Finite Group Databasebeta

← #25082050

Subgroups — #25082050

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145553C211yesmaximal, characteristic, complemented
2#19144746C211yesmaximal, characteristic
3#19144666C211yesmaximal, characteristic, complemented
4#19134039C211yesmaximal, characteristic, complemented
5#19134032C211yesmaximal, characteristic, complemented
6#19134025C211yesmaximal, characteristic, complemented
7#19134018C211yesmaximal, characteristic, complemented
8#19133965C211yesmaximal, characteristic, complemented
9#19133960C211yesmaximal, characteristic, complemented
10#19133943C211yesmaximal, characteristic, complemented
11#19133936C211yesmaximal, characteristic, complemented
12#19133375C211yesmaximal, characteristic, complemented
13#19133293C211yesmaximal, characteristic, complemented
14#19133245C211yesmaximal, characteristic, complemented
15C43×#2988C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18#14583279C2211yescharacteristic
19#14583272C2211yescharacteristic
20#14583250C2211yescharacteristic
21#14583246C2211yescharacteristic
22#14583240—21no—
23#14583223—21no—
24#14583184C2211yescharacteristic
25#14583184C2211yescharacteristic
26#14583179C2211yescharacteristic
27#14583179C2211yescharacteristic
28#14583122—21no—
29#14583122—21no—
30#14583109C2211yescharacteristic
31#14583104C2211yescharacteristic
32#14583099C2211yescharacteristic
33#14583094C2211yescharacteristic
34#14583063—21no—
35#14583063—21no—
36#14583061—21no—
37#14583044—21no—
38#14583009—21no—
39#14582997—21no—
40C4×#10621885—21no—
41C4×#10621883—21no—
42#14582956C2211yescharacteristic
43#14582952C2211yescharacteristic
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582646C2211yescharacteristic
51#14582646C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C4×#41×C43C2211yescharacteristic
57C8×Q8×C43C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C8×D4×C43—21no—
60C8×D4×C43—21no—
61C8×D4×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#431—21no—
64C43×#431C2211yescharacteristic
65C2×C4⋊C8×C43—21no—
66C2×C4⋊C8×C43C2211yescharacteristic
67C2×#10621898—21no—
68C2×Dic172—21no—
69C2×Dic172—21no—
70C2×#10621885—21no—
71C2×#10621873—21no—
72C2×#10621873—21no—
73C2×#10621883—21no—
74C2×#10621884—21no—
75C2×#10621882—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063322C2311yescharacteristic
80#13063317—21no—
81#13063313—21no—
82#13063304—21no—
83#13063304—21no—
84#13063299—21no—
85#13063299—21no—
86C4×Dic86—21no—
87C4×Dic86—21no—
88C4×D172—21no—
89C4×D172—21no—
90#13063284—21no—
91#13063258—21no—
92#13063258—21no—
93#13063256—21no—
94#13063256—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063250—21no—
100#13063250—21no—
101#13063249—21no—
102#13063249—21no—
103#13063248—21no—
104#13063248—21no—
105#13063247—21no—
106#13063247—21no—
107#13063246—21no—
108#13063246—21no—
109#13063245—21no—
110#13063245—21no—
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113#13063236—21no—
114C4×C43⋊C8—21no—
115C2×#41×C43D411yescharacteristic
116C22×C8×C43—21no—
117C22×C8×C43—21no—
118C22×C8×C43—21no—
119C4×Q8×C43D411yescharacteristic
120C4×Q8×C43C2311yescharacteristic
121C4×D4×C43—21no—
122C4×D4×C43—21no—
123C4×D4×C43D411yescharacteristic
124C4×D4×C43C2311yescharacteristic
125#117×C43—21no—
126#117×C43D411yescharacteristic
127C2×C42×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—21no—
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43D411yescharacteristic
133C4⋊C8×C43D411yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—22no—
145#41×C43—22no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C2×C22⋊D43—41no—
156#10621898—81no—
157#10621898—81no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×C4×D43—41no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—81no—
168C2×C8×C43—81no—
169C2×C8×C43—81no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43C2×D411yescharacteristic
185C42×C43C2×D411yescharacteristic
186C42×C43#4111yescharacteristic
187C42×C43C2411yescharacteristic
188C22⋊Dic43—41no—
189#10621885—42no—
190#10621884—42no—
191#10621883—42no—
192#10621882—42no—
193(C2×D43)⋊C4—41no—
194(C2×D43)⋊C4—41no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201Dic43⋊C4—41no—
202Dic43⋊C4—41no—
203C4×Dic43—41no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208Dic172—81no—
209Dic172—81no—
210#10621873—81no—
211#10621873—81no—
212C23×C43—21no—
213C23×C43#12111yescharacteristic
214C22×D43—41no—
215Q8×C43—21no—
216Q8×C43#13512yes—
217D4×C43—24no—
218D4×C43—21no—
219D4×C43#13512yes—
220C2×C4×C43—24no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—81no—
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C22⋊D43—82no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242D172—41no—
243D172—41no—
244D172—41no—
245D172—41no—
246D172—81no—
247C4×D43—82no—
248Dic86—41no—
249Dic86—41no—
250Dic86—41no—
251Dic86—41no—
252Dic86—41no—
253Dic86—41no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—41no—
259C8×C43—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264#19413—431nomaximal, Sylow
265C22×C43—21no—
266C22×C43—22no—
267C22×C43—21no—
268C22×C43—21no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43C2×#12111yescharacteristic
272C2×D43—81no—
273C2×D43—81no—
274C2×D43—81no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—22no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43C2×#13511yescharacteristic
283C4×C43C2×#13511yescharacteristic
284C4×C43#57611yescharacteristic
285C4×C43#57711yescharacteristic
286Dic43—81no—
287Dic43—81no—
288Dic43—81no—
289#3210—431no—
290#3115—431no—
291#3107—431no—
292#2988D4311yescharacteristic, complemented
293#1682—431no—
294#1681—431no—
295#1680—431no—
296#1679—431no—
297#1670—431no—
298#1669—431no—
299#1666—431no—
300#1665—431no—
301#1572—431no—
302#1552—431no—
303#1540—431no—
304C2×C43—41no—
305C2×C43—42no—
306C2×C43#304511yescharacteristic
307C2×C43#305011yescharacteristic
308C2×C43#306911yescharacteristic
309D43—161no—
310#533—431no—
311#532—431no—
312C4×#41C2×D4311yescharacteristic
313#494—431no—
314#492—431no—
315#487—431no—
316#486—431no—
317#485—861no—
318#482—861no—
319#475—431no—
320#475—431no—
321#474—431no—
322#474—431no—
323#464—861no—
324#464—861no—
325#462—431no—
326#461—431no—
327#460—431no—
328#459—431no—
329#452—861no—
330#452—861no—
331#452—861no—
332#449—861no—
333C8×Q8C2×D4311yescharacteristic
334C8×Q8C2×D4311yescharacteristic
335#442—861no—
336#440—861no—
337C4×Q16—861no—
338C4×SD16—861no—
339C8×D4—21no—
340C8×D4—21no—
341C8×D4C2×D4311yescharacteristic
342C8×D4C2×D4311yescharacteristic
343#432—431no—
344#431—21no—
345#431—431no—
346#431C2×D4311yescharacteristic
347C2×C4⋊C8—21no—
348C2×C4⋊C8C2×D4311yescharacteristic
349#335—431no—
350#335—431no—
351#334—431no—
352#334—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#332—431no—
357#332—431no—
358#332—431no—
359#331—431no—
360#331—431no—
361C43#1941311yescharacteristic, complemented, Sylow
362C2×#41—861no—
363C2×#41D17211yescharacteristic
364C2×Q16—861no—
365C2×Q16—861no—
366C2×Q16—861no—
367C2×SD16—861no—
368C2×SD16—861no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×D8—861no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C4⋊Q8—431no—
376C4⋊Q8—431no—
377C4⋊Q8—431no—
378#127—431no—
379#125—861no—
380#124—861no—
381C22⋊Q8—861no—
382C22⋊Q8—861no—
383#121—861no—
384#121—861no—
385C4×Q8—861no—
386C4×Q8—861no—
387C4×Q8D17211yescharacteristic
388C4×Q8C22×D4311yescharacteristic
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—861no—
392C4×D4—861no—
393C4×D4D17211yescharacteristic
394C4×D4C22×D4311yescharacteristic
395#117—21no—
396#117—861no—
397#117D17211yescharacteristic
398C2×C42—21no—
399C2×C42C22×D4311yescharacteristic
400#107—861no—
401#107—861no—
402#106—861no—
403#106—861no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8C22⋊D4311yescharacteristic
412C4⋊C8C22⋊D4311yescharacteristic
413C4⋊C8C22×D4311yescharacteristic
414C4⋊C8C22×D4311yescharacteristic
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—861no—
420#103—861no—
421#102—861no—
422#102—861no—
423#102—861no—
424#102—861no—
425#102—861no—
426#102—861no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431C22⋊C8C22⋊D4311yescharacteristic
432C22⋊C8C22⋊D4311yescharacteristic
433#97—861no—
434C4×C8—21no—
435C4×C8—21no—
436C4×C8—861no—
437C4×C8C22×D4311yescharacteristic
438C4×C8C22×D4311yescharacteristic
439#41—22no—
440#41—22no—
441#41—3441no—
442#41—3441no—
443C2×Q8—861no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×Q8C2×D17211yescharacteristic
447C2×D4—21no—
448C2×D4—861no—
449C2×D4—861no—
450C2×D4—861no—
451C2×D4—1721no—
452C2×D4C2×D17211yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—1721no—
457C22×C4C2×D17211yescharacteristic
458C22×C4#1062189811yescharacteristic
459C22×C4C2×C22⋊D4311yescharacteristic
460Q16—3441no—
461Q16—3441no—
462Q16—1722no—
463SD16—3441no—
464SD16—3441no—
465SD16—1722no—
466SD16—1722no—
467D8—1722no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—81no—
471C2×C8—81no—
472C2×C8—81no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8C2×C22⋊D4311yescharacteristic
478C2×C8C2×C22⋊D4311yescharacteristic
479C2×C8C2×C22⋊D4311yescharacteristic
480C2×C8C2×C22⋊D4311yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—1721no—
490C4⋊C4—1721no—
491C4⋊C4C2×D17211yescharacteristic
492C4⋊C4C2×D17211yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—1721no—
497C22⋊C4—1721no—
498C22⋊C4—1721no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—1721no—
503C42C2×D17211yescharacteristic
504C42#1062189811yescharacteristic
505C42C2×C22⋊D4311yescharacteristic
506C42C23×D4311yescharacteristic
507C23—21no—
508C23—1721no—
509C23#1306329911yescharacteristic
510Q8—21no—
511Q8—1721no—
512Q8—1721no—
513Q8—1721no—
514Q8—1721no—
515Q8—1721no—
516Q8—1721no—
517Q8#1306334712yes—
518D4—24no—
519D4—21no—
520D4—3441no—
521D4—3442no—
522D4—1721no—
523D4—1721no—
524D4—1721no—
525D4—1721no—
526D4#1306334712yes—
527C2×C4—24no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—81no—
539C2×C4—3442no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4#1306329911yescharacteristic
544C2×C4#1306329911yescharacteristic
545C2×C4#1306329911yescharacteristic
546C2×C4C22×C22⋊D4311yescharacteristic
547C2×C4C22×D17211yescharacteristic
548C2×C4C2×#1062189811yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—1721no—
556C8—1721no—
557C8—1721no—
558C8—1721no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—3441no—
566C22—3441no—
567C22—3441no—
568C22C2×#1306329911yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—22no—
574C4—41no—
575C4—41no—
576C4—3441no—
577C4—3441no—
578C4—3441no—
579C4C2×#1306334711yescharacteristic
580C4C2×#1306334711yescharacteristic
581C4#1458370211yescharacteristic
582C4#1458370711yescharacteristic
583C2—41no—
584C2—42no—
585C2—6881no—
586C2#1914413411yescharacteristic
587C2#1914417611yescharacteristic
588C2#1914433211yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2988C2
socleC22×C43C2×#121
prime radical#19144746C2
hypercenter#2988D43
hypocenterC43#19413
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #19145553C2semidirect
3. #19144666C2semidirect
4. #19134039C2semidirect
5. #19134032C2semidirect
6. #19134025C2semidirect
7. #19134018C2semidirect
8. #19133965C2semidirect
9. #19133960C2semidirect
10. #19133943C2semidirect
11. #19133936C2semidirect
12. #19133375C2semidirect
13. #19133293C2semidirect
14. #19133245C2semidirect
15. C43×#2988C2semidirect
292. #2988D43semidirect
361. C43#19413semidirect

Maximal subgroups

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

subgroupindex
#191455532
#191447462
#191446662
#191340392
#191340322
#191340252
#191340182
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C43×#29882
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