102—21no—
369#335—431no—
370#335—431no—
371#333—431no—
372#332—431no—
373#332—431no—
374#331—431no—
375D4⋊C8—431no—
376D4⋊C8—431no—
377D4⋊C8—431no—
378D4⋊C8—431no—
379C82—431no—
380C43#1989911yescharacteristic, complemented, Sylow
381C2×#41—21no—
382C2×#41—861no—
383C22×D4—21no—
384C22×D4—21no—
385C2×SD16—861no—
386C2×SD16—861no—
387C2×D8—21no—
388C2×D8—431no—
389C2×D8—861no—
390C2×D8C22⋊D4311yescharacteristic
391C2×M16—861no—
392C2×M16—861no—
393C22×C8—21no—
394C22×C8—861no—
395C4⋊Q8—431no—
396C4⋊Q8—431no—
397C4⋊Q8C22×D4311yescharacteristic
398#127C22×D4311yescharacteristic
399#124—1721no—
400#123—41no—
401#123—1721no—
402C22⋊Q8—21no—
403C22⋊Q8—861no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—861no—
408#121—861no—
409#121—861no—
410#120—41no—
411C4×D4—431no—
412C4×D4C22×D4311yescharacteristic
413C4×D4C22×D4311yescharacteristic
414C4×D4C22×D4311yescharacteristic
415#117—861no—
416#117—861no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—861no—
419#107—21no—
420#107—431no—
421#107—861no—
422#107C22⋊D4311yescharacteristic
423#106—861no—
424#106—861no—
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8C22×D4311yescharacteristic
429#103—861no—
430#103—861no—
431#103—861no—
432#103—861no—
433#103—861no—
434#103—861no—
435#103—1721no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—431no—
441#102—431no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102—861no—
446#102—861no—
447#102—861no—
448#102—1721no—
449#102C22⋊D4311yescharacteristic
450#102C22⋊D4311yescharacteristic
451C22⋊C8—21no—
452C22⋊C8—861no—
453C22⋊C8—861no—
454C22⋊C8—861no—
455C4×C8—431no—
456C4×C8—431no—
457C4×C8C22×D4311yescharacteristic
458C24—41no—
459#41—42no—
460#41—81no—
461#41—3441no—
462#41—1722no—
463C2×Q8—21no—
464C2×Q8—861no—
465C2×Q8—861no—
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×D4—431no—
477C2×D4—1721no—
478C2×D4—1721no—
479C2×D4D4×D4311yescharacteristic
480C2×D4C2×C22⋊D4311yescharacteristic
481C2×D4C2×C22⋊D4311yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—41no—
486C22×C4—861no—
487C22×C4—1721no—
488SD16—3441no—
489SD16—3441no—
490D8—41no—
491D8—81no—
492D8—862no—
493D8—3441no—
494M16—3441no—
495M16—3441no—
496C2×C8—21no—
497C2×C8—81no—
498C2×C8—431no—
499C2×C8—431no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—3441no—
505C2×C8C2×C22⋊D4311yescharacteristic
506C2×C8C2×C22⋊D4311yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—431no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—1721no—
516C4⋊C4D4×D4311yescharacteristic
517C4⋊C4C2×C22⋊D4311yescharacteristic
518C4⋊C4C2×C22⋊D4311yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—861no—
525C22⋊C4—1721no—
526C22⋊C4—1721no—
527C22⋊C4—1721no—
528C42—1721no—
529C42C23×D4311yescharacteristic
530C23—21no—
531C23—21no—
532C23—21no—
533C23—41no—
534C23—82no—
535C23—82no—
536C23—161no—
537C23—861no—
538Q8—41no—
539Q8—41no—
540Q8—3441no—
541Q8—1721no—
542Q8—1721no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—81no—
553D4—82no—
554D4—82no—
555D4—82no—
556D4—861no—
557D4—861no—
558D4—3442no—
559D4—6881no—
560D4#1306334412yes—
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—3442no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4C2×D4×D4311yescharacteristic
579C2×C4C22×C22⋊D4311yescharacteristic
580C2×C4#1306337011yescharacteristic
581C8—21no—
582C8—21no—
583C8—41no—
584C8—861no—
585C8—861no—
586C8—1721no—
587C8—1721no—
588C8—1721no—
589C8—1721no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—164no—
603C22—1721no—
604C22—1721no—
605C22—1721no—
606C22D4×C22⋊D4311yescharacteristic
607C4—21no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4—3441no—
613C4—3441no—
614C4—1721no—
615C4C2×#1306334411yescharacteristic
616C4#1458369711yescharacteristic
617C4#1458370011yescharacteristic
618C4#1458370211yescharacteristic
619C2—42no—
620C2—81no—
621C2—81no—
622C2—161no—
623C2—3441no—
624C2#1914620211yescharacteristic
625C2#1914628011yescharacteristic
626C2#1914637511yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3294C2
socleC22×C43D42
hypercenter#3294D43
hypocenterC43#19899
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. #19146900C2semidirect
2. #19146837C2semidirect
3. #19146525C2semidirect
4. #19134206C2semidirect
5. #19134140C2semidirect
6. #19134126C2semidirect
7. #19134046C2semidirect
8. #19134029C2semidirect
9. #19133822C2semidirect
10. #19133774C2semidirect
11. #19133746C2semidirect
12. #19133682C2semidirect
13. #19133480C2semidirect
14. C8×#10621882C2semidirect
15. C43×#3294C2semidirect
17. #14583553C22semidirect
18. #14583251C22semidirect
19. #14583250C22semidirect
20. #14583249C22semidirect
27. #14583189C22semidirect
33. #14583101C22semidirect
40. #14582977C22semidirect
41. C8×D172C22semidirect
45. #14582652C22semidirect
46. #14582651C22semidirect
47. #14582647C22semidirect
48. #14582646C22semidirect
49. #14582645C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. C8×C43⋊C8C22semidirect
309. #3294D43semidirect
380. C43#19899semidirect

Maximal subgroups

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

subgroupindex
#191469002
#191468372
#191465252
#191342062
#191341402
#191341262
#191340462
#191340292
#191338222
#191337742
#191337462
#191336822
#191334802
C8×#106218822
C43×#32942
#1989943