Finite Group Databasebeta

← #25088092

Subgroups — #25088092

Order 11008.

648 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147244C211yesmaximal, characteristic, complemented
2#19146828C211yesmaximal, characteristic, complemented
3#19146402C211yesmaximal, characteristic
4#19134198C211yesmaximal, characteristic, complemented
5#19134167C211yesmaximal, characteristic, complemented
6#19134156C211yesmaximal, characteristic, complemented
7#19134048C211yesmaximal, characteristic, complemented
8#19134041C211yesmaximal, characteristic, complemented
9#19133879C211yesmaximal, characteristic, complemented
10#19133863C211yesmaximal, characteristic, complemented
11#19133710C211yesmaximal, characteristic, complemented
12#19133667C211yesmaximal, characteristic, complemented
13#19133478C211yesmaximal, characteristic, complemented
14SD16×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3331C211yesmaximal, characteristic, complemented
16#14583622C2211yescharacteristic
17D4×D172C2211yescharacteristic
18#14583295C2211yescharacteristic, complemented
19#14583273C2211yescharacteristic
20#14583256—21no—
21#14583251C2211yescharacteristic, complemented
22#14583247C2211yescharacteristic
23#14583246C2211yescharacteristic
24#14583225—21no—
25#14583212—21no—
26#14583203—21no—
27#14583186C2211yescharacteristic
28#14583179C2211yescharacteristic
29#14583176C2211yescharacteristic
30#14583148—21no—
31#14583133—21no—
32#14583114—21no—
33#14583104C2211yescharacteristic, complemented
34#14583099C2211yescharacteristic
35#14583094C2211yescharacteristic
36#14583048—21no—
37#14583032—21no—
38Q8×C43⋊C8C2211yescharacteristic, complemented
39C4×#10621883—21no—
40C4×#10621882C2211yescharacteristic
41#14582978C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582902—21no—
44C2×#13063245—21no—
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582644C2211yescharacteristic, 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, complemented
57C43×#547C2211yescharacteristic
58C43×#487C2211yescharacteristic, complemented
59C43×#483—21no—
60C43×#476C2211yescharacteristic
61C43×#470—21no—
62C43×#462C2211yescharacteristic, complemented
63C43×#452—21no—
64C4×SD16×C43C2211yescharacteristic
65C43×#436C2211yescharacteristic, complemented
66C43×#417—21no—
67C22×D172—21no—
68C2×D4×D43—21no—
69C2×#10621883—21no—
70C2×#10621884—21no—
71C2×#10621884—41no—
72C2×#10621882—21no—
73C2×#10621882D411yescharacteristic
74C2×#10621872—21no—
75C22×C43⋊C8—21no—
76#13063325C2311yescharacteristic
77#13063322C2311yescharacteristic
78#13063320—41no—
79#13063313—21no—
80#13063301—21no—
81#13063300—21no—
82#13063299—21no—
83#13063295—41no—
84C4×Dic86—21no—
85C4×D172C2311yescharacteristic
86#13063283—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258D411yescharacteristic
90#13063256—21no—
91#13063256—41no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96#13063248—21no—
97#13063248—21no—
98#13063248—21no—
99#13063247—21no—
100#13063247—21no—
101#13063246—21no—
102#13063246D411yescharacteristic
103#13063245—21no—
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—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×#41×C43—21no—
116C2×Q16×C43—21no—
117C2×SD16×C43D411yescharacteristic
118C2×M16×C43—21no—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#125×C43—21no—
122#123×C43—41no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—41no—
126#121×C43—21no—
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133#106×C43—21no—
134#106×C43D411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#103×C43D411yescharacteristic
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×C43—21no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—41no—
151C2×D4×C43C2×D411yescharacteristic
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—41no—
156C22×C4×C43—41no—
157C2×C22⋊D43—41no—
158D4×D43—42no—
159D4×D43—81no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—41no—
164C2×D172—42no—
165C2×D172—81no—
166C2×D172C2×D411yescharacteristic
167C2×C4×D43—21no—
168C2×Dic86—21no—
169Q16×C43—81no—
170SD16×C43—22no—
171M16×C43—81no—
172C2×C8×C43—21no—
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—41no—
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
192#10621884—82no—
193#10621884—81no—
194#10621883—42no—
195#10621882—41no—
196#10621882—81no—
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—41no—
199(C2×D43)⋊C4—41no—
200(C2×D43)⋊C4—41no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43C2×D411yescharacteristic
204Dic43⋊C4—41no—
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⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213#10621872—81no—
214C23×C43—21no—
215C23×C43—21no—
216C22×D43—21no—
217C22×D43—41no—
218C22×D43—82no—
219C22×D43—82no—
220C22×D43—161no—
221Q8×C43—21no—
222Q8×C43—21no—
223Q8×C43—41no—
224Q8×C43—41no—
225Q8×C43—81no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—82no—
230D4×C43#13512yes—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—82no—
242C2×C4×C43—161no—
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C22⋊D43—82no—
247C2×Dic43—21no—
248C2×Dic43—41no—
249D172—21no—
250D172—21no—
251D172—41no—
252D172—41no—
253D172—41no—
254D172—41no—
255D172—81no—
256D172—82no—
257C4×D43—41no—
258C4×D43—41no—
259Dic86—41no—
260Dic86—41no—
261C8×C43—21no—
262C8×C43—21no—
263C8×C43—41no—
264C43⋊C8—22no—
265C43⋊C8—21no—
266C43⋊C8—21no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270#19901—431nomaximal, Sylow
271C22×C43—22no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43D4211yescharacteristic
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—81no—
284C2×D43—164no—
285C4×C43—21no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—81no—
291C4×C43—81no—
292C4×C43C2×#13511yescharacteristic
293C4×C43#57511yescharacteristic
294C4×C43#57611yescharacteristic
295C4×C43#57711yescharacteristic
296Dic43—41no—
297Dic43—81no—
298#3360—431no—
299#3331D4311yescharacteristic, complemented
300#3324—431no—
301#3294—431no—
302#1708—431no—
303#1703—431no—
304#1701—431no—
305#1683—431no—
306#1682—431no—
307#1654—431no—
308#1652—431no—
309#1629—431no—
310#1622—431no—
311#1589—431no—
312C8×SD16—431no—
313C2×C43—42no—
314C2×C43—81no—
315C2×C43#327511yescharacteristic
316C2×C43#328011yescharacteristic
317C2×C43#329111yescharacteristic
318D43—81no—
319D43—161no—
320#556—431no—
321#554C2×D4311yescharacteristic, complemented
322#547C2×D4311yescharacteristic
323D42—431no—
324#498—431no—
325#492—431no—
326#488—861no—
327#487—431no—
328#487C2×D4311yescharacteristic, complemented
329#486—431no—
330#486—431no—
331#483—21no—
332#482—861no—
333#480—861no—
334#479—861no—
335#476—431no—
336#476C2×D4311yescharacteristic
337#474—431no—
338#474—431no—
339#470—21no—
340#468—861no—
341#466—861no—
342#463—861no—
343#462C2×D4311yescharacteristic, complemented
344#461—431no—
345#460—431no—
346#459—431no—
347#452—21no—
348#450—861no—
349#447—861no—
350C8×Q8—431no—
351C4×SD16—861no—
352C4×SD16C2×D4311yescharacteristic
353C4×D8—431no—
354#436—431no—
355#436C2×D4311yescharacteristic, complemented
356C8×D4—431no—
357#418—861no—
358#417—21no—
359C2×#102—861no—
360#335—431no—
361#334—431no—
362#333—431no—
363#332—431no—
364#332—431no—
365#331—431no—
366Q8⋊C8—431no—
367D4⋊C8—431no—
368D4⋊C8—431no—
369D4⋊C8—431no—
370C82—431no—
371C43#1990111yescharacteristic, complemented, Sylow
372C2×#41—21no—
373C22×D4—861no—
374C22×D4—861no—
375C2×Q16—21no—
376C2×SD16—861no—
377C2×SD16—861no—
378C2×SD16—1721no—
379C2×SD16C22⋊D4311yescharacteristic
380C2×D8—431no—
381C2×D8—861no—
382C2×M16—21no—
383C2×M16—861no—
384C22×C8—861no—
385C4⋊Q8—431no—
386C4⋊Q8C22×D4311yescharacteristic
387C4⋊Q8C22×D4311yescharacteristic
388#127—431no—
389#126—1721no—
390#125—21no—
391#124—861no—
392#123—41no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395C22⋊Q8—41no—
396C22⋊Q8—861no—
397#121—21no—
398#121—861no—
399#121—861no—
400#120—1721no—
401C4×Q8—861no—
402C4×Q8C22×D4311yescharacteristic
403C4×D4—21no—
404C4×D4—431no—
405C4×D4C22×D4311yescharacteristic
406C4×D4C22×D4311yescharacteristic
407#117—861no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410#107—431no—
411#107—861no—
412#107—861no—
413#106—21no—
414#106—861no—
415#106—1721no—
416#106C22⋊D4311yescharacteristic
417C4⋊C8—431no—
418C4⋊C8—431no—
419C4⋊C8—431no—
420C4⋊C8—861no—
421C4⋊C8C22×D4311yescharacteristic
422#103—21no—
423#103—21no—
424#103—21no—
425#103—861no—
426#103—861no—
427#103—861no—
428#103C22⋊D4311yescharacteristic
429#102—21no—
430#102—431no—
431#102—431no—
432#102—861no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441#102C22⋊D4311yescharacteristic
442C22⋊C8—21no—
443C22⋊C8—861no—
444C22⋊C8—861no—
445C4×C8—431no—
446C4×C8—431no—
447C4×C8—861no—
448C4×C8C22×D4311yescharacteristic
449C24—1721no—
450#41—42no—
451#41—81no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—861no—
455C2×Q8C2×C22⋊D4311yescharacteristic
456C2×D4—41no—
457C2×D4—431no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4—3441no—
462C2×D4—3441no—
463C2×D4—1721no—
464C2×D4—1722no—
465C2×D4—1721no—
466C2×D4—1722no—
467C2×D4D4×D4311yescharacteristic
468C2×D4C2×C22⋊D4311yescharacteristic
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—861no—
474Q16—81no—
475SD16—22no—
476SD16—3442no—
477SD16—3441no—
478SD16—1722no—
479D8—3441no—
480D8—1721no—
481M16—81no—
482M16—3441no—
483C2×C8—21no—
484C2×C8—431no—
485C2×C8—431no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—3441no—
491C2×C8C2×C22⋊D4311yescharacteristic
492C2×C8C2×C22⋊D4311yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—431no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—1721no—
505C4⋊C4D4×D4311yescharacteristic
506C4⋊C4C2×C22⋊D4311yescharacteristic
507C4⋊C4C2×C22⋊D4311yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—861no—
513C22⋊C4—1721no—
514C22⋊C4—1721no—
515C22⋊C4—1721no—
516C42—21no—
517C42—1721no—
518C42C23×D4311yescharacteristic
519C23—21no—
520C23—21no—
521C23—861no—
522C23—3442no—
523C23—3442no—
524C23—1721no—
525C23—6881no—
526Q8—21no—
527Q8—21no—
528Q8—41no—
529Q8—41no—
530Q8—81no—
531Q8—1721no—
532Q8—1721no—
533D4—21no—
534D4—21no—
535D4—21no—
536D4—82no—
537D4—861no—
538D4—861no—
539D4—3441no—
540D4—3442no—
541D4—3442no—
542D4—1721no—
543D4—1721no—
544D4—1721no—
545D4—1721no—
546D4#1306334512yes—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—82no—
558C2×C4—161no—
559C2×C4—861no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4C2×D4×D4311yescharacteristic
564C2×C4C22×C22⋊D4311yescharacteristic
565C2×C4#1306337011yescharacteristic
566C8—21no—
567C8—21no—
568C8—41no—
569C8—862no—
570C8—861no—
571C8—861no—
572C8—1721no—
573C8—1721no—
574C8—1721no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—3441no—
582C22—3441no—
583C22—3441no—
584C22—1721no—
585C22—1721no—
586C22—1721no—
587C22—6884no—
588C22D4×C22⋊D4311yescharacteristic
589C4—21no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—81no—
596C4—3441no—
597C4—1721no—
598C4C2×#1306334511yescharacteristic
599C4#1458369811yescharacteristic
600C4#1458370211yescharacteristic
601C4#1458370811yescharacteristic
602C2—42no—
603C2—81no—
604C2—3441no—
605C2—6881no—
606C2#1914622011yescharacteristic
607C2#1914627611yescharacteristic
608C2#1914638611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3331C2
socleC22×C43D42
prime radical#19146402C2
hypercenter#3331D43
hypocenterC43#19901
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3331

Complements

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

NH ≅ G/Ntype
1. #19147244C2semidirect
2. #19146828C2semidirect
4. #19134198C2semidirect
5. #19134167C2semidirect
6. #19134156C2semidirect
7. #19134048C2semidirect
8. #19134041C2semidirect
9. #19133879C2semidirect
10. #19133863C2semidirect
11. #19133710C2semidirect
12. #19133667C2semidirect
13. #19133478C2semidirect
14. SD16×C43⋊C8C2semidirect
15. C43×#3331C2semidirect
18. #14583295C22semidirect
21. #14583251C22semidirect
33. #14583104C22semidirect
38. Q8×C43⋊C8C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582648C22semidirect
48. #14582645C22semidirect
49. #14582644C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. C8×C43⋊C8C22semidirect
56. C43×#554C22semidirect
58. C43×#487C22semidirect
62. C43×#462C22semidirect
65. C43×#436C22semidirect
299. #3331D43semidirect
321. #554C2×D43semidirect
328. #487C2×D43semidirect
343. #462C2×D43semidirect
355. #436C2×D43semidirect
371. C43#19901semidirect

Maximal subgroups

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

subgroupindex
#191472442
#191468282
#191464022
#191341982
#191341672
#191341562
#191340482
#191340412
#191338792
#191338632
#191337102
#191336672
#191334782
SD16×C43⋊C82
C43×#33312
#1990143