Finite Group Databasebeta

← #25086275

Subgroups — #25086275

Order 11008.

648 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146820C211yesmaximal, characteristic, complemented
2#19146506C211yesmaximal, characteristic, complemented
3#19146410C211yesmaximal, characteristic
4#19134258C211yesmaximal, characteristic, complemented
5#19134144C211yesmaximal, characteristic, complemented
6#19134039C211yesmaximal, characteristic, complemented
7#19134034C211yesmaximal, characteristic, complemented
8#19133957C211yesmaximal, characteristic, complemented
9#19133877C211yesmaximal, characteristic, complemented
10#19133865C211yesmaximal, characteristic, complemented
11#19133772C211yesmaximal, characteristic, complemented
12#19133705C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic, complemented
14#19133405C211yesmaximal, characteristic, complemented
15C43×#3393C211yesmaximal, characteristic, complemented
16#14583554C2211yescharacteristic
17D4×D172C2211yescharacteristic
18#14583295C2211yescharacteristic, complemented
19#14583251C2211yescharacteristic, complemented
20#14583247C2211yescharacteristic
21#14583247C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583240—21no—
24#14583223—21no—
25#14583214—21no—
26#14583179C2211yescharacteristic
27#14583176C2211yescharacteristic
28#14583176C2211yescharacteristic
29#14583147—21no—
30#14583138—21no—
31#14583134—21no—
32#14583109C2211yescharacteristic, complemented
33#14583099C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583059—21no—
36#14583049—21no—
37#14583031—21no—
38C4×#10621884C2211yescharacteristic
39#14582977C2211yescharacteristic
40C8×D172C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic, complemented
42#14582903—21no—
43#14582893—21no—
44#102×D43—21no—
45#14582652C2211yescharacteristic, complemented
46#14582651C2211yescharacteristic, complemented
47#14582645C2211yescharacteristic, 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
55#14582621C2211yescharacteristic, complemented
56C43×#556C2211yescharacteristic
57C43×#556C2211yescharacteristic, complemented
58C43×#495—21no—
59C43×#494C2211yescharacteristic, complemented
60C43×#464—21no—
61C43×#464—21no—
62C43×#461C2211yescharacteristic
63C43×#461C2211yescharacteristic, complemented
64C8×Q8×C43C2211yescharacteristic, complemented
65C4×Q16×C43—21no—
66C4×D8×C43C2211yescharacteristic
67C2×#10621898—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70C2×#10621885—21no—
71C2×#10621884—21no—
72C2×#10621884D411yescharacteristic
73C2×#10621882—21no—
74C2×#10621877—21no—
75C22×C43⋊C8—21no—
76C2×C8×D43—21no—
77#13063325C2311yescharacteristic
78#13063322C2311yescharacteristic
79#13063307—41no—
80#13063304—21no—
81#13063300—21no—
82#13063299—21no—
83#13063296—21no—
84#13063295—41no—
85C4×D172C2311yescharacteristic
86C4⋊C4×D43—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063256—41no—
91#13063256D411yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063249D411yescharacteristic
96#13063248—21no—
97#13063248—21no—
98#13063248—21no—
99#13063247—21no—
100#13063247—21no—
101#13063246—21no—
102#13063245—21no—
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×Q16×C43—21no—
116C2×Q16×C43—21no—
117C2×SD16×C43—21no—
118C2×SD16×C43—21no—
119C2×D8×C43D411yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122#126×C43—41no—
123#126×C43—41no—
124#124×C43—21no—
125#124×C43—21no—
126C22⋊Q8×C43—21no—
127C22⋊Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C4×Q8×C43C2311yescharacteristic
131C4×D4×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#117×C43—21no—
134#117×C43—21no—
135#107×C43D411yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C23×D43—41no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43C2×D411yescharacteristic
149C2×D4×C43C2×D411yescharacteristic
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C2×C22⋊D43—41no—
153C2×C22⋊D43—41no—
154D4×D43—42no—
155D4×D43—81no—
156#10621898—42no—
157#10621898—81no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—41no—
162C2×D172—42no—
163C2×D172—81no—
164C2×D172C2×D411yescharacteristic
165C2×C4×D43—21no—
166C2×C4×D43—41no—
167C2×Dic86—21no—
168Q16×C43—42no—
169Q16×C43—81no—
170SD16×C43—81no—
171SD16×C43—81no—
172D8×C43—41no—
173C2×C8×C43—21no—
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
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—
190C22⋊C4×C43—41no—
191C22⋊C4×C43—41no—
192C42×C43—21no—
193C42×C43—41no—
194C42×C43—41no—
195C42×C43C2411yescharacteristic
196C22⋊Dic43—41no—
197#10621885—81no—
198#10621884—22no—
199#10621884—81no—
200#10621882—81no—
201(C2×D43)⋊C4—21no—
202(C2×D43)⋊C4—41no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43C2×D411yescharacteristic
206Dic43⋊C4—41no—
207#10621877—81no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—81no—
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215C8×D43—81no—
216C23×C43—21no—
217C23×C43—21no—
218C22×D43—21no—
219C22×D43—41no—
220C22×D43—82no—
221C22×D43—82no—
222C22×D43—161no—
223Q8×C43—21no—
224Q8×C43—21no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—21no—
232D4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C22⋊D43—82no—
247C22⋊D43—82no—
248C2×Dic43—21no—
249C2×Dic43—41no—
250D172—21no—
251D172—41no—
252D172—41no—
253D172—41no—
254D172—41no—
255D172—81no—
256D172—82no—
257D172#13512yes—
258C4×D43—41no—
259C4×D43—41no—
260C4×D43—82no—
261Dic86—41no—
262Dic86—41no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—41no—
266C43⋊C8—21no—
267C43⋊C8—21no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272#19777—431nomaximal, Sylow
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43D4211yescharacteristic
280C2×D43—22no—
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—81no—
284C2×D43—81no—
285C2×D43—81no—
286C2×D43—164no—
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43C2×#13511yescharacteristic
295C4×C43#57511yescharacteristic
296C4×C43#57611yescharacteristic
297C4×C43#57611yescharacteristic
298Dic43—41no—
299Dic43—81no—
300#3393D4311yescharacteristic, complemented
301#3324—431no—
302#3302—431no—
303#3294—431no—
304#1720—431no—
305#1699—431no—
306#1682—431no—
307#1681—431no—
308#1669—431no—
309#1654—431no—
310#1652—431no—
311#1639—431no—
312#1628—431no—
313#1581—431no—
314SD16⋊C8—431no—
315C2×C43—81no—
316C2×C43—81no—
317C2×C43#326811yescharacteristic
318C2×C43#328011yescharacteristic
319C2×C43#328911yescharacteristic
320D43—42no—
321D43—161no—
322#556C2×D4311yescharacteristic
323#556C2×D4311yescharacteristic, complemented
324#547—431no—
325D42—431no—
326#498—431no—
327#495—21no—
328#494C2×D4311yescharacteristic, complemented
329#487—431no—
330#486—431no—
331#486—431no—
332#486—431no—
333#485—861no—
334#482—861no—
335#480—861no—
336#474—431no—
337#474—431no—
338#474—431no—
339#468—861no—
340#467—861no—
341#466—861no—
342#464—21no—
343#464—21no—
344#462—431no—
345#461C2×D4311yescharacteristic
346#461C2×D4311yescharacteristic, complemented
347#460—431no—
348#459—431no—
349#452—861no—
350#450—861no—
351#447—861no—
352C8×Q8C2×D4311yescharacteristic, complemented
353C4×Q16—21no—
354C4×SD16—431no—
355C4×D8C2×D4311yescharacteristic
356#436—431no—
357C8×D4—431no—
358C8×D4—431no—
359#418—861no—
360#416—861no—
361C2×#102—861no—
362#335—431no—
363#335—431no—
364#332—431no—
365#332—431no—
366#332—431no—
367#331—431no—
368Q8⋊C8—431no—
369D4⋊C8—431no—
370D4⋊C8—431no—
371D4⋊C8—431no—
372#322—431no—
373C43#1977711yescharacteristic, complemented, Sylow
374C2×#41—861no—
375C22×D4—861no—
376C22×D4—861no—
377C2×Q16—21no—
378C2×Q16—21no—
379C2×Q16—861no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—431no—
383C2×SD16—861no—
384C2×D8—861no—
385C2×D8C22⋊D4311yescharacteristic
386C2×M16—861no—
387C22×C8—861no—
388C22×C8—861no—
389C4⋊Q8—431no—
390C4⋊Q8C22×D4311yescharacteristic
391C4⋊Q8C22×D4311yescharacteristic
392#127—431no—
393#126—41no—
394#126—41no—
395#124—21no—
396#124—21no—
397#123—1721no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—861no—
401#121—861no—
402#121—861no—
403#121—861no—
404#120—1721no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8C22×D4311yescharacteristic
408C4×D4—431no—
409C4×D4C22×D4311yescharacteristic
410C4×D4C22×D4311yescharacteristic
411#117—21no—
412#117—21no—
413C2×C4⋊C4—861no—
414#107—861no—
415#107—861no—
416#107—861no—
417#107C22⋊D4311yescharacteristic
418#106—431no—
419#106—1721no—
420C4⋊C8—21no—
421C4⋊C8—431no—
422C4⋊C8—431no—
423C4⋊C8—431no—
424C4⋊C8C22×D4311yescharacteristic
425#103—21no—
426#103—21no—
427#103—431no—
428#103—861no—
429#103—861no—
430#103—861no—
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#102—1721no—
442#102C22⋊D4311yescharacteristic
443#102C22⋊D4311yescharacteristic
444C22⋊C8—861no—
445C22⋊C8—861no—
446C22⋊C8—861no—
447C4×C8—21no—
448C4×C8—431no—
449C4×C8—431no—
450C4×C8C22×D4311yescharacteristic
451C24—1721no—
452#41—3441no—
453#41—1722no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—861no—
457C2×Q8D4×D4311yescharacteristic
458C2×D4—431no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—3441no—
463C2×D4—3441no—
464C2×D4—1721no—
465C2×D4—1722no—
466C2×D4—1721no—
467C2×D4—1722no—
468C2×D4—1721no—
469C2×D4C2×C22⋊D4311yescharacteristic
470C2×D4C2×C22⋊D4311yescharacteristic
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—861no—
474C22×C4—1721no—
475Q16—42no—
476Q16—81no—
477Q16—3441no—
478SD16—81no—
479SD16—81no—
480SD16—862no—
481SD16—3441no—
482D8—41no—
483D8—3441no—
484M16—3441no—
485C2×C8—21no—
486C2×C8—431no—
487C2×C8—431no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—3441no—
493C2×C8—3441no—
494C2×C8C2×C22⋊D4311yescharacteristic
495C2×C8C2×C22⋊D4311yescharacteristic
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—431no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—1721no—
507C4⋊C4D4×D4311yescharacteristic
508C4⋊C4C2×C22⋊D4311yescharacteristic
509C4⋊C4C2×C22⋊D4311yescharacteristic
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—861no—
517C22⋊C4—1721no—
518C22⋊C4—1721no—
519C42—21no—
520C42—41no—
521C42—41no—
522C42C23×D4311yescharacteristic
523C23—21no—
524C23—21no—
525C23—861no—
526C23—3442no—
527C23—3442no—
528C23—1721no—
529C23—6881no—
530Q8—21no—
531Q8—21no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—1721no—
537Q8—1721no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—432no—
543D4—861no—
544D4—3441no—
545D4—3442no—
546D4—3442no—
547D4—3442no—
548D4—1721no—
549D4—1721no—
550D4—1721no—
551D4—1721no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—861no—
563C2×C4—3442no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4C2×D4×D4311yescharacteristic
568C2×C4C22×C22⋊D4311yescharacteristic
569C2×C4#1306337011yescharacteristic
570C8—21no—
571C8—21no—
572C8—41no—
573C8—861no—
574C8—861no—
575C8—1721no—
576C8—1721no—
577C8—1721no—
578C8—1721no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—862no—
586C22—3441no—
587C22—3441no—
588C22—3441no—
589C22—1721no—
590C22—1721no—
591C22—6884no—
592C22D4×C22⋊D4311yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4—3441no—
601C4—1721no—
602C4#135×D4311yescharacteristic
603C4#1458369711yescharacteristic
604C4#1458370111yescharacteristic
605C4#1458370211yescharacteristic
606C2—81no—
607C2—81no—
608C2—1722no—
609C2—6881no—
610C2#1914613611yescharacteristic
611C2#1914627411yescharacteristic
612C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3393C2
socleC22×C43D42
prime radical#19146410C2
hypercenter#3393D43
hypocenterC43#19777
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3393

Complements

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

NH ≅ G/Ntype
1. #19146820C2semidirect
2. #19146506C2semidirect
4. #19134258C2semidirect
5. #19134144C2semidirect
6. #19134039C2semidirect
7. #19134034C2semidirect
8. #19133957C2semidirect
9. #19133877C2semidirect
10. #19133865C2semidirect
11. #19133772C2semidirect
12. #19133705C2semidirect
13. #19133425C2semidirect
14. #19133405C2semidirect
15. C43×#3393C2semidirect
18. #14583295C22semidirect
19. #14583251C22semidirect
32. #14583109C22semidirect
41. D4×C43⋊C8C22semidirect
45. #14582652C22semidirect
46. #14582651C22semidirect
47. #14582645C22semidirect
48. #14582645C22semidirect
49. #14582644C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. #14582621C22semidirect
57. C43×#556C22semidirect
59. C43×#494C22semidirect
63. C43×#461C22semidirect
64. C8×Q8×C43C22semidirect
300. #3393D43semidirect
323. #556C2×D43semidirect
328. #494C2×D43semidirect
346. #461C2×D43semidirect
352. C8×Q8C2×D43semidirect
373. C43#19777semidirect

Maximal subgroups

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

subgroupindex
#191468202
#191465062
#191464102
#191342582
#191341442
#191340392
#191340342
#191339572
#191338772
#191338652
#191337722
#191337052
#191334252
#191334052
C43×#33932
#1977743