Finite Group Databasebeta

← #25087952

Subgroups — #25087952

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147494C211yesmaximal, characteristic, complemented
2#19146462C211yesmaximal, characteristic, complemented
3#19146191C211yesmaximal, characteristic
4#19134195C211yesmaximal, characteristic, complemented
5#19134096C211yesmaximal, characteristic, complemented
6#19134065C211yesmaximal, characteristic, complemented
7#19134018C211yesmaximal, characteristic, complemented
8#19134001C211yesmaximal, characteristic, complemented
9#19133802C211yesmaximal, characteristic, complemented
10#19133774C211yesmaximal, characteristic, complemented
11#19133745C211yesmaximal, characteristic, complemented
12#19133696C211yesmaximal, characteristic, complemented
13#19133486C211yesmaximal, characteristic, complemented
14C8×#10621882C211yesmaximal, characteristic, complemented
15C43×#3295C211yesmaximal, characteristic, complemented
16C2×#13063351—21no—
17Q8×D172C2211yescharacteristic, complemented
18#14583554C2211yescharacteristic
19#14583309—21no—
20#14583295C2211yescharacteristic, complemented
21#14583271C2211yescharacteristic
22#14583250C2211yescharacteristic, complemented
23#14583249C2211yescharacteristic, complemented
24#14583245C2211yescharacteristic
25#14583231—21no—
26#14583196—21no—
27#14583189—21no—
28#14583186C2211yescharacteristic, complemented
29#14583184C2211yescharacteristic, complemented
30#14583179C2211yescharacteristic
31#14583143—21no—
32#14583127—21no—
33#14583104C2211yescharacteristic
34#14583104C2211yescharacteristic
35#14583091C2211yescharacteristic
36#14583050—21no—
37#14583042—21no—
38#14583036—21no—
39#14583030C2211yescharacteristic, complemented
40#14583009—21no—
41C4×#10621882C2211yescharacteristic
42#14582977C2211yescharacteristic
43C8×D172C2211yescharacteristic, complemented
44#103×D43—21no—
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582646C2211yescharacteristic, complemented
49#14582644C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic, complemented
55C8×C43⋊C8C2211yescharacteristic, complemented
56C43×#554C2211yescharacteristic
57D42×C43C2211yescharacteristic
58C43×#486C2211yescharacteristic
59C43×#481—21no—
60C43×#476C2211yescharacteristic
61C43×#465—21no—
62C43×#460C2211yescharacteristic
63C43×#450—21no—
64C4×SD16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C2×#102×C43—21no—
67C2×#10621898—21no—
68C2×Q8×D43—21no—
69#13063351—44no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621883—21no—
74C2×#10621882—21no—
75C2×#10621882D411yescharacteristic
76C2×#10621877—21no—
77C2×C8×D43—21no—
78#13063325—21no—
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063307—41no—
82#13063305—21no—
83#13063305—41no—
84#13063304—21no—
85#13063296—21no—
86C4×D172—21no—
87C4×D172C2311yescharacteristic
88C4⋊C4×D43—21no—
89#13063258—21no—
90#13063258D411yescharacteristic
91#13063256—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256—21no—
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063250—21no—
100#13063250—21no—
101#13063249—21no—
102#13063249—41no—
103#13063248—21no—
104#13063248—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—41no—
108#13063246D411yescharacteristic
109#13063245—21no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113#13063236—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43D411yescharacteristic
120C22×C8×C43—21no—
121C4⋊Q8×C43C2311yescharacteristic
122#127×C43C2311yescharacteristic
123#125×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—41no—
126#121×C43—21no—
127#121×C43—21no—
128#120×C43—41no—
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133C2×C4⋊C4×C43—21no—
134#106×C43—21no—
135#106×C43D411yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43D411yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—41no—
152C2×D4×C43—41no—
153C2×D4×C43—42no—
154C2×D4×C43—42no—
155C2×D4×C43—81no—
156C2×D4×C43—81no—
157C2×D4×C43C2×D411yescharacteristic
158C2×D4×C43C2×D411yescharacteristic
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—41no—
162C2×C22⋊D43—41no—
163Q8×D43—42no—
164Q8×D43—81no—
165#10621898—42no—
166#10621898—81no—
167C2×D172C2×D411yescharacteristic
168C2×C4×D43—21no—
169C2×C4×D43—41no—
170C2×C4×D43—41no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—41no—
174SD16×C43—41no—
175SD16×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—21no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43—41no—
185C4⋊C4×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C4⋊C4×C43C2×D411yescharacteristic
188C22⋊C4×C43—21no—
189C22⋊C4×C43—21no—
190C22⋊C4×C43—41no—
191C22⋊C4×C43—41no—
192C42×C43—21no—
193C42×C43C2411yescharacteristic
194C22⋊Dic43—41no—
195#10621883—42no—
196#10621883—42no—
197#10621883—81no—
198#10621883—81no—
199#10621882—42no—
200#10621882SD1614yescomplemented
201(C2×D43)⋊C4—21no—
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—
210#10621877—42no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8C2×D411yescharacteristic
216C2×C43⋊C8C2×D411yescharacteristic
217C8×D43—81no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—41no—
221C23×C43—82no—
222C23×C43—82no—
223C23×C43—161no—
224C22×D43—21no—
225Q8×C43—21no—
226Q8×C43—21no—
227Q8×C43—81no—
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×C43C2×SD1612yes—
239C2×C4×C43—21no—
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—161no—
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43H(5,𝔽2)11yescharacteristic
252C22⋊D43—82no—
253C2×Dic43—21no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256D172—21no—
257D172C2×SD1612yes—
258C4×D43—41no—
259C4×D43—41no—
260C4×D43—82no—
261C4×D43—82no—
262Dic86—41no—
263Dic86—41no—
264Dic86—41no—
265Dic86—41no—
266Dic86—82no—
267C8×C43—21no—
268C8×C43—21no—
269C8×C43—41no—
270C43⋊C8—21no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8C2×SD1612yes—
276#19891—431nomaximal, Sylow
277C22×C43—22no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—164no—
287C22×C43D4211yescharacteristic
288C2×D43—22no—
289C2×D43—41no—
290C2×D43—41no—
291C4×C43—21no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—81no—
297C4×C43C22×SD1611yescharacteristic
298C4×C43#57511yescharacteristic
299C4×C43#57611yescharacteristic
300C4×C43#57711yescharacteristic
301Dic43—41no—
302Dic43—81no—
303Dic43—81no—
304#3384—431no—
305#3298—431no—
306#3295D4311yescharacteristic, complemented
307#3272—431no—
308#1708—431no—
309#1691—431no—
310#1686—431no—
311#1679—431no—
312#1677—431no—
313#1643—431no—
314#1639—431no—
315#1635—431no—
316#1627—431no—
317#1590—431no—
318C8×D8—431no—
319C2×C43—42no—
320C2×C43—81no—
321C2×C43—161no—
322C2×C43#327311yescharacteristic
323C2×C43D4×SD1611yescharacteristic
324C2×C43#329011yescharacteristic
325D43—42no—
326C2×AGL(1,ℤ/8)—861no—
327#554C2×D4311yescharacteristic
328D4×Q8—431no—
329#547—431no—
330D42C2×D4311yescharacteristic
331#501—861no—
332#498—431no—
333#492—431no—
334#487—431no—
335#487—431no—
336#486—431no—
337#486C2×D4311yescharacteristic
338#483—861no—
339#481—21no—
340#478—861no—
341#476—431no—
342#476—861no—
343#476C2×D4311yescharacteristic
344#475—431no—
345#474—431no—
346#468—861no—
347#465—21no—
348#465—861no—
349#461—431no—
350#461—431no—
351#460C2×D4311yescharacteristic
352#459—431no—
353#450—21no—
354#450—861no—
355#449—861no—
356#448—861no—
357#446—431no—
358#442—861no—
359C4×SD16C2×D4311yescharacteristic
360C4×D8—431no—
361#436—431no—
362C8×D4—431no—
363C8×D4C2×D4311yescharacteristic
364C2×#103—861no—
365C2×#102—21no—
366#335—431no—
367#334—431no—
368#333—431no—
369#332—431no—
370#332—431no—
371#331—431no—
372Q8⋊C8—431no—
373D4⋊C8—431no—
374D4⋊C8—431no—
375D4⋊C8—431no—
376C82—431no—
377C43#1989111yescharacteristic, complemented, Sylow
378C2×#41—861no—
379C22×Q8—861no—
380C22×D4—21no—
381C22×D4—21no—
382AGL(1,ℤ/8)—1724no—
383C2×SD16—21no—
384C2×SD16—861no—
385C2×SD16—861no—
386C2×SD16—861no—
387C2×SD16—861no—
388C2×SD16C22⋊D4311yescharacteristic
389C2×D8—431no—
390C2×D8—861no—
391C2×M16—861no—
392C22×C8—21no—
393C22×C8—861no—
394C4⋊Q8—431no—
395C4⋊Q8—431no—
396C4⋊Q8—861no—
397C4⋊Q8C22×D4311yescharacteristic
398#127C22×D4311yescharacteristic
399#125—21no—
400#123—1721no—
401C22⋊Q8—21no—
402C22⋊Q8—41no—
403C22⋊Q8—861no—
404C22⋊Q8—861no—
405C22⋊Q8—1721no—
406#121—21no—
407#121—21no—
408#121—861no—
409#120—41no—
410C4×Q8C22×D4311yescharacteristic
411C4×D4—21no—
412C4×D4—431no—
413C4×D4—861no—
414C4×D4C22×D4311yescharacteristic
415C4×D4C22×D4311yescharacteristic
416C2×C4⋊C4—21no—
417C2×C4⋊C4—861no—
418#107—431no—
419#107—861no—
420#106—21no—
421#106—861no—
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⋊C8C22×D4311yescharacteristic
431#103—861no—
432#103—861no—
433#103—861no—
434#103—861no—
435#103—861no—
436#103—1721no—
437#103C22⋊D4311yescharacteristic
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—431no—
443#102—431no—
444#102—861no—
445#102—861no—
446#102—861no—
447#102—1721no—
448#102C22⋊D4311yescharacteristic
449C22⋊C8—21no—
450C22⋊C8—861no—
451C22⋊C8—861no—
452#97—861no—
453C4×C8—431no—
454C4×C8—431no—
455C4×C8C22×D4311yescharacteristic
456C24—41no—
457#41—3441no—
458#41—1722no—
459C2×Q8—21no—
460C2×Q8—861no—
461C2×Q8—861no—
462C2×Q8—3441no—
463C2×Q8—1721no—
464C2×Q8—1722no—
465C2×Q8C2×C22⋊D4311yescharacteristic
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—81no—
474C2×D4—81no—
475C2×D4—431no—
476C2×D4—1721no—
477C2×D4D4×D4311yescharacteristic
478C2×D4C2×C22⋊D4311yescharacteristic
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—41no—
482C22×C4—861no—
483C22×C4—1721no—
484C22×C4—1721no—
485SD16—41no—
486SD16—81no—
487SD16—3441no—
488SD16—3441no—
489SD16—1722no—
490SD16—1722no—
491D8—434no—
492D8—1722no—
493M16—1722no—
494C2×C8—21no—
495C2×C8—81no—
496C2×C8—431no—
497C2×C8—431no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—3441no—
503C2×C8C2×C22⋊D4311yescharacteristic
504C2×C8C2×C22⋊D4311yescharacteristic
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—41no—
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—
527C42—21no—
528C42C23×D4311yescharacteristic
529C23—21no—
530C23—21no—
531C23—41no—
532C23—82no—
533C23—82no—
534C23—161no—
535C23—861no—
536Q8—21no—
537Q8—21no—
538Q8—81no—
539Q8—3442no—
540Q8—1721no—
541Q8—1721no—
542Q8—1721no—
543Q8—1721no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—81no—
552D4—82no—
553D4—82no—
554D4—432no—
555D4—861no—
556D4—3442no—
557D4SD16×D4312yes—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—161no—
568C2×C4—861no—
569C2×C4—3442no—
570C2×C4—3442no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4C2×D4×D4311yescharacteristic
576C2×C4C22×C22⋊D4311yescharacteristic
577C2×C4#1306337011yescharacteristic
578C8—21no—
579C8—21no—
580C8—41no—
581C8—432no—
582C8—861no—
583C8—1721no—
584C8—1721no—
585C8—1721no—
586C8—1721no—
587C22—22no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22—164no—
597C22—862no—
598C22—1721no—
599C22—1721no—
600C22D4×C22⋊D4311yescharacteristic
601C4—21no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—81no—
607C4—3441no—
608C4—3441no—
609C4—1721no—
610C4C2×SD16×D4311yescharacteristic
611C4#1458369711yescharacteristic
612C4#1458370211yescharacteristic
613C4#1458370511yescharacteristic
614C2—42no—
615C2—81no—
616C2—161no—
617C2—1722no—
618C2#1914620211yescharacteristic
619C2SD16×C22⋊D4311yescharacteristic
620C2#1914637711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3295C2
socleC22×C43D42
prime radical#19146191C2
hypercenter#3295D43
hypocenterC43#19891
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3295

Complements

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

NH ≅ G/Ntype
1. #19147494C2semidirect
2. #19146462C2semidirect
4. #19134195C2semidirect
5. #19134096C2semidirect
6. #19134065C2semidirect
7. #19134018C2semidirect
8. #19134001C2semidirect
9. #19133802C2semidirect
10. #19133774C2semidirect
11. #19133745C2semidirect
12. #19133696C2semidirect
13. #19133486C2semidirect
14. C8×#10621882C2semidirect
15. C43×#3295C2semidirect
17. Q8×D172C22semidirect
20. #14583295C22semidirect
22. #14583250C22semidirect
23. #14583249C22semidirect
28. #14583186C22semidirect
29. #14583184C22semidirect
39. #14583030C22semidirect
43. C8×D172C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582648C22semidirect
48. #14582646C22semidirect
49. #14582644C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. C8×C43⋊C8C22semidirect
200. #10621882SD16semidirect
306. #3295D43semidirect
377. C43#19891semidirect

Maximal subgroups

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

subgroupindex
#191474942
#191464622
#191461912
#191341952
#191340962
#191340652
#191340182
#191340012
#191338022
#191337742
#191337452
#191336962
#191334862
C8×#106218822
C43×#32952
#1989143