Finite Group Databasebeta

← #25086420

Subgroups — #25086420

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147313C211yesmaximal, characteristic, complemented
2#19146514C211yesmaximal, characteristic, complemented
3#19146408C211yesmaximal, characteristic
4#19134246C211yesmaximal, characteristic, complemented
5#19134161C211yesmaximal, characteristic, complemented
6#19134020C211yesmaximal, characteristic, complemented
7#19134018C211yesmaximal, characteristic, complemented
8#19133933C211yesmaximal, characteristic, complemented
9#19133844C211yesmaximal, characteristic, complemented
10#19133828C211yesmaximal, characteristic, complemented
11#19133774C211yesmaximal, characteristic, complemented
12#19133704C211yesmaximal, characteristic, complemented
13#19133432C211yesmaximal, characteristic, complemented
14#19133417C211yesmaximal, characteristic, complemented
15D4×SD16×C43C211yesmaximal, characteristic, complemented
16#14583622C2211yescharacteristic, complemented
17#14583553C2211yescharacteristic
18#14583302C2211yescharacteristic, complemented
19#14583261—21no—
20#14583251C2211yescharacteristic, complemented
21#14583250C2211yescharacteristic, complemented
22#14583245C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583243—21no—
25#14583210—21no—
26#14583191—21no—
27#14583179C2211yescharacteristic
28#14583179C2211yescharacteristic
29#14583176C2211yescharacteristic, complemented
30#14583139—21no—
31#14583133—21no—
32#14583114—21no—
33#14583109C2211yescharacteristic, complemented
34#14583104C2211yescharacteristic
35#14583091C2211yescharacteristic
36#14583058—21no—
37#14583033—21no—
38#14583030C2211yescharacteristic, complemented
39#14582999—21no—
40C4×#10621882C2211yescharacteristic
41C8×D172C2211yescharacteristic, complemented
42D4×C43⋊C8C2211yescharacteristic
43#14582892—21no—
44C2×#13063246—21no—
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, 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#14582621C2211yescharacteristic, complemented
56C22×SD16×C43—21no—
57D4×Q8×C43C2211yescharacteristic
58D42×C43C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#465—21no—
61C43×#461C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C43×#450—21no—
64C43×#448—21no—
65C4×SD16×C43C2211yescharacteristic
66C8×D4×C43C2211yescharacteristic
67C2×#10621900—21no—
68C2×#10621885—21no—
69C2×#10621883—21no—
70C2×#10621882—21no—
71C2×#10621882D411yescharacteristic
72C22×C43⋊C8—21no—
73C2×C8×D43—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063320—41no—
77#13063313—21no—
78#13063309—41no—
79#13063305—21no—
80#13063301—21no—
81#13063299—21no—
82C4×Dic86—21no—
83C4×D172C2311yescharacteristic
84#13063283—21no—
85C2×C4⋊Dic43—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—41no—
90#13063258D411yescharacteristic
91C4⋊(C43⋊C8)—21no—
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063250—21no—
96#13063250—21no—
97#13063248—21no—
98#13063248—21no—
99#13063248—21no—
100#13063248—21no—
101#13063246—21no—
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—41no—
107#13063246D411yescharacteristic
108#13063245—21no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111(C2×D43)⋊C8—21no—
112#13063236—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C22×Q8×C43—21no—
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43—21no—
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×SD16×C43—44no—
123C2×SD16×C43D411yescharacteristic
124C22×C8×C43—21no—
125C4⋊Q8×C43—21no—
126C4⋊Q8×C43C2311yescharacteristic
127#127×C43C2311yescharacteristic
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43—41no—
130#121×C43—21no—
131#121×C43—21no—
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×C43—21no—
140#103×C43D411yescharacteristic
141#102×C43—21no—
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146C2×Q8×C43—21no—
147C2×Q8×C43—41no—
148C2×Q8×C43—42no—
149C2×Q8×C43—81no—
150C2×Q8×C43C2×D411yescharacteristic
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—41no—
155C2×D4×C43—41no—
156C2×D4×C43—42no—
157C2×D4×C43—42no—
158C2×D4×C43—81no—
159C2×D4×C43—81no—
160C2×D4×C43C2×D411yescharacteristic
161C2×D4×C43C2×D411yescharacteristic
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—41no—
165C2×C22⋊D43—41no—
166C22×Dic43—41no—
167#10621900—42no—
168#10621900—81no—
169C2×D172C2×D411yescharacteristic
170C2×C4×D43—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173SD16×C43—22no—
174SD16×C43—42no—
175SD16×C43—42no—
176SD16×C43—42no—
177SD16×C43—81no—
178C2×C8×C43—21no—
179C2×C8×C43—42no—
180C2×C8×C43C2×D411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43C2×D411yescharacteristic
187C4⋊C4×C43C2×D411yescharacteristic
188C4⋊C4×C43C2×D411yescharacteristic
189C22⋊C4×C43—21no—
190C22⋊C4×C43—21no—
191C22⋊C4×C43—41no—
192C22⋊C4×C43—41no—
193C42×C43—21no—
194C42×C43C2411yescharacteristic
195#10621885—81no—
196#10621883—42no—
197#10621882—22no—
198#10621882—81no—
199(C2×D43)⋊C4—21no—
200(C2×D43)⋊C4—41no—
201(C2×D43)⋊C4—41no—
202(C2×D43)⋊C4—41no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—41no—
208C4⋊Dic43C2×D411yescharacteristic
209Dic43⋊C4—41no—
210C4×Dic43—41no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—81no—
216C2×C43⋊C8C2×D411yescharacteristic
217C2×C43⋊C8C2×D411yescharacteristic
218C8×D43—81no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—41no—
222C23×C43—82no—
223C23×C43—82no—
224C23×C43—161no—
225C22×D43—21no—
226Q8×C43—21no—
227Q8×C43—21no—
228Q8×C43—41no—
229Q8×C43—41no—
230Q8×C43—82no—
231D4×C43—21no—
232D4×C43—21no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—81no—
238D4×C43—82no—
239D4×C43—82no—
240D4×C43#13512yes—
241D4×C43AGL(1,ℤ/8)12yes—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—82no—
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C22⋊D43—82no—
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—41no—
267Dic86—41no—
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—41no—
271C43⋊C8—21no—
272C43⋊C8—21no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277#19787—431nomaximal, Sylow
278C22×C43—22no—
279C22×C43—22no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—164no—
288C22×C43D4211yescharacteristic
289C2×D43—41no—
290C2×D43—41no—
291C2×D43—41no—
292C4×C43—21no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—81no—
298C4×C43C2×#13511yescharacteristic
299C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C43#57611yescharacteristic
301C4×C43#57711yescharacteristic
302Dic43—41no—
303Dic43—81no—
304Dic43—81no—
305#3367—431no—
306#3302—431no—
307#3294—431no—
308D4×SD16D4311yescharacteristic, complemented
309#1719—431no—
310#1702—431no—
311#1679—431no—
312#1679—431no—
313#1665—431no—
314#1649—431no—
315#1647—431no—
316#1639—431no—
317#1628—431no—
318#1582—431no—
319#1580—431no—
320C2×C43—42no—
321C2×C43—42no—
322C2×C43—161no—
323C2×C43#326411yescharacteristic
324C2×C43#328211yescharacteristic
325C2×C43#328911yescharacteristic
326D43—81no—
327C22×SD16—21no—
328#556—431no—
329D4×Q8C2×D4311yescharacteristic
330#547—431no—
331D42C2×D4311yescharacteristic
332#500—431no—
333#492C2×D4311yescharacteristic
334#489—861no—
335#487—431no—
336#487—431no—
337#486—431no—
338#486—431no—
339#485—861no—
340#480—861no—
341#477—861no—
342#474—431no—
343#474—431no—
344#474—431no—
345#467—861no—
346#466—861no—
347#465—21no—
348#463—861no—
349#462—431no—
350#461—431no—
351#461C2×D4311yescharacteristic
352#460C2×D4311yescharacteristic
353#459—431no—
354#452—861no—
355#450—21no—
356#448—21no—
357#447—861no—
358#446—431no—
359#440—861no—
360C4×SD16C2×D4311yescharacteristic
361C4×D8—431no—
362C8×D4—431no—
363C8×D4—431no—
364C8×D4C2×D4311yescharacteristic
365#416—861no—
366C2×#102—861no—
367#334—431no—
368#334—431no—
369#332—431no—
370#332—431no—
371#332—431no—
372#331—431no—
373Q8⋊C8—431no—
374D4⋊C8—431no—
375D4⋊C8—431no—
376D4⋊C8—431no—
377#322—431no—
378C43#1978711yescharacteristic, complemented, Sylow
379C2×#41—861no—
380C22×Q8—21no—
381C22×D4—21no—
382C22×D4—21no—
383C2×Q16—861no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×SD16—44no—
389C2×SD16—861no—
390C2×SD16C22⋊D4311yescharacteristic
391C2×D8—431no—
392C2×D8—861no—
393C22×C8—21no—
394C22×C8—861no—
395C22×C8—861no—
396C4⋊Q8—21no—
397C4⋊Q8—431no—
398C4⋊Q8—431no—
399C4⋊Q8C22×D4311yescharacteristic
400#127C22×D4311yescharacteristic
401#126—1721no—
402#124—861no—
403#123—1721no—
404C22⋊Q8—21no—
405C22⋊Q8—41no—
406C22⋊Q8—861no—
407C22⋊Q8—861no—
408#121—21no—
409#121—21no—
410#121—861no—
411#120—41no—
412C4×Q8—861no—
413C4×Q8C22×D4311yescharacteristic
414C4×D4—21no—
415C4×D4—431no—
416C4×D4C22×D4311yescharacteristic
417C4×D4C22×D4311yescharacteristic
418#117—861no—
419C2×C4⋊C4—861no—
420#107—431no—
421#107—861no—
422#107—861no—
423#107—861no—
424#107—1721no—
425#106C22⋊D4311yescharacteristic
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8—861no—
430C4⋊C8C22×D4311yescharacteristic
431#103—21no—
432#103—861no—
433#103—861no—
434#103—861no—
435#103—861no—
436#103—861no—
437#103—861no—
438#103C22⋊D4311yescharacteristic
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
450C22⋊C8—21no—
451C22⋊C8—861no—
452C22⋊C8—861no—
453#97—861no—
454C4×C8—431no—
455C4×C8—431no—
456C4×C8C22×D4311yescharacteristic
457C24—41no—
458#41—3441no—
459#41—1722no—
460C2×Q8—21no—
461C2×Q8—41no—
462C2×Q8—42no—
463C2×Q8—81no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8C2×C22⋊D4311yescharacteristic
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—81no—
475C2×D4—81no—
476C2×D4—431no—
477C2×D4—1721no—
478C2×D4D4×D4311yescharacteristic
479C2×D4C2×C22⋊D4311yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4—861no—
484C22×C4—1721no—
485Q16—3441no—
486SD16—22no—
487SD16—42no—
488SD16—42no—
489SD16—42no—
490SD16—81no—
491SD16—1722no—
492D8—862no—
493D8—3441no—
494C2×C8—21no—
495C2×C8—42no—
496C2×C8—431no—
497C2×C8—431no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—3441no—
503C2×C8—3441no—
504C2×C8C2×C22⋊D4311yescharacteristic
505C2×C8C2×C22⋊D4311yescharacteristic
506C4⋊C4—21no—
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⋊C4—1721no—
517C4⋊C4D4×D4311yescharacteristic
518C4⋊C4C2×C22⋊D4311yescharacteristic
519C4⋊C4C2×C22⋊D4311yescharacteristic
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—21no—
529C42—1721no—
530C42C23×D4311yescharacteristic
531C23—21no—
532C23—21no—
533C23—41no—
534C23—82no—
535C23—82no—
536C23—161no—
537C23—861no—
538Q8—21no—
539Q8—21no—
540Q8—41no—
541Q8—41no—
542Q8—82no—
543Q8—1721no—
544Q8—1721no—
545Q8—1721no—
546Q8—1721no—
547D4—21no—
548D4—21no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—81no—
554D4—82no—
555D4—82no—
556D4—861no—
557D4—861no—
558D4—3442no—
559D4#1306334612yes—
560D4#1306335112yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—82no—
571C2×C4—861no—
572C2×C4—3442no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4C2×D4×D4311yescharacteristic
578C2×C4C22×C22⋊D4311yescharacteristic
579C2×C4#1306337011yescharacteristic
580C8—21no—
581C8—21no—
582C8—41no—
583C8—861no—
584C8—861no—
585C8—1721no—
586C8—1721no—
587C8—1721no—
588C8—1721no—
589C22—22no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—164no—
599C22—1721no—
600C22—1721no—
601C22—1721no—
602C22D4×C22⋊D4311yescharacteristic
603C4—21no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—81no—
609C4—3441no—
610C4—3441no—
611C4—1721no—
612C4C2×#1306334611yescharacteristic
613C4C2×#1306335111yescharacteristic
614C4#1458370211yescharacteristic
615C4#1458370511yescharacteristic
616C2—42no—
617C2—42no—
618C2—161no—
619C2—3441no—
620C2#1914607111yescharacteristic
621C2#1914630211yescharacteristic
622C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingD4×SD16×C43C2
socleC22×C43D42
prime radical#19146408C2
hypercenterD4×SD16D43
hypocenterC43#19787
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ D4×SD16

Complements

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

NH ≅ G/Ntype
1. #19147313C2semidirect
2. #19146514C2semidirect
4. #19134246C2semidirect
5. #19134161C2semidirect
6. #19134020C2semidirect
7. #19134018C2semidirect
8. #19133933C2semidirect
9. #19133844C2semidirect
10. #19133828C2semidirect
11. #19133774C2semidirect
12. #19133704C2semidirect
13. #19133432C2semidirect
14. #19133417C2semidirect
15. D4×SD16×C43C2semidirect
16. #14583622C22semidirect
18. #14583302C22semidirect
20. #14583251C22semidirect
21. #14583250C22semidirect
29. #14583176C22semidirect
33. #14583109C22semidirect
38. #14583030C22semidirect
41. C8×D172C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582646C22semidirect
48. #14582645C22semidirect
49. #14582644C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. #14582621C22semidirect
308. D4×SD16D43semidirect
378. C43#19787semidirect

Maximal subgroups

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

subgroupindex
#191473132
#191465142
#191464082
#191342462
#191341612
#191340202
#191340182
#191339332
#191338442
#191338282
#191337742
#191337042
#191334322
#191334172
D4×SD16×C432
#1978743