Finite Group Databasebeta

← #25087986

Subgroups — #25087986

Order 11008.

684 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147503C211yesmaximal, characteristic, complemented
2#19147262C211yesmaximal, characteristic, complemented
3#19146419C211yesmaximal, characteristic, complemented
4#19134184C211yesmaximal, characteristic, complemented
5#19134118C211yesmaximal, characteristic, complemented
6#19134076C211yesmaximal, characteristic, complemented
7#19134009C211yesmaximal, characteristic, complemented
8#19134002C211yesmaximal, characteristic, complemented
9#19133722C211yesmaximal, characteristic, complemented
10#19133711C211yesmaximal, characteristic, complemented
11#19133672C211yesmaximal, characteristic, complemented
12#19133665C211yesmaximal, characteristic, complemented
13#19133483C211yesmaximal, characteristic, complemented
14SD16×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3274C211yesmaximal, characteristic
16Q8×Dic86C2211yescharacteristic, complemented
17#14583606C2211yescharacteristic
18#14583306—21no—
19#14583304C2211yescharacteristic, complemented
20#14583271C2211yescharacteristic
21#14583271C2211yescharacteristic, complemented
22#14583245—21no—
23#14583245C2211yescharacteristic
24#14583245C2211yescharacteristic, complemented
25#14583215—21no—
26#14583208—21no—
27#14583194C2211yescharacteristic, complemented
28#14583189—21no—
29#14583189C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583189C2211yescharacteristic
32#14583177—21no—
33#14583126—21no—
34#14583096—21no—
35#14583096C2211yescharacteristic
36#14583096C2211yescharacteristic, complemented
37#14583050—21no—
38#14583029C2211yescharacteristic, complemented
39Q8×C43⋊C8C2211yescharacteristic, complemented
40#14583000—21no—
41C4×#10621883—21no—
42C4×#10621883C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063246—21no—
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, complemented
48#14582647C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic
50#14582643C2211yescharacteristic, complemented
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52#14582629C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic, complemented
56C2×AGL(1,ℤ/8)×C43—21no—
57C43×#550C2211yescharacteristic
58D42×C43C2211yescharacteristic
59C43×#493C2211yescharacteristic
60C43×#469—21no—
61C43×#460C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#449—21no—
64C43×#447—21no—
65C4×SD16×C43C2211yescharacteristic
66C43×#436C2211yescharacteristic
67C2×#10621883—21no—
68C2×#10621883—21no—
69C2×#10621883—41no—
70C2×#10621883—41no—
71C2×#10621883D411yescharacteristic
72C22×C43⋊C8—21no—
73#13063325—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063324—21no—
77#13063324—41no—
78#13063316—21no—
79#13063304—21no—
80#13063302—41no—
81Q8×Dic43—21no—
82C4×Dic86—21no—
83C4×Dic86C2311yescharacteristic
84D4×Dic43—21no—
85C2×C4⋊Dic43—21no—
86#13063259—21no—
87#13063259—21no—
88#13063258—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256D411yescharacteristic
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97Dic43⋊C8—21no—
98#13063249—21no—
99#13063248D411yescharacteristic
100#13063246—21no—
101#13063246—21no—
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111#13063235—21no—
112C4×C43⋊C8—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×C43D411yescharacteristic
121C2×D8×C43—21no—
122C2×D8×C43—21no—
123C2×D8×C43—21no—
124C2×M16×C43—21no—
125#127×C43—21no—
126#127×C43C2311yescharacteristic
127#127×C43C2311yescharacteristic
128#121×C43—21no—
129#121×C43—21no—
130#121×C43—21no—
131#121×C43—41no—
132#120×C43—41no—
133C4×Q8×C43C2311yescharacteristic
134C4×D4×C43—21no—
135C4×D4×C43C2311yescharacteristic
136C4×D4×C43C2311yescharacteristic
137#106×C43D411yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43D411yescharacteristic
140#102×C43—21no—
141#102×C43—21no—
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146#41×C43—42no—
147#41×C43—81no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—41no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43—81no—
162C2×D4×C43—81no—
163C2×D4×C43C2×D411yescharacteristic
164C2×D4×C43C2×D411yescharacteristic
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—41no—
168C22×Dic43—41no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—41no—
172C2×Dic86C2×D411yescharacteristic
173SD16×C43—42no—
174SD16×C43SD1614yescomplemented
175D8×C43—42no—
176D8×C43—42no—
177D8×C43—81no—
178M16×C43—42no—
179C2×C8×C43—21no—
180C2×C8×C43C2×D411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C4⋊C4×C43—21no—
183C4⋊C4×C43C2×D411yescharacteristic
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C22⋊C4×C43—21no—
187C22⋊C4×C43—21no—
188C22⋊C4×C43—41no—
189C22⋊C4×C43—41no—
190C42×C43—21no—
191C42×C43C2411yescharacteristic
192C22⋊Dic43—41no—
193#10621883—41no—
194#10621883—42no—
195#10621883—82no—
196#10621883—82no—
197#10621883—81no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—41no—
203C4⋊Dic43—41no—
204C4⋊Dic43C2×D411yescharacteristic
205Dic43⋊C4—21no—
206Dic43⋊C4—41no—
207Dic43⋊C4—41no—
208C4×Dic43—21no—
209C4×Dic43—41no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—81no—
215C2×C43⋊C8C2×D411yescharacteristic
216C2×C43⋊C8C2×D411yescharacteristic
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—82no—
222C23×C43—82no—
223C23×C43—161no—
224Q8×C43—21no—
225Q8×C43C2×SD1612yes—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—82no—
238D4×C43—81no—
239D4×C43—81no—
240D4×C43—82no—
241D4×C43—82no—
242D4×C43—161no—
243D4×C43C2×SD1612yes—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
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—161no—
261Dic86—21no—
262Dic86—21no—
263Dic86—81no—
264Dic86—81no—
265Dic86—161no—
266C8×C43—21no—
267C8×C43—41no—
268C8×C43C2×SD1612yes—
269C43⋊C8—22no—
270C43⋊C8—21no—
271C43⋊C8—21no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275#19893—431nomaximal, Sylow
276C22×C43—22no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—164no—
289C22×C43D4211yescharacteristic
290C4×C43—22no—
291C4×C43—21no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43C22×SD1611yescharacteristic
296C4×C43#57511yescharacteristic
297C4×C43#57711yescharacteristic
298C4×C43#57711yescharacteristic
299Dic43—41no—
300Dic43—41no—
301Dic43—81no—
302Dic43—81no—
303#3385—431no—
304#3362—431no—
305#3295—431no—
306#3274D4311yescharacteristic
307#1706—431no—
308#1695—431no—
309#1688—431no—
310#1678—431no—
311#1677—431no—
312#1631—431no—
313#1629—431no—
314#1623—431no—
315#1622—431no—
316#1590—431no—
317C8×SD16—431no—
318C2×C43—42no—
319C2×C43—81no—
320C2×C43—161no—
321C2×C43—161no—
322C2×C43#327511yescharacteristic
323C2×C43D4×SD1611yescharacteristic
324C2×C43#329211yescharacteristic
325C2×AGL(1,ℤ/8)—21no—
326Q82—431no—
327#554—431no—
328#550C2×D4311yescharacteristic
329D42C2×D4311yescharacteristic
330#501—861no—
331#500—431no—
332#493C2×D4311yescharacteristic
333#492—431no—
334#492—431no—
335#486—431no—
336#486—431no—
337#486—861no—
338#481—861no—
339#479—861no—
340#477—431no—
341#476—431no—
342#476—431no—
343#476—431no—
344#476—861no—
345#474—861no—
346#469—21no—
347#465—861no—
348#460—431no—
349#460—431no—
350#460—861no—
351#460C2×D4311yescharacteristic
352#459C2×D4311yescharacteristic
353#450—861no—
354#449—21no—
355#447—21no—
356#446—431no—
357C8×Q8—431no—
358#440—861no—
359C4×SD16—431no—
360C4×SD16—861no—
361C4×SD16C2×D4311yescharacteristic
362#436C2×D4311yescharacteristic
363C8×D4—431no—
364C2×#102—861no—
365#334—431no—
366#334—431no—
367#333—431no—
368#333—431no—
369#331—431no—
370#331—431no—
371Q8⋊C8—431no—
372Q8⋊C8—431no—
373D4⋊C8—431no—
374D4⋊C8—431no—
375C82—431no—
376C43#1989311yescharacteristic, complemented, Sylow
377C2×#41—21no—
378C22×D4—21no—
379C22×D4—21no—
380AGL(1,ℤ/8)—44no—
381C2×SD16—21no—
382C2×SD16—431no—
383C2×SD16—861no—
384C2×SD16—861no—
385C2×SD16—1721no—
386C2×SD16—1721no—
387C2×SD16C22⋊D4311yescharacteristic
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—21no—
391C2×M16—21no—
392C22×C8—861no—
393C4⋊Q8—431no—
394C4⋊Q8—431no—
395C4⋊Q8—861no—
396C4⋊Q8—861no—
397C4⋊Q8—1721no—
398#127—21no—
399#127C22×D4311yescharacteristic
400#127C22×D4311yescharacteristic
401#125—861no—
402C22⋊Q8—861no—
403C22⋊Q8—1721no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—41no—
408#120—41no—
409C4×Q8—431no—
410C4×Q8—861no—
411C4×Q8—861no—
412C4×Q8C22×D4311yescharacteristic
413C4×D4—21no—
414C4×D4—861no—
415C4×D4C22×D4311yescharacteristic
416C4×D4C22×D4311yescharacteristic
417C2×C4⋊C4—861no—
418#107—861no—
419#107—861no—
420#107—861no—
421#106—431no—
422#106—861no—
423#106—861no—
424#106—861no—
425#106C22⋊D4311yescharacteristic
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8—861no—
430C4⋊C8—861no—
431C4⋊C8C22×D4311yescharacteristic
432#103—431no—
433#103—861no—
434#103C22⋊D4311yescharacteristic
435#102—21no—
436#102—21no—
437#102—431no—
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#102C22⋊D4311yescharacteristic
448C22⋊C8—21no—
449C22⋊C8—861no—
450#97—861no—
451C4×C8—431no—
452C4×C8—431no—
453C4×C8—861no—
454C4×C8C22×D4311yescharacteristic
455C24—41no—
456#41—42no—
457#41—81no—
458C2×Q8—431no—
459C2×Q8—861no—
460C2×Q8—861no—
461C2×Q8—1721no—
462C2×Q8C2×C22⋊D4311yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—81no—
476C2×D4—81no—
477C2×D4D4×D4311yescharacteristic
478C2×D4C2×C22⋊D4311yescharacteristic
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—41no—
482C22×C4—1721no—
483SD16—42no—
484SD16—3442no—
485SD16—3442no—
486SD16—3441no—
487SD16—1721no—
488SD16—1722no—
489SD16#1062188314yescomplemented
490D8—42no—
491D8—42no—
492D8—81no—
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×C8C2×C22⋊D4311yescharacteristic
503C2×C8C2×C22⋊D4311yescharacteristic
504C4⋊C4—21no—
505C4⋊C4—431no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—1721no—
512C4⋊C4—1721no—
513C4⋊C4—1721no—
514C4⋊C4—1721no—
515C4⋊C4D4×D4311yescharacteristic
516C4⋊C4C2×C22⋊D4311yescharacteristic
517C4⋊C4C2×C22⋊D4311yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—1721no—
523C42—21no—
524C42—861no—
525C42—1721no—
526C42C23×D4311yescharacteristic
527C23—21no—
528C23—21no—
529C23—41no—
530C23—41no—
531C23—82no—
532C23—82no—
533C23—161no—
534Q8—21no—
535Q8—861no—
536Q8—861no—
537Q8—3441no—
538Q8—3441no—
539Q8—6881no—
540Q8C2×#1062188312yes—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—82no—
553D4—81no—
554D4—81no—
555D4—82no—
556D4—82no—
557D4—161no—
558D4C2×#1062188312yes—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—82no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—6881no—
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4C22×C22⋊D4311yescharacteristic
575C2×C4#1306337011yescharacteristic
576C8—21no—
577C8—41no—
578C8—862no—
579C8—861no—
580C8—861no—
581C8—1721no—
582C8—1721no—
583C8—1721no—
584C8C2×#1062188312yes—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—164no—
598C22D4×C22⋊D4311yescharacteristic
599C4—22no—
600C4—21no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—3441no—
605C4—3441no—
606C4—1721no—
607C4—1721no—
608C4C22×#1062188311yescharacteristic
609C4#1458369511yescharacteristic
610C4#1458370911yescharacteristic
611C4#1458371011yescharacteristic
612C2—42no—
613C2—81no—
614C2—161no—
615C2—161no—
616C2#1914622611yescharacteristic
617C2D4×#1062188311yescharacteristic
618C2#1914639211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3274C2
socleC22×C43D42
hypercenter#3274D43
hypocenterC43#19893
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3274

Complements

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

NH ≅ G/Ntype
1. #19147503C2semidirect
2. #19147262C2semidirect
3. #19146419C2semidirect
4. #19134184C2semidirect
5. #19134118C2semidirect
6. #19134076C2semidirect
7. #19134009C2semidirect
8. #19134002C2semidirect
9. #19133722C2semidirect
10. #19133711C2semidirect
11. #19133672C2semidirect
12. #19133665C2semidirect
13. #19133483C2semidirect
14. SD16×C43⋊C8C2semidirect
16. Q8×Dic86C22semidirect
19. #14583304C22semidirect
21. #14583271C22semidirect
24. #14583245C22semidirect
27. #14583194C22semidirect
36. #14583096C22semidirect
38. #14583029C22semidirect
39. Q8×C43⋊C8C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582647C22semidirect
48. #14582647C22semidirect
50. #14582643C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. #14582629C22semidirect
55. C8×C43⋊C8C22semidirect
174. SD16×C43SD16semidirect
376. C43#19893semidirect
489. SD16#10621883semidirect

Maximal subgroups

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

subgroupindex
#191475032
#191472622
#191464192
#191341842
#191341182
#191340762
#191340092
#191340022
#191337222
#191337112
#191336722
#191336652
#191334832
SD16×C43⋊C82
C43×#32742
#1989343