Finite Group Databasebeta

← #25088066

Subgroups — #25088066

Order 11008.

666 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146839C211yesmaximal, characteristic, complemented
2#19146523C211yesmaximal, characteristic, complemented
3#19146402C211yesmaximal, characteristic, complemented
4#19134208C211yesmaximal, characteristic, complemented
5#19134139C211yesmaximal, characteristic, complemented
6#19134128C211yesmaximal, characteristic, complemented
7#19134044C211yesmaximal, characteristic, complemented
8#19134034C211yesmaximal, characteristic, complemented
9#19133821C211yesmaximal, characteristic, complemented
10#19133773C211yesmaximal, characteristic, complemented
11#19133746C211yesmaximal, characteristic, complemented
12#19133684C211yesmaximal, characteristic, complemented
13#19133478C211yesmaximal, characteristic, complemented
14D8×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3330C211yesmaximal, characteristic, complemented
16#14583614C2211yescharacteristic
17D4×D172C2211yescharacteristic
18#14583251C2211yescharacteristic, complemented
19#14583249C2211yescharacteristic, complemented
20#14583247C2211yescharacteristic
21#14583247C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583237—21no—
24#14583226—21no—
25#14583212—21no—
26#14583189C2211yescharacteristic
27#14583189C2211yescharacteristic, complemented
28#14583176C2211yescharacteristic
29#14583151—21no—
30#14583133—21no—
31#14583130—21no—
32#14583101C2211yescharacteristic
33#14583094C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583044—21no—
36#14583032—21no—
37#14583031—21no—
38C4×#10621882C2211yescharacteristic
39#14582978C2211yescharacteristic
40D4×C43⋊C8C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic, complemented
42#14582902—21no—
43#14582895—21no—
44C2×#13063245—21no—
45#14582652C2211yescharacteristic, complemented
46#14582651C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582645C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51D4⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic, complemented
56C43×#547C2211yescharacteristic
57C43×#547C2211yescharacteristic, complemented
58C43×#487C2211yescharacteristic, complemented
59C43×#484—21no—
60C43×#474C2211yescharacteristic
61C43×#468—21no—
62C43×#461C2211yescharacteristic, complemented
63C43×#449—21no—
64C4×D8×C43C2211yescharacteristic
65C43×#436C2211yescharacteristic, complemented
66C43×#417—21no—
67C22×D172—21no—
68C2×D4×D43—21no—
69C2×#10621884—21no—
70C2×#10621882—21no—
71C2×#10621882—21no—
72C2×#10621882D411yescharacteristic
73C2×#10621872—21no—
74C22×C43⋊C8—21no—
75C22×C43⋊C8—21no—
76#13063325C2311yescharacteristic
77#13063322C2311yescharacteristic
78#13063311—41no—
79#13063300—21no—
80#13063299—21no—
81#13063299—21no—
82#13063296—21no—
83#13063295—41no—
84C4×D172C2311yescharacteristic
85#13063284—21no—
86#13063283—21no—
87#13063258—21no—
88#13063258D411yescharacteristic
89#13063256—21no—
90#13063256—21no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94#13063249—21no—
95#13063249—21no—
96#13063249—21no—
97#13063248—41no—
98#13063247—21no—
99#13063247—21no—
100#13063246—21no—
101#13063246—21no—
102#13063246D411yescharacteristic
103#13063245—21no—
104#13063245—21no—
105#13063245—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—41no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×#41×C43—21no—
116C2×#41×C43—21no—
117C2×SD16×C43—21no—
118C2×D8×C43D411yescharacteristic
119C2×M16×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122#123×C43—41no—
123#123×C43—41no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—21no—
126#121×C43—21no—
127#121×C43—21no—
128C4×D4×C43C2311yescharacteristic
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133#107×C43—21no—
134#107×C43D411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#102×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C23×D43—41no—
145#41×C43—42no—
146#41×C43—42no—
147#41×C43—81no—
148#41×C43—81no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×D4×C43—41no—
152C2×D4×C43—41no—
153C2×D4×C43C2×D411yescharacteristic
154C2×D4×C43C2×D411yescharacteristic
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—41no—
160C22×C4×C43—41no—
161C2×C22⋊D43—41no—
162C2×C22⋊D43—41no—
163D4×D43—42no—
164D4×D43—81no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—41no—
169C2×D172—42no—
170C2×D172—81no—
171C2×D172C2×D411yescharacteristic
172C2×C4×D43—21no—
173C2×Dic86—21no—
174SD16×C43—81no—
175D8×C43—22no—
176M16×C43—81no—
177C2×C8×C43—21no—
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—41no—
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—21no—
192C22⋊C4×C43—41no—
193C22⋊C4×C43—41no—
194C42×C43C2411yescharacteristic
195C22⋊Dic43—41no—
196#10621884—81no—
197#10621882—41no—
198#10621882—81no—
199#10621882—81no—
200(C2×D43)⋊C4—21no—
201(C2×D43)⋊C4—41no—
202(C2×D43)⋊C4—41no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43C2×D411yescharacteristic
206C4×Dic43—41no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—81no—
212C2×C43⋊C8—81no—
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215#10621872—81no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C22×D43—21no—
220C22×D43—41no—
221C22×D43—82no—
222C22×D43—82no—
223C22×D43—161no—
224Q8×C43—41no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—41no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—21no—
232D4×C43—21no—
233D4×C43—82no—
234D4×C43—82no—
235D4×C43#13512yes—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—82no—
248C2×C4×C43—82no—
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43H(5,𝔽2)11yescharacteristic
252C22⋊D43—82no—
253C22⋊D43—161no—
254C2×Dic43—21no—
255C2×Dic43—41no—
256D172—21no—
257D172—21no—
258D172—41no—
259D172—41no—
260D172—41no—
261D172—41no—
262D172—81no—
263D172—82no—
264C4×D43—41no—
265C4×D43—41no—
266Dic86—81no—
267C8×C43—21no—
268C8×C43—21no—
269C8×C43—41no—
270C43⋊C8—21no—
271C43⋊C8—21no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276#19899—431nomaximal, Sylow
277C22×C43—22no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43D4211yescharacteristic
287C2×D43—41no—
288C2×D43—41no—
289C2×D43—41no—
290C2×D43—81no—
291C2×D43—81no—
292C2×D43—81no—
293C2×D43—164no—
294C4×C43—21no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—81no—
299C4×C43—81no—
300C4×C43C2×#13511yescharacteristic
301C4×C43#57511yescharacteristic
302C4×C43#57611yescharacteristic
303C4×C43#57611yescharacteristic
304Dic43—41no—
305Dic43—81no—
306#3330D4311yescharacteristic, complemented
307#3325—431no—
308#3303—431no—
309#3294—431no—
310#1711—431no—
311#1699—431no—
312#1697—431no—
313#1683—431no—
314#1681—431no—
315#1646—431no—
316#1639—431no—
317#1635—431no—
318#1625—431no—
319#1589—431no—
320C8×D8—431no—
321C2×C43—42no—
322C2×C43—81no—
323C2×C43—81no—
324C2×C43#327311yescharacteristic
325C2×C43#328011yescharacteristic
326C2×C43#329011yescharacteristic
327D43—81no—
328D43—161no—
329#555—431no—
330#547C2×D4311yescharacteristic
331#547C2×D4311yescharacteristic, complemented
332D42—431no—
333#487—431no—
334#487—431no—
335#487C2×D4311yescharacteristic, complemented
336#486—431no—
337#486—431no—
338#486—431no—
339#485—861no—
340#484—21no—
341#482—861no—
342#480—861no—
343#476—431no—
344#476—431no—
345#474—431no—
346#474C2×D4311yescharacteristic
347#469—861no—
348#468—21no—
349#466—861no—
350#465—861no—
351#461—431no—
352#461C2×D4311yescharacteristic, complemented
353#459—431no—
354#459—431no—
355#449—21no—
356#449—861no—
357#447—861no—
358#447—861no—
359C4×D8—431no—
360C4×D8C2×D4311yescharacteristic
361#436—431no—
362#436C2×D4311yescharacteristic, complemented
363C8×D4—431no—
364C8×D4—431no—
365#418—861no—
366#417—21no—
367#416—861no—
368C2×#102—861no—
369#335—431no—
370#335—431no—
371#333—431no—
372#332—431no—
373#332—431no—
374#331—431no—
375D4⋊C8—431no—
376D4⋊C8—431no—
377D4⋊C8—431no—
378D4⋊C8—431no—
379C82—431no—
380C43#1989911yescharacteristic, complemented, Sylow
381C2×#41—21no—
382C2×#41—21no—
383C22×D4—861no—
384C22×D4—861no—
385C2×SD16—21no—
386C2×SD16—861no—
387C2×D8—431no—
388C2×D8—861no—
389C2×D8—861no—
390C2×D8C22⋊D4311yescharacteristic
391C2×M16—21no—
392C2×M16—861no—
393C22×C8—861no—
394C22×C8—861no—
395C4⋊Q8—431no—
396C4⋊Q8C22×D4311yescharacteristic
397C4⋊Q8C22×D4311yescharacteristic
398#127—431no—
399#124—1721no—
400#123—41no—
401#123—41no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404#121—21no—
405#121—21no—
406#121—861no—
407#121—861no—
408#121—861no—
409#121—861no—
410#120—1721no—
411C4×D4—431no—
412C4×D4C22×D4311yescharacteristic
413C4×D4C22×D4311yescharacteristic
414C4×D4C22×D4311yescharacteristic
415#117—861no—
416#117—861no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419#107—21no—
420#107—431no—
421#107—861no—
422#107C22⋊D4311yescharacteristic
423#106—861no—
424#106—861no—
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8C22×D4311yescharacteristic
429#103—21no—
430#103—21no—
431#103—21no—
432#103—861no—
433#103—861no—
434#103—861no—
435#103—1721no—
436#102—21no—
437#102—431no—
438#102—431no—
439#102—861no—
440#102—861no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102—861no—
446#102—861no—
447#102—861no—
448#102—1721no—
449#102C22⋊D4311yescharacteristic
450#102C22⋊D4311yescharacteristic
451C22⋊C8—21no—
452C22⋊C8—861no—
453C22⋊C8—861no—
454C22⋊C8—861no—
455C4×C8—431no—
456C4×C8—431no—
457C4×C8C22×D4311yescharacteristic
458C24—1721no—
459#41—42no—
460#41—42no—
461#41—81no—
462#41—81no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—861no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—431no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—3441no—
473C2×D4—3441no—
474C2×D4—1721no—
475C2×D4—1722no—
476C2×D4—1721no—
477C2×D4—1722no—
478C2×D4—1721no—
479C2×D4D4×D4311yescharacteristic
480C2×D4C2×C22⋊D4311yescharacteristic
481C2×D4C2×C22⋊D4311yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—861no—
488SD16—81no—
489SD16—3441no—
490D8—22no—
491D8—3441no—
492D8—3441no—
493D8—1721no—
494M16—81no—
495M16—3441no—
496C2×C8—21no—
497C2×C8—431no—
498C2×C8—431no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—3441no—
504C2×C8—3441no—
505C2×C8C2×C22⋊D4311yescharacteristic
506C2×C8C2×C22⋊D4311yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—431no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4D4×D4311yescharacteristic
517C4⋊C4C2×C22⋊D4311yescharacteristic
518C4⋊C4C2×C22⋊D4311yescharacteristic
519C22⋊C4—21no—
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—1721no—
529C42C23×D4311yescharacteristic
530C23—21no—
531C23—21no—
532C23—21no—
533C23—861no—
534C23—3442no—
535C23—3442no—
536C23—1721no—
537C23—6881no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—3441no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—82no—
549D4—82no—
550D4—861no—
551D4—861no—
552D4—3441no—
553D4—3442no—
554D4—3442no—
555D4—1721no—
556D4—1721no—
557D4—1721no—
558D4—1721no—
559D4—6881no—
560D4#1306334512yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4—861no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4C2×D4×D4311yescharacteristic
579C2×C4C22×C22⋊D4311yescharacteristic
580C2×C4#1306337011yescharacteristic
581C8—21no—
582C8—21no—
583C8—41no—
584C8—861no—
585C8—861no—
586C8—1721no—
587C8—1721no—
588C8—1721no—
589C8—1721no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—3441no—
600C22—3441no—
601C22—3441no—
602C22—1721no—
603C22—1721no—
604C22—1721no—
605C22—6884no—
606C22D4×C22⋊D4311yescharacteristic
607C4—21no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4—81no—
613C4—3441no—
614C4—1721no—
615C4C2×#1306334511yescharacteristic
616C4#1458369511yescharacteristic
617C4#1458370211yescharacteristic
618C4#1458370311yescharacteristic
619C2—42no—
620C2—81no—
621C2—81no—
622C2—3441no—
623C2—6881no—
624C2#1914620011yescharacteristic
625C2#1914627611yescharacteristic
626C2#1914638111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3330C2
socleC22×C43D42
hypercenter#3330D43
hypocenterC43#19899
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3330

Complements

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

NH ≅ G/Ntype
1. #19146839C2semidirect
2. #19146523C2semidirect
3. #19146402C2semidirect
4. #19134208C2semidirect
5. #19134139C2semidirect
6. #19134128C2semidirect
7. #19134044C2semidirect
8. #19134034C2semidirect
9. #19133821C2semidirect
10. #19133773C2semidirect
11. #19133746C2semidirect
12. #19133684C2semidirect
13. #19133478C2semidirect
14. D8×C43⋊C8C2semidirect
15. C43×#3330C2semidirect
18. #14583251C22semidirect
19. #14583249C22semidirect
27. #14583189C22semidirect
41. D4×C43⋊C8C22semidirect
45. #14582652C22semidirect
46. #14582651C22semidirect
47. #14582647C22semidirect
48. #14582645C22semidirect
49. #14582645C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. C8×C43⋊C8C22semidirect
57. C43×#547C22semidirect
58. C43×#487C22semidirect
62. C43×#461C22semidirect
65. C43×#436C22semidirect
306. #3330D43semidirect
331. #547C2×D43semidirect
335. #487C2×D43semidirect
352. #461C2×D43semidirect
362. #436C2×D43semidirect
380. C43#19899semidirect

Maximal subgroups

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

subgroupindex
#191468392
#191465232
#191464022
#191342082
#191341392
#191341282
#191340442
#191340342
#191338212
#191337732
#191337462
#191336842
#191334782
D8×C43⋊C82
C43×#33302
#1989943