Finite Group Databasebeta

← #25250053

Subgroups — #25250053

Order 11008.

646 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#19147727C211yesmaximal, characteristic
2#19143509C211yesmaximal, characteristic, complemented
3#19143477C211yesmaximal, characteristic, complemented
4#19136496C211yesmaximal, characteristic, complemented
5#19136494C211yesmaximal, characteristic, complemented
6#19136491C211yesmaximal, characteristic, complemented
7#19136488C211yesmaximal, characteristic, complemented
8#19136486C211yesmaximal, characteristic, complemented
9#19136485C211yesmaximal, characteristic, complemented
10#19136483C211yesmaximal, characteristic, complemented
11#365×D43C211yesmaximal, characteristic, complemented
12#19136341C211yesmaximal, characteristic, complemented
13#360×D43C211yesmaximal, characteristic, complemented
14#19136198C211yesmaximal, characteristic, complemented
15C43×AGL(1,ℤ/16)C211yesmaximal, characteristic, complemented
16C2×#13063344C2211yescharacteristic
17#135×D43C2211yescharacteristic
18#14583664—21no—
19#14583378—21no—
20#14583342C2211yescharacteristic
21#14583339C2211yescharacteristic
22#14583338C412yescomplemented
23#14583335C2211yescharacteristic
24#14583333C412yescomplemented
25#14583330C412yescomplemented
26#14583328C412yescomplemented
27M32×D43C2211yescharacteristic
28M32×D43C2211yescharacteristic
29#14583022C2211yescharacteristic
30#14583021C2211yescharacteristic
31#14583020C2211yescharacteristic
32#14583014—21no—
33#14583013—21no—
34#14583011C2211yescharacteristic, complemented
35#14583007C2211yescharacteristic, complemented
36#14583005C2211yescharacteristic, complemented
37#14582990—21no—
38C4×#10621883—21no—
39#108×D43C2211yescharacteristic
40#106×D43C2211yescharacteristic
41#14582914—21no—
42#14582897—21no—
43#14582856C2211yescharacteristic
44#14582723C2211yescharacteristic, complemented
45#14582722C2211yescharacteristic, complemented
46#14582721C2211yescharacteristic, complemented
47#14582716C2211yescharacteristic, complemented
48#14582714C2211yescharacteristic, complemented
49#14582712C2211yescharacteristic, complemented
50#14582710C2211yescharacteristic
51#14582709C2211yescharacteristic
52#14582708C2211yescharacteristic
53#14582677C2211yescharacteristic, complemented
54#14582676C2211yescharacteristic, complemented
55#14582676C2211yescharacteristic, complemented
56C43×#509C2211yescharacteristic
57C43×#444C2211yescharacteristic
58C43×#442C2211yescharacteristic, complemented
59C43×#365C2211yescharacteristic, complemented
60C43×#361C2211yescharacteristic, complemented
61C43×#360C2211yescharacteristic
62C43×#347C2211yescharacteristic, complemented
63C2×#10621900—21no—
64#41×D43—21no—
65#13063348C2×C411yescharacteristic, complemented
66#13063347C2311yescharacteristic
67#13063346—21no—
68#13063345—21no—
69#13063344—21no—
70#13063344—21no—
71#13063344C2×C412yes—
72#13063344C2×C412yes—
73#13063344C2×C411yescharacteristic, complemented
74C2×Dic172C2311yescharacteristic
75Q16×D43C2×C411yescharacteristic, complemented
76C2×#10621883—21no—
77SD16×D43—21no—
78D8×D43C2×C411yescharacteristic, complemented
79#13063333—21no—
80#13063333—41no—
81#13063332—21no—
82#13063331—21no—
83#13063331—41no—
84C2×#10621872—41no—
85C2×#10621872D411yescharacteristic
86M16×D43—21no—
87M16×D43—41no—
88C2×C8×D43C2311yescharacteristic
89C4×Dic86—21no—
90#13063290—21no—
91D4×Dic43—21no—
92C4×C22⋊D43—41no—
93(C22⋊D43)⋊C4—41no—
94#13063282D411yescharacteristic
95#13063281—41no—
96C2×Dic43⋊C4—41no—
97C4⋊C4×D43—21no—
98Dic344C2×C412yescomplemented
99#13063271C2×C412yescomplemented
100#13063270C2×C412yescomplemented
101#13063269C2×C412yescomplemented
102#13063269C2×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#13063257C2311yescharacteristic
113#13063256—21no—
114#13063253—21no—
115#13063252—21no—
116#13063251—21no—
117#13063250—21no—
118#13063248—21no—
119#13063246—21no—
120#13063235C2311yescharacteristic
121C4×C43⋊C8D411yescharacteristic
122C8×Dic43D411yescharacteristic
123#135×C43C2311yescharacteristic
124C2×D8×C43C2311yescharacteristic
125#131×C43—21no—
126C4×D4×C43—21no—
127SD32×C43C2×C412yescomplemented
128D16×C43C2×C412yescomplemented
129M32×C43C2311yescharacteristic
130M32×C43C2311yescharacteristic
131#108×C43C2311yescharacteristic
132#106×C43C2311yescharacteristic
133#104×C43—21no—
134#102×C43—21no—
135#97×C43C2311yescharacteristic
136#41×C43—21no—
137C2×D4×C43—21no—
138C22×C4×C43—41no—
139C2×C22⋊D43—41no—
140C22×Dic43—41no—
141C22×Dic43—41no—
142#10621902—21no—
143Q8×D43—21no—
144#10621900—22no—
145#10621900—22no—
146#10621900—21no—
147#10621900—41no—
148#10621900—41no—
149#10621900—41no—
150D4×D43—21no—
151D4×D43—41no—
152#10621898—21no—
153#10621898—41no—
154C2×C4×D43—41no—
155C2×C4×D43—41no—
156C2×C4×D43C2×D411yescharacteristic
157C2×Dic86—21no—
158Q16×C43C22×C411yescharacteristic
159SD16×C43—21no—
160D8×C43—21no—
161D8×C43C22×C411yescharacteristic
162D8×C43C22×C412yes—
163M16×C43—21no—
164M16×C43—41no—
165C2×C8×C43—41no—
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2411yescharacteristic
168C4⋊C4×C43—21no—
169C22⋊C4×C43—41no—
170C42×C43C2×D411yescharacteristic
171C22⋊Dic43—41no—
172#10621885—21no—
173#10621884—21no—
174#10621883—21no—
175#10621883—22no—
176#10621883—22no—
177#10621882—21no—
178(C2×D43)⋊C4—21no—
179C4⋊Dic43—21no—
180Dic43⋊C4—21no—
181Dic43⋊C4—41no—
182Dic43⋊C4—41no—
183Dic43⋊C4—41no—
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
192Dic172—21no—
193Dic172C22×C411yescharacteristic
194Dic172C22×C412yes—
195D344C22×C411yescharacteristic
196#10621873—21no—
197#10621872—21no—
198#10621872—21no—
199#10621872—41no—
200#10621872—41no—
201#10621872—41no—
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—
213C23×C43—41no—
214C22×D43—41no—
215C22×D43AGL(1,ℤ/8)11yescharacteristic
216Q8×C43—21no—
217D4×C43—21no—
218D4×C43—22no—
219D4×C43—41no—
220D4×C43—41no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—161no—
225C2×C4×C43C22×D411yescharacteristic
226C22⋊D43—41no—
227C22⋊D43—41no—
228C22⋊D43—42no—
229C22⋊D43—42no—
230C22⋊D43—41no—
231C2×Dic43—21no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236C2×Dic43—41no—
237C2×Dic43—161no—
238C2×Dic43AGL(1,ℤ/8)11yescharacteristic
239D172—21no—
240D172—41no—
241C4×D43—41no—
242C4×D43—41no—
243C4×D43—41no—
244C4×D43—161no—
245C4×D43C4×D411yescharacteristic
246C4×D43C4×D411yescharacteristic
247C4×D43AGL(1,ℤ/8)11yescharacteristic
248C4×D43AGL(1,ℤ/8)11yescharacteristic
249Dic86—21no—
250Dic86—22no—
251Dic86—41no—
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#33469—431nomaximal, Sylow
262C22×C43—41no—
263C22×C43—42no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
267C2×D43—41no—
268C2×D43—41no—
269C2×D43—161no—
270C2×D43#44211yescharacteristic
271C2×D43#44211yescharacteristic
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—81no—
275C4×C43C2×C4×D411yescharacteristic
276C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
277Dic43—41no—
278Dic43—41no—
279Dic43—42no—
280Dic43—81no—
281Dic43#44211yescharacteristic
282Dic43#44211yescharacteristic
283#3414—431no—
284#2957—431no—
285#2952—431no—
286AGL(1,ℤ/16)—431no—
287AGL(1,ℤ/16)—431no—
288AGL(1,ℤ/16)—431no—
289AGL(1,ℤ/16)D4311yescharacteristic, complemented
290#2180—431no—
291#2180—431no—
292#2180—431no—
293#2180—431no—
294C2×#365—431no—
295#2148—431no—
296C2×#360—431no—
297#2110—431no—
298C2×C43—21no—
299C2×C43—81no—
300C2×C43—82no—
301C2×C43C2×#44211yescharacteristic
302D43—21no—
303D43—21no—
304D43—81no—
305C2×#135—431no—
306C2×#135—431no—
307#568—861no—
308#520—861no—
309#510—431no—
310#510—432no—
311#510—431no—
312#509—431no—
313#509—432no—
314#509C2×D4311yescharacteristic
315#508—432no—
316#508—432no—
317C2×M32—431no—
318C2×M32—431no—
319#444—431no—
320#444—431no—
321#444—431no—
322#444C2×D4311yescharacteristic
323#443—861no—
324#443—861no—
325#442—431no—
326#442C2×D4311yescharacteristic, complemented
327#441—431no—
328#441—431no—
329C4×SD16—861no—
330C4×SD16—861no—
331C2×#108—431no—
332C2×#106—431no—
333#421—861no—
334#417—861no—
335#405—431no—
336#365—431no—
337#365—431no—
338#365—431no—
339#365C2×D4311yescharacteristic, complemented
340#362—431no—
341#362—431no—
342#361—431no—
343#361C2×D4311yescharacteristic, complemented
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#3346911yescharacteristic, complemented, Sylow
353C2×#41—861no—
354C2×#41—861no—
355#135—431no—
356#135—432no—
357#135—432no—
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×Q16—431no—
367C2×SD16—861no—
368C2×SD16—861no—
369C2×D8—431no—
370C2×D8C22×D4311yescharacteristic
371#131—21no—
372#131—861no—
373#131—861no—
374#131—861no—
375#131—1721no—
376#131—1721no—
377C2×M16—431no—
378C2×M16—861no—
379C2×M16—1721no—
380C2×M16—1721no—
381C22×C8—431no—
382C4×Q8—861no—
383C4×Q8—861no—
384C4×D4—21no—
385C4×D4—861no—
386C4×D4—1721no—
387C4×D4—1721no—
388#117—431no—
389#117—1721no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—1721no—
392Q32—432no—
393Q32—432no—
394SD32—432no—
395SD32—432no—
396SD32—432no—
397SD32C4×D4312yescomplemented
398D16—432no—
399D16C4×D4312yescomplemented
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#106—431no—
412#106—861no—
413#106C22×D4311yescharacteristic
414#104—21no—
415#104—861no—
416#104—861no—
417#104—861no—
418#103—861no—
419#103—861no—
420#102—21no—
421#102—861no—
422#97—431no—
423#97C22×D4311yescharacteristic
424C4×C8—431no—
425C4×C8—431no—
426#41—21no—
427#41—862no—
428#41—862no—
429#41—861no—
430#41—861no—
431#41—861no—
432#41—1721no—
433#41—1721no—
434#41—1721no—
435#41—1721no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×D4—21no—
439C2×D4—861no—
440C2×D4—1721no—
441C2×D4—1721no—
442C22×C4—41no—
443C22×C4—431no—
444C22×C4—1721no—
445C22×C4—1721no—
446C22×C4—1721no—
447C22×C4—1721no—
448Q16—431no—
449Q16—432no—
450Q16—861no—
451Q16—861no—
452Q16C2×C4×D4311yescharacteristic
453SD16—21no—
454SD16—862no—
455SD16—862no—
456SD16—861no—
457SD16—861no—
458SD16—861no—
459D8—21no—
460D8—431no—
461D8—861no—
462D8C2×C4×D4312yes—
463D8C2×C4×D4311yescharacteristic
464M16—21no—
465M16—41no—
466M16—861no—
467M16—861no—
468M16—861no—
469M16—1721no—
470M16—1721no—
471M16—1721no—
472M16—1721no—
473C2×C8—41no—
474C2×C8—431no—
475C2×C8—431no—
476C2×C8—431no—
477C2×C8—431no—
478C2×C8—431no—
479C2×C8—431no—
480C2×C8—1721no—
481C2×C8—1721no—
482C2×C8—1721no—
483C2×C8—1721no—
484C2×C8D4×D4311yescharacteristic
485C2×C8C23×D4311yescharacteristic
486C4⋊C4—21no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—1721no—
490C4⋊C4—1721no—
491C4⋊C4—1721no—
492C22⋊C4—41no—
493C22⋊C4—861no—
494C22⋊C4—1721no—
495C42—431no—
496C42—1721no—
497C42—1721no—
498C42D4×D4311yescharacteristic
499C16—21no—
500C16—432no—
501C16—861no—
502C16C2×C4×D4312yes—
503C23—41no—
504C23—431no—
505C23—1721no—
506Q8—21no—
507Q8—862no—
508Q8—861no—
509Q8—1721no—
510Q8—1721no—
511D4—22no—
512D4—21no—
513D4—41no—
514D4—41no—
515D4—861no—
516D4—1721no—
517D4—1721no—
518D4—1721no—
519D4—1722no—
520D4—1722no—
521D4—1721no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—161no—
526C2×C4—431no—
527C2×C4—431no—
528C2×C4—431no—
529C2×C4—431no—
530C2×C4—431no—
531C2×C4—861no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1722no—
536C2×C4—1722no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—6881no—
541C2×C4—6881no—
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—42no—
553C22—81no—
554C22—81no—
555C22—431no—
556C22—431no—
557C22—1721no—
558C22—1721no—
559C22—6881no—
560C22AGL(1,ℤ/8)×D4311yescharacteristic
561C4—41no—
562C4—41no—
563C4—81no—
564C4—431no—
565C4—431no—
566C4—3441no—
567C4—1721no—
568C4—1721no—
569C4—1722no—
570C4C4×D4×D4311yescharacteristic
571C4AGL(1,ℤ/8)×D4311yescharacteristic
572C2—21no—
573C2—82no—
574C2—81no—
575C2—861no—
576C2—861no—
577C2—3441no—
578C2#442×D4311yescharacteristic
subgroupG/H
centerC2#442×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC43×AGL(1,ℤ/16)C2
socleC2×C43C2×#442
prime radical#19147727C2
cosocleC2×C8×C43C24
hypercenterAGL(1,ℤ/16)D43
hypocenterC43#33469
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ AGL(1,ℤ/16)

Complements

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

NH ≅ G/Ntype
2. #19143509C2semidirect
3. #19143477C2semidirect
4. #19136496C2semidirect
5. #19136494C2semidirect
6. #19136491C2semidirect
7. #19136488C2semidirect
8. #19136486C2semidirect
9. #19136485C2semidirect
10. #19136483C2semidirect
11. #365×D43C2semidirect
12. #19136341C2semidirect
13. #360×D43C2semidirect
14. #19136198C2semidirect
15. C43×AGL(1,ℤ/16)C2semidirect
22. #14583338C4semidirect
24. #14583333C4semidirect
25. #14583330C4semidirect
26. #14583328C4semidirect
34. #14583011C22semidirect
35. #14583007C22semidirect
36. #14583005C22semidirect
44. #14582723C22semidirect
45. #14582722C22semidirect
46. #14582721C22semidirect
47. #14582716C22semidirect
48. #14582714C22semidirect
49. #14582712C22semidirect
53. #14582677C22semidirect
54. #14582676C22semidirect
55. #14582676C22semidirect
58. C43×#442C22semidirect
59. C43×#365C22semidirect
60. C43×#361C22semidirect
62. C43×#347C22semidirect
65. #13063348C2×C4semidirect
73. #13063344C2×C4semidirect
75. Q16×D43C2×C4semidirect
78. D8×D43C2×C4semidirect
98. Dic344C2×C4semidirect
99. #13063271C2×C4semidirect
100. #13063270C2×C4semidirect
101. #13063269C2×C4semidirect
102. #13063269C2×C4semidirect
103. #13063266C2×C4semidirect
107. #13063264C2×C4semidirect
109. C16×D43C2×C4semidirect
127. SD32×C43C2×C4semidirect
128. D16×C43C2×C4semidirect
289. AGL(1,ℤ/16)D43semidirect
326. #442C2×D43semidirect
339. #365C2×D43semidirect
343. #361C2×D43semidirect
351. #347C2×D43semidirect
352. C43#33469semidirect
397. SD32C4×D43semidirect
399. D16C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191477272
#191435092
#191434772
#191364962
#191364942
#191364912
#191364882
#191364862
#191364852
#191364832
#365×D432
#191363412
#360×D432
#191361982
C43×AGL(1,ℤ/16)2
#3346943