Finite Group Databasebeta

← #25080341

Subgroups — #25080341

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#19145926C211yesmaximal, characteristic, complemented
2#19145571C211yesmaximal, characteristic
3#19143599C211yesmaximal, characteristic, complemented
4#19134160C211yesmaximal, characteristic, complemented
5#19134146C211yesmaximal, characteristic, complemented
6#19134105C211yesmaximal, characteristic, complemented
7#19134057C211yesmaximal, characteristic, complemented
8#19134029C211yesmaximal, characteristic, complemented
9#19134015C211yesmaximal, characteristic, complemented
10#19133986C211yesmaximal, characteristic, complemented
11#19133940C211yesmaximal, characteristic, complemented
12#19133347C211yesmaximal, characteristic, complemented
13#19133260C211yesmaximal, characteristic, complemented
14#19133244C211yesmaximal, characteristic, complemented
15C43×#3182C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583281—21no—
18#14583253—21no—
19#14583206—21no—
20#14583181C2211yescharacteristic
21#14583176C2211yescharacteristic
22#14583138—21no—
23#14583130—21no—
24#14583121—21no—
25#14583106C2211yescharacteristic
26#14583106C2211yescharacteristic
27#14583101C2211yescharacteristic
28#14583101C2211yescharacteristic
29#14583096C2211yescharacteristic
30#14583091C2211yescharacteristic
31#14583061—21no—
32#14583044—21no—
33#14583029C2211yescharacteristic
34C8×Dic86C2211yescharacteristic
35#14582978C2211yescharacteristic
36#14582975—21no—
37#14582968—21no—
38C8×D172C2211yescharacteristic
39#14582961—21no—
40#14582952C2211yescharacteristic
41#14582952C2211yescharacteristic
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43#14582856—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#532C2211yescharacteristic
58C43×#500C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#486C2211yescharacteristic
62C43×#468—21no—
63C43×#468—21no—
64C43×#440—21no—
65C43×#440—21no—
66C4×M16×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621883—21no—
70C2×#10621884—21no—
71C2×#10621884—21no—
72C2×#10621882—21no—
73C2×#10621872—21no—
74C22×C43⋊C8—21no—
75C2×C8×D43—21no—
76#13063319—21no—
77#13063317D411yescharacteristic
78#13063313D411yescharacteristic
79#13063308—21no—
80#13063304D411yescharacteristic
81#13063299D411yescharacteristic
82C4×Dic86C2311yescharacteristic
83C4×D172C2311yescharacteristic
84C4×C22⋊D43—21no—
85#13063282—21no—
86#13063258—21no—
87#13063256—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)C2311yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95Dic43⋊C8—21no—
96Dic43⋊C8—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101#13063248—21no—
102#13063246—21no—
103#13063246—21no—
104#13063245—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)—21no—
107(C2×D43)⋊C8—21no—
108(C2×D43)⋊C8—21no—
109#13063235—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8—21no—
112C8×Dic43—21no—
113C2×#41×C43—21no—
114C2×SD16×C43—21no—
115C2×SD16×C43—21no—
116C2×M16×C43D411yescharacteristic
117C2×M16×C43D411yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#127×C43C2311yescharacteristic
122#125×C43—21no—
123#124×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—21no—
126#121×C43—21no—
127#121×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132#117×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#107×C43—21no—
135#107×C43—21no—
136#103×C43—21no—
137#103×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140#97×C43D411yescharacteristic
141#97×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—81no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—41no—
153C22×C4×C43—41no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43#4111yescharacteristic
157C2×C22⋊D43—21no—
158C2×D172C2×D411yescharacteristic
159C2×C4×D43—21no—
160C2×Dic86C2×D411yescharacteristic
161SD16×C43—42no—
162SD16×C43—42no—
163M16×C43—22no—
164M16×C43—41no—
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43—41no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C42×C43—41no—
181C42×C43C2×D411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C42×C43#4111yescharacteristic
184C42×C43C2411yescharacteristic
185C22⋊Dic43—21no—
186#10621885—81no—
187#10621885—81no—
188#10621884—81no—
189#10621884—81no—
190#10621883—81no—
191#10621882—81no—
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—21no—
194(C2×D43)⋊C4—21no—
195(C2×D43)⋊C4—21no—
196C4⋊Dic43C2×D411yescharacteristic
197C4⋊Dic43C2×D411yescharacteristic
198Dic43⋊C4—21no—
199Dic43⋊C4—21no—
200Dic43⋊C4—21no—
201Dic43⋊C4—21no—
202C4×Dic43—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—81no—
210#10621872—42no—
211C8×D43—42no—
212C23×C43—41no—
213C23×C43#12111yescharacteristic
214C22×D43—21no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—81no—
226D4×C43—82no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
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—82no—
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43#12111yescharacteristic
238C2×C4×C43#12111yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C22⋊D43—81no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246D172—21no—
247D172—21no—
248C4×D43—41no—
249C4×D43—41no—
250Dic86—21no—
251Dic86—21no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43#13512yes—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
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×C43—81no—
279C4×C43—81no—
280C4×C43C2×#13511yescharacteristic
281C4×C43#57511yescharacteristic
282C4×C43#57611yescharacteristic
283C4×C43#57711yescharacteristic
284Dic43—41no—
285Dic43—41no—
286Dic43—41no—
287#3248—431no—
288#3212—431no—
289#3182D4311yescharacteristic, complemented
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#1540—431no—
302C2×C43—41no—
303C2×C43—161no—
304C2×C43#303511yescharacteristic
305C2×C43#306211yescharacteristic
306C2×C43#306911yescharacteristic
307D43—81no—
308#533C2×D4311yescharacteristic
309#532C2×D4311yescharacteristic
310#529—431no—
311#500C2×D4311yescharacteristic
312#495—861no—
313#492C2×D4311yescharacteristic
314#488—861no—
315#487C2×D4311yescharacteristic
316#486C2×D4311yescharacteristic
317#479—861no—
318#475—431no—
319#474—431no—
320#468—21no—
321#468—21no—
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—21no—
336#440—21no—
337#436—431no—
338#436—861no—
339#435—861no—
340C8×D4—431no—
341#433—861no—
342#431—431no—
343#431—431no—
344C2×C4⋊C8—431no—
345#405—861no—
346C4×M16C2×D4311yescharacteristic
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#332—431no—
356#332—431no—
357#331—431no—
358#331—431no—
359C43#1925211yescharacteristic, complemented, Sylow
360C2×#41—21no—
361C2×Q16—861no—
362C2×Q16—861no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—861no—
366C2×SD16—861no—
367C2×SD16—861no—
368C2×D8—861no—
369C2×M16—861no—
370C2×M16C22⋊D4311yescharacteristic
371C2×M16C22⋊D4311yescharacteristic
372C22×C8—861no—
373C22×C8—861no—
374C4⋊Q8C22×D4311yescharacteristic
375C4⋊Q8C22×D4311yescharacteristic
376C4⋊Q8C22×D4311yescharacteristic
377#127C22×D4311yescharacteristic
378#126—861no—
379#125—21no—
380#125—431no—
381#124—21no—
382#124—431no—
383#123—861no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—431no—
387#121—21no—
388#121—21no—
389#121—431no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8—431no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—431no—
396C4×D4—861no—
397#117—21no—
398#117—861no—
399C2×C42C22×D4311yescharacteristic
400#107—21no—
401#107—21no—
402#107—861no—
403#106—861no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—861no—
411C4⋊C8—861no—
412C4⋊C8—861no—
413#103—21no—
414#103—21no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—861no—
420#102—21no—
421#102—21no—
422#102—861no—
423#102—861no—
424#102—861no—
425C22⋊C8—861no—
426C22⋊C8—861no—
427C22⋊C8—861no—
428C22⋊C8—861no—
429#97—861no—
430#97C22⋊D4311yescharacteristic
431#97C22⋊D4311yescharacteristic
432C4×C8—861no—
433C4×C8—861no—
434C4×C8—861no—
435C4×C8C22×D4311yescharacteristic
436C4×C8C22×D4311yescharacteristic
437#41—81no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—431no—
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×C4D4×D4311yescharacteristic
452C22×C4#1062190011yescharacteristic
453C22×C4C2×C22⋊D4311yescharacteristic
454Q16—3441no—
455Q16—3441no—
456SD16—42no—
457SD16—42no—
458SD16—3441no—
459SD16—3441no—
460SD16—3441no—
461D8—3441no—
462M16—22no—
463M16—41no—
464M16—1722no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—3441no—
472C2×C8—1722no—
473C2×C8C2×C22⋊D4311yescharacteristic
474C2×C8C2×C22⋊D4311yescharacteristic
475C2×C8C2×C22⋊D4311yescharacteristic
476C2×C8C2×C22⋊D4311yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—431no—
486C4⋊C4—431no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—861no—
495C22⋊C4—861no—
496C22⋊C4—861no—
497C22⋊C4—861no—
498C22⋊C4—861no—
499C42—41no—
500C42—861no—
501C42D4×D4311yescharacteristic
502C42#1062190011yescharacteristic
503C42C2×C22⋊D4311yescharacteristic
504C42C23×D4311yescharacteristic
505C23—41no—
506C23—861no—
507C23#1306329611yescharacteristic
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—861no—
515Q8—861no—
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—41no—
532C2×C4—41no—
533C2×C4—82no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4#1306329611yescharacteristic
540C2×C4#1306329611yescharacteristic
541C2×C4#1306329611yescharacteristic
542C2×C4C2×D4×D4311yescharacteristic
543C2×C4C22×C22⋊D4311yescharacteristic
544C2×C4C2×#1062190011yescharacteristic
545C8—21no—
546C8—21no—
547C8—21no—
548C8—1721no—
549C8—1721no—
550C8—1721no—
551C8—1721no—
552C8—1721no—
553C8—1721no—
554C8#1306334512yes—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—1721no—
562C22—1721no—
563C22—1721no—
564C22C2×#1306329611yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—1721no—
573C4—1721no—
574C4—1721no—
575C4C2×#1306334511yescharacteristic
576C4#1458369711yescharacteristic
577C4#1458370311yescharacteristic
578C4#1458370911yescharacteristic
579C2—41no—
580C2—161no—
581C2—3441no—
582C2#1914404411yescharacteristic
583C2#1914426911yescharacteristic
584C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3182C2
socleC22×C43C2×#121
prime radical#19145571C2
hypercenter#3182D43
hypocenterC43#19252
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3182

Complements

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

NH ≅ G/Ntype
1. #19145926C2semidirect
3. #19143599C2semidirect
4. #19134160C2semidirect
5. #19134146C2semidirect
6. #19134105C2semidirect
7. #19134057C2semidirect
8. #19134029C2semidirect
9. #19134015C2semidirect
10. #19133986C2semidirect
11. #19133940C2semidirect
12. #19133347C2semidirect
13. #19133260C2semidirect
14. #19133244C2semidirect
15. C43×#3182C2semidirect
289. #3182D43semidirect
359. C43#19252semidirect

Maximal subgroups

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

subgroupindex
#191459262
#191455712
#191435992
#191341602
#191341462
#191341052
#191340572
#191340292
#191340152
#191339862
#191339402
#191333472
#191332602
#191332442
C43×#31822
#1925243