Finite Group Databasebeta

← #25088225

Subgroups — #25088225

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#19147298C211yesmaximal, characteristic, complemented
2#19146831C211yesmaximal, characteristic, complemented
3#19146421C211yesmaximal, characteristic, complemented
4#19134199C211yesmaximal, characteristic, complemented
5#19134137C211yesmaximal, characteristic, complemented
6#19134126C211yesmaximal, characteristic, complemented
7#19134004C211yesmaximal, characteristic, complemented
8#19134001C211yesmaximal, characteristic, complemented
9#19133740C211yesmaximal, characteristic, complemented
10#19133728C211yesmaximal, characteristic, complemented
11#19133660C211yesmaximal, characteristic, complemented
12#19133648C211yesmaximal, characteristic, complemented
13#19133486C211yesmaximal, characteristic, complemented
14C8×#10621882C211yesmaximal, characteristic, complemented
15C43×#3305C211yesmaximal, characteristic, complemented
16#14583609C2211yescharacteristic
17D4×D172C2211yescharacteristic
18#14583278C2211yescharacteristic, complemented
19#14583275C2211yescharacteristic
20#14583263—21no—
21#14583247C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583245C2211yescharacteristic, complemented
24#14583223—21no—
25#14583219—21no—
26#14583199—21no—
27#14583189C2211yescharacteristic
28#14583189C2211yescharacteristic, complemented
29#14583186C2211yescharacteristic
30#14583150—21no—
31#14583131—21no—
32#14583099C2211yescharacteristic
33#14583094C2211yescharacteristic
34#14583091—21no—
35#14583091C2211yescharacteristic
36#14583048—21no—
37#14583032—21no—
38#14583030C2211yescharacteristic, complemented
39#14583009—21no—
40C4×#10621882C2211yescharacteristic
41#14582977C2211yescharacteristic
42C8×D172C2211yescharacteristic
43#14582903—21no—
44#102×D43—21no—
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582647C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic, complemented
56C43×#555C2211yescharacteristic
57C43×#550C2211yescharacteristic, complemented
58C43×#486C2211yescharacteristic, complemented
59C43×#482—21no—
60C43×#477C2211yescharacteristic, complemented
61C43×#466—21no—
62C43×#459C2211yescharacteristic
63C43×#449—21no—
64C4×SD16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic, complemented
66C43×#416—21no—
67C22×D172—21no—
68C2×D4×D43—21no—
69C2×#10621885—41no—
70C2×#10621884—21no—
71C2×#10621882—21no—
72C2×#10621882—21no—
73C2×#10621882—41no—
74C2×#10621882D411yescharacteristic
75C2×#10621877—21no—
76C2×C8×D43—21no—
77#13063325C2311yescharacteristic
78#13063322C2311yescharacteristic
79#13063317—21no—
80#13063303—41no—
81#13063301—21no—
82#13063300—21no—
83#13063299—21no—
84#13063295—41no—
85C4×D172—21no—
86C4×D172C2311yescharacteristic
87C4⋊C4×D43—21no—
88#13063258D411yescharacteristic
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96#13063247—21no—
97#13063247—21no—
98#13063246—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
115C2×#41×C43—21no—
116C2×SD16×C43D411yescharacteristic
117C2×D8×C43—21no—
118C22×C8×C43—21no—
119C4⋊Q8×C43C2311yescharacteristic
120#127×C43—21no—
121#127×C43C2311yescharacteristic
122#124×C43—41no—
123#121×C43—21no—
124#121×C43—21no—
125#121×C43—21no—
126#121×C43—41no—
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131#117×C43—21no—
132#117×C43—21no—
133#107×C43—21no—
134#106×C43D411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43D411yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C23×D43—41no—
145#41×C43—42no—
146#41×C43—81no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—41no—
153C2×D4×C43—41no—
154C2×D4×C43—41no—
155C2×D4×C43C2×D411yescharacteristic
156C2×D4×C43C2×D411yescharacteristic
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—41no—
160C2×C22⋊D43—41no—
161D4×D43—42no—
162D4×D43—81no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—41no—
167C2×D172—42no—
168C2×D172—81no—
169C2×D172C2×D411yescharacteristic
170C2×C4×D43—21no—
171C2×C4×D43—41no—
172C2×Dic86—21no—
173SD16×C43—41no—
174D8×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×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—
189C22⋊C4×C43—41no—
190C42×C43—21no—
191C42×C43—41no—
192C42×C43C2411yescharacteristic
193#10621885—82no—
194#10621884—81no—
195#10621882—22no—
196#10621882—42no—
197#10621882—82no—
198#10621882—81no—
199(C2×D43)⋊C4—21no—
200(C2×D43)⋊C4—41no—
201(C2×D43)⋊C4—41no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43C2×D411yescharacteristic
205Dic43⋊C4—41no—
206Dic43⋊C4—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—
218C22×D43—21no—
219C22×D43—41no—
220C22×D43—82no—
221C22×D43—82no—
222C22×D43—161no—
223Q8×C43—21no—
224Q8×C43—21no—
225Q8×C43—81no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—81no—
235D4×C43—82no—
236D4×C43—161no—
237D4×C43—161no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
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×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C22⋊D43—82no—
252C2×Dic43—21no—
253C2×Dic43—41no—
254D172—21no—
255D172—41no—
256D172—41no—
257D172—41no—
258D172—41no—
259D172—81no—
260D172—82no—
261D172#13512yes—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—161no—
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—41no—
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×C43D4211yescharacteristic
286C2×D43—22no—
287C2×D43—41no—
288C2×D43—41no—
289C2×D43—81no—
290C2×D43—81no—
291C2×D43—81no—
292C2×D43—164no—
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#3305D4311yescharacteristic, complemented
308#3295—431no—
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—81no—
321C2×C43—81no—
322C2×C43—161no—
323C2×C43#327311yescharacteristic
324C2×C43#328211yescharacteristic
325C2×C43#329211yescharacteristic
326D43—42no—
327D43—161no—
328#555C2×D4311yescharacteristic
329#554—431no—
330#550C2×D4311yescharacteristic, complemented
331D42—431no—
332#494—431no—
333#493—431no—
334#490—861no—
335#486—431no—
336#486—431no—
337#486—431no—
338#486C2×D4311yescharacteristic, complemented
339#482—21no—
340#482—861no—
341#481—861no—
342#478—861no—
343#477C2×D4311yescharacteristic, complemented
344#476—431no—
345#476—431no—
346#476—431no—
347#469—861no—
348#466—21no—
349#465—861no—
350#460—431no—
351#459—431no—
352#459—431no—
353#459—861no—
354#459C2×D4311yescharacteristic
355#450—861no—
356#449—21no—
357#447—861no—
358#446—431no—
359#442—861no—
360C4×SD16C2×D4311yescharacteristic
361C4×D8—431no—
362#436—431no—
363C8×D4—431no—
364C8×D4C2×D4311yescharacteristic, complemented
365#418—861no—
366#416—21no—
367C2×#102—861no—
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—21no—
381C22×D4—861no—
382C22×D4—861no—
383C2×Q16—1721no—
384C2×SD16—861no—
385C2×SD16C22⋊D4311yescharacteristic
386C2×D8—21no—
387C2×D8—431no—
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—21no—
397#127—431no—
398#127C22×D4311yescharacteristic
399#125—861no—
400#124—41no—
401C22⋊Q8—861no—
402C22⋊Q8—1721no—
403#121—21no—
404#121—21no—
405#121—21no—
406#121—41no—
407#121—861no—
408#121—861no—
409#120—1721no—
410C4×Q8C22×D4311yescharacteristic
411C4×D4—21no—
412C4×D4—431no—
413C4×D4—861no—
414C4×D4C22×D4311yescharacteristic
415C4×D4C22×D4311yescharacteristic
416#117—21no—
417#117—21no—
418C2×C4⋊C4—861no—
419#107—21no—
420#107—431no—
421#106—861no—
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—21no—
431#103C22⋊D4311yescharacteristic
432#102—21no—
433#102—21no—
434#102—21no—
435#102—431no—
436#102—431no—
437#102—861no—
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—1721no—
458#41—42no—
459#41—81no—
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—41no—
469C2×D4—431no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—3441no—
474C2×D4—3441no—
475C2×D4—1721no—
476C2×D4—1722no—
477C2×D4—1721no—
478C2×D4—1722no—
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—3441no—
489D8—81no—
490D8—862no—
491D8—3442no—
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—431no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—1721no—
513C4⋊C4—1721no—
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—41no—
522C22⋊C4—861no—
523C22⋊C4—1721no—
524C22⋊C4—1721no—
525C42—21no—
526C42—41no—
527C42C23×D4311yescharacteristic
528C23—21no—
529C23—21no—
530C23—41no—
531C23—861no—
532C23—3442no—
533C23—3442no—
534C23—1721no—
535C23—6881no—
536Q8—21no—
537Q8—21no—
538Q8—81no—
539Q8—3441no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—81no—
549D4—82no—
550D4—161no—
551D4—161no—
552D4—432no—
553D4—861no—
554D4—3441no—
555D4—3442no—
556D4—3442no—
557D4—1721no—
558D4—1721no—
559D4—1721no—
560D4—1721no—
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—82no—
571C2×C4—861no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—6881no—
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—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—862no—
598C22—3441no—
599C22—3441no—
600C22—3441no—
601C22—1721no—
602C22—1721no—
603C22—6884no—
604C22D4×C22⋊D4311yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—3441no—
612C4—1721no—
613C4#135×D4311yescharacteristic
614C4#1458369711yescharacteristic
615C4#1458370211yescharacteristic
616C4#1458370611yescharacteristic
617C2—81no—
618C2—81no—
619C2—161no—
620C2—1722no—
621C2—6881no—
622C2#1914620211yescharacteristic
623C2#1914629611yescharacteristic
624C2#1914639211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3305C2
socleC22×C43D42
hypercenter#3305D43
hypocenterC43#19911
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3305

Complements

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

NH ≅ G/Ntype
1. #19147298C2semidirect
2. #19146831C2semidirect
3. #19146421C2semidirect
4. #19134199C2semidirect
5. #19134137C2semidirect
6. #19134126C2semidirect
7. #19134004C2semidirect
8. #19134001C2semidirect
9. #19133740C2semidirect
10. #19133728C2semidirect
11. #19133660C2semidirect
12. #19133648C2semidirect
13. #19133486C2semidirect
14. C8×#10621882C2semidirect
15. C43×#3305C2semidirect
18. #14583278C22semidirect
23. #14583245C22semidirect
28. #14583189C22semidirect
38. #14583030C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582648C22semidirect
48. #14582647C22semidirect
49. #14582643C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. C8×C43⋊C8C22semidirect
57. C43×#550C22semidirect
58. C43×#486C22semidirect
60. C43×#477C22semidirect
65. C8×D4×C43C22semidirect
307. #3305D43semidirect
330. #550C2×D43semidirect
338. #486C2×D43semidirect
343. #477C2×D43semidirect
364. C8×D4C2×D43semidirect
379. C43#19911semidirect

Maximal subgroups

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

subgroupindex
#191472982
#191468312
#191464212
#191341992
#191341372
#191341262
#191340042
#191340012
#191337402
#191337282
#191336602
#191336482
#191334862
C8×#106218822
C43×#33052
#1991143