Finite Group Databasebeta

← #25080546

Subgroups — #25080546

Order 11008.

722 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#486×D43C211yesmaximal, characteristic, complemented
2#19144407C211yesmaximal, characteristic, complemented
3#19144070C211yesmaximal, characteristic
4C8×#10621900C211yesmaximal, characteristic, complemented
5#19134014C211yesmaximal, characteristic, complemented
6#19134012C211yesmaximal, characteristic, complemented
7#19134010C211yesmaximal, characteristic, complemented
8#19134008C211yesmaximal, characteristic, complemented
9#19134006C211yesmaximal, characteristic, complemented
10#19134004C211yesmaximal, characteristic, complemented
11#19134002C211yesmaximal, characteristic, complemented
12#19133349C211yesmaximal, characteristic, complemented
13#19133274C211yesmaximal, characteristic, complemented
14#19133261C211yesmaximal, characteristic, complemented
15C43×#1677C211yesmaximal, characteristic, complemented
16C2×#13063349—21no—
17C4⋊Q8×D43C2211yescharacteristic
18#127×D43C2211yescharacteristic
19C4×#10621900C2211yescharacteristic
20#14583247C2211yescharacteristic
21#14583246C2211yescharacteristic
22#14583245C2211yescharacteristic
23#14583244—21no—
24#14583244—21no—
25#14583195C2211yescharacteristic, complemented
26#14583191C2211yescharacteristic, complemented
27#14583189C2211yescharacteristic, complemented
28#14583183—21no—
29#14583177—21no—
30#14583100C2211yescharacteristic
31#14583098—21no—
32#14583096C2211yescharacteristic
33#14583094C2211yescharacteristic
34#14583092—21no—
35C8×Dic86C2211yescharacteristic, complemented
36#14583023C2211yescharacteristic, complemented
37D4×C43⋊C8C2211yescharacteristic, complemented
38C8×C22⋊D43—21no—
39(C22⋊D43)⋊C8—21no—
40#14582951C2211yescharacteristic
41#14582949—21no—
42#14582938—21no—
43#14582921C2211yescharacteristic
44#14582921C2211yescharacteristic
45#14582902—21no—
46#14582897—21no—
47#102×D43—21no—
48#102×D43—21no—
49C2×C8×Dic43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582650C2211yescharacteristic, complemented
52#14582649C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582647C2211yescharacteristic, complemented
57#14582643C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#476C2211yescharacteristic, complemented
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic, complemented
64C43×#334C2211yescharacteristic, complemented
65C43×#333C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic
67C2×#10621900D411yescharacteristic
68C2×Q8×D43—21no—
69C2×D4×D43—21no—
70C2×D4×D43—21no—
71C2×D4×D43—21no—
72#13063349—44no—
73C2×#10621873—21no—
74C2×#10621883—21no—
75C2×#10621882—21no—
76C2×#10621872—21no—
77C2×#10621872—21no—
78C22×C43⋊C8—21no—
79C2×C8×D43D411yescharacteristic
80C2×C8×D43D411yescharacteristic
81#13063325C2311yescharacteristic
82#13063324—21no—
83#13063324—21no—
84#13063323—21no—
85#13063322C2311yescharacteristic
86#13063321—21no—
87#13063321—21no—
88#13063321—21no—
89C4×Dic86C2311yescharacteristic
90#13063290D411yescharacteristic
91D4×Dic43D411yescharacteristic
92C4×C22⋊D43—21no—
93(C22⋊D43)⋊C4—21no—
94#13063283D411yescharacteristic
95#13063281—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—21no—
98C2×C4×Dic43—21no—
99C42×D43C2311yescharacteristic
100#13063259—21no—
101#13063258—21no—
102#13063256—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110#13063250—21no—
111#13063248—21no—
112#13063247—21no—
113#13063247—21no—
114#13063247—21no—
115#13063246—21no—
116#13063246—21no—
117#13063246—21no—
118#13063246—21no—
119#13063245—21no—
120#13063245—21no—
121#13063245—21no—
122C22⋊(C43⋊C8)—21no—
123(C2×D43)⋊C8—21no—
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C2×D8×C43—21no—
131C22×C8×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133#127×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—41no—
146C2×Q8×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C2×C22⋊D43—21no—
153C2×C22⋊D43—41no—
154C2×C22⋊D43—41no—
155C2×C22⋊D43—41no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158Q8×D43—82no—
159#10621900—22no—
160#10621900SD1614yes—
161D4×D43—42no—
162D4×D43—42no—
163D4×D43—42no—
164D4×D43—42no—
165D4×D43—82no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×C4×D43—41no—
170C2×C4×D43C2×D411yescharacteristic
171C2×C4×D43C2×D411yescharacteristic
172C2×C4×D43#4111yescharacteristic
173C2×Dic86—21no—
174C2×Dic86—41no—
175C2×Dic86C2×D411yescharacteristic
176D8×C43—42no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—42no—
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43C2×D411yescharacteristic
186C22⋊C4×C43—21no—
187C42×C43C2411yescharacteristic
188C22⋊Dic43—21no—
189#10621883—42no—
190#10621882—42no—
191(C2×D43)⋊C4—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197Dic43⋊C4—41no—
198Dic43⋊C4—41no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43C2×D411yescharacteristic
203C4×Dic43C2×D411yescharacteristic
204C4×Dic43#4111yescharacteristic
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—42no—
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211#10621873—42no—
212#10621872—42no—
213#10621872—42no—
214C8×D43—41no—
215C8×D43—41no—
216C23×C43—21no—
217C23×C43—41no—
218C22×D43—41no—
219C22×D43—82no—
220C22×D43—82no—
221C22×D43—82no—
222C22×D43#12111yescharacteristic
223Q8×C43—81no—
224D4×C43—21no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—81no—
230D4×C43C2×SD1612yes—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C22⋊D43—24no—
239C22⋊D43—82no—
240C22⋊D43—82no—
241C22⋊D43—82no—
242C2×Dic43—21no—
243C2×Dic43—24no—
244C2×Dic43—21no—
245C2×Dic43—42no—
246C2×Dic43—41no—
247C2×Dic43#12111yescharacteristic
248C2×Dic43#12111yescharacteristic
249C2×Dic43#12111yescharacteristic
250D172—41no—
251D172—41no—
252D172—41no—
253D172—41no—
254D172—81no—
255C4×D43—21no—
256C4×D43—21no—
257C4×D43—22no—
258C4×D43—82no—
259C4×D43C2×SD1612yes—
260C4×D43#13512yes—
261Dic86—21no—
262Dic86—82no—
263Dic86—81no—
264Dic86C2×SD1612yes—
265C8×C43—21no—
266C8×C43—21no—
267C8×C43—41no—
268C8×C43—41no—
269C8×C43—41no—
270C43⋊C8—21no—
271C43⋊C8—21no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275#19274—431nomaximal, Sylow
276C22×C43—22no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43C2×#12111yescharacteristic
283C2×D43—21no—
284C2×D43—21no—
285C2×D43—81no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—164no—
289C2×D43#46512yes—
290C4×C43—21no—
291C4×C43—41no—
292C4×C43—81no—
293C4×C43C22×SD1611yescharacteristic
294C4×C43C2×#13511yescharacteristic
295C4×C43#57511yescharacteristic
296C4×C43#57511yescharacteristic
297Dic43—21no—
298Dic43—22no—
299Dic43—41no—
300Dic43—81no—
301Dic43#46512yes—
302Dic43#47212yes—
303C2×#486—431no—
304#3079—431no—
305#3038—431no—
306C8×#41—431no—
307#1678—431no—
308#1678—431no—
309#1678—431no—
310#1678—431no—
311#1677—431no—
312#1677—431no—
313#1677—431no—
314#1677D4311yescharacteristic, complemented
315#1566—431no—
316#1548—431no—
317#1545—431no—
318C2×C43—42no—
319C2×C43—161no—
320C2×C43#304011yescharacteristic
321C2×C43C2×#46511yescharacteristic
322C2×C43C2×#47211yescharacteristic
323D43—22no—
324D43—161no—
325C2×AGL(1,ℤ/8)—861no—
326C2×C4⋊Q8—431no—
327C2×#127—431no—
328C4×#41—431no—
329#486—431no—
330#486—431no—
331#486—431no—
332#486—861no—
333#486—861no—
334#486C2×D4311yescharacteristic
335#477—431no—
336#477—431no—
337#476—431no—
338#476C2×D4311yescharacteristic, complemented
339#475—861no—
340#474—861no—
341#460—431no—
342#460—431no—
343#460—861no—
344#459—431no—
345#459—861no—
346#459C2×D4311yescharacteristic
347C8×Q8—431no—
348C8×Q8—431no—
349C8×D4—431no—
350C8×D4—861no—
351C8×D4—861no—
352C8×D4C2×D4311yescharacteristic, complemented
353#431—431no—
354#431—861no—
355#428—861no—
356#423—431no—
357#423—431no—
358#418—861no—
359#417—861no—
360C2×#102—861no—
361C2×#102—861no—
362C2×C4×C8—431no—
363C2×C4×C8—861no—
364#334—431no—
365#334—431no—
366#334—431no—
367#334C2×D4311yescharacteristic, complemented
368#333—431no—
369#333—431no—
370#333—431no—
371#333C2×D4311yescharacteristic, complemented
372#331—431no—
373#331—431no—
374#331—431no—
375#331C2×D4311yescharacteristic
376C43#1927411yescharacteristic, complemented, Sylow
377C2×#41—431no—
378C22×Q8—861no—
379C22×D4—861no—
380C22×D4—861no—
381C22×D4—861no—
382AGL(1,ℤ/8)—1724no—
383C2×SD16—861no—
384C2×SD16—861no—
385C2×D8—21no—
386C2×D8—861no—
387C2×M16—861no—
388C2×M16—861no—
389C22×C8—21no—
390C22×C8—431no—
391C22×C8—431no—
392C22×C8—861no—
393C4⋊Q8—431no—
394C4⋊Q8—861no—
395C4⋊Q8—861no—
396C4⋊Q8—861no—
397C4⋊Q8C22×D4311yescharacteristic
398#127—431no—
399#127—861no—
400#127—861no—
401#127—861no—
402#127C22×D4311yescharacteristic
403C4×Q8—431no—
404C4×Q8—431no—
405C4×D4—431no—
406C4×D4—861no—
407C4×D4—861no—
408C4×D4C22×D4311yescharacteristic
409#117—431no—
410#117—861no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C42—431no—
414C2×C42—861no—
415#107—861no—
416#107—861no—
417#106—21no—
418#106—861no—
419C4⋊C8—431no—
420C4⋊C8—431no—
421C4⋊C8—431no—
422C4⋊C8—861no—
423C4⋊C8—861no—
424C4⋊C8—861no—
425C4⋊C8—861no—
426C4⋊C8C22×D4311yescharacteristic
427C4⋊C8C22×D4311yescharacteristic
428C4⋊C8C22×D4311yescharacteristic
429#103—861no—
430#103—861no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—861no—
445C22⋊C8—21no—
446C22⋊C8—861no—
447C22⋊C8—861no—
448C4×C8—431no—
449C4×C8—431no—
450C4×C8—431no—
451C4×C8—861no—
452C4×C8—861no—
453C4×C8—861no—
454C4×C8C22×D4311yescharacteristic
455C24—1721no—
456#41—434no—
457#41—862no—
458C2×Q8—21no—
459C2×Q8—431no—
460C2×Q8—861no—
461C2×Q8—3442no—
462C2×Q8—1721no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—3442no—
471C2×D4—1722no—
472C2×D4—1722no—
473C2×D4—1721no—
474C2×D4—1721no—
475C2×D4—1721no—
476C2×D4—1722no—
477C2×D4—1722no—
478C2×D4D4×D4311yescharacteristic
479C22×C4—21no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—1721no—
486SD16—1722no—
487SD16—1722no—
488D8—42no—
489D8—1722no—
490M16—1722no—
491M16—1722no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—42no—
496C2×C8—431no—
497C2×C8—431no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—1721no—
502C2×C8—1721no—
503C2×C8—1722no—
504C2×C8D4×D4311yescharacteristic
505C2×C8D4×D4311yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—431no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—1721no—
514C4⋊C4—1721no—
515C4⋊C4D4×D4311yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—861no—
518C22⋊C4—861no—
519C42—431no—
520C42—431no—
521C42—431no—
522C42—861no—
523C42—861no—
524C42—861no—
525C42C23×D4311yescharacteristic
526C23—21no—
527C23—41no—
528C23—431no—
529C23—3442no—
530C23—3442no—
531C23—3442no—
532C23—1721no—
533Q8—81no—
534Q8—432no—
535Q8—861no—
536Q8—3441no—
537Q8—3442no—
538D4—21no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—81no—
544D4—864no—
545D4—3441no—
546D4—3442no—
547D4—3442no—
548D4—3442no—
549D4—1721no—
550D4—1721no—
551D4—1721no—
552D4—1721no—
553D4SD16×D4312yes—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—431no—
559C2×C4—431no—
560C2×C4—432no—
561C2×C4—432no—
562C2×C4—431no—
563C2×C4—862no—
564C2×C4—864no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—3442no—
570C2×C4—1722no—
571C2×C4—1721no—
572C2×C4C2×D4×D4311yescharacteristic
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4#41×D4311yescharacteristic
575C8—21no—
576C8—21no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—861no—
581C8—861no—
582C8—1721no—
583C8—1721no—
584C8—1721no—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—432no—
592C22—861no—
593C22—861no—
594C22—3441no—
595C22—3441no—
596C22—3441no—
597C22—6884no—
598C22#121×D4311yescharacteristic
599C4—21no—
600C4—41no—
601C4—81no—
602C4—432no—
603C4—432no—
604C4—861no—
605C4—862no—
606C4—3441no—
607C4—1721no—
608C4C2×SD16×D4311yescharacteristic
609C4#135×D4311yescharacteristic
610C4#1458369511yescharacteristic
611C4#1458369611yescharacteristic
612C2—42no—
613C2—161no—
614C2—862no—
615C2—6881no—
616C2#1914408411yescharacteristic
617C2#465×D4311yescharacteristic
618C2#472×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1677C2
socleC22×C43C2×#121
prime radical#19144070C2
hypercenter#1677D43
hypocenterC43#19274
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1677

Complements

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

NH ≅ G/Ntype
1. #486×D43C2semidirect
2. #19144407C2semidirect
4. C8×#10621900C2semidirect
5. #19134014C2semidirect
6. #19134012C2semidirect
7. #19134010C2semidirect
8. #19134008C2semidirect
9. #19134006C2semidirect
10. #19134004C2semidirect
11. #19134002C2semidirect
12. #19133349C2semidirect
13. #19133274C2semidirect
14. #19133261C2semidirect
15. C43×#1677C2semidirect
25. #14583195C22semidirect
26. #14583191C22semidirect
27. #14583189C22semidirect
35. C8×Dic86C22semidirect
36. #14583023C22semidirect
37. D4×C43⋊C8C22semidirect
51. #14582650C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582648C22semidirect
55. #14582647C22semidirect
56. #14582647C22semidirect
61. C43×#476C22semidirect
63. C8×D4×C43C22semidirect
64. C43×#334C22semidirect
65. C43×#333C22semidirect
314. #1677D43semidirect
338. #476C2×D43semidirect
352. C8×D4C2×D43semidirect
367. #334C2×D43semidirect
371. #333C2×D43semidirect
376. C43#19274semidirect

Maximal subgroups

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

subgroupindex
#486×D432
#191444072
#191440702
C8×#106219002
#191340142
#191340122
#191340102
#191340082
#191340062
#191340042
#191340022
#191333492
#191332742
#191332612
C43×#16772
#1927443