Finite Group Databasebeta

← #25087980

Subgroups — #25087980

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#19147266C211yesmaximal, characteristic, complemented
2#19146413C211yesmaximal, characteristic, complemented
3#19146216C211yesmaximal, characteristic
4#19134188C211yesmaximal, characteristic, complemented
5#19134115C211yesmaximal, characteristic, complemented
6#19134079C211yesmaximal, characteristic, complemented
7#19134013C211yesmaximal, characteristic, complemented
8#19134006C211yesmaximal, characteristic, complemented
9#19133720C211yesmaximal, characteristic, complemented
10#19133710C211yesmaximal, characteristic, complemented
11#19133673C211yesmaximal, characteristic, complemented
12#19133667C211yesmaximal, characteristic, complemented
13#19133485C211yesmaximal, characteristic, complemented
14SD16×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3385C211yesmaximal, characteristic, complemented
16C2×#13063352—21no—
17#14583571C2211yescharacteristic
18D4×D172C2211yescharacteristic
19#14583276C2211yescharacteristic
20#14583273C2211yescharacteristic
21#14583273C2211yescharacteristic, complemented
22#14583247—21no—
23#14583247C2211yescharacteristic
24#14583247C2211yescharacteristic, complemented
25#14583217—21no—
26#14583186—21no—
27#14583186C2211yescharacteristic
28#14583186C2211yescharacteristic
29#14583153—21no—
30#14583130—21no—
31#14583099—21no—
32#14583099C2211yescharacteristic
33#14583099C2211yescharacteristic
34#14583099C2211yescharacteristic, complemented
35#14583094C2211yescharacteristic
36#14583049—21no—
37#14583047—21no—
38#14583034—21no—
39Q8×C43⋊C8C2211yescharacteristic, complemented
40C4×#10621884—21no—
41C4×#10621884C2211yescharacteristic
42#14582978C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063245—21no—
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582648C2211yescharacteristic, complemented
49#14582642C2211yescharacteristic
50#14582642C2211yescharacteristic, complemented
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic, complemented
56Q82×C43C2211yescharacteristic, complemented
57C43×#554C2211yescharacteristic
58C43×#501—21no—
59C43×#500C2211yescharacteristic, complemented
60C43×#479—21no—
61C43×#477C2211yescharacteristic, complemented
62C43×#476C2211yescharacteristic
63C43×#474—21no—
64C43×#446C2211yescharacteristic, complemented
65C43×#440—21no—
66C4×SD16×C43C2211yescharacteristic
67C2×#10621902—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70#13063352—44no—
71C2×#10621884—21no—
72C2×#10621884—21no—
73C2×#10621884—21no—
74C2×#10621884—41no—
75C2×#10621884—41no—
76C2×#10621884D411yescharacteristic
77C2×D344—21no—
78C2×D344—21no—
79C2×#10621882—21no—
80C2×#10621872—21no—
81C22×C43⋊C8—21no—
82#13063322—21no—
83#13063322C2311yescharacteristic
84#13063322C2311yescharacteristic
85#13063300—21no—
86#13063300—21no—
87#13063300—41no—
88#13063299—21no—
89#13063295—41no—
90C4×D172—21no—
91C4×D172C2311yescharacteristic
92#13063256—21no—
93#13063256—21no—
94#13063256D411yescharacteristic
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063249D411yescharacteristic
100#13063245—21no—
101#13063245—21no—
102#13063245—21no—
103#13063245—21no—
104#13063245—21no—
105#13063245—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245—21no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C2×SD16×C43D411yescharacteristic
117C4⋊Q8×C43—21no—
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—41no—
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122#125×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43C2311yescharacteristic
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43—21no—
130C4×D4×C43C2311yescharacteristic
131C2×C4⋊C4×C43—21no—
132#107×C43—21no—
133#107×C43—21no—
134#107×C43—21no—
135#106×C43—21no—
136#106×C43D411yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#102×C43—21no—
142#102×C43D411yescharacteristic
143#97×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—41no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×Q8×C43C2×D411yescharacteristic
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—41no—
154C2×C22⋊D43—41no—
155#10621902—42no—
156#10621902—81no—
157D4×D43—42no—
158D4×D43—81no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—41no—
166C2×D172—41no—
167C2×D172—41no—
168C2×D172—42no—
169C2×D172—81no—
170C2×D172C2×D411yescharacteristic
171C2×C4×D43—21no—
172C2×C4×D43—41no—
173SD16×C43SD1614yescomplemented
174C2×C8×C43—21no—
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43—41no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43C2×D411yescharacteristic
188C4⋊C4×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C22⋊C4×C43—21no—
191C22⋊C4×C43—41no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43—41no—
195C42×C43C2411yescharacteristic
196#10621884—41no—
197#10621884—42no—
198#10621884—42no—
199#10621884—82no—
200#10621884—82no—
201#10621884—81no—
202#10621882—42no—
203(C2×D43)⋊C4—21no—
204(C2×D43)⋊C4—41no—
205(C2×D43)⋊C4—41no—
206C4⋊Dic43C2×D411yescharacteristic
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—81no—
212C2×C43⋊C8C2×D411yescharacteristic
213C2×C43⋊C8C2×D411yescharacteristic
214D344—42no—
215D344—81no—
216#10621872—42no—
217C23×C43—21no—
218C22×D43—21no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—82no—
222C22×D43—82no—
223C22×D43—161no—
224Q8×C43—21no—
225Q8×C43—21no—
226Q8×C43—21no—
227Q8×C43—81no—
228Q8×C43—81no—
229Q8×C43—161no—
230Q8×C43C2×SD1612yes—
231D4×C43—21no—
232D4×C43C2×SD1612yes—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—161no—
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C22⋊D43—82no—
247C2×Dic43—21no—
248D172—21no—
249D172—21no—
250D172—41no—
251D172—41no—
252D172—41no—
253D172—41no—
254D172—41no—
255D172—41no—
256D172—41no—
257D172—41no—
258D172—82no—
259D172—81no—
260D172—81no—
261D172—82no—
262D172—161no—
263C4×D43—41no—
264C4×D43—41no—
265C4×D43—82no—
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×C43D4211yescharacteristic
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—81no—
284C2×D43—81no—
285C2×D43—81no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—164no—
290C4×C43—22no—
291C4×C43—21no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43C22×SD1611yescharacteristic
299C4×C43#57511yescharacteristic
300C4×C43#57711yescharacteristic
301C4×C43#57711yescharacteristic
302Dic43—41no—
303#3385D4311yescharacteristic, complemented
304#3362—431no—
305#3295—431no—
306#3274—431no—
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#327511yescharacteristic
320C2×C43D4×SD1611yescharacteristic
321C2×C43#329211yescharacteristic
322D43—81no—
323D43—161no—
324D43—161no—
325C2×AGL(1,ℤ/8)—861no—
326Q82C2×D4311yescharacteristic, complemented
327#554C2×D4311yescharacteristic
328#550—431no—
329D42—431no—
330#501—21no—
331#500C2×D4311yescharacteristic, complemented
332#493—431no—
333#492—431no—
334#492—431no—
335#486—431no—
336#486—431no—
337#486—861no—
338#481—861no—
339#479—21no—
340#477C2×D4311yescharacteristic, complemented
341#476—431no—
342#476—431no—
343#476—861no—
344#476C2×D4311yescharacteristic
345#474—21no—
346#469—861no—
347#465—861no—
348#460—431no—
349#460—431no—
350#460—431no—
351#460—861no—
352#459—431no—
353#450—861no—
354#449—861no—
355#447—861no—
356#446C2×D4311yescharacteristic, complemented
357C8×Q8—431no—
358#440—21no—
359C4×SD16—431no—
360C4×SD16—861no—
361C4×SD16C2×D4311yescharacteristic
362#436—431no—
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—861no—
378C22×D4—861no—
379C22×D4—861no—
380AGL(1,ℤ/8)—1724no—
381C2×SD16—431no—
382C2×SD16—861no—
383C2×SD16—861no—
384C2×SD16—861no—
385C2×SD16—1721no—
386C2×SD16—1721no—
387C2×SD16C22⋊D4311yescharacteristic
388C2×D8—861no—
389C2×D8—861no—
390C2×D8—861no—
391C2×M16—861no—
392C22×C8—861no—
393C4⋊Q8—21no—
394C4⋊Q8—21no—
395C4⋊Q8—41no—
396C4⋊Q8C22×D4311yescharacteristic
397C4⋊Q8C22×D4311yescharacteristic
398#127—431no—
399#127—431no—
400#127—861no—
401#125—21no—
402C22⋊Q8—21no—
403C22⋊Q8—41no—
404#121—861no—
405#121—861no—
406#121—861no—
407#121—1721no—
408#120—1721no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8C22×D4311yescharacteristic
412C4×Q8C22×D4311yescharacteristic
413C4×D4—21no—
414C4×D4—431no—
415C4×D4—861no—
416C4×D4C22×D4311yescharacteristic
417C2×C4⋊C4—21no—
418#107—21no—
419#107—21no—
420#107—21no—
421#106—21no—
422#106—431no—
423#106—861no—
424#106—861no—
425#106C22⋊D4311yescharacteristic
426C4⋊C8—21no—
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8—431no—
430C4⋊C8—861no—
431C4⋊C8C22×D4311yescharacteristic
432#103—21no—
433#103—431no—
434#103C22⋊D4311yescharacteristic
435#102—21no—
436#102—431no—
437#102—861no—
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—861no—
449C22⋊C8—861no—
450#97—21no—
451C4×C8—431no—
452C4×C8—431no—
453C4×C8—861no—
454C4×C8C22×D4311yescharacteristic
455C24—1721no—
456#41—3441no—
457#41—1722no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—41no—
461C2×Q8D4×D4311yescharacteristic
462C2×Q8C2×C22⋊D4311yescharacteristic
463C2×D4—431no—
464C2×D4—861no—
465C2×D4—861no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—3441no—
471C2×D4—3441no—
472C2×D4—1721no—
473C2×D4—1721no—
474C2×D4—1721no—
475C2×D4—1722no—
476C2×D4—1721no—
477C2×D4—1722no—
478C2×D4C2×C22⋊D4311yescharacteristic
479C22×C4—21no—
480C22×C4—41no—
481C22×C4—861no—
482C22×C4—1721no—
483SD16—3442no—
484SD16—3442no—
485SD16—3441no—
486SD16—1721no—
487SD16—1722no—
488SD16—1722no—
489SD16#1062188414yescomplemented
490D8—3441no—
491D8—1722no—
492D8—1722no—
493M16—1722no—
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—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—431no—
515C4⋊C4D4×D4311yescharacteristic
516C4⋊C4C2×C22⋊D4311yescharacteristic
517C4⋊C4C2×C22⋊D4311yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—41no—
520C22⋊C4—861no—
521C22⋊C4—1721no—
522C22⋊C4—1721no—
523C42—21no—
524C42—21no—
525C42—41no—
526C42C23×D4311yescharacteristic
527C23—21no—
528C23—861no—
529C23—3442no—
530C23—3442no—
531C23—1721no—
532C23—1721no—
533C23—6881no—
534Q8—21no—
535Q8—21no—
536Q8—21no—
537Q8—81no—
538Q8—81no—
539Q8—161no—
540Q8C2×#1062188412yes—
541D4—21no—
542D4—861no—
543D4—861no—
544D4—3441no—
545D4—3441no—
546D4—3442no—
547D4—3442no—
548D4—3442no—
549D4—1721no—
550D4—1721no—
551D4—1721no—
552D4—1721no—
553D4—1721no—
554D4—1721no—
555D4—1721no—
556D4—1721no—
557D4—6881no—
558D4C2×#1062188412yes—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—161no—
569C2×C4—861no—
570C2×C4—3442no—
571C2×C4—1721no—
572C2×C4—1721no—
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×#1062188412yes—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—3441no—
589C22—3441no—
590C22—3441no—
591C22—3441no—
592C22—3441no—
593C22—3441no—
594C22—1721no—
595C22—1721no—
596C22—1721no—
597C22—6884no—
598C22D4×C22⋊D4311yescharacteristic
599C4—22no—
600C4—21no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—81no—
606C4—81no—
607C4—1721no—
608C4C22×#1062188411yescharacteristic
609C4#1458369811yescharacteristic
610C4#1458370711yescharacteristic
611C4#1458370811yescharacteristic
612C2—42no—
613C2—3441no—
614C2—6881no—
615C2—6881no—
616C2#1914622011yescharacteristic
617C2D4×#1062188411yescharacteristic
618C2#1914639211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3385C2
socleC22×C43D42
prime radical#19146216C2
hypercenter#3385D43
hypocenterC43#19893
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3385

Complements

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

NH ≅ G/Ntype
1. #19147266C2semidirect
2. #19146413C2semidirect
4. #19134188C2semidirect
5. #19134115C2semidirect
6. #19134079C2semidirect
7. #19134013C2semidirect
8. #19134006C2semidirect
9. #19133720C2semidirect
10. #19133710C2semidirect
11. #19133673C2semidirect
12. #19133667C2semidirect
13. #19133485C2semidirect
14. SD16×C43⋊C8C2semidirect
15. C43×#3385C2semidirect
21. #14583273C22semidirect
24. #14583247C22semidirect
34. #14583099C22semidirect
39. Q8×C43⋊C8C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582648C22semidirect
48. #14582648C22semidirect
50. #14582642C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. Q8⋊(C43⋊C8)C22semidirect
55. C8×C43⋊C8C22semidirect
56. Q82×C43C22semidirect
59. C43×#500C22semidirect
61. C43×#477C22semidirect
64. C43×#446C22semidirect
173. SD16×C43SD16semidirect
303. #3385D43semidirect
326. Q82C2×D43semidirect
331. #500C2×D43semidirect
340. #477C2×D43semidirect
356. #446C2×D43semidirect
376. C43#19893semidirect
489. SD16#10621884semidirect

Maximal subgroups

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

subgroupindex
#191472662
#191464132
#191462162
#191341882
#191341152
#191340792
#191340132
#191340062
#191337202
#191337102
#191336732
#191336672
#191334852
SD16×C43⋊C82
C43×#33852
#1989343