Finite Group Databasebeta

← #25086270

Subgroups — #25086270

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#19147581C211yesmaximal, characteristic, complemented
2#19146826C211yesmaximal, characteristic, complemented
3#19146512C211yesmaximal, characteristic, complemented
4#19134254C211yesmaximal, characteristic, complemented
5#19134140C211yesmaximal, characteristic, complemented
6#19134036C211yesmaximal, characteristic, complemented
7#19134030C211yesmaximal, characteristic, complemented
8#19133960C211yesmaximal, characteristic, complemented
9#19133879C211yesmaximal, characteristic, complemented
10#19133864C211yesmaximal, characteristic, complemented
11#19133774C211yesmaximal, characteristic, complemented
12#19133703C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic, complemented
15C43×#3294C211yesmaximal, characteristic
16#14583619C2211yescharacteristic
17#14583619C2211yescharacteristic, complemented
18#14583295C2211yescharacteristic, complemented
19#14583282—21no—
20#14583279C2211yescharacteristic, complemented
21#14583249C2211yescharacteristic, complemented
22#14583245C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583237—21no—
25#14583220—21no—
26#14583179C2211yescharacteristic
27#14583179C2211yescharacteristic
28#14583143—21no—
29#14583138—21no—
30#14583120—21no—
31#14583120—21no—
32#14583106C2211yescharacteristic, complemented
33#14583104C2211yescharacteristic
34#14583104C2211yescharacteristic, complemented
35#14583096C2211yescharacteristic
36#14583061—21no—
37#14583050—21no—
38C8×Dic86C2211yescharacteristic, complemented
39#14582993—21no—
40C4×#10621883C2211yescharacteristic
41#14582977C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic, complemented
43#14582904—21no—
44#14582895—21no—
45#14582652C2211yescharacteristic, complemented
46#14582651C2211yescharacteristic, complemented
47#14582646C2211yescharacteristic, complemented
48#14582646C2211yescharacteristic, complemented
49#14582645C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic
51#14582629C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic, complemented
55#14582621C2211yescharacteristic, complemented
56C43×#547C2211yescharacteristic
57D42×C43C2211yescharacteristic
58C43×#486C2211yescharacteristic
59C43×#480—21no—
60C43×#474C2211yescharacteristic
61C43×#466—21no—
62C43×#459C2211yescharacteristic
63C43×#447—21no—
64C4×D8×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C2×#102×C43—21no—
67C2×Dic172—21no—
68C2×Dic172—21no—
69C2×#10621885—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621883D411yescharacteristic
74C2×#10621877—21no—
75C22×C43⋊C8—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063318—41no—
79#13063318—41no—
80#13063312—21no—
81#13063312—21no—
82#13063304—21no—
83#13063304—21no—
84C4×Dic86C2311yescharacteristic
85#13063290—21no—
86#13063290—21no—
87#13063284—21no—
88#13063284—21no—
89#13063258—21no—
90#13063258—21no—
91#13063256—41no—
92#13063256D411yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96Dic43⋊C8—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063248—21no—
101#13063248—21no—
102#13063248D411yescharacteristic
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246—41no—
109#13063246D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×#41×C43—21no—
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118C2×D8×C43—21no—
119C2×D8×C43D411yescharacteristic
120C22×C8×C43—21no—
121C4⋊Q8×C43C2311yescharacteristic
122#127×C43C2311yescharacteristic
123#123×C43—41no—
124C22⋊Q8×C43—21no—
125#121×C43—21no—
126#121×C43—21no—
127#121×C43—21no—
128#120×C43—41no—
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131C4×D4×C43C2311yescharacteristic
132C2×C4⋊C4×C43—21no—
133#107×C43—21no—
134#107×C43D411yescharacteristic
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
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C24×C43—41no—
145#41×C43—42no—
146#41×C43—81no—
147C2×Q8×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—41no—
152C2×D4×C43—41no—
153C2×D4×C43—41no—
154C2×D4×C43—42no—
155C2×D4×C43—42no—
156C2×D4×C43—81no—
157C2×D4×C43—81no—
158C2×D4×C43C2×D411yescharacteristic
159C2×D4×C43C2×D411yescharacteristic
160C2×D4×C43C2×D411yescharacteristic
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—41no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86C2×D411yescharacteristic
168D8×C43—41no—
169D8×C43—81no—
170C2×C8×C43—21no—
171C2×C8×C43—81no—
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43C2×D411yescharacteristic
178C4⋊C4×C43C2×D411yescharacteristic
179C4⋊C4×C43C2×D411yescharacteristic
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—41no—
184C22⋊C4×C43—41no—
185C42×C43C2411yescharacteristic
186C22⋊Dic43—41no—
187C22⋊Dic43—41no—
188C22⋊Dic43—41no—
189C22⋊Dic43—41no—
190#10621885—81no—
191#10621883—22no—
192#10621883—81no—
193#10621883—81no—
194#10621883—81no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43C2×D411yescharacteristic
200Dic43⋊C4—21no—
201Dic43⋊C4—41no—
202Dic43⋊C4—41no—
203C4×Dic43—21no—
204C4×Dic43—41no—
205C4×Dic43—41no—
206#10621877—81no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—81no—
212C2×C43⋊C8C2×D411yescharacteristic
213C2×C43⋊C8C2×D411yescharacteristic
214Dic172—42no—
215Dic172—81no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—41no—
220C23×C43—82no—
221C23×C43—82no—
222C23×C43—161no—
223Q8×C43—41no—
224Q8×C43—41no—
225D4×C43—21no—
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—82no—
237D4×C43—82no—
238D4×C43#13512yes—
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—41no—
248C2×C4×C43—41no—
249C2×C4×C43—82no—
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43H(5,𝔽2)11yescharacteristic
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257Dic86—21no—
258Dic86—21no—
259Dic86—41no—
260Dic86—41no—
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—22no—
274C22×C43—41no—
275C22×C43—41no—
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×C43—164no—
286C22×C43D4211yescharacteristic
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—81no—
292C4×C43C2×#13511yescharacteristic
293C4×C43#57511yescharacteristic
294C4×C43#57611yescharacteristic
295C4×C43#57611yescharacteristic
296Dic43—41no—
297Dic43—41no—
298Dic43—81no—
299Dic43—81no—
300#3393—431no—
301#3324—431no—
302#3302—431no—
303#3294D4311yescharacteristic
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—42no—
316C2×C43—81no—
317C2×C43—81no—
318C2×C43—161no—
319C2×C43#326811yescharacteristic
320C2×C43#328011yescharacteristic
321C2×C43#328911yescharacteristic
322#556—431no—
323#556—431no—
324#547C2×D4311yescharacteristic
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—21no—
336#474—431no—
337#474—431no—
338#474C2×D4311yescharacteristic
339#468—861no—
340#467—861no—
341#466—21no—
342#464—861no—
343#464—861no—
344#462—431no—
345#461—431no—
346#461—431no—
347#460—431no—
348#459C2×D4311yescharacteristic
349#452—861no—
350#450—861no—
351#447—21no—
352C8×Q8—431no—
353C4×Q16—861no—
354C4×SD16—431no—
355C4×D8C2×D4311yescharacteristic
356#436—431no—
357C8×D4—431no—
358C8×D4C2×D4311yescharacteristic
359#418—861no—
360#416—861no—
361C2×#102—21no—
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—21no—
375C22×D4—21no—
376C22×D4—21no—
377C2×Q16—861no—
378C2×Q16—861no—
379C2×Q16—861no—
380C2×SD16—431no—
381C2×SD16—861no—
382C2×SD16—861no—
383C2×SD16—861no—
384C2×D8—21no—
385C2×D8C22⋊D4311yescharacteristic
386C2×M16—861no—
387C22×C8—21no—
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—41no—
398C22⋊Q8—21no—
399C22⋊Q8—861no—
400C22⋊Q8—861no—
401#121—21no—
402#121—21no—
403#121—21no—
404#120—41no—
405C4×Q8—431no—
406C4×Q8—861no—
407C4×Q8—861no—
408C4×D4C22×D4311yescharacteristic
409C4×D4C22×D4311yescharacteristic
410C4×D4C22×D4311yescharacteristic
411#117—861no—
412#117—861no—
413C2×C4⋊C4—21no—
414#107—21no—
415#107—861no—
416#107—861no—
417#107C22⋊D4311yescharacteristic
418#106—431no—
419#106—1721no—
420C4⋊C8—431no—
421C4⋊C8—431no—
422C4⋊C8—431no—
423C4⋊C8—861no—
424C4⋊C8C22×D4311yescharacteristic
425#103—431no—
426#103—861no—
427#103—861no—
428#103—861no—
429#103—861no—
430#103—861no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—431no—
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—21no—
445C22⋊C8—861no—
446C22⋊C8—861no—
447C4×C8—431no—
448C4×C8—431no—
449C4×C8—861no—
450C4×C8C22×D4311yescharacteristic
451C24—41no—
452#41—42no—
453#41—81no—
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—41no—
466C2×D4—81no—
467C2×D4—81no—
468C2×D4D4×D4311yescharacteristic
469C2×D4C2×C22⋊D4311yescharacteristic
470C2×D4C2×C22⋊D4311yescharacteristic
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—41no—
475Q16—3441no—
476Q16—3441no—
477Q16—1722no—
478SD16—862no—
479SD16—3441no—
480SD16—3441no—
481SD16—3441no—
482D8—41no—
483D8—81no—
484M16—3441no—
485C2×C8—21no—
486C2×C8—81no—
487C2×C8—431no—
488C2×C8—431no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—3441no—
494C2×C8C2×C22⋊D4311yescharacteristic
495C2×C8C2×C22⋊D4311yescharacteristic
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—41no—
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⋊C4D4×D4311yescharacteristic
508C4⋊C4C2×C22⋊D4311yescharacteristic
509C4⋊C4C2×C22⋊D4311yescharacteristic
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—41no—
514C22⋊C4—41no—
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—21no—
526C23—41no—
527C23—82no—
528C23—82no—
529C23—161no—
530Q8—41no—
531Q8—41no—
532Q8—861no—
533Q8—861no—
534Q8—1721no—
535Q8—1721no—
536Q8—1721no—
537Q8—1721no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—81no—
548D4—82no—
549D4—82no—
550D4—82no—
551D4#1306334412yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—82no—
563C2×C4—861no—
564C2×C4—861no—
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—22no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—164no—
592C22D4×C22⋊D4311yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—81no—
598C4—3441no—
599C4—3441no—
600C4—1721no—
601C4—1721no—
602C4C2×#1306334411yescharacteristic
603C4#1458369711yescharacteristic
604C4#1458370011yescharacteristic
605C4#1458370211yescharacteristic
606C2—42no—
607C2—81no—
608C2—81no—
609C2—161no—
610C2#1914613111yescharacteristic
611C2#1914628011yescharacteristic
612C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3294C2
socleC22×C43D42
hypercenter#3294D43
hypocenterC43#19777
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3294

Complements

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

NH ≅ G/Ntype
1. #19147581C2semidirect
2. #19146826C2semidirect
3. #19146512C2semidirect
4. #19134254C2semidirect
5. #19134140C2semidirect
6. #19134036C2semidirect
7. #19134030C2semidirect
8. #19133960C2semidirect
9. #19133879C2semidirect
10. #19133864C2semidirect
11. #19133774C2semidirect
12. #19133703C2semidirect
13. #19133425C2semidirect
14. #19133407C2semidirect
17. #14583619C22semidirect
18. #14583295C22semidirect
20. #14583279C22semidirect
21. #14583249C22semidirect
32. #14583106C22semidirect
34. #14583104C22semidirect
38. C8×Dic86C22semidirect
42. D4×C43⋊C8C22semidirect
45. #14582652C22semidirect
46. #14582651C22semidirect
47. #14582646C22semidirect
48. #14582646C22semidirect
49. #14582645C22semidirect
51. #14582629C22semidirect
54. D4⋊(C43⋊C8)C22semidirect
55. #14582621C22semidirect
373. C43#19777semidirect

Maximal subgroups

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

subgroupindex
#191475812
#191468262
#191465122
#191342542
#191341402
#191340362
#191340302
#191339602
#191338792
#191338642
#191337742
#191337032
#191334252
#191334072
C43×#32942
#1977743