Finite Group Databasebeta

← #25080345

Subgroups — #25080345

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145933C211yesmaximal, characteristic, complemented
2#19145571C211yesmaximal, characteristic
3#19145309C211yesmaximal, characteristic, complemented
4#19143593C211yesmaximal, characteristic, complemented
5#19134162C211yesmaximal, characteristic, complemented
6#19134152C211yesmaximal, characteristic, complemented
7#19134107C211yesmaximal, characteristic, complemented
8#19134059C211yesmaximal, characteristic, complemented
9#19134031C211yesmaximal, characteristic, complemented
10#19134021C211yesmaximal, characteristic, complemented
11#19133988C211yesmaximal, characteristic, complemented
12#19133942C211yesmaximal, characteristic, complemented
13#19133345C211yesmaximal, characteristic, complemented
14#19133259C211yesmaximal, characteristic, complemented
15C43×#1540C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583433C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583281—21no—
20#14583271C2211yescharacteristic
21#14583253—21no—
22#14583251C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583207—21no—
25#14583185C2211yescharacteristic
26#14583180C2211yescharacteristic
27#14583143—21no—
28#14583143—21no—
29#14583140—21no—
30#14583128—21no—
31#14583122—21no—
32#14583110C2211yescharacteristic
33#14583106C2211yescharacteristic
34#14583105C2211yescharacteristic
35#14583101C2211yescharacteristic
36#14583096C2211yescharacteristic
37#14583091C2211yescharacteristic
38#14583061—21no—
39#14583044—21no—
40#14583026C2211yescharacteristic
41#14583023C2211yescharacteristic
42#14582999—21no—
43#14582999—21no—
44#14582976C2211yescharacteristic
45#14582974—21no—
46#14582973—21no—
47#14582964C2211yescharacteristic
48#14582958—21no—
49#14582952C2211yescharacteristic
50#14582853—21no—
51C4×#10621877C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#532C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×Dic172—21no—
68C2×#10621885—21no—
69C2×#10621873—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621884—21no—
74C2×#10621882—21no—
75C2×#10621877D411yescharacteristic
76C2×#10621877D411yescharacteristic
77C2×#10621872—21no—
78C2×C8×D43—21no—
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063319—21no—
82#13063317—21no—
83#13063317D411yescharacteristic
84#13063313D411yescharacteristic
85#13063308—21no—
86#13063304—21no—
87#13063304—21no—
88#13063304D411yescharacteristic
89#13063299D411yescharacteristic
90C4×Dic86—21no—
91C4×Dic86—21no—
92C4×Dic86C2311yescharacteristic
93C4×D172C2311yescharacteristic
94C4×C22⋊D43—21no—
95#13063284—21no—
96#13063282—21no—
97#13063259—21no—
98#13063258—21no—
99#13063258—21no—
100#13063257—21no—
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105#13063250—21no—
106#13063250—21no—
107#13063250—21no—
108#13063249—21no—
109#13063249—21no—
110#13063248—21no—
111#13063248—21no—
112#13063247—21no—
113#13063246—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120#13063236D411yescharacteristic
121#13063236D411yescharacteristic
122#13063235—21no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C2×#41×C43—21no—
128C22×C8×C43—21no—
129C4⋊Q8×C43C2311yescharacteristic
130#127×C43C2311yescharacteristic
131#124×C43—21no—
132#121×C43—21no—
133#121×C43—21no—
134C4×D4×C43—21no—
135C4×D4×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43—21no—
144#41×C43—81no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—41no—
151C22×C4×C43—41no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C2×C22⋊D43—21no—
156C2×D172C2×D411yescharacteristic
157C2×C4×D43—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86C2×D411yescharacteristic
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—81no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C22⋊C4×C43—41no—
169C22⋊C4×C43—41no—
170C42×C43C2×D411yescharacteristic
171C42×C43C2×D411yescharacteristic
172C42×C43#4111yescharacteristic
173C42×C43C2411yescharacteristic
174C22⋊Dic43—21no—
175C22⋊Dic43—41no—
176#10621885—81no—
177#10621884—81no—
178#10621883—42no—
179#10621883—42no—
180#10621883—81no—
181#10621882—81no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C2×D411yescharacteristic
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198C4×Dic43—21no—
199C4×Dic43—41no—
200#10621877—22no—
201#10621877—41no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208Dic172—81no—
209#10621873—81no—
210#10621872—42no—
211C8×D43—42no—
212C23×C43—41no—
213C23×C43#12111yescharacteristic
214C22×D43—21no—
215Q8×C43—41no—
216Q8×C43—41no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—81no—
222D4×C43—82no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—82no—
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C22⋊D43—81no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242D172—21no—
243D172—21no—
244C4×D43—41no—
245C4×D43—41no—
246Dic86—21no—
247Dic86—21no—
248Dic86—41no—
249Dic86—41no—
250Dic86—41no—
251Dic86—41no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43—41no—
255C8×C43—41no—
256C43⋊C8—21no—
257C43⋊C8—21no—
258C43⋊C8—21no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8#13512yes—
262#19252—431nomaximal, Sylow
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43C2×#12111yescharacteristic
270C2×D43—41no—
271C2×D43—41no—
272C2×D43—41no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—81no—
278C4×C43C2×#13511yescharacteristic
279C4×C43#57511yescharacteristic
280C4×C43#57611yescharacteristic
281C4×C43#57711yescharacteristic
282Dic43—41no—
283Dic43—41no—
284Dic43—41no—
285Dic43—81no—
286Dic43—81no—
287#3248—431no—
288#3212—431no—
289#3182—431no—
290#2969—431no—
291#1702—431no—
292#1700—431no—
293#1693—431no—
294#1685—431no—
295#1681—431no—
296#1679—431no—
297#1674—431no—
298#1666—431no—
299#1565—431no—
300#1544—431no—
301#1540D4311yescharacteristic, complemented
302C2×C43—41no—
303C2×C43—161no—
304C2×C43#303511yescharacteristic
305C2×C43#306211yescharacteristic
306C2×C43#306911yescharacteristic
307D43—81no—
308#533—431no—
309#532C2×D4311yescharacteristic
310#529—431no—
311#500—431no—
312#495—861no—
313#492—431no—
314#488—861no—
315#487—431no—
316#486—431no—
317#479—861no—
318#475—431no—
319#474—431no—
320#468—861no—
321#468—861no—
322#467—861no—
323#465—861no—
324#464—861no—
325#462—431no—
326#462—431no—
327#461—431no—
328#461—431no—
329#460—431no—
330#459—431no—
331#452—861no—
332#449—861no—
333#446—431no—
334C8×Q8—431no—
335#440—861no—
336#440—861no—
337#436—431no—
338#436—861no—
339#435—861no—
340C8×D4—431no—
341#433—861no—
342#431—431no—
343#431C2×D4311yescharacteristic
344C2×C4⋊C8C2×D4311yescharacteristic
345#405—861no—
346C4×M16—431no—
347#335—431no—
348#335—431no—
349#334—431no—
350#334—431no—
351#332—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#332C2×D4311yescharacteristic
356#332C2×D4311yescharacteristic
357#331C2×D4311yescharacteristic
358#331C2×D4311yescharacteristic
359C43#1925211yescharacteristic, complemented, Sylow
360C2×#41—21no—
361C2×Q16—861no—
362C2×Q16—861no—
363C2×SD16—861no—
364C2×SD16—861no—
365C2×SD16—861no—
366C2×SD16—861no—
367C2×SD16—861no—
368C2×D8—861no—
369C2×M16—431no—
370C2×M16—431no—
371C2×M16—861no—
372C22×C8—21no—
373C22×C8—861no—
374C4⋊Q8—431no—
375C4⋊Q8—431no—
376C4⋊Q8C22×D4311yescharacteristic
377#127C22×D4311yescharacteristic
378#126—861no—
379#125—431no—
380#125—861no—
381#124—21no—
382#124—431no—
383#123—861no—
384C22⋊Q8—431no—
385C22⋊Q8—861no—
386C22⋊Q8—861no—
387#121—21no—
388#121—21no—
389#121—431no—
390C4×Q8—431no—
391C4×Q8—861no—
392C4×Q8—861no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—431no—
396C4×D4—861no—
397#117—861no—
398#117—861no—
399C2×C42C22×D4311yescharacteristic
400#107—861no—
401#107—861no—
402#107—861no—
403#106—861no—
404C4⋊C8—21no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—861no—
408C4⋊C8—861no—
409C4⋊C8C22×D4311yescharacteristic
410C4⋊C8C22×D4311yescharacteristic
411C4⋊C8C22×D4311yescharacteristic
412C4⋊C8C22×D4311yescharacteristic
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—861no—
420#102—861no—
421#102—861no—
422#102—861no—
423#102—861no—
424#102—861no—
425C22⋊C8—21no—
426C22⋊C8—861no—
427C22⋊C8—861no—
428C22⋊C8—861no—
429#97—431no—
430#97—431no—
431#97—861no—
432C4×C8—21no—
433C4×C8—431no—
434C4×C8—431no—
435C4×C8—861no—
436C4×C8—861no—
437#41—81no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—431no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—41no—
447C2×D4—431no—
448C2×D4—861no—
449C22×C4—41no—
450C22×C4—861no—
451C22×C4#1062189811yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4D4×D4311yescharacteristic
454Q16—3441no—
455Q16—3441no—
456SD16—3441no—
457SD16—3441no—
458SD16—3441no—
459SD16—1722no—
460SD16—1722no—
461D8—3441no—
462M16—862no—
463M16—1722no—
464M16—1721no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—81no—
470C2×C8—431no—
471C2×C8—431no—
472C2×C8—431no—
473C2×C8—431no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—1722no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—431no—
480C4⋊C4—431no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—1721no—
490C4⋊C4—1721no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—861no—
494C22⋊C4—861no—
495C22⋊C4—861no—
496C22⋊C4—861no—
497C22⋊C4—861no—
498C22⋊C4—1721no—
499C42—861no—
500C42—1721no—
501C42#1062189811yescharacteristic
502C42D4×D4311yescharacteristic
503C42D4×D4311yescharacteristic
504C42C23×D4311yescharacteristic
505C23—41no—
506C23—861no—
507C23#1306329811yescharacteristic
508Q8—41no—
509Q8—41no—
510Q8—861no—
511Q8—861no—
512Q8—1721no—
513Q8—1721no—
514Q8—1721no—
515Q8—1721no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—81no—
521D4—82no—
522D4—861no—
523D4—861no—
524D4—3441no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—82no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4#1306329811yescharacteristic
540C2×C4#1306329811yescharacteristic
541C2×C4#1306329811yescharacteristic
542C2×C4C2×D4×D4311yescharacteristic
543C2×C4C2×D4×D4311yescharacteristic
544C2×C4C2×#1062189811yescharacteristic
545C8—41no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—432no—
550C8—861no—
551C8—861no—
552C8—861no—
553C8—1721no—
554C8—1721no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—1721no—
562C22—1721no—
563C22—1721no—
564C22C2×#1306329811yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—81no—
570C4—3441no—
571C4—3441no—
572C4—1721no—
573C4—1721no—
574C4—1721no—
575C4#135×D4311yescharacteristic
576C4#1458369611yescharacteristic
577C4#1458370011yescharacteristic
578C4#1458370511yescharacteristic
579C2—41no—
580C2—161no—
581C2—3441no—
582C2#1914404811yescharacteristic
583C2#1914427311yescharacteristic
584C2#1914433511yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1540C2
socleC22×C43C2×#121
prime radical#19145571C2
hypercenter#1540D43
hypocenterC43#19252
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
1. #19145933C2semidirect
3. #19145309C2semidirect
4. #19143593C2semidirect
5. #19134162C2semidirect
6. #19134152C2semidirect
7. #19134107C2semidirect
8. #19134059C2semidirect
9. #19134031C2semidirect
10. #19134021C2semidirect
11. #19133988C2semidirect
12. #19133942C2semidirect
13. #19133345C2semidirect
14. #19133259C2semidirect
15. C43×#1540C2semidirect
301. #1540D43semidirect
359. C43#19252semidirect

Maximal subgroups

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

subgroupindex
#191459332
#191455712
#191453092
#191435932
#191341622
#191341522
#191341072
#191340592
#191340312
#191340212
#191339882
#191339422
#191333452
#191332592
C43×#15402
#1925243