Finite Group Databasebeta

← #25088220

Subgroups — #25088220

Order 11008.

666 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147302C211yesmaximal, characteristic, complemented
2#19146837C211yesmaximal, characteristic, complemented
3#19146547C211yesmaximal, characteristic, complemented
4#19134199C211yesmaximal, characteristic, complemented
5#19134133C211yesmaximal, characteristic, complemented
6#19134130C211yesmaximal, characteristic, complemented
7#19134004C211yesmaximal, characteristic, complemented
8#19134001C211yesmaximal, characteristic, complemented
9#19133739C211yesmaximal, characteristic, complemented
10#19133729C211yesmaximal, characteristic, complemented
11#19133658C211yesmaximal, characteristic, complemented
12#19133649C211yesmaximal, characteristic, complemented
13#19133486C211yesmaximal, characteristic, complemented
14C8×#10621882C211yesmaximal, characteristic, complemented
15C43×#3295C211yesmaximal, characteristic, complemented
16#14583614C2211yescharacteristic
17#14583571C2211yescharacteristic, complemented
18#14583278C2211yescharacteristic, complemented
19#14583275C2211yescharacteristic
20#14583265—21no—
21#14583247C2211yescharacteristic, complemented
22#14583246C2211yescharacteristic, complemented
23#14583245C2211yescharacteristic
24#14583225—21no—
25#14583220—21no—
26#14583196—21no—
27#14583194C2211yescharacteristic, complemented
28#14583189C2211yescharacteristic
29#14583186C2211yescharacteristic, complemented
30#14583150—21no—
31#14583134—21no—
32#14583094—21no—
33#14583094C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583091C2211yescharacteristic
36#14583043—21no—
37#14583033—21no—
38#14583030C2211yescharacteristic, complemented
39#14583009—21no—
40C4×#10621882C2211yescharacteristic
41#14582977C2211yescharacteristic
42C8×D172C2211yescharacteristic, complemented
43#14582904—21no—
44#14582894—21no—
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582647C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic
50#14582642C2211yescharacteristic, complemented
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×#10621902—21no—
68C2×#10621885—41no—
69C2×#10621882—21no—
70C2×#10621882—21no—
71C2×#10621882—21no—
72C2×#10621882—41no—
73C2×#10621882D411yescharacteristic
74C2×#10621877—21no—
75C2×C8×D43—21no—
76#13063325C2311yescharacteristic
77#13063322—21no—
78#13063322C2311yescharacteristic
79#13063311—41no—
80#13063300—21no—
81#13063300—41no—
82#13063299—21no—
83#13063296—21no—
84C4×D172—21no—
85C4×D172C2311yescharacteristic
86#13063284—21no—
87#13063283—21no—
88#13063258—21no—
89#13063258D411yescharacteristic
90#13063256—21no—
91#13063256—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96#13063249—21no—
97#13063247—21no—
98#13063247—21no—
99#13063246—21no—
100#13063246—21no—
101#13063246—21no—
102#13063246—21no—
103#13063246D411yescharacteristic
104#13063245—21no—
105#13063245—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111(C2×D43)⋊C8—21no—
112#13063236—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C22×D4×C43—21no—
116C22×D4×C43—21no—
117C2×SD16×C43—21no—
118C2×SD16×C43D411yescharacteristic
119C22×C8×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121#127×C43C2311yescharacteristic
122#125×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125#121×C43—21no—
126#121×C43—21no—
127#120×C43—41no—
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43—21no—
130C4×D4×C43C2311yescharacteristic
131C4×D4×C43C2311yescharacteristic
132C2×C4⋊C4×C43—21no—
133#106×C43—21no—
134#106×C43D411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136#103×C43D411yescharacteristic
137#102×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C24×C43—41no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—41no—
151C2×D4×C43—41no—
152C2×D4×C43—42no—
153C2×D4×C43—42no—
154C2×D4×C43—81no—
155C2×D4×C43—81no—
156C2×D4×C43C2×D411yescharacteristic
157C2×D4×C43C2×D411yescharacteristic
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—41no—
161C2×C22⋊D43—41no—
162#10621902—42no—
163#10621902—81no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—41no—
168C2×D172—41no—
169C2×D172C2×D411yescharacteristic
170C2×C4×D43—21no—
171C2×C4×D43—41no—
172C2×Dic86—21no—
173SD16×C43—41no—
174SD16×C43—81no—
175C2×C8×C43—21no—
176C2×C8×C43—81no—
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C22⋊C4×C43—21no—
188C22⋊C4×C43—21no—
189C22⋊C4×C43—41no—
190C22⋊C4×C43—41no—
191C42×C43—21no—
192C42×C43C2411yescharacteristic
193C22⋊Dic43—41no—
194#10621885—82no—
195#10621882—22no—
196#10621882—42no—
197#10621882—82no—
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—
207#10621877—81no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8C2×D411yescharacteristic
213C2×C43⋊C8C2×D411yescharacteristic
214C8×D43—81no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—41no—
218C23×C43—82no—
219C23×C43—82no—
220C23×C43—161no—
221C22×D43—21no—
222C22×D43—41no—
223Q8×C43—21no—
224Q8×C43—21no—
225Q8×C43—81no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—81no—
234D4×C43—82no—
235D4×C43—82no—
236D4×C43#13512yes—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—161no—
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C22⋊D43—161no—
251C2×Dic43—21no—
252C2×Dic43—41no—
253D172—21no—
254D172—21no—
255D172—41no—
256D172—41no—
257D172—41no—
258D172—41no—
259D172—81no—
260D172—82no—
261D172—161no—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—82no—
265Dic86—81no—
266C8×C43—21no—
267C8×C43—21no—
268C8×C43—41no—
269C43⋊C8—22no—
270C43⋊C8—21no—
271C43⋊C8—21no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275#19911—431nomaximal, Sylow
276C22×C43—22no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—164no—
286C22×C43D4211yescharacteristic
287C2×D43—41no—
288C2×D43—41no—
289C2×D43—41no—
290C2×D43—81no—
291C2×D43—81no—
292C2×D43—81no—
293C4×C43—21no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—81no—
299C4×C43C2×#13511yescharacteristic
300C4×C43#57511yescharacteristic
301C4×C43#57611yescharacteristic
302C4×C43#57711yescharacteristic
303Dic43—41no—
304Dic43—81no—
305#3366—431no—
306#3325—431no—
307#3305—431no—
308#3295D4311yescharacteristic, complemented
309#1709—431no—
310#1698—431no—
311#1697—431no—
312#1677—431no—
313#1677—431no—
314#1634—431no—
315#1632—431no—
316#1621—431no—
317#1619—431no—
318#1590—431no—
319C8×D8—431no—
320C2×C43—42no—
321C2×C43—81no—
322C2×C43—161no—
323C2×C43#327311yescharacteristic
324C2×C43#328211yescharacteristic
325C2×C43#329211yescharacteristic
326D43—81no—
327D43—161no—
328#555—431no—
329#554C2×D4311yescharacteristic
330#550—431no—
331D42C2×D4311yescharacteristic
332#494—431no—
333#493—431no—
334#490—861no—
335#486—431no—
336#486—431no—
337#486—431no—
338#486C2×D4311yescharacteristic
339#482—861no—
340#482—861no—
341#481—21no—
342#478—861no—
343#477—431no—
344#476—431no—
345#476—431no—
346#476C2×D4311yescharacteristic
347#469—861no—
348#466—861no—
349#465—21no—
350#460C2×D4311yescharacteristic
351#459—431no—
352#459—431no—
353#459—431no—
354#459—861no—
355#450—21no—
356#449—861no—
357#447—861no—
358#446—431no—
359#442—861no—
360C4×SD16C2×D4311yescharacteristic
361C4×D8—431no—
362#436—431no—
363C8×D4—431no—
364C8×D4C2×D4311yescharacteristic
365#418—861no—
366#416—861no—
367C2×#102—21no—
368#335—431no—
369#334—431no—
370#333—431no—
371#333—431no—
372#331—431no—
373#331—431no—
374Q8⋊C8—431no—
375D4⋊C8—431no—
376D4⋊C8—431no—
377D4⋊C8—431no—
378C82—431no—
379C43#1991111yescharacteristic, complemented, Sylow
380C2×#41—861no—
381C22×D4—21no—
382C22×D4—21no—
383C2×Q16—1721no—
384C2×SD16—21no—
385C2×SD16C22⋊D4311yescharacteristic
386C2×D8—431no—
387C2×D8—861no—
388C2×D8—861no—
389C2×D8—861no—
390C2×D8—1721no—
391C2×M16—861no—
392C22×C8—21no—
393C22×C8—861no—
394C4⋊Q8—431no—
395C4⋊Q8C22×D4311yescharacteristic
396#127—431no—
397#127—861no—
398#127C22×D4311yescharacteristic
399#125—21no—
400#124—1721no—
401C22⋊Q8—21no—
402C22⋊Q8—41no—
403#121—21no—
404#121—21no—
405#121—861no—
406#121—861no—
407#121—861no—
408#121—1721no—
409#120—41no—
410C4×Q8C22×D4311yescharacteristic
411C4×D4—21no—
412C4×D4—431no—
413C4×D4—861no—
414C4×D4C22×D4311yescharacteristic
415C4×D4C22×D4311yescharacteristic
416#117—861no—
417#117—861no—
418C2×C4⋊C4—21no—
419#107—431no—
420#107—861no—
421#106—21no—
422#106—861no—
423#106—861no—
424#106C22⋊D4311yescharacteristic
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8—861no—
429C4⋊C8C22×D4311yescharacteristic
430#103—861no—
431#103C22⋊D4311yescharacteristic
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—431no—
437#102—431no—
438#102—861no—
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—861no—
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—861no—
462C2×Q8C2×C22⋊D4311yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—81no—
471C2×D4—81no—
472C2×D4—431no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—1721no—
477C2×D4—1721no—
478C2×D4—1721no—
479C2×D4D4×D4311yescharacteristic
480C2×D4C2×C22⋊D4311yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—41no—
484C22×C4—861no—
485C22×C4—1721no—
486Q16—3442no—
487SD16—41no—
488SD16—81no—
489D8—862no—
490D8—3442no—
491D8—3441no—
492D8—3441no—
493D8—1722no—
494M16—3441no—
495C2×C8—21no—
496C2×C8—81no—
497C2×C8—431no—
498C2×C8—431no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
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—41no—
511C4⋊C4—431no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4D4×D4311yescharacteristic
515C4⋊C4C2×C22⋊D4311yescharacteristic
516C4⋊C4C2×C22⋊D4311yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—861no—
522C22⋊C4—1721no—
523C22⋊C4—1721no—
524C22⋊C4—1721no—
525C42—21no—
526C42—1721no—
527C42C23×D4311yescharacteristic
528C23—21no—
529C23—21no—
530C23—41no—
531C23—82no—
532C23—82no—
533C23—161no—
534C23—861no—
535C23—1721no—
536Q8—21no—
537Q8—21no—
538Q8—81no—
539Q8—3441no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—81no—
548D4—82no—
549D4—82no—
550D4—861no—
551D4—861no—
552D4—3441no—
553D4—3442no—
554D4—1721no—
555D4—1721no—
556D4—1721no—
557D4—1721no—
558D4—6881no—
559D4—6881no—
560D4#1306334612yes—
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—161no—
571C2×C4—861no—
572C2×C4—3442no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4C2×D4×D4311yescharacteristic
577C2×C4C22×C22⋊D4311yescharacteristic
578C2×C4#1306337011yescharacteristic
579C8—21no—
580C8—21no—
581C8—41no—
582C8—862no—
583C8—861no—
584C8—861no—
585C8—1721no—
586C8—1721no—
587C8—1721no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—164no—
598C22—3441no—
599C22—3441no—
600C22—3441no—
601C22—1721no—
602C22—1721no—
603C22—1721no—
604C22D4×C22⋊D4311yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—3441no—
612C4—1721no—
613C4C2×#1306334611yescharacteristic
614C4#1458369711yescharacteristic
615C4#1458370211yescharacteristic
616C4#1458370511yescharacteristic
617C2—42no—
618C2—81no—
619C2—161no—
620C2—3441no—
621C2—6881no—
622C2#1914620211yescharacteristic
623C2#1914630211yescharacteristic
624C2#1914639211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3295C2
socleC22×C43D42
hypercenter#3295D43
hypocenterC43#19911
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. #19147302C2semidirect
2. #19146837C2semidirect
3. #19146547C2semidirect
4. #19134199C2semidirect
5. #19134133C2semidirect
6. #19134130C2semidirect
7. #19134004C2semidirect
8. #19134001C2semidirect
9. #19133739C2semidirect
10. #19133729C2semidirect
11. #19133658C2semidirect
12. #19133649C2semidirect
13. #19133486C2semidirect
14. C8×#10621882C2semidirect
15. C43×#3295C2semidirect
17. #14583571C22semidirect
18. #14583278C22semidirect
21. #14583247C22semidirect
22. #14583246C22semidirect
27. #14583194C22semidirect
29. #14583186C22semidirect
38. #14583030C22semidirect
42. C8×D172C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582648C22semidirect
48. #14582647C22semidirect
50. #14582642C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. C8×C43⋊C8C22semidirect
308. #3295D43semidirect
379. C43#19911semidirect

Maximal subgroups

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

subgroupindex
#191473022
#191468372
#191465472
#191341992
#191341332
#191341302
#191340042
#191340012
#191337392
#191337292
#191336582
#191336492
#191334862
C8×#106218822
C43×#32952
#1991143