Finite Group Databasebeta

← #25086718

Subgroups — #25086718

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#19147576C211yesmaximal, characteristic, complemented
2#19147468C211yesmaximal, characteristic, complemented
3#19146419C211yesmaximal, characteristic, complemented
4#19134221C211yesmaximal, characteristic, complemented
5#19134094C211yesmaximal, characteristic, complemented
6#19134009C211yesmaximal, characteristic, complemented
7#19133952C211yesmaximal, characteristic, complemented
8#19133934C211yesmaximal, characteristic, complemented
9#19133774C211yesmaximal, characteristic, complemented
10#19133722C211yesmaximal, characteristic, complemented
11#19133690C211yesmaximal, characteristic, complemented
12#19133665C211yesmaximal, characteristic, complemented
13#19133436C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C43×#3274C211yesmaximal, characteristic
16#14583628C2211yescharacteristic, complemented
17#14583606C2211yescharacteristic
18#14583299—21no—
19#14583297C2211yescharacteristic, complemented
20#14583271—21no—
21#14583271C2211yescharacteristic, complemented
22#14583271C2211yescharacteristic, complemented
23#14583245C2211yescharacteristic
24#14583245C2211yescharacteristic
25#14583215—21no—
26#14583204—21no—
27#14583201—21no—
28#14583194C2211yescharacteristic, complemented
29#14583189C2211yescharacteristic
30#14583179C2211yescharacteristic
31#14583126—21no—
32#14583104—21no—
33#14583104C2211yescharacteristic
34#14583096—21no—
35#14583096C2211yescharacteristic
36#14583096C2211yescharacteristic, complemented
37#14583050—21no—
38Q8×C43⋊C8C2211yescharacteristic, complemented
39C8×Dic86C2211yescharacteristic, complemented
40SD16×Dic43—21no—
41C4×#10621883—21no—
42C4×#10621883C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063246—21no—
45#14582652C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, complemented
48#14582644C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic
50#14582643C2211yescharacteristic, complemented
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52#14582629C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582620C2211yescharacteristic, complemented
56C2×AGL(1,ℤ/8)×C43—21no—
57C43×#550C2211yescharacteristic
58D42×C43C2211yescharacteristic
59C43×#493C2211yescharacteristic
60C43×#469—21no—
61C43×#460C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#449—21no—
64C43×#447—21no—
65C4×SD16×C43C2211yescharacteristic
66C43×#436C2211yescharacteristic
67C2×#10621883—21no—
68C2×#10621883—21no—
69C2×#10621883—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—41no—
73C2×#10621883D411yescharacteristic
74C22×C43⋊C8—21no—
75#13063325—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063316—21no—
79#13063316—21no—
80#13063316—41no—
81#13063304—21no—
82#13063302—41no—
83Q8×Dic43—21no—
84C4×Dic86—21no—
85C4×Dic86C2311yescharacteristic
86D4×Dic43—21no—
87C2×C4⋊Dic43—21no—
88#13063258—21no—
89#13063258—21no—
90#13063257—21no—
91#13063257—21no—
92#13063256—21no—
93#13063256D411yescharacteristic
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98Dic43⋊C8—21no—
99#13063249—21no—
100#13063248—21no—
101#13063248D411yescharacteristic
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246—41no—
109#13063246D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×#41×C43—21no—
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118AGL(1,ℤ/8)×C43—44no—
119C2×SD16×C43—21no—
120C2×SD16×C43D411yescharacteristic
121C2×D8×C43—21no—
122C2×D8×C43—21no—
123C2×D8×C43—21no—
124C2×M16×C43—21no—
125#127×C43—21no—
126#127×C43C2311yescharacteristic
127#127×C43C2311yescharacteristic
128#121×C43—21no—
129#121×C43—21no—
130#121×C43—21no—
131#121×C43—41no—
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×C43D411yescharacteristic
140#102×C43—21no—
141#102×C43—21no—
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146#41×C43—42no—
147#41×C43—81no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—41no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43—81no—
162C2×D4×C43—81no—
163C2×D4×C43C2×D411yescharacteristic
164C2×D4×C43C2×D411yescharacteristic
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—41no—
168C22×Dic43—41no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86C2×D411yescharacteristic
172SD16×C43—42no—
173SD16×C43SD1614yescomplemented
174D8×C43—42no—
175D8×C43—42no—
176D8×C43—81no—
177M16×C43—42no—
178C2×C8×C43—21no—
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C4⋊C4×C43—21no—
182C4⋊C4×C43C2×D411yescharacteristic
183C4⋊C4×C43C2×D411yescharacteristic
184C4⋊C4×C43C2×D411yescharacteristic
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C22⋊C4×C43—41no—
188C22⋊C4×C43—41no—
189C42×C43—21no—
190C42×C43C2411yescharacteristic
191C22⋊Dic43—41no—
192#10621883—41no—
193#10621883—42no—
194#10621883—81no—
195#10621883—81no—
196#10621883—81no—
197#10621883—81no—
198#10621883—82no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—41no—
204C4⋊Dic43—41no—
205C4⋊Dic43—41no—
206C4⋊Dic43C2×D411yescharacteristic
207Dic43⋊C4—21no—
208Dic43⋊C4—41no—
209Dic43⋊C4—41no—
210C4×Dic43—21no—
211C4×Dic43—41no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—81no—
217C2×C43⋊C8C2×D411yescharacteristic
218C2×C43⋊C8C2×D411yescharacteristic
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—82no—
224C23×C43—82no—
225C23×C43—161no—
226Q8×C43—21no—
227Q8×C43C2×SD1612yes—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—82no—
240D4×C43—81no—
241D4×C43—81no—
242D4×C43—82no—
243D4×C43—82no—
244D4×C43—161no—
245D4×C43C2×SD1612yes—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—82no—
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—161no—
263Dic86—21no—
264Dic86—21no—
265Dic86—41no—
266Dic86—41no—
267Dic86—81no—
268C8×C43—21no—
269C8×C43—41no—
270C8×C43C2×SD1612yes—
271C43⋊C8—21no—
272C43⋊C8—21no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8—41no—
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—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—164no—
291C22×C43D4211yescharacteristic
292C4×C43—22no—
293C4×C43—21no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43C22×SD1611yescharacteristic
298C4×C43#57511yescharacteristic
299C4×C43#57611yescharacteristic
300C4×C43#57711yescharacteristic
301Dic43—41no—
302Dic43—41no—
303Dic43—81no—
304Dic43—81no—
305#3392—431no—
306#3381—431no—
307#3295—431no—
308#3274D4311yescharacteristic
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—161no—
324C2×C43#326811yescharacteristic
325C2×C43D4×SD1611yescharacteristic
326C2×C43#328811yescharacteristic
327C2×AGL(1,ℤ/8)—21no—
328#557—431no—
329#554—431no—
330#550C2×D4311yescharacteristic
331D42C2×D4311yescharacteristic
332#499—861no—
333#498—431no—
334#493C2×D4311yescharacteristic
335#492—431no—
336#492—431no—
337#492—861no—
338#486—431no—
339#486—431no—
340#481—861no—
341#479—861no—
342#478—861no—
343#477—431no—
344#476—431no—
345#474—431no—
346#469—21no—
347#465—861no—
348#461—431no—
349#461—861no—
350#460—431no—
351#460—431no—
352#460—861no—
353#460C2×D4311yescharacteristic
354#459C2×D4311yescharacteristic
355#450—861no—
356#449—21no—
357#447—21no—
358C8×Q8—431no—
359C8×Q8—431no—
360C4×SD16—431no—
361C4×SD16—861no—
362C4×SD16—861no—
363C4×SD16C2×D4311yescharacteristic
364#436C2×D4311yescharacteristic
365C8×D4—431no—
366C2×#102—861no—
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—21no—
380C22×D4—21no—
381C22×D4—21no—
382AGL(1,ℤ/8)—44no—
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—21no—
393C2×D8—21no—
394C2×D8—21no—
395C2×M16—21no—
396C22×C8—861no—
397C4⋊Q8—431no—
398C4⋊Q8—431no—
399C4⋊Q8—861no—
400#127—21no—
401#127C22×D4311yescharacteristic
402#127C22×D4311yescharacteristic
403#125—861no—
404#125—861no—
405#125—1721no—
406C22⋊Q8—861no—
407C22⋊Q8—1721no—
408#121—21no—
409#121—21no—
410#121—21no—
411#121—41no—
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—861no—
422#107—861no—
423#107—861no—
424#106—431no—
425#106—861no—
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—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—
452C4×C8—431no—
453C4×C8—431no—
454C4×C8—861no—
455C4×C8—861no—
456C4×C8C22×D4311yescharacteristic
457C24—41no—
458#41—42no—
459#41—81no—
460C2×Q8—431no—
461C2×Q8—861no—
462C2×Q8—861no—
463C2×Q8C2×C22⋊D4311yescharacteristic
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—81no—
477C2×D4—81no—
478C2×D4D4×D4311yescharacteristic
479C2×D4C2×C22⋊D4311yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4—1721no—
484SD16—42no—
485SD16—3441no—
486SD16—3441no—
487SD16—3441no—
488SD16—3441no—
489SD16—3442no—
490SD16—1721no—
491SD16—1722no—
492SD16#1062188314yescomplemented
493D8—42no—
494D8—42no—
495D8—81no—
496M16—42no—
497C2×C8—21no—
498C2×C8—431no—
499C2×C8—431no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—3441no—
505C2×C8C2×C22⋊D4311yescharacteristic
506C2×C8C2×C22⋊D4311yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—431no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—1721no—
515C4⋊C4—1721no—
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—41no—
535C23—82no—
536C23—82no—
537C23—161no—
538Q8—21no—
539Q8—861no—
540Q8—861no—
541Q8—3441no—
542Q8—1721no—
543Q8—1721no—
544Q8C2×#1062188312yes—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—82no—
557D4—81no—
558D4—81no—
559D4—82no—
560D4—82no—
561D4—161no—
562D4C2×#1062188312yes—
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—82no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—6881no—
577C2×C4C2×D4×D4311yescharacteristic
578C2×C4C22×C22⋊D4311yescharacteristic
579C2×C4#1306337011yescharacteristic
580C8—21no—
581C8—41no—
582C8—861no—
583C8—861no—
584C8—1721no—
585C8—1721no—
586C8—1721no—
587C8—1721no—
588C8C2×#1062188312yes—
589C22—22no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—164no—
602C22D4×C22⋊D4311yescharacteristic
603C4—22no—
604C4—21no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—3441no—
609C4—3441no—
610C4—1721no—
611C4—1721no—
612C4C22×#1062188311yescharacteristic
613C4#1458369511yescharacteristic
614C4#1458370311yescharacteristic
615C4#1458371011yescharacteristic
616C2—42no—
617C2—81no—
618C2—161no—
619C2—161no—
620C2#1914612911yescharacteristic
621C2D4×#1062188311yescharacteristic
622C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3274C2
socleC22×C43D42
hypercenter#3274D43
hypocenterC43#19807
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3274

Complements

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

NH ≅ G/Ntype
1. #19147576C2semidirect
2. #19147468C2semidirect
3. #19146419C2semidirect
4. #19134221C2semidirect
5. #19134094C2semidirect
6. #19134009C2semidirect
7. #19133952C2semidirect
8. #19133934C2semidirect
9. #19133774C2semidirect
10. #19133722C2semidirect
11. #19133690C2semidirect
12. #19133665C2semidirect
13. #19133436C2semidirect
14. SD16⋊(C43⋊C8)C2semidirect
16. #14583628C22semidirect
19. #14583297C22semidirect
21. #14583271C22semidirect
22. #14583271C22semidirect
28. #14583194C22semidirect
36. #14583096C22semidirect
38. Q8×C43⋊C8C22semidirect
39. C8×Dic86C22semidirect
45. #14582652C22semidirect
46. #14582649C22semidirect
47. #14582647C22semidirect
48. #14582644C22semidirect
50. #14582643C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. #14582629C22semidirect
55. #14582620C22semidirect
173. SD16×C43SD16semidirect
378. C43#19807semidirect
492. SD16#10621883semidirect

Maximal subgroups

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

subgroupindex
#191475762
#191474682
#191464192
#191342212
#191340942
#191340092
#191339522
#191339342
#191337742
#191337222
#191336902
#191336652
#191334362
SD16⋊(C43⋊C8)2
C43×#32742
#1980743