Finite Group Databasebeta

← #25086472

Subgroups — #25086472

Order 11008.

626 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147466C211yesmaximal, characteristic, complemented
2#19147372C211yesmaximal, characteristic, complemented
3#19146422C211yesmaximal, characteristic
4#19146422C211yesmaximal, characteristic
5#19134254C211yesmaximal, characteristic, complemented
6#19134133C211yesmaximal, characteristic, complemented
7#19134045C211yesmaximal, characteristic, complemented
8#19134009C211yesmaximal, characteristic, complemented
9#19133969C211yesmaximal, characteristic, complemented
10#19133771C211yesmaximal, characteristic
11#19133732C211yesmaximal, characteristic, complemented
12#19133732C211yesmaximal, characteristic, complemented
13#19133434C211yesmaximal, characteristic, complemented
14#19133410C211yesmaximal, characteristic, complemented
15C43×#1626C211yesmaximal, characteristic, complemented
16#14583609C2211yescharacteristic
17#14583609C2211yescharacteristic
18#14583534C2211yescharacteristic
19#14583298—21no—
20#14583295C2211yescharacteristic, complemented
21#14583279C2211yescharacteristic, complemented
22#14583267—21no—
23#14583249C2211yescharacteristic, complemented
24#14583245C2211yescharacteristic
25#14583245C2211yescharacteristic
26#14583216—21no—
27#14583216—21no—
28#14583206—21no—
29#14583206—21no—
30#14583196—21no—
31#14583194C2211yescharacteristic, complemented
32#14583194C2211yescharacteristic, complemented
33#14583190C2211yescharacteristic
34#14583190C2211yescharacteristic
35#14583176C2211yescharacteristic
36#14583125—21no—
37#14583125—21no—
38#14583101—21no—
39#14583101C2211yescharacteristic
40#14583048—21no—
41#14583048—21no—
42#14583030C2211yescharacteristic, complemented
43Q8×C43⋊C8C2211yescharacteristic, complemented
44#14582997—21no—
45C4×#10621884—21no—
46C4×#10621884C2211yescharacteristic
47C4×#10621884C2211yescharacteristic
48#14582964C2211yescharacteristic
49#14582964C2211yescharacteristic
50#102×D43—21no—
51#102×D43—21no—
52#14582651C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582647C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582643C2211yescharacteristic
57#14582628C2211yescharacteristic
58#14582628C2211yescharacteristic
59#14582621C2211yescharacteristic, complemented
60C43×#557C2211yescharacteristic, complemented
61C43×#486C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C43×#460C2211yescharacteristic
64C43×#332C2211yescharacteristic, complemented
65C43×Q8⋊C8C2211yescharacteristic, complemented
66C43×Q8⋊C8C2211yescharacteristic, complemented
67C2×D4×D43—21no—
68C2×D4×D43—21no—
69C2×Dic172—41no—
70C2×#10621884—21no—
71C2×#10621884D411yescharacteristic
72C2×#10621884D411yescharacteristic
73C2×C8×D43—21no—
74C2×C8×D43—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063317—21no—
78#13063317—21no—
79#13063303—41no—
80#13063303—41no—
81#13063301—21no—
82#13063301—21no—
83#13063296—21no—
84#13063296—21no—
85#13063293—41no—
86C4×D172—21no—
87C4×D172—21no—
88C4×D172C2311yescharacteristic
89C4×D172C2311yescharacteristic
90C4⋊C4×D43—21no—
91C4⋊C4×D43—21no—
92#13063258—21no—
93#13063258—21no—
94#13063258—21no—
95#13063257—21no—
96#13063257—21no—
97#13063256—21no—
98#13063256—21no—
99#13063256D411yescharacteristic
100#13063256D411yescharacteristic
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105#13063249—21no—
106#13063249—21no—
107#13063249—21no—
108#13063249—21no—
109#13063249—21no—
110#13063249D411yescharacteristic
111#13063249D411yescharacteristic
112#13063247—21no—
113#13063247—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117#13063246—21no—
118#13063245—21no—
119#13063245D411yescharacteristic
120#13063245D411yescharacteristic
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123#13063236—21no—
124C4×C43⋊C8—21no—
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C2×SD16×C43—21no—
128C2×SD16×C43—21no—
129C4⋊Q8×C43—21no—
130C4⋊Q8×C43C2311yescharacteristic
131#127×C43C2311yescharacteristic
132#125×C43—21no—
133#125×C43—41no—
134C4×Q8×C43—21no—
135C4×Q8×C43—21no—
136C4×Q8×C43C2311yescharacteristic
137C4×Q8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#102×C43—21no—
141#102×C43—21no—
142#102×C43—41no—
143C4×C8×C43C2311yescharacteristic
144C23×D43—41no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×C22⋊D43—41no—
152C2×C22⋊D43—41no—
153D4×D43—42no—
154D4×D43—42no—
155D4×D43—81no—
156D4×D43—81no—
157C2×D172C2×D411yescharacteristic
158C2×D172C2×D411yescharacteristic
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—41no—
162C2×C4×D43—41no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165SD16×C43—81no—
166SD16×C43—81no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43C2×D411yescharacteristic
178C4⋊C4×C43C2×D411yescharacteristic
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—41no—
182C42×C43C2411yescharacteristic
183C22⋊Dic43—41no—
184#10621884—22no—
185#10621884—22no—
186#10621884—42no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4—41no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43C2×D411yescharacteristic
196C4⋊Dic43C2×D411yescharacteristic
197Dic43⋊C4—41no—
198Dic43⋊C4—41no—
199Dic43⋊C4—41no—
200Dic43⋊C4—41no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207Dic172—82no—
208C8×D43—81no—
209C8×D43—81no—
210C23×C43—41no—
211C22×D43—21no—
212C22×D43—21no—
213C22×D43—82no—
214C22×D43—82no—
215C22×D43—161no—
216Q8×C43—21no—
217Q8×C43—21no—
218Q8×C43—21no—
219Q8×C43—21no—
220Q8×C43—41no—
221Q8×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—81no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43H(5,𝔽2)11yescharacteristic
235C22⋊D43—82no—
236C22⋊D43—82no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241D172—21no—
242D172—21no—
243D172#13512yes—
244D172#13712yes—
245C4×D43—41no—
246C4×D43—41no—
247C4×D43—41no—
248C4×D43—41no—
249C4×D43—161no—
250C4×D43—161no—
251Dic86—81no—
252Dic86—81no—
253C8×C43—41no—
254C8×C43—41no—
255C8×C43—41no—
256C43⋊C8—21no—
257C43⋊C8—21no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262#19790—431nomaximal, Sylow
263C22×C43—81no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43D4211yescharacteristic
267C2×D43—22no—
268C2×D43—22no—
269C2×D43—41no—
270C2×D43—41no—
271C2×D43—41no—
272C2×D43—41no—
273C2×D43—164no—
274C4×C43—21no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—81no—
280C4×C43C2×#13511yescharacteristic
281C4×C43C2×#13711yescharacteristic
282C4×C43#57711yescharacteristic
283C4×C43#57711yescharacteristic
284Dic43—41no—
285Dic43—41no—
286Dic43—81no—
287Dic43—81no—
288#3381—431no—
289#3372—431no—
290#3295—431no—
291#3295—431no—
292#1720—431no—
293#1698—431no—
294#1683—431no—
295#1678—431no—
296#1671—431no—
297#1639—431no—
298#1632—431no—
299#1632—431no—
300#1626D4311yescharacteristic, complemented
301#1582—431no—
302SD16⋊C8—431no—
303C2×C43—161no—
304C2×C43#326611yescharacteristic
305C2×C43#328211yescharacteristic
306C2×C43#328811yescharacteristic
307D43—42no—
308D43—42no—
309#557C2×D4311yescharacteristic, complemented
310#554—431no—
311#554—431no—
312D42—431no—
313#499—861no—
314#498—431no—
315#494—431no—
316#491—861no—
317#487—431no—
318#486—431no—
319#486—431no—
320#486C2×D4311yescharacteristic
321#481—861no—
322#481—861no—
323#479—861no—
324#479—861no—
325#478—861no—
326#477—431no—
327#477—431no—
328#476—431no—
329#476—431no—
330#474—431no—
331#465—861no—
332#465—861no—
333#461—431no—
334#461—861no—
335#460C2×D4311yescharacteristic
336#460C2×D4311yescharacteristic
337#450—861no—
338#450—861no—
339#446—431no—
340C8×Q8—431no—
341#440—861no—
342C4×SD16—431no—
343C4×SD16—431no—
344C4×SD16—861no—
345C8×D4—431no—
346C8×D4—431no—
347C2×#102—861no—
348C2×#102—861no—
349#335—431no—
350#334—431no—
351#333—431no—
352#333—431no—
353#332C2×D4311yescharacteristic, complemented
354#331—431no—
355Q8⋊C8C2×D4311yescharacteristic, complemented
356Q8⋊C8C2×D4311yescharacteristic, complemented
357D4⋊C8—431no—
358D4⋊C8—431no—
359#322—431no—
360C43#1979011yescharacteristic, complemented, Sylow
361C22×D4—861no—
362C22×D4—861no—
363C2×Q16—1721no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—431no—
367C2×SD16—431no—
368C2×SD16—861no—
369C22×C8—861no—
370C22×C8—861no—
371C4⋊Q8—21no—
372C4⋊Q8—431no—
373C4⋊Q8—431no—
374C4⋊Q8C22×D4311yescharacteristic
375#127C22×D4311yescharacteristic
376#125—21no—
377#125—41no—
378#125—861no—
379#125—861no—
380C22⋊Q8—861no—
381C22⋊Q8—861no—
382C22⋊Q8—1721no—
383C22⋊Q8—1721no—
384#121—861no—
385#121—861no—
386#120—1721no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8C22×D4311yescharacteristic
390C4×Q8C22×D4311yescharacteristic
391C4×D4—431no—
392C4×D4—431no—
393C4×D4—861no—
394C4×D4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397#107—861no—
398#107—861no—
399#107—861no—
400#106—431no—
401#106—431no—
402#106—861no—
403#106—861no—
404#106—861no—
405#106—861no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—861no—
409C4⋊C8—861no—
410C4⋊C8C22×D4311yescharacteristic
411C4⋊C8C22×D4311yescharacteristic
412#103—431no—
413#103—431no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#102—21no—
420#102—21no—
421#102—41no—
422#102—431no—
423#102—431no—
424#102—861no—
425#102—861no—
426#102—861no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433#97—861no—
434C4×C8—431no—
435C4×C8—431no—
436C4×C8—861no—
437C4×C8C22×D4311yescharacteristic
438C24—1721no—
439C2×Q8—21no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8D4×D4311yescharacteristic
443C2×Q8D4×D4311yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—431no—
448C2×D4—431no—
449C2×D4—3441no—
450C2×D4—3441no—
451C2×D4—1721no—
452C2×D4—1721no—
453C2×D4—1722no—
454C2×D4—1722no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—1721no—
458C22×C4—1721no—
459Q16—3442no—
460SD16—81no—
461SD16—81no—
462SD16—862no—
463SD16—862no—
464SD16—1722no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—431no—
469C2×C8—431no—
470C2×C8—431no—
471C2×C8—431no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—3441no—
475C2×C8—3441no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—431no—
484C4⋊C4—431no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—1721no—
490C4⋊C4—1721no—
491C4⋊C4—1721no—
492C4⋊C4—1721no—
493C4⋊C4D4×D4311yescharacteristic
494C4⋊C4D4×D4311yescharacteristic
495C22⋊C4—861no—
496C22⋊C4—861no—
497C22⋊C4—1721no—
498C22⋊C4—1721no—
499C22⋊C4—1721no—
500C42—21no—
501C42—21no—
502C42—41no—
503C42C23×D4311yescharacteristic
504C23—41no—
505C23—861no—
506C23—861no—
507C23—3442no—
508C23—3442no—
509C23—6881no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—3441no—
517Q8—3441no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—81no—
523D4—432no—
524D4—432no—
525D4—861no—
526D4—861no—
527D4—3442no—
528D4—3442no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—6881no—
543C2×C4—6881no—
544C2×C4C2×D4×D4311yescharacteristic
545C2×C4C2×D4×D4311yescharacteristic
546C2×C4#1306337011yescharacteristic
547C8—41no—
548C8—41no—
549C8—41no—
550C8—861no—
551C8—861no—
552C8—861no—
553C8—861no—
554C8—1721no—
555C8—1721no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—862no—
560C22—862no—
561C22—1721no—
562C22—1721no—
563C22—1721no—
564C22—1721no—
565C22—6884no—
566C22#1458353111yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—3441no—
574C4—3441no—
575C4—1721no—
576C4—1721no—
577C4#135×D4311yescharacteristic
578C4#137×D4311yescharacteristic
579C4#1458370511yescharacteristic
580C4#1458370911yescharacteristic
581C2—161no—
582C2—1722no—
583C2—1722no—
584C2#1914610811yescharacteristic
585C2#1914630511yescharacteristic
586C2#1914636311yescharacteristic
subgroupG/H
centerC22#14583531
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1626C2
socleC22×C43D42
prime radical#14583534C22
hypercenter#1626D43
hypocenterC43#19790
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1626

Complements

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

NH ≅ G/Ntype
1. #19147466C2semidirect
2. #19147372C2semidirect
5. #19134254C2semidirect
6. #19134133C2semidirect
7. #19134045C2semidirect
8. #19134009C2semidirect
9. #19133969C2semidirect
11. #19133732C2semidirect
12. #19133732C2semidirect
13. #19133434C2semidirect
14. #19133410C2semidirect
15. C43×#1626C2semidirect
20. #14583295C22semidirect
21. #14583279C22semidirect
23. #14583249C22semidirect
31. #14583194C22semidirect
32. #14583194C22semidirect
42. #14583030C22semidirect
43. Q8×C43⋊C8C22semidirect
52. #14582651C22semidirect
53. #14582649C22semidirect
54. #14582647C22semidirect
55. #14582647C22semidirect
59. #14582621C22semidirect
60. C43×#557C22semidirect
64. C43×#332C22semidirect
65. C43×Q8⋊C8C22semidirect
66. C43×Q8⋊C8C22semidirect
300. #1626D43semidirect
309. #557C2×D43semidirect
353. #332C2×D43semidirect
355. Q8⋊C8C2×D43semidirect
356. Q8⋊C8C2×D43semidirect
360. C43#19790semidirect

Maximal subgroups

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

subgroupindex
#191474662
#191473722
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