Finite Group Databasebeta

← #25088218

Subgroups — #25088218

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#19146839C211yesmaximal, characteristic, complemented
2#19146545C211yesmaximal, characteristic, complemented
3#19146413C211yesmaximal, characteristic, complemented
4#19134199C211yesmaximal, characteristic, complemented
5#19134135C211yesmaximal, characteristic, complemented
6#19134125C211yesmaximal, characteristic, complemented
7#19134006C211yesmaximal, characteristic, complemented
8#19134002C211yesmaximal, characteristic, complemented
9#19133739C211yesmaximal, characteristic, complemented
10#19133729C211yesmaximal, characteristic, complemented
11#19133660C211yesmaximal, characteristic, complemented
12#19133648C211yesmaximal, characteristic, complemented
13#19133485C211yesmaximal, characteristic, complemented
14D8×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3366C211yesmaximal, characteristic, complemented
16#14583614C2211yescharacteristic
17D4×D172C2211yescharacteristic
18#14583278C2211yescharacteristic, complemented
19#14583275C2211yescharacteristic
20#14583247C2211yescharacteristic
21#14583246C2211yescharacteristic
22#14583245C2211yescharacteristic, complemented
23#14583226—21no—
24#14583220—21no—
25#14583217—21no—
26#14583194C2211yescharacteristic, complemented
27#14583189C2211yescharacteristic
28#14583186C2211yescharacteristic
29#14583151—21no—
30#14583133—21no—
31#14583130—21no—
32#14583099C2211yescharacteristic
33#14583094C2211yescharacteristic
34#14583091C2211yescharacteristic
35#14583049—21no—
36#14583044—21no—
37#14583031—21no—
38C4×#10621884C2211yescharacteristic
39#14582978C2211yescharacteristic
40D4×C43⋊C8C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic, complemented
42#14582902—21no—
43#14582895—21no—
44C2×#13063245—21no—
45#14582652C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, 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×#554C2211yescharacteristic
57C43×#550C2211yescharacteristic, complemented
58C43×#490—21no—
59C43×#486C2211yescharacteristic, complemented
60C43×#478—21no—
61C43×#476C2211yescharacteristic, complemented
62C43×#459—21no—
63C43×#459C2211yescharacteristic
64C43×#446C2211yescharacteristic, complemented
65C43×#442—21no—
66C4×D8×C43C2211yescharacteristic
67C22×D172—21no—
68C2×D4×D43—21no—
69C2×#10621885—41no—
70C2×#10621884—21no—
71C2×#10621884D411yescharacteristic
72C2×#10621882—21no—
73C2×#10621882—21no—
74C2×#10621882—41no—
75C2×#10621872—21no—
76C22×C43⋊C8—21no—
77C22×C43⋊C8—21no—
78#13063325C2311yescharacteristic
79#13063322C2311yescharacteristic
80#13063311—41no—
81#13063300—21no—
82#13063299—21no—
83#13063299—21no—
84#13063296—21no—
85#13063295—41no—
86C4×D172C2311yescharacteristic
87#13063284—21no—
88#13063283—21no—
89#13063258—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256D411yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96#13063249—21no—
97#13063249D411yescharacteristic
98#13063247—21no—
99#13063247—21no—
100#13063246—21no—
101#13063246—21no—
102#13063246—21no—
103#13063246—21no—
104#13063245—21no—
105#13063245—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
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×D8×C43—21no—
117C2×D8×C43D411yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119#127×C43—21no—
120#127×C43C2311yescharacteristic
121#125×C43—21no—
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43—41no—
124#121×C43—21no—
125#121×C43—41no—
126C4×Q8×C43C2311yescharacteristic
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131C2×C4⋊C4×C43—21no—
132#107×C43D411yescharacteristic
133#106×C43—21no—
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#102×C43—21no—
137#102×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142#97×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×C43C2×D411yescharacteristic
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—41no—
159C22×C4×C43—41no—
160C2×C22⋊D43—41no—
161C2×C22⋊D43—41no—
162D4×D43—42no—
163D4×D43—81no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—41no—
168C2×D172—42no—
169C2×D172—81no—
170C2×D172C2×D411yescharacteristic
171C2×C4×D43—21no—
172C2×Dic86—21no—
173D8×C43—22no—
174D8×C43—42no—
175C2×C8×C43—21no—
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
192C22⋊Dic43—41no—
193#10621885—82no—
194#10621884—41no—
195#10621884—81no—
196#10621882—82no—
197#10621882—81no—
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
205C4×Dic43—41no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—81no—
211C2×C43⋊C8—81no—
212C2×C43⋊C8C2×D411yescharacteristic
213C2×C43⋊C8C2×D411yescharacteristic
214#10621872—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—41no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—81no—
234D4×C43—82no—
235D4×C43—161no—
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—82no—
247C2×C4×C43—161no—
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C22⋊D43—82no—
252C22⋊D43—161no—
253C2×Dic43—21no—
254C2×Dic43—41no—
255D172—21no—
256D172—21no—
257D172—41no—
258D172—41no—
259D172—41no—
260D172—41no—
261D172—81no—
262D172—82no—
263C4×D43—41no—
264C4×D43—41no—
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×C43D4211yescharacteristic
286C2×D43—41no—
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#3366D4311yescharacteristic, complemented
306#3325—431no—
307#3305—431no—
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—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#550C2×D4311yescharacteristic, complemented
331D42—431no—
332#494—431no—
333#493—431no—
334#490—21no—
335#486—431no—
336#486—431no—
337#486—431no—
338#486C2×D4311yescharacteristic, complemented
339#482—861no—
340#482—861no—
341#481—861no—
342#478—21no—
343#477—431no—
344#476—431no—
345#476—431no—
346#476C2×D4311yescharacteristic, complemented
347#469—861no—
348#466—861no—
349#465—861no—
350#460—431no—
351#459—21no—
352#459—431no—
353#459—431no—
354#459C2×D4311yescharacteristic
355#450—861no—
356#449—861no—
357#447—861no—
358#446C2×D4311yescharacteristic, complemented
359#442—21no—
360C4×SD16—431no—
361C4×D8C2×D4311yescharacteristic
362#436—431no—
363C8×D4—431no—
364C8×D4—431no—
365#418—861no—
366#416—861no—
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—431no—
385C2×SD16—861no—
386C2×D8—21no—
387C2×D8—861no—
388C2×D8—861no—
389C2×D8—1721no—
390C2×D8C22⋊D4311yescharacteristic
391C2×M16—861no—
392C22×C8—861no—
393C22×C8—861no—
394C4⋊Q8—431no—
395C4⋊Q8C22×D4311yescharacteristic
396#127—21no—
397#127—431no—
398#127C22×D4311yescharacteristic
399#125—21no—
400#124—1721no—
401C22⋊Q8—21no—
402C22⋊Q8—41no—
403#121—21no—
404#121—41no—
405#121—861no—
406#121—861no—
407#121—861no—
408#121—861no—
409#120—1721no—
410C4×Q8C22×D4311yescharacteristic
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—431no—
414C4×D4C22×D4311yescharacteristic
415C4×D4C22×D4311yescharacteristic
416#117—861no—
417#117—861no—
418C2×C4⋊C4—21no—
419#107—861no—
420#107C22⋊D4311yescharacteristic
421#106—21no—
422#106—431no—
423#106—861no—
424#106—861no—
425C4⋊C8—21no—
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8C22×D4311yescharacteristic
430#103—431no—
431#103—861no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
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#102C22⋊D4311yescharacteristic
449#102C22⋊D4311yescharacteristic
450C22⋊C8—861no—
451C22⋊C8—861no—
452C22⋊C8—861no—
453#97—21no—
454C4×C8—431no—
455C4×C8—431no—
456C4×C8C22×D4311yescharacteristic
457C24—1721no—
458#41—42no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—861no—
462C2×Q8D4×D4311yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
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×D4C2×C22⋊D4311yescharacteristic
480C2×D4C2×C22⋊D4311yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—861no—
486Q16—3442no—
487SD16—3441no—
488SD16—1721no—
489D8—22no—
490D8—42no—
491D8—3442no—
492D8—3441no—
493D8—3441no—
494M16—3441no—
495C2×C8—21no—
496C2×C8—431no—
497C2×C8—431no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—3441no—
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—861no—
532C23—3442no—
533C23—3442no—
534C23—1721no—
535C23—6881no—
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—161no—
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—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—82no—
571C2×C4—161no—
572C2×C4—861no—
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—3441no—
598C22—3441no—
599C22—3441no—
600C22—1721no—
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—
613C4C2×#1306334511yescharacteristic
614C4#1458369511yescharacteristic
615C4#1458370311yescharacteristic
616C4#1458370711yescharacteristic
617C2—42no—
618C2—81no—
619C2—161no—
620C2—3441no—
621C2—6881no—
622C2#1914620011yescharacteristic
623C2#1914630311yescharacteristic
624C2#1914639211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3366C2
socleC22×C43D42
hypercenter#3366D43
hypocenterC43#19911
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3366

Complements

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

NH ≅ G/Ntype
1. #19146839C2semidirect
2. #19146545C2semidirect
3. #19146413C2semidirect
4. #19134199C2semidirect
5. #19134135C2semidirect
6. #19134125C2semidirect
7. #19134006C2semidirect
8. #19134002C2semidirect
9. #19133739C2semidirect
10. #19133729C2semidirect
11. #19133660C2semidirect
12. #19133648C2semidirect
13. #19133485C2semidirect
14. D8×C43⋊C8C2semidirect
15. C43×#3366C2semidirect
18. #14583278C22semidirect
22. #14583245C22semidirect
26. #14583194C22semidirect
41. D4×C43⋊C8C22semidirect
45. #14582652C22semidirect
46. #14582649C22semidirect
47. #14582648C22semidirect
48. #14582647C22semidirect
49. #14582643C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. C8×C43⋊C8C22semidirect
57. C43×#550C22semidirect
59. C43×#486C22semidirect
61. C43×#476C22semidirect
64. C43×#446C22semidirect
305. #3366D43semidirect
330. #550C2×D43semidirect
338. #486C2×D43semidirect
346. #476C2×D43semidirect
358. #446C2×D43semidirect
379. C43#19911semidirect

Maximal subgroups

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

subgroupindex
#191468392
#191465452
#191464132
#191341992
#191341352
#191341252
#191340062
#191340022
#191337392
#191337292
#191336602
#191336482
#191334852
D8×C43⋊C82
C43×#33662
#1991143