Finite Group Databasebeta

← #25086272

Subgroups — #25086272

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#19147582C211yesmaximal, characteristic, complemented
2#19146826C211yesmaximal, characteristic, complemented
3#19146509C211yesmaximal, characteristic, complemented
4#19146408C211yesmaximal, characteristic
5#19134257C211yesmaximal, characteristic, complemented
6#19134144C211yesmaximal, characteristic, complemented
7#19134038C211yesmaximal, characteristic, complemented
8#19134031C211yesmaximal, characteristic, complemented
9#19133958C211yesmaximal, characteristic, complemented
10#19133882C211yesmaximal, characteristic, complemented
11#19133868C211yesmaximal, characteristic, complemented
12#19133702C211yesmaximal, characteristic, complemented
13#19133427C211yesmaximal, characteristic, complemented
14#19133404C211yesmaximal, characteristic, complemented
15C43×#1639C211yesmaximal, characteristic, complemented
16#14583623C2211yescharacteristic, complemented
17#14583619C2211yescharacteristic
18#14583553C2211yescharacteristic
19#14583297C2211yescharacteristic, complemented
20#14583280—21no—
21#14583278C2211yescharacteristic, complemented
22#14583251C2211yescharacteristic, complemented
23#14583245C2211yescharacteristic
24#14583245C2211yescharacteristic
25#14583242—21no—
26#14583220—21no—
27#14583210—21no—
28#14583179C2211yescharacteristic
29#14583179C2211yescharacteristic
30#14583143—21no—
31#14583141—21no—
32#14583133—21no—
33#14583124—21no—
34#14583119—21no—
35#14583110C2211yescharacteristic, complemented
36#14583105C2211yescharacteristic, complemented
37#14583096C2211yescharacteristic
38#14583091C2211yescharacteristic
39#14583062—21no—
40#14583050—21no—
41#14583033—21no—
42#14583023C2211yescharacteristic, complemented
43#14582991—21no—
44C4×#10621883C2211yescharacteristic
45C4×#10621882C2211yescharacteristic
46#14582977C2211yescharacteristic
47D4×C43⋊C8C2211yescharacteristic
48#14582964C2211yescharacteristic, complemented
49#14582904—21no—
50#14582892—21no—
51C2×#13063246—21no—
52#14582651C2211yescharacteristic, complemented
53#14582651C2211yescharacteristic, complemented
54#14582645C2211yescharacteristic, complemented
55#14582644C2211yescharacteristic, complemented
56#14582644C2211yescharacteristic, complemented
57#14582631C2211yescharacteristic, complemented
58#14582628C2211yescharacteristic, complemented
59#14582621C2211yescharacteristic, complemented
60D42×C43C2211yescharacteristic
61C43×#486C2211yescharacteristic
62C43×#474C2211yescharacteristic
63C43×#461C2211yescharacteristic
64C43×#331C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×D4⋊C8C2211yescharacteristic
67C2×#10621900—21no—
68C2×Dic172—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621873—21no—
72C2×#10621883—21no—
73C2×#10621883D411yescharacteristic
74C2×#10621882—21no—
75C2×#10621882D411yescharacteristic
76C2×#10621877—21no—
77C22×C43⋊C8—21no—
78C2×C8×D43—21no—
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063320—41no—
82#13063318—41no—
83#13063314—21no—
84#13063312—21no—
85#13063309—41no—
86#13063305—21no—
87#13063305—21no—
88#13063304—21no—
89#13063299—21no—
90Q8×Dic43—21no—
91C4×Dic86C2311yescharacteristic
92#13063290—21no—
93C4×D172C2311yescharacteristic
94#13063284—21no—
95#13063283—21no—
96C2×C4⋊Dic43—21no—
97#13063258—21no—
98#13063258—21no—
99#13063258D411yescharacteristic
100#13063257—41no—
101#13063256D411yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104Dic43⋊C8—21no—
105#13063250—21no—
106#13063250—21no—
107#13063248—21no—
108#13063248—21no—
109#13063248D411yescharacteristic
110#13063246—21no—
111#13063246—21no—
112#13063246—21no—
113#13063246—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117#13063246—21no—
118#13063246D411yescharacteristic
119#13063246D411yescharacteristic
120#13063245D411yescharacteristic
121C22⋊(C43⋊C8)—21no—
122C22⋊(C43⋊C8)—21no—
123(C2×D43)⋊C8—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C22×D4×C43—21no—
128C22×D4×C43—21no—
129C2×SD16×C43—21no—
130C4⋊Q8×C43C2311yescharacteristic
131#127×C43C2311yescharacteristic
132#121×C43—21no—
133#121×C43—21no—
134#120×C43—41no—
135C4×D4×C43C2311yescharacteristic
136C4×D4×C43C2311yescharacteristic
137#107×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#102×C43—21no—
142#102×C43—41no—
143C4×C8×C43C2311yescharacteristic
144C24×C43—41no—
145C2×Q8×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—41no—
150C2×D4×C43—41no—
151C2×D4×C43—42no—
152C2×D4×C43—42no—
153C2×D4×C43—81no—
154C2×D4×C43—81no—
155C2×D4×C43C2×D411yescharacteristic
156C2×D4×C43C2×D411yescharacteristic
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C2×C22⋊D43—41no—
160C22×Dic43—41no—
161#10621900—42no—
162#10621900—81no—
163C2×D172C2×D411yescharacteristic
164C2×C4×D43—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86C2×D411yescharacteristic
168SD16×C43—81no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—41no—
179C42×C43C2411yescharacteristic
180C22⋊Dic43—41no—
181C22⋊Dic43—41no—
182#10621885—42no—
183#10621885—81no—
184#10621883—22no—
185#10621883—81no—
186#10621882—41no—
187#10621882—81no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—41no—
197C4⋊Dic43—41no—
198C4⋊Dic43C2×D411yescharacteristic
199C4⋊Dic43C2×D411yescharacteristic
200Dic43⋊C4—21no—
201Dic43⋊C4—41no—
202C4×Dic43—21no—
203C4×Dic43—41no—
204C4×Dic43—41no—
205#10621877—81no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—81no—
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213Dic172—81no—
214#10621873—81no—
215C8×D43—81no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—41no—
219C23×C43—82no—
220C23×C43—82no—
221C23×C43—161no—
222C22×D43—21no—
223Q8×C43—41no—
224Q8×C43—41no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—81no—
233D4×C43—82no—
234D4×C43—82no—
235D4×C43#13512yes—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
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—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—82no—
253D172—21no—
254D172—21no—
255C4×D43—41no—
256C4×D43—41no—
257Dic86—21no—
258Dic86—21no—
259Dic86—41no—
260Dic86—41no—
261Dic86—41no—
262Dic86—41no—
263C8×C43—41no—
264C8×C43—41no—
265C8×C43—41no—
266C43⋊C8—21no—
267C43⋊C8—21no—
268C43⋊C8—21no—
269C43⋊C8—21no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272#19777—431nomaximal, Sylow
273C22×C43—22no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—164no—
283C22×C43D4211yescharacteristic
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—41no—
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—81no—
291C4×C43C2×#13511yescharacteristic
292C4×C43#57511yescharacteristic
293C4×C43#57611yescharacteristic
294C4×C43#57611yescharacteristic
295Dic43—41no—
296Dic43—41no—
297Dic43—41no—
298Dic43—81no—
299Dic43—81no—
300#3393—431no—
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#1639D4311yescharacteristic, complemented
312#1628—431no—
313#1581—431no—
314SD16⋊C8—431no—
315C2×C43—42no—
316C2×C43—81no—
317C2×C43—161no—
318C2×C43#326811yescharacteristic
319C2×C43#328011yescharacteristic
320C2×C43#328911yescharacteristic
321D43—81no—
322#556—431no—
323#556—431no—
324#547—431no—
325D42C2×D4311yescharacteristic
326#498—431no—
327#495—861no—
328#494—431no—
329#487—431no—
330#486—431no—
331#486—431no—
332#486C2×D4311yescharacteristic
333#485—861no—
334#482—861no—
335#480—861no—
336#474—431no—
337#474—431no—
338#474C2×D4311yescharacteristic
339#468—861no—
340#467—861no—
341#466—861no—
342#464—861no—
343#464—861no—
344#462—431no—
345#461—431no—
346#461C2×D4311yescharacteristic
347#460—431no—
348#459—431no—
349#452—861no—
350#450—861no—
351#447—861no—
352C8×Q8—431no—
353C4×Q16—861no—
354C4×SD16—431no—
355C4×D8—431no—
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#331C2×D4311yescharacteristic
368Q8⋊C8—431no—
369D4⋊C8—431no—
370D4⋊C8C2×D4311yescharacteristic
371D4⋊C8C2×D4311yescharacteristic
372#322—431no—
373C43#1977711yescharacteristic, complemented, Sylow
374C2×#41—861no—
375C22×D4—21no—
376C22×D4—21no—
377C2×Q16—861no—
378C2×Q16—861no—
379C2×Q16—861no—
380C2×SD16—21no—
381C2×SD16—431no—
382C2×SD16—861no—
383C2×SD16—861no—
384C2×D8—431no—
385C2×D8—861no—
386C2×M16—861no—
387C22×C8—861no—
388C22×C8—861no—
389C4⋊Q8—431no—
390C4⋊Q8—431no—
391C4⋊Q8C22×D4311yescharacteristic
392#127C22×D4311yescharacteristic
393#126—1721no—
394#126—1721no—
395#124—861no—
396#124—861no—
397#123—1721no—
398C22⋊Q8—861no—
399C22⋊Q8—861no—
400C22⋊Q8—861no—
401#121—21no—
402#121—21no—
403#121—861no—
404#120—41no—
405C4×Q8—431no—
406C4×Q8—861no—
407C4×Q8—861no—
408C4×D4—431no—
409C4×D4C22×D4311yescharacteristic
410C4×D4C22×D4311yescharacteristic
411#117—861no—
412#117—861no—
413C2×C4⋊C4—861no—
414#107—21no—
415#107—431no—
416#107—861no—
417#107—861no—
418#106—431no—
419#106—1721no—
420C4⋊C8—431no—
421C4⋊C8—431no—
422C4⋊C8—861no—
423C4⋊C8C22×D4311yescharacteristic
424C4⋊C8C22×D4311yescharacteristic
425#103—21no—
426#103—431no—
427#103—861no—
428#103—861no—
429#103—861no—
430#103—861no—
431#102—21no—
432#102—41no—
433#102—431no—
434#102—431no—
435#102—431no—
436#102—861no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441#102—861no—
442#102—861no—
443#102—861no—
444C22⋊C8—861no—
445C22⋊C8—861no—
446C22⋊C8—861no—
447C4×C8—431no—
448C4×C8—431no—
449C4×C8—861no—
450C4×C8C22×D4311yescharacteristic
451C24—41no—
452#41—3441no—
453#41—1722no—
454C2×Q8—21no—
455C2×Q8—431no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—81no—
466C2×D4—81no—
467C2×D4—431no—
468C2×D4—1721no—
469C2×D4D4×D4311yescharacteristic
470C2×D4D4×D4311yescharacteristic
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—861no—
474C22×C4—1721no—
475Q16—3441no—
476Q16—3441no—
477Q16—1722no—
478SD16—81no—
479SD16—862no—
480SD16—3441no—
481SD16—3441no—
482D8—3441no—
483D8—1721no—
484M16—3441no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—431no—
489C2×C8—431no—
490C2×C8—431no—
491C2×C8—431no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—3441no—
495C2×C8—3441no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—431no—
499C4⋊C4—431no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—1721no—
506C4⋊C4—1721no—
507C4⋊C4—1721no—
508C4⋊C4D4×D4311yescharacteristic
509C4⋊C4D4×D4311yescharacteristic
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—41no—
513C22⋊C4—861no—
514C22⋊C4—1721no—
515C22⋊C4—1721no—
516C22⋊C4—1721no—
517C22⋊C4—1721no—
518C22⋊C4—1721no—
519C42—861no—
520C42—1721no—
521C42—1721no—
522C42C23×D4311yescharacteristic
523C23—21no—
524C23—21no—
525C23—41no—
526C23—82no—
527C23—82no—
528C23—161no—
529C23—861no—
530Q8—41no—
531Q8—41no—
532Q8—861no—
533Q8—861no—
534Q8—1721no—
535Q8—1721no—
536Q8—1721no—
537Q8—1721no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—81no—
546D4—82no—
547D4—82no—
548D4—861no—
549D4—861no—
550D4—3442no—
551D4#1306334612yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—3442no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4C2×D4×D4311yescharacteristic
568C2×C4C2×D4×D4311yescharacteristic
569C2×C4#1306337011yescharacteristic
570C8—41no—
571C8—41no—
572C8—41no—
573C8—861no—
574C8—861no—
575C8—861no—
576C8—861no—
577C8—1721no—
578C8—1721no—
579C22—22no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—164no—
589C22—1721no—
590C22—1721no—
591C22—1721no—
592C22#1458353111yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—81no—
597C4—3441no—
598C4—3441no—
599C4—1721no—
600C4—1721no—
601C4—1721no—
602C4C2×#1306334611yescharacteristic
603C4#1458369511yescharacteristic
604C4#1458370011yescharacteristic
605C4#1458370311yescharacteristic
606C2—42no—
607C2—81no—
608C2—161no—
609C2—3441no—
610C2#1914613311yescharacteristic
611C2#1914627311yescharacteristic
612C2#1914637311yescharacteristic
subgroupG/H
centerC22#14583531
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1639C2
socleC22×C43D42
prime radical#19146408C2
hypercenter#1639D43
hypocenterC43#19777
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1639

Complements

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

NH ≅ G/Ntype
1. #19147582C2semidirect
2. #19146826C2semidirect
3. #19146509C2semidirect
5. #19134257C2semidirect
6. #19134144C2semidirect
7. #19134038C2semidirect
8. #19134031C2semidirect
9. #19133958C2semidirect
10. #19133882C2semidirect
11. #19133868C2semidirect
12. #19133702C2semidirect
13. #19133427C2semidirect
14. #19133404C2semidirect
15. C43×#1639C2semidirect
16. #14583623C22semidirect
19. #14583297C22semidirect
21. #14583278C22semidirect
22. #14583251C22semidirect
35. #14583110C22semidirect
36. #14583105C22semidirect
42. #14583023C22semidirect
48. #14582964C22semidirect
52. #14582651C22semidirect
53. #14582651C22semidirect
54. #14582645C22semidirect
55. #14582644C22semidirect
56. #14582644C22semidirect
57. #14582631C22semidirect
58. #14582628C22semidirect
59. #14582621C22semidirect
311. #1639D43semidirect
373. C43#19777semidirect

Maximal subgroups

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

subgroupindex
#191475822
#191468262
#191465092
#191464082
#191342572
#191341442
#191340382
#191340312
#191339582
#191338822
#191338682
#191337022
#191334272
#191334042
C43×#16392
#1977743