Finite Group Databasebeta

← #25086473

Subgroups — #25086473

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#19147474C211yesmaximal, characteristic, complemented
2#19147380C211yesmaximal, characteristic, complemented
3#19146419C211yesmaximal, characteristic
4#19146419C211yesmaximal, characteristic
5#19134254C211yesmaximal, characteristic, complemented
6#19134134C211yesmaximal, characteristic, complemented
7#19134044C211yesmaximal, characteristic, complemented
8#19134010C211yesmaximal, characteristic, complemented
9#19133968C211yesmaximal, characteristic, complemented
10#19133731C211yesmaximal, characteristic, complemented
11#19133731C211yesmaximal, characteristic, complemented
12#19133688C211yesmaximal, characteristic, complemented
13#19133428C211yesmaximal, characteristic, complemented
14#19133404C211yesmaximal, characteristic, complemented
15C43×#1639C211yesmaximal, characteristic
16#14583624C2211yescharacteristic, complemented
17#14583606C2211yescharacteristic
18#14583606C2211yescharacteristic
19#14583300—21no—
20#14583295C2211yescharacteristic, complemented
21#14583279C2211yescharacteristic, complemented
22#14583266—21no—
23#14583249C2211yescharacteristic, complemented
24#14583245C2211yescharacteristic
25#14583245C2211yescharacteristic
26#14583215—21no—
27#14583215—21no—
28#14583208—21no—
29#14583205—21no—
30#14583197—21no—
31#14583195C2211yescharacteristic, complemented
32#14583195C2211yescharacteristic, complemented
33#14583189C2211yescharacteristic
34#14583189C2211yescharacteristic
35#14583126—21no—
36#14583126—21no—
37#14583102—21no—
38#14583096C2211yescharacteristic
39#14583096C2211yescharacteristic
40#14583050—21no—
41#14583050—21no—
42#14583026C2211yescharacteristic, complemented
43#14583023C2211yescharacteristic, complemented
44#14583000—21no—
45#14582990—21no—
46C4×#10621883C2211yescharacteristic
47C4×#10621883C2211yescharacteristic
48D4×C43⋊C8C2211yescharacteristic
49D4×C43⋊C8C2211yescharacteristic
50C2×#13063246—21no—
51C2×#13063246—21no—
52#14582651C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582647C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582645C2211yescharacteristic, complemented
57#14582631C2211yescharacteristic, complemented
58#14582631C2211yescharacteristic, complemented
59#14582621C2211yescharacteristic, complemented
60D42×C43C2211yescharacteristic
61C43×#486C2211yescharacteristic
62C43×#474C2211yescharacteristic
63C43×#461C2211yescharacteristic
64C43×#331C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×D4⋊C8C2211yescharacteristic
67C2×Dic172—41no—
68C2×#10621883—21no—
69C2×#10621883—21no—
70C2×#10621883D411yescharacteristic
71C2×#10621883D411yescharacteristic
72C22×C43⋊C8—21no—
73C22×C43⋊C8—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063323—21no—
77#13063316—21no—
78#13063316—21no—
79#13063316—21no—
80#13063315—41no—
81#13063304—21no—
82#13063304—21no—
83#13063302—41no—
84#13063302—41no—
85Q8×Dic43—21no—
86C4×Dic86C2311yescharacteristic
87C4×Dic86C2311yescharacteristic
88#13063290—21no—
89D4×Dic43—21no—
90D4×Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—21no—
93#13063259—21no—
94#13063259—21no—
95#13063256—21no—
96#13063256—21no—
97#13063256—21no—
98#13063256—21no—
99#13063256D411yescharacteristic
100#13063256D411yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105#13063250—21no—
106#13063250—21no—
107#13063249—21no—
108#13063249—21no—
109#13063248D411yescharacteristic
110#13063248D411yescharacteristic
111#13063246—21no—
112#13063246—21no—
113#13063246—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117#13063246—21no—
118#13063246—21no—
119#13063246D411yescharacteristic
120#13063246D411yescharacteristic
121C22⋊(C43⋊C8)—21no—
122C22⋊(C43⋊C8)—21no—
123#13063235—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—
159C22×Dic43—41no—
160C22×Dic43—41no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86C2×D411yescharacteristic
164C2×Dic86C2×D411yescharacteristic
165SD16×C43—42no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43C2×D411yescharacteristic
172C4⋊C4×C43C2×D411yescharacteristic
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—41no—
176C42×C43C2411yescharacteristic
177C22⋊Dic43—41no—
178C22⋊Dic43—41no—
179#10621883—22no—
180#10621883—22no—
181#10621883—81no—
182#10621883—81no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—41no—
188C4⋊Dic43—41no—
189C4⋊Dic43—41no—
190C4⋊Dic43C2×D411yescharacteristic
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—41no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—81no—
204C2×C43⋊C8—81no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209Dic172—82no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—41no—
213C23×C43—82no—
214C23×C43—82no—
215C23×C43—161no—
216Q8×C43—41no—
217Q8×C43—41no—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—81no—
225D4×C43—82no—
226D4×C43—82no—
227D4×C43#13512yes—
228D4×C43#13712yes—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43H(5,𝔽2)11yescharacteristic
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—161no—
246C2×Dic43—161no—
247Dic86—21no—
248Dic86—21no—
249Dic86—21no—
250Dic86—21no—
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—22no—
264C22×C43—22no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—164no—
273C22×C43D4211yescharacteristic
274C4×C43—21no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—81no—
278C4×C43C2×#13511yescharacteristic
279C4×C43C2×#13711yescharacteristic
280C4×C43#57711yescharacteristic
281C4×C43#57711yescharacteristic
282Dic43—41no—
283Dic43—41no—
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#1639D4311yescharacteristic
298#1632—431no—
299#1632—431no—
300#1626—431no—
301#1582—431no—
302SD16⋊C8—431no—
303C2×C43—42no—
304C2×C43—42no—
305C2×C43—161no—
306C2×C43#326611yescharacteristic
307C2×C43#328211yescharacteristic
308C2×C43#328811yescharacteristic
309#557—431no—
310#554—431no—
311#554—431no—
312D42C2×D4311yescharacteristic
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#474C2×D4311yescharacteristic
331#465—861no—
332#465—861no—
333#461—861no—
334#461C2×D4311yescharacteristic
335#460—431no—
336#460—431no—
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#332—431no—
354#331C2×D4311yescharacteristic
355Q8⋊C8—431no—
356Q8⋊C8—431no—
357D4⋊C8C2×D4311yescharacteristic
358D4⋊C8C2×D4311yescharacteristic
359#322—431no—
360C43#1979011yescharacteristic, complemented, Sylow
361C22×D4—21no—
362C22×D4—21no—
363C2×Q16—1721no—
364C2×SD16—21no—
365C2×SD16—431no—
366C2×SD16—431no—
367C2×SD16—861no—
368C2×SD16—861no—
369C22×C8—861no—
370C22×C8—861no—
371C4⋊Q8—431no—
372C4⋊Q8—431no—
373C4⋊Q8—861no—
374C4⋊Q8C22×D4311yescharacteristic
375#127C22×D4311yescharacteristic
376#125—861no—
377#125—861no—
378#125—861no—
379#125—1721no—
380C22⋊Q8—861no—
381C22⋊Q8—861no—
382C22⋊Q8—1721no—
383C22⋊Q8—1721no—
384#121—21no—
385#121—21no—
386#120—41no—
387C4×Q8—431no—
388C4×Q8—431no—
389C4×Q8—861no—
390C4×Q8—861no—
391C4×D4—861no—
392C4×D4—861no—
393C4×D4C22×D4311yescharacteristic
394C4×D4C22×D4311yescharacteristic
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397#107—21no—
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—21no—
413#103—431no—
414#103—431no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#102—21no—
420#102—41no—
421#102—431no—
422#102—431no—
423#102—861no—
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—41no—
439C2×Q8—21no—
440C2×Q8—431no—
441C2×Q8—431no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—81no—
452C2×D4—81no—
453C2×D4D4×D4311yescharacteristic
454C2×D4D4×D4311yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—1721no—
458C22×C4—1721no—
459Q16—3442no—
460SD16—42no—
461SD16—862no—
462SD16—862no—
463SD16—3441no—
464SD16—3441no—
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—431no—
479C4⋊C4—431no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—1721no—
487C4⋊C4—1721no—
488C4⋊C4—1721no—
489C4⋊C4—1721no—
490C4⋊C4—1721no—
491C4⋊C4—1721no—
492C4⋊C4—1721no—
493C4⋊C4D4×D4311yescharacteristic
494C4⋊C4D4×D4311yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—41no—
498C22⋊C4—1721no—
499C22⋊C4—1721no—
500C42—861no—
501C42—861no—
502C42—1721no—
503C42C23×D4311yescharacteristic
504C23—21no—
505C23—21no—
506C23—41no—
507C23—82no—
508C23—82no—
509C23—161no—
510Q8—41no—
511Q8—41no—
512Q8—861no—
513Q8—861no—
514Q8—861no—
515Q8—861no—
516Q8—3441no—
517Q8—3441no—
518D4—21no—
519D4—21no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526D4—82no—
527D4#1306334412yes—
528D4#1306335412yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
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—22no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—164no—
566C22#1458353111yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—3441no—
572C4—3441no—
573C4—1721no—
574C4—1721no—
575C4—1721no—
576C4—1721no—
577C4C2×#1306334411yescharacteristic
578C4C2×#1306335411yescharacteristic
579C4#1458370911yescharacteristic
580C4#1458370911yescharacteristic
581C2—42no—
582C2—42no—
583C2—161no—
584C2#1914610911yescharacteristic
585C2#1914630611yescharacteristic
586C2#1914636411yescharacteristic
subgroupG/H
centerC22#14583531
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1639C2
socleC22×C43D42
prime radicalD42×C43C22
hypercenter#1639D43
hypocenterC43#19790
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. #19147474C2semidirect
2. #19147380C2semidirect
5. #19134254C2semidirect
6. #19134134C2semidirect
7. #19134044C2semidirect
8. #19134010C2semidirect
9. #19133968C2semidirect
10. #19133731C2semidirect
11. #19133731C2semidirect
12. #19133688C2semidirect
13. #19133428C2semidirect
14. #19133404C2semidirect
16. #14583624C22semidirect
20. #14583295C22semidirect
21. #14583279C22semidirect
23. #14583249C22semidirect
31. #14583195C22semidirect
32. #14583195C22semidirect
42. #14583026C22semidirect
43. #14583023C22semidirect
52. #14582651C22semidirect
53. #14582649C22semidirect
54. #14582647C22semidirect
55. #14582647C22semidirect
56. #14582645C22semidirect
57. #14582631C22semidirect
58. #14582631C22semidirect
59. #14582621C22semidirect
360. C43#19790semidirect

Maximal subgroups

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

subgroupindex
#191474742
#191473802
#191464192
#191342542
#191341342
#191340442
#191340102
#191339682
#191337312
#191336882
#191334282
#191334042
C43×#16392
#1979043