Finite Group Databasebeta

← #25250042

Subgroups — #25250042

Order 11008.

652 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147730C211yesmaximal, characteristic
2#444×D43C211yesmaximal, characteristic, complemented
3#19143394C211yesmaximal, characteristic, complemented
4#19136495C211yesmaximal, characteristic, complemented
5#19136493C211yesmaximal, characteristic, complemented
6#19136492C211yesmaximal, characteristic, complemented
7#19136490C211yesmaximal, characteristic, complemented
8#19136489C211yesmaximal, characteristic, complemented
9#19136487C211yesmaximal, characteristic, complemented
10#19136484C211yesmaximal, characteristic, complemented
11#19136366C211yesmaximal, characteristic, complemented
12#19136343C211yesmaximal, characteristic, complemented
13#19136329C211yesmaximal, characteristic, complemented
14#347×D43C211yesmaximal, characteristic, complemented
15C43×#2180C211yesmaximal, characteristic, complemented
16C2×#13063348C2211yescharacteristic
17#135×D43C2211yescharacteristic
18#131×D43—21no—
19C4×#10621902—21no—
20#14583341C412yescomplemented
21#14583340C2211yescharacteristic
22#14583337C2211yescharacteristic
23#14583336C412yescomplemented
24#14583334C2211yescharacteristic
25#14583332C412yescomplemented
26#14583330C412yescomplemented
27M32×D43C2211yescharacteristic
28M32×D43C2211yescharacteristic
29#14583022C2211yescharacteristic
30#14583021C2211yescharacteristic
31#14583020C2211yescharacteristic
32#14583019—21no—
33#14583018—21no—
34#14583012C2211yescharacteristic, complemented
35#14583010C2211yescharacteristic, complemented
36#14583006C2211yescharacteristic, complemented
37#14583002—21no—
38#14582997—21no—
39#108×D43C2211yescharacteristic
40#14582934C2211yescharacteristic
41#104×D43—21no—
42#14582894—21no—
43#97×D43C2211yescharacteristic
44#14582723C2211yescharacteristic, complemented
45#14582722C2211yescharacteristic, complemented
46#14582721C2211yescharacteristic, complemented
47#14582715C2211yescharacteristic, complemented
48#14582713C2211yescharacteristic, complemented
49#14582711C2211yescharacteristic, complemented
50#14582710C2211yescharacteristic
51#14582709C2211yescharacteristic
52#14582708C2211yescharacteristic
53#14582677C2211yescharacteristic, complemented
54#14582676C2211yescharacteristic, complemented
55#14582676C2211yescharacteristic, complemented
56C43×#510C2211yescharacteristic
57C43×#444C2211yescharacteristic
58C43×#441C2211yescharacteristic, complemented
59C43×#365C2211yescharacteristic, complemented
60C43×#362C2211yescharacteristic, complemented
61C43×#360C2211yescharacteristic
62C43×#347C2211yescharacteristic, complemented
63C2×#10621902—21no—
64#41×D43—21no—
65#13063348—21no—
66#13063348—21no—
67#13063348C2×C412yes—
68#13063348C2×C412yes—
69#13063348C2×C411yescharacteristic, complemented
70#13063347C2311yescharacteristic
71#13063346—21no—
72#13063345—21no—
73#13063344C2×C411yescharacteristic, complemented
74Q16×D43C2×C411yescharacteristic, complemented
75C2×#10621884—21no—
76SD16×D43—21no—
77C2×D344C2311yescharacteristic
78D8×D43C2×C411yescharacteristic, complemented
79#13063333—21no—
80#13063333—41no—
81#13063332—21no—
82#13063331—21no—
83#13063331—41no—
84M16×D43—21no—
85M16×D43—41no—
86C2×C8×D43—41no—
87C2×C8×D43D411yescharacteristic
88C2×C8×D43C2311yescharacteristic
89Q8×Dic43—21no—
90C4×D172—21no—
91C4×D172—41no—
92#13063287—21no—
93#13063287—41no—
94#13063283—21no—
95#13063283—41no—
96C42×D43—41no—
97C42×D43D411yescharacteristic
98#13063271C2×C412yescomplemented
99#13063270C2×C412yescomplemented
100#13063268C2×C412yescomplemented
101#13063268C2×C412yescomplemented
102D688C2×C412yescomplemented
103#13063266C2×C412yescomplemented
104#13063265C2311yescharacteristic
105#13063265C2311yescharacteristic
106#13063264—21no—
107#13063264C2×C412yescomplemented
108C16×D43—21no—
109C16×D43C2×C412yescomplemented
110#13063261C2311yescharacteristic
111#13063260—21no—
112#13063258—21no—
113#13063257C2311yescharacteristic
114#13063253—21no—
115#13063252—21no—
116#13063251—21no—
117#13063249—21no—
118#13063247—21no—
119#13063245—21no—
120#13063236D411yescharacteristic
121#13063235D411yescharacteristic
122#13063235C2311yescharacteristic
123#135×C43C2311yescharacteristic
124C2×Q16×C43C2311yescharacteristic
125#131×C43—21no—
126C4×Q8×C43—21no—
127Q32×C43C2×C412yescomplemented
128SD32×C43C2×C412yescomplemented
129M32×C43C2311yescharacteristic
130M32×C43C2311yescharacteristic
131#108×C43C2311yescharacteristic
132#106×C43C2311yescharacteristic
133#104×C43—21no—
134#103×C43—21no—
135#97×C43C2311yescharacteristic
136#41×C43—21no—
137C2×Q8×C43—21no—
138#10621902—21no—
139#10621902—22no—
140#10621902—22no—
141#10621902—41no—
142#10621902—41no—
143Q8×D43—21no—
144#10621900—21no—
145#10621900—41no—
146D4×D43—21no—
147D4×D43—41no—
148#10621898—21no—
149#10621898—41no—
150C2×D172—21no—
151C2×D172—41no—
152C2×C4×D43—21no—
153C2×C4×D43—41no—
154C2×C4×D43—41no—
155C2×C4×D43—41no—
156C2×C4×D43—41no—
157C2×C4×D43C2×D411yescharacteristic
158Q16×C43—21no—
159Q16×C43C22×C412yes—
160Q16×C43C22×C411yescharacteristic
161SD16×C43—21no—
162D8×C43C22×C411yescharacteristic
163M16×C43—21no—
164M16×C43—41no—
165C2×C8×C43—41no—
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2411yescharacteristic
168C4⋊C4×C43—21no—
169C4⋊C4×C43—41no—
170C42×C43—41no—
171C42×C43C2×D411yescharacteristic
172#10621885—21no—
173#10621884—21no—
174#10621884—22no—
175#10621884—22no—
176#10621883—21no—
177#10621882—21no—
178(C2×D43)⋊C4—41no—
179(C2×D43)⋊C4—41no—
180(C2×D43)⋊C4—41no—
181C4⋊Dic43—21no—
182C4⋊Dic43—41no—
183C4×Dic43—21no—
184C4×Dic43—41no—
185C4×Dic43—41no—
186C4×Dic43C2×D411yescharacteristic
187#10621877—21no—
188#10621877—41no—
189C2×C43⋊C8—41no—
190C2×C43⋊C8C2×D411yescharacteristic
191C2×C43⋊C8C2×D411yescharacteristic
192Dic172C22×C411yescharacteristic
193D344—21no—
194D344C22×C412yes—
195D344C22×C411yescharacteristic
196#10621873—21no—
197#10621872—41no—
198#10621872—41no—
199#10621872—41no—
200C8×D43—21no—
201C8×D43—21no—
202C8×D43—41no—
203C8×D43—41no—
204C8×D43—41no—
205C8×D43C22×C411yescharacteristic
206C8×D43C22×C411yescharacteristic
207C8×D43#4111yescharacteristic
208C8×D43#4111yescharacteristic
209C16×C43—21no—
210C16×C43C22×C412yes—
211C43⋊C16—21no—
212C43⋊C16C22×C412yes—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43AGL(1,ℤ/8)11yescharacteristic
216Q8×C43—22no—
217Q8×C43—21no—
218Q8×C43—41no—
219D4×C43—21no—
220D4×C43—41no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43C22×D411yescharacteristic
226C22⋊D43—41no—
227C22⋊D43—41no—
228C22⋊D43—41no—
229C2×Dic43—21no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43AGL(1,ℤ/8)11yescharacteristic
233D172—21no—
234D172—22no—
235D172—42no—
236D172—42no—
237D172—41no—
238D172—41no—
239C4×D43—41no—
240C4×D43—41no—
241C4×D43—41no—
242C4×D43—42no—
243C4×D43—42no—
244C4×D43—81no—
245C4×D43—82no—
246C4×D43—82no—
247C4×D43C4×D411yescharacteristic
248C4×D43C4×D411yescharacteristic
249C4×D43AGL(1,ℤ/8)11yescharacteristic
250C4×D43AGL(1,ℤ/8)11yescharacteristic
251Dic86—21no—
252Dic86—41no—
253C8×C43—21no—
254C8×C43—41no—
255C8×C43C23×C411yescharacteristic
256C8×C43C2×#4111yescharacteristic
257C43⋊C8—21no—
258C43⋊C8—41no—
259C43⋊C8C4×D411yescharacteristic
260C43⋊C8C4×D411yescharacteristic
261#33468—431nomaximal, Sylow
262C22×C43—41no—
263C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
264C2×D43—41no—
265C2×D43—42no—
266C2×D43—41no—
267C2×D43—82no—
268C2×D43—81no—
269C2×D43—81no—
270C2×D43#44211yescharacteristic
271C2×D43#44211yescharacteristic
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—42no—
275C4×C43—81no—
276C4×C43C2×C4×D411yescharacteristic
277C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
278Dic43—41no—
279Dic43—41no—
280Dic43—81no—
281Dic43#44211yescharacteristic
282Dic43#44211yescharacteristic
283#3414—431no—
284C2×#444—431no—
285#2943—431no—
286AGL(1,ℤ/16)—431no—
287AGL(1,ℤ/16)—431no—
288AGL(1,ℤ/16)—431no—
289AGL(1,ℤ/16)—431no—
290#2180—431no—
291#2180—431no—
292#2180—431no—
293#2180D4311yescharacteristic, complemented
294#2155—431no—
295#2148—431no—
296#2145—431no—
297C2×#347—431no—
298C2×C43—21no—
299C2×C43—81no—
300C2×C43C2×#44211yescharacteristic
301D43—21no—
302D43—21no—
303D43—82no—
304D43—81no—
305C2×#135—431no—
306C2×#135—431no—
307C2×#131—861no—
308C4×#41—861no—
309#510—431no—
310#510—432no—
311#510C2×D4311yescharacteristic
312#509—431no—
313#509—432no—
314#509—431no—
315#508—432no—
316#508—432no—
317C2×M32—431no—
318C2×M32—431no—
319#444—431no—
320#444—431no—
321#444—431no—
322#444—861no—
323#444—861no—
324#444C2×D4311yescharacteristic
325#442—431no—
326#442—431no—
327#441—431no—
328#441C2×D4311yescharacteristic, complemented
329#440—861no—
330#440—861no—
331C2×#108—431no—
332#427—431no—
333C2×#104—861no—
334#416—861no—
335C2×#97—431no—
336#365—431no—
337#365—431no—
338#365—431no—
339#365C2×D4311yescharacteristic, complemented
340#362—431no—
341#362C2×D4311yescharacteristic, complemented
342#361—431no—
343#361—431no—
344#360—431no—
345#360—431no—
346#360—431no—
347#360C2×D4311yescharacteristic
348#347—431no—
349#347—431no—
350#347—431no—
351#347C2×D4311yescharacteristic, complemented
352C43#3346811yescharacteristic, complemented, Sylow
353C2×#41—861no—
354C2×#41—861no—
355#135—432no—
356#135—432no—
357#135—431no—
358#135—431no—
359#135—431no—
360#135—861no—
361#135—861no—
362#135—861no—
363#135—861no—
364#135C22×D4311yescharacteristic
365C2×Q16—431no—
366C2×Q16C22×D4311yescharacteristic
367C2×SD16—861no—
368C2×SD16—861no—
369C2×D8—431no—
370C2×D8—431no—
371#131—21no—
372#131—861no—
373#131—861no—
374#131—861no—
375#131—1721no—
376#131—1721no—
377C2×M16—861no—
378C2×M16—1721no—
379C22×C8—431no—
380C22×C8—431no—
381C22×C8—1721no—
382C4×Q8—21no—
383C4×Q8—861no—
384C4×D4—861no—
385C4×D4—861no—
386C4×D4—1721no—
387C4×D4—1721no—
388#117—861no—
389#117—1721no—
390C2×C42—431no—
391C2×C42—1721no—
392Q32—432no—
393Q32C4×D4312yescomplemented
394SD32—432no—
395SD32—432no—
396SD32—432no—
397SD32C4×D4312yescomplemented
398D16—432no—
399D16—432no—
400M32—431no—
401M32—432no—
402M32—431no—
403M32—861no—
404M32C22×D4311yescharacteristic
405M32C22×D4311yescharacteristic
406C2×C16—432no—
407C2×C16—861no—
408#108—431no—
409#108—861no—
410#108C22×D4311yescharacteristic
411#107—861no—
412#106—431no—
413#106C22×D4311yescharacteristic
414#104—21no—
415#104—861no—
416#104—861no—
417#104—861no—
418#103—21no—
419#103—861no—
420#102—861no—
421#102—861no—
422#97—431no—
423#97—431no—
424#97—431no—
425#97C22×D4311yescharacteristic
426#41—21no—
427#41—861no—
428#41—862no—
429#41—861no—
430#41—862no—
431#41—861no—
432#41—1721no—
433#41—1721no—
434#41—1721no—
435#41—1721no—
436C2×Q8—21no—
437C2×Q8—861no—
438C2×D4—861no—
439C2×D4—861no—
440C2×D4—1721no—
441C2×D4—1721no—
442C22×C4—431no—
443C22×C4—861no—
444C22×C4—1721no—
445C22×C4—1721no—
446C22×C4—1721no—
447C22×C4—1721no—
448Q16—21no—
449Q16—431no—
450Q16—861no—
451Q16C2×C4×D4311yescharacteristic
452Q16C2×C4×D4312yes—
453SD16—21no—
454SD16—861no—
455SD16—862no—
456SD16—861no—
457SD16—862no—
458SD16—861no—
459D8—432no—
460D8—431no—
461D8—861no—
462D8—861no—
463D8C2×C4×D4311yescharacteristic
464M16—21no—
465M16—41no—
466M16—861no—
467M16—1721no—
468M16—1721no—
469M16—1721no—
470M16—1721no—
471C2×C8—41no—
472C2×C8—431no—
473C2×C8—431no—
474C2×C8—431no—
475C2×C8—431no—
476C2×C8—431no—
477C2×C8—431no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—1721no—
481C2×C8—1721no—
482C2×C8—1721no—
483C2×C8—1721no—
484C2×C8D4×D4311yescharacteristic
485C2×C8C23×D4311yescharacteristic
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—861no—
489C4⋊C4—1721no—
490C22⋊C4—1721no—
491C22⋊C4—1721no—
492C22⋊C4—1721no—
493C42—41no—
494C42—431no—
495C42—861no—
496C42—1721no—
497C42—1721no—
498C42D4×D4311yescharacteristic
499C16—21no—
500C16—432no—
501C16—861no—
502C16C2×C4×D4312yes—
503C23—431no—
504C23—1721no—
505C23—1721no—
506Q8—21no—
507Q8—22no—
508Q8—41no—
509Q8—861no—
510Q8—1721no—
511D4—21no—
512D4—41no—
513D4—861no—
514D4—862no—
515D4—1721no—
516D4—1722no—
517D4—1722no—
518D4—1721no—
519D4—1721no—
520D4—1721no—
521D4—1721no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—431no—
527C2×C4—431no—
528C2×C4—431no—
529C2×C4—431no—
530C2×C4—431no—
531C2×C4—861no—
532C2×C4—3442no—
533C2×C4—3441no—
534C2×C4—3442no—
535C2×C4—1721no—
536C2×C4—1722no—
537C2×C4—1722no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4C2×D4×D4311yescharacteristic
543C8—21no—
544C8—41no—
545C8—431no—
546C8—431no—
547C8—861no—
548C8—1721no—
549C8C22×C4×D4311yescharacteristic
550C8#41×D4311yescharacteristic
551C22—41no—
552C22—431no—
553C22—431no—
554C22—3441no—
555C22—3441no—
556C22—3442no—
557C22—1721no—
558C22—1722no—
559C22—1721no—
560C22AGL(1,ℤ/8)×D4311yescharacteristic
561C4—41no—
562C4—41no—
563C4—42no—
564C4—81no—
565C4—431no—
566C4—431no—
567C4—3441no—
568C4—1721no—
569C4—1721no—
570C4C4×D4×D4311yescharacteristic
571C4AGL(1,ℤ/8)×D4311yescharacteristic
572C2—21no—
573C2—81no—
574C2—861no—
575C2—861no—
576C2—3442no—
577C2—3441no—
578C2#442×D4311yescharacteristic
subgroupG/H
centerC2#442×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC43×#2180C2
socleC2×C43C2×#442
prime radical#19147730C2
cosocleC2×C8×C43C24
hypercenter#2180D43
hypocenterC43#33468
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #2180

Complements

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

NH ≅ G/Ntype
2. #444×D43C2semidirect
3. #19143394C2semidirect
4. #19136495C2semidirect
5. #19136493C2semidirect
6. #19136492C2semidirect
7. #19136490C2semidirect
8. #19136489C2semidirect
9. #19136487C2semidirect
10. #19136484C2semidirect
11. #19136366C2semidirect
12. #19136343C2semidirect
13. #19136329C2semidirect
14. #347×D43C2semidirect
15. C43×#2180C2semidirect
20. #14583341C4semidirect
23. #14583336C4semidirect
25. #14583332C4semidirect
26. #14583330C4semidirect
34. #14583012C22semidirect
35. #14583010C22semidirect
36. #14583006C22semidirect
44. #14582723C22semidirect
45. #14582722C22semidirect
46. #14582721C22semidirect
47. #14582715C22semidirect
48. #14582713C22semidirect
49. #14582711C22semidirect
53. #14582677C22semidirect
54. #14582676C22semidirect
55. #14582676C22semidirect
58. C43×#441C22semidirect
59. C43×#365C22semidirect
60. C43×#362C22semidirect
62. C43×#347C22semidirect
69. #13063348C2×C4semidirect
73. #13063344C2×C4semidirect
74. Q16×D43C2×C4semidirect
78. D8×D43C2×C4semidirect
98. #13063271C2×C4semidirect
99. #13063270C2×C4semidirect
100. #13063268C2×C4semidirect
101. #13063268C2×C4semidirect
102. D688C2×C4semidirect
103. #13063266C2×C4semidirect
107. #13063264C2×C4semidirect
109. C16×D43C2×C4semidirect
127. Q32×C43C2×C4semidirect
128. SD32×C43C2×C4semidirect
293. #2180D43semidirect
328. #441C2×D43semidirect
339. #365C2×D43semidirect
341. #362C2×D43semidirect
351. #347C2×D43semidirect
352. C43#33468semidirect
393. Q32C4×D43semidirect
397. SD32C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191477302
#444×D432
#191433942
#191364952
#191364932
#191364922
#191364902
#191364892
#191364872
#191364842
#191363662
#191363432
#191363292
#347×D432
C43×#21802
#3346843