Finite Group Databasebeta

← #25086720

Subgroups — #25086720

Order 11008.

684 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#19147574C211yesmaximal, characteristic, complemented
2#19147470C211yesmaximal, characteristic, complemented
3#19146211C211yesmaximal, characteristic
4#19134225C211yesmaximal, characteristic, complemented
5#19134096C211yesmaximal, characteristic, complemented
6#19134008C211yesmaximal, characteristic, complemented
7#19133953C211yesmaximal, characteristic, complemented
8#19133936C211yesmaximal, characteristic, complemented
9#19133774C211yesmaximal, characteristic, complemented
10#19133721C211yesmaximal, characteristic, complemented
11#19133689C211yesmaximal, characteristic, complemented
12#19133667C211yesmaximal, characteristic, complemented
13#19133439C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic, complemented
15C43×#3295C211yesmaximal, characteristic, complemented
16C2×#13063351—21no—
17#14583627C2211yescharacteristic, complemented
18#14583570C2211yescharacteristic
19#14583298—21no—
20#14583295C2211yescharacteristic, complemented
21#14583275C2211yescharacteristic
22#14583273C2211yescharacteristic, complemented
23#14583272C2211yescharacteristic, complemented
24#14583270—21no—
25#14583245C2211yescharacteristic
26#14583203—21no—
27#14583199—21no—
28#14583191C2211yescharacteristic, complemented
29#14583179C2211yescharacteristic
30#14583150—21no—
31#14583104C2211yescharacteristic
32#14583103—21no—
33#14583099C2211yescharacteristic, complemented
34#14583098—21no—
35#14583096C2211yescharacteristic
36#14583094C2211yescharacteristic
37#14583042—21no—
38#14583033—21no—
39Q8×C43⋊C8C2211yescharacteristic, complemented
40C8×Dic86C2211yescharacteristic, complemented
41#14582986—21no—
42C4×#10621883—21no—
43C4×#10621883C2211yescharacteristic
44#14582977C2211yescharacteristic
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582646C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic
50#14582642C2211yescharacteristic, complemented
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52#14582629C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic, 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—
68#13063351—44no—
69C2×#10621873—21no—
70C2×#10621873—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621883D411yescharacteristic
74C2×#10621884—21no—
75C2×#10621884—41no—
76C2×#10621882—21no—
77C2×#10621882—21no—
78C2×#10621882—21no—
79C2×#10621877—21no—
80#13063325C2311yescharacteristic
81#13063323—21no—
82#13063322C2311yescharacteristic
83#13063321—21no—
84#13063317—21no—
85#13063315—41no—
86#13063299—21no—
87#13063298—41no—
88C4×Dic86—21no—
89C4×Dic86C2311yescharacteristic
90#13063290—21no—
91#13063287—21no—
92#13063258—21no—
93#13063258—21no—
94#13063256—21no—
95#13063256—21no—
96#13063256D411yescharacteristic
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101Dic43⋊C8—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248D411yescharacteristic
105#13063246—21no—
106#13063246—21no—
107#13063246—41no—
108#13063246D411yescharacteristic
109#13063245—21no—
110#13063245—21no—
111C22⋊(C43⋊C8)—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C8×Dic43—21no—
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—
163C2×C22⋊D43—41no—
164#10621898—42no—
165#10621898—81no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×C4×D43—41no—
170C2×Dic86—21no—
171C2×Dic86C2×D411yescharacteristic
172SD16×C43—41no—
173SD16×C43—81no—
174C2×C8×C43—21no—
175C2×C8×C43—81no—
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—41no—
182C4⋊C4×C43—41no—
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
192#10621884—81no—
193#10621884—82no—
194#10621883—42no—
195#10621883—81no—
196#10621883SD1614yescomplemented
197#10621882—42no—
198#10621882—42no—
199#10621882—81no—
200(C2×D43)⋊C4—41no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43C2×D411yescharacteristic
204Dic43⋊C4—21no—
205Dic43⋊C4—41no—
206Dic43⋊C4—41no—
207Dic43⋊C4—41no—
208C4×Dic43—21no—
209C4×Dic43—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
217#10621873—42no—
218#10621873—81no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—41no—
222C23×C43—82no—
223C23×C43—82no—
224C23×C43—161no—
225C22×D43—41no—
226Q8×C43—21no—
227Q8×C43—21no—
228Q8×C43—81no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—21no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—81no—
237D4×C43—82no—
238D4×C43—82no—
239D4×C43C2×SD1612yes—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—161no—
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43H(5,𝔽2)11yescharacteristic
253C22⋊D43—82no—
254C22⋊D43—161no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—41no—
258D172—41no—
259D172—41no—
260D172—41no—
261D172—41no—
262D172—81no—
263C4×D43—82no—
264Dic86—21no—
265Dic86—41no—
266Dic86—41no—
267Dic86C2×SD1612yes—
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—41no—
271C43⋊C8—21no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8C2×SD1612yes—
277#19807—431nomaximal, Sylow
278C22×C43—22no—
279C22×C43—41no—
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—81no—
290C2×D43—81no—
291C2×D43—81no—
292C4×C43—21no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—81no—
298C4×C43C22×SD1611yescharacteristic
299C4×C43#57511yescharacteristic
300C4×C43#57611yescharacteristic
301C4×C43#57711yescharacteristic
302Dic43—22no—
303Dic43—41no—
304Dic43—81no—
305#3392—431no—
306#3381—431no—
307#3295D4311yescharacteristic, complemented
308#3274—431no—
309#1715—431no—
310#1691—431no—
311#1678—431no—
312#1668—431no—
313#1665—431no—
314#1639—431no—
315#1631—431no—
316#1626—431no—
317#1622—431no—
318#1583—431no—
319SD16⋊C8—431no—
320C2×C43—42no—
321C2×C43—81no—
322C2×C43—161no—
323C2×C43#326811yescharacteristic
324C2×C43D4×SD1611yescharacteristic
325C2×C43#328811yescharacteristic
326D43—161no—
327C2×AGL(1,ℤ/8)—861no—
328#557—431no—
329#554C2×D4311yescharacteristic
330#550—431no—
331D42C2×D4311yescharacteristic
332#499—861no—
333#498—431no—
334#493—431no—
335#492—431no—
336#492—431no—
337#492—861no—
338#486—431no—
339#486C2×D4311yescharacteristic
340#481—21no—
341#479—861no—
342#478—861no—
343#477—431no—
344#476C2×D4311yescharacteristic
345#474—431no—
346#469—861no—
347#465—21no—
348#461—431no—
349#461—861no—
350#460—431no—
351#460—431no—
352#460—861no—
353#460C2×D4311yescharacteristic
354#459—431no—
355#450—21no—
356#449—861no—
357#447—861no—
358C8×Q8—431no—
359C8×Q8—431no—
360C4×SD16—431no—
361C4×SD16—861no—
362C4×SD16—861no—
363C4×SD16C2×D4311yescharacteristic
364#436—431no—
365C8×D4C2×D4311yescharacteristic
366C2×#102—21no—
367#335—431no—
368#334—431no—
369#333—431no—
370#332—431no—
371#331—431no—
372#331—431no—
373Q8⋊C8—431no—
374Q8⋊C8—431no—
375D4⋊C8—431no—
376D4⋊C8—431no—
377#322—431no—
378C43#1980711yescharacteristic, complemented, Sylow
379C2×#41—861no—
380C22×D4—21no—
381C22×D4—21no—
382AGL(1,ℤ/8)—1724no—
383C2×SD16—21no—
384C2×SD16—431no—
385C2×SD16—861no—
386C2×SD16—861no—
387C2×SD16—861no—
388C2×SD16—861no—
389C2×SD16—861no—
390C2×SD16—1721no—
391C2×SD16C22⋊D4311yescharacteristic
392C2×D8—861no—
393C2×D8—861no—
394C2×D8—861no—
395C2×M16—861no—
396C22×C8—21no—
397C4⋊Q8—431no—
398C4⋊Q8—861no—
399C4⋊Q8C22×D4311yescharacteristic
400#127—431no—
401#127—861no—
402#127C22×D4311yescharacteristic
403#125—21no—
404#125—861no—
405#125—1721no—
406C22⋊Q8—21no—
407C22⋊Q8—41no—
408#121—21no—
409#121—21no—
410#121—861no—
411#121—1721no—
412#120—41no—
413C4×Q8—431no—
414C4×Q8—861no—
415C4×Q8—861no—
416C4×Q8C22×D4311yescharacteristic
417C4×D4—21no—
418C4×D4—861no—
419C4×D4C22×D4311yescharacteristic
420C4×D4C22×D4311yescharacteristic
421C2×C4⋊C4—21no—
422#107—861no—
423#107—861no—
424#106—21no—
425#106—431no—
426#106—861no—
427#106—861no—
428#106C22⋊D4311yescharacteristic
429C4⋊C8—431no—
430C4⋊C8—431no—
431C4⋊C8—431no—
432C4⋊C8—861no—
433C4⋊C8—861no—
434C4⋊C8C22×D4311yescharacteristic
435#103—431no—
436#103—861no—
437#103—861no—
438#103C22⋊D4311yescharacteristic
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—431no—
444#102—861no—
445#102—861no—
446#102—861no—
447#102—861no—
448#102—1721no—
449#102C22⋊D4311yescharacteristic
450C22⋊C8—21no—
451C22⋊C8—861no—
452C4×C8—431no—
453C4×C8—431no—
454C4×C8—861no—
455C4×C8—861no—
456C4×C8C22×D4311yescharacteristic
457C24—41no—
458#41—3441no—
459#41—1722no—
460C2×Q8—21no—
461C2×Q8—431no—
462C2×Q8—861no—
463C2×Q8C2×C22⋊D4311yescharacteristic
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—81no—
472C2×D4—81no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—1721no—
477C2×D4—1721no—
478C2×D4D4×D4311yescharacteristic
479C2×D4C2×C22⋊D4311yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4—1721no—
484SD16—41no—
485SD16—81no—
486SD16—434no—
487SD16—3441no—
488SD16—3441no—
489SD16—3442no—
490SD16—3441no—
491SD16—1722no—
492SD16—1722no—
493D8—3441no—
494D8—1722no—
495D8—1722no—
496M16—1722no—
497C2×C8—21no—
498C2×C8—81no—
499C2×C8—431no—
500C2×C8—431no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8C2×C22⋊D4311yescharacteristic
506C2×C8C2×C22⋊D4311yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—431no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—1721no—
517C4⋊C4—1721no—
518C4⋊C4—1721no—
519C4⋊C4D4×D4311yescharacteristic
520C4⋊C4C2×C22⋊D4311yescharacteristic
521C4⋊C4C2×C22⋊D4311yescharacteristic
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—1721no—
527C42—21no—
528C42—861no—
529C42—1721no—
530C42C23×D4311yescharacteristic
531C23—21no—
532C23—21no—
533C23—41no—
534C23—82no—
535C23—82no—
536C23—161no—
537C23—1721no—
538Q8—21no—
539Q8—21no—
540Q8—81no—
541Q8—432no—
542Q8—861no—
543Q8—1721no—
544Q8—1721no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—81no—
553D4—82no—
554D4—82no—
555D4—3441no—
556D4—3442no—
557D4—1721no—
558D4—1721no—
559D4—1721no—
560D4—1721no—
561D4—6881no—
562D4SD16×D4312yes—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—161no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—3442no—
576C2×C4—1721no—
577C2×C4C2×D4×D4311yescharacteristic
578C2×C4C22×C22⋊D4311yescharacteristic
579C2×C4#1306337011yescharacteristic
580C8—21no—
581C8—21no—
582C8—41no—
583C8—432no—
584C8—861no—
585C8—1721no—
586C8—1721no—
587C8—1721no—
588C8—1721no—
589C22—22no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—164no—
599C22—3441no—
600C22—3441no—
601C22—3441no—
602C22D4×C22⋊D4311yescharacteristic
603C4—21no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—81no—
609C4—862no—
610C4—3441no—
611C4—1721no—
612C4C2×SD16×D4311yescharacteristic
613C4#1458369711yescharacteristic
614C4#1458370211yescharacteristic
615C4#1458370511yescharacteristic
616C2—42no—
617C2—81no—
618C2—161no—
619C2—6881no—
620C2#1914613111yescharacteristic
621C2SD16×C22⋊D4311yescharacteristic
622C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3295C2
socleC22×C43D42
prime radical#19146211C2
hypercenter#3295D43
hypocenterC43#19807
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. #19147574C2semidirect
2. #19147470C2semidirect
4. #19134225C2semidirect
5. #19134096C2semidirect
6. #19134008C2semidirect
7. #19133953C2semidirect
8. #19133936C2semidirect
9. #19133774C2semidirect
10. #19133721C2semidirect
11. #19133689C2semidirect
12. #19133667C2semidirect
13. #19133439C2semidirect
14. #19133407C2semidirect
15. C43×#3295C2semidirect
17. #14583627C22semidirect
20. #14583295C22semidirect
22. #14583273C22semidirect
23. #14583272C22semidirect
28. #14583191C22semidirect
33. #14583099C22semidirect
39. Q8×C43⋊C8C22semidirect
40. C8×Dic86C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582648C22semidirect
48. #14582646C22semidirect
50. #14582642C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. #14582629C22semidirect
55. #14582621C22semidirect
196. #10621883SD16semidirect
307. #3295D43semidirect
378. C43#19807semidirect

Maximal subgroups

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

subgroupindex
#191475742
#191474702
#191462112
#191342252
#191340962
#191340082
#191339532
#191339362
#191337742
#191337212
#191336892
#191336672
#191334392
#191334072
C43×#32952
#1980743