Finite Group Databasebeta

← #25250060

Subgroups — #25250060

Order 11008.

632 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#510×D43C211yesmaximal, characteristic
2#19143509C211yesmaximal, characteristic
3#19143460C211yesmaximal, characteristic, complemented
4#19136489C211yesmaximal, characteristic, complemented
5#19136488C211yesmaximal, characteristic, complemented
6#19136487C211yesmaximal, characteristic, complemented
7#19136486C211yesmaximal, characteristic, complemented
8#19136485C211yesmaximal, characteristic, complemented
9#19136484C211yesmaximal, characteristic, complemented
10#19136483C211yesmaximal, characteristic, complemented
11#19136366C211yesmaximal, characteristic, complemented
12#362×D43C211yesmaximal, characteristic, complemented
13#19136329C211yesmaximal, characteristic
14#19136198C211yesmaximal, characteristic, complemented
15C43×#2180C211yesmaximal, characteristic, complemented
16#135×D43C2211yescharacteristic
17C2×Q16×D43C2211yescharacteristic
18#14583664—21no—
19#14583375—21no—
20#14583342C2211yescharacteristic
21#14583341C412yescomplemented
22#14583340C2211yescharacteristic
23#14583339C2211yescharacteristic
24#14583338C412yescomplemented
25Q32×D43C412yescomplemented
26SD32×D43C412yescomplemented
27M32×D43C2211yescharacteristic
28M32×D43C2211yescharacteristic
29#14583022C2211yescharacteristic
30#14583021C2211yescharacteristic
31#14583020C2211yescharacteristic
32#14583014—21no—
33#14583013—21no—
34#14583007C2211yescharacteristic, complemented
35#14583006C2211yescharacteristic, complemented
36#14583005C2211yescharacteristic, complemented
37C4×#10621885—21no—
38#14582991—21no—
39#108×D43C2211yescharacteristic
40#14582934C2211yescharacteristic
41#14582914—21no—
42#14582906—21no—
43#14582856C2211yescharacteristic
44#14582723C2211yescharacteristic, complemented
45#14582722C2211yescharacteristic, complemented
46#14582721C2211yescharacteristic, complemented
47#14582716C2211yescharacteristic, complemented
48#14582715C2211yescharacteristic, complemented
49#14582714C2211yescharacteristic, 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
63#41×D43—21no—
64C2×Q8×D43—21no—
65#13063348C2×C411yescharacteristic
66#13063347C2311yescharacteristic
67#13063346—21no—
68#13063345—21no—
69#13063344C2×C411yescharacteristic
70C2×Dic172C2311yescharacteristic
71C2×#10621885—21no—
72Q16×D43—21no—
73Q16×D43—21no—
74Q16×D43C2×C412yes—
75Q16×D43C2×C411yescharacteristic
76Q16×D43C2×C412yes—
77SD16×D43—21no—
78D8×D43C2×C411yescharacteristic
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
89Q8×Dic43—21no—
90C4×Dic86—21no—
91C4×Dic86—41no—
92#13063290—21no—
93#13063290—41no—
94#13063283—21no—
95#13063283—41no—
96#13063282—41no—
97#13063282D411yescharacteristic
98Dic344C2×C412yes—
99#13063271C2×C412yes—
100#13063271C2×C412yes—
101#13063270C2×C412yes—
102#13063269C2×C412yes—
103#13063268C2×C412yes—
104#13063265C2311yescharacteristic
105#13063265C2311yescharacteristic
106#13063264—21no—
107#13063264C2×C412yes—
108C16×D43—21no—
109C16×D43C2×C412yes—
110#13063261C2311yescharacteristic
111#13063260—21no—
112#13063258—21no—
113#13063257C2311yescharacteristic
114#13063253—21no—
115#13063252—21no—
116#13063251—21no—
117#13063250—21no—
118#13063249—21no—
119#13063248—21no—
120#13063235C2311yescharacteristic
121C4×C43⋊C8D411yescharacteristic
122C8×Dic43D411yescharacteristic
123#135×C43C2311yescharacteristic
124C2×Q16×C43C2311yescharacteristic
125#131×C43—21no—
126C4×Q8×C43—21no—
127Q32×C43C2×C412yes—
128SD32×C43C2×C412yes—
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—
139Q8×D43—21no—
140Q8×D43—22no—
141Q8×D43—22no—
142Q8×D43—41no—
143Q8×D43—41no—
144#10621900—21no—
145#10621900—41no—
146D4×D43—21no—
147D4×D43—41no—
148#10621898—21no—
149#10621898—41no—
150C2×C4×D43—41no—
151C2×C4×D43—41no—
152C2×C4×D43C2×D411yescharacteristic
153C2×Dic86—21no—
154C2×Dic86—41no—
155Q16×C43—21no—
156Q16×C43C22×C412yes—
157Q16×C43C22×C411yescharacteristic
158SD16×C43—21no—
159D8×C43C22×C411yescharacteristic
160M16×C43—21no—
161M16×C43—41no—
162C2×C8×C43—41no—
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2411yescharacteristic
165C4⋊C4×C43—21no—
166C4⋊C4×C43—41no—
167C42×C43—41no—
168C42×C43C2×D411yescharacteristic
169#10621885—22no—
170#10621885—22no—
171#10621885—21no—
172#10621884—21no—
173#10621883—21no—
174#10621882—21no—
175(C2×D43)⋊C4—21no—
176(C2×D43)⋊C4—41no—
177C4⋊Dic43—21no—
178C4⋊Dic43—41no—
179Dic43⋊C4—21no—
180Dic43⋊C4—41no—
181Dic43⋊C4—41no—
182C4×Dic43—41no—
183C4×Dic43—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×C412yes—
194Dic172C22×C411yescharacteristic
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—
213C22×D43—41no—
214C22×D43AGL(1,ℤ/8)11yescharacteristic
215Q8×C43—21no—
216Q8×C43—22no—
217Q8×C43—41no—
218D4×C43—21no—
219D4×C43—41no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43C22×D411yescharacteristic
225C22⋊D43—41no—
226C22⋊D43—41no—
227C22⋊D43—41no—
228C2×Dic43—21no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43AGL(1,ℤ/8)11yescharacteristic
233D172—21no—
234D172—41no—
235C4×D43—41no—
236C4×D43—42no—
237C4×D43—42no—
238C4×D43—41no—
239C4×D43—41no—
240C4×D43C4×D411yescharacteristic
241C4×D43C4×D411yescharacteristic
242C4×D43AGL(1,ℤ/8)11yescharacteristic
243C4×D43AGL(1,ℤ/8)11yescharacteristic
244Dic86—21no—
245Dic86—22no—
246Dic86—41no—
247Dic86—42no—
248Dic86—42no—
249Dic86—41no—
250C8×C43—21no—
251C8×C43—41no—
252C8×C43C23×C411yescharacteristic
253C8×C43C2×#4111yescharacteristic
254C43⋊C8—21no—
255C43⋊C8—41no—
256C43⋊C8C4×D411yescharacteristic
257C43⋊C8C4×D411yescharacteristic
258#33470—431nomaximal, Sylow
259C22×C43—41no—
260C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
261C2×D43—41no—
262C2×D43—41no—
263C2×D43—161no—
264C2×D43#44211yescharacteristic
265C2×D43#44211yescharacteristic
266C4×C43—41no—
267C4×C43—42no—
268C4×C43—41no—
269C4×C43—81no—
270C4×C43C2×C4×D411yescharacteristic
271C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
272Dic43—41no—
273Dic43—42no—
274Dic43—41no—
275Dic43—81no—
276Dic43#44211yescharacteristic
277Dic43#44211yescharacteristic
278C2×#510—431no—
279#2957—431no—
280#2950—431no—
281#2180—431no—
282#2180—431no—
283#2180—431no—
284#2180—431no—
285#2180—431no—
286#2180—431no—
287#2180—431no—
288#2180D4311yescharacteristic, complemented
289#2155—431no—
290C2×#362—431no—
291#2145—431no—
292#2110—431no—
293C2×C43—21no—
294C2×C43—81no—
295C2×C43C2×#44211yescharacteristic
296D43—21no—
297D43—21no—
298D43—81no—
299C2×#135—431no—
300C22×Q16—431no—
301#568—861no—
302#519—861no—
303#510—431no—
304#510—431no—
305#510—432no—
306#510—432no—
307#510—431no—
308#510C2×D4311yescharacteristic
309C2×Q32—432no—
310C2×SD32—432no—
311C2×M32—431no—
312C2×M32—431no—
313#444—431no—
314#444—431no—
315#444—431no—
316#444C2×D4311yescharacteristic
317#443—861no—
318#443—861no—
319#441—431no—
320#441—431no—
321#441—431no—
322#441C2×D4311yescharacteristic, complemented
323C4×Q16—861no—
324C4×Q16—861no—
325C2×#108—431no—
326#427—431no—
327#421—861no—
328#419—861no—
329#405—431no—
330#365—431no—
331#365—431no—
332#365—431no—
333#365C2×D4311yescharacteristic, complemented
334#362—431no—
335#362—431no—
336#362—431no—
337#362C2×D4311yescharacteristic, complemented
338#360—431no—
339#360—431no—
340#360—431no—
341#360C2×D4311yescharacteristic
342#347—431no—
343#347—431no—
344#347—431no—
345#347C2×D4311yescharacteristic, complemented
346C43#3347011yescharacteristic, complemented, Sylow
347C2×#41—861no—
348C22×Q8—861no—
349#135—431no—
350#135—431no—
351#135—431no—
352#135—861no—
353#135—861no—
354#135C22×D4311yescharacteristic
355C2×Q16—432no—
356C2×Q16—432no—
357C2×Q16—431no—
358C2×Q16—431no—
359C2×Q16—861no—
360C2×Q16—861no—
361C2×Q16—861no—
362C2×Q16C22×D4311yescharacteristic
363C2×SD16—861no—
364C2×D8—431no—
365#131—21no—
366#131—861no—
367#131—861no—
368#131—861no—
369#131—1721no—
370#131—1721no—
371C2×M16—431no—
372C2×M16—861no—
373C2×M16—1721no—
374C2×M16—1721no—
375C22×C8—431no—
376C4×Q8—21no—
377C4×Q8—861no—
378C4×Q8—861no—
379C4×Q8—861no—
380C4×Q8—1721no—
381C4×Q8—1721no—
382#117—431no—
383#117—861no—
384#117—1721no—
385#117—1721no—
386Q32—432no—
387Q32—432no—
388Q32—432no—
389Q32C4×D4312yes—
390SD32—432no—
391SD32—432no—
392SD32—432no—
393SD32C4×D4312yes—
394M32—431no—
395M32—432no—
396M32—431no—
397M32—861no—
398M32C22×D4311yescharacteristic
399M32C22×D4311yescharacteristic
400C2×C16—432no—
401C2×C16—861no—
402#108—431no—
403#108—861no—
404#108C22×D4311yescharacteristic
405#107—861no—
406#106—431no—
407#106C22×D4311yescharacteristic
408#104—21no—
409#104—861no—
410#104—861no—
411#104—861no—
412#103—21no—
413#103—861no—
414#103—861no—
415#103—861no—
416#97—431no—
417#97C22×D4311yescharacteristic
418C4×C8—431no—
419C4×C8—431no—
420#41—21no—
421#41—861no—
422#41—861no—
423#41—861no—
424#41—1721no—
425#41—1721no—
426C2×Q8—21no—
427C2×Q8—861no—
428C2×Q8—862no—
429C2×Q8—862no—
430C2×Q8—861no—
431C2×Q8—1721no—
432C2×Q8—1721no—
433C2×Q8—1721no—
434C2×D4—861no—
435C2×D4—1721no—
436C22×C4—431no—
437C22×C4—1721no—
438C22×C4—1721no—
439Q16—21no—
440Q16—432no—
441Q16—431no—
442Q16—862no—
443Q16—862no—
444Q16—861no—
445Q16—861no—
446Q16C2×C4×D4312yes—
447Q16C2×C4×D4311yescharacteristic
448SD16—21no—
449SD16—861no—
450SD16—861no—
451SD16—861no—
452D8—431no—
453D8—861no—
454D8C2×C4×D4311yescharacteristic
455M16—21no—
456M16—41no—
457M16—861no—
458M16—861no—
459M16—861no—
460M16—1721no—
461M16—1721no—
462M16—1721no—
463M16—1721no—
464C2×C8—41no—
465C2×C8—431no—
466C2×C8—431no—
467C2×C8—431no—
468C2×C8—431no—
469C2×C8—431no—
470C2×C8—431no—
471C2×C8—1721no—
472C2×C8—1721no—
473C2×C8—1721no—
474C2×C8—1721no—
475C2×C8D4×D4311yescharacteristic
476C2×C8C23×D4311yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—41no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—1721no—
482C4⋊C4—1721no—
483C4⋊C4—1721no—
484C22⋊C4—861no—
485C22⋊C4—1721no—
486C42—41no—
487C42—431no—
488C42—1721no—
489C42—1721no—
490C42—1721no—
491C42—1721no—
492C42D4×D4311yescharacteristic
493C16—21no—
494C16—432no—
495C16—861no—
496C16C2×C4×D4312yes—
497C23—431no—
498C23—1721no—
499Q8—21no—
500Q8—22no—
501Q8—41no—
502Q8—861no—
503Q8—862no—
504Q8—1722no—
505Q8—1722no—
506Q8—1721no—
507Q8—1721no—
508D4—21no—
509D4—41no—
510D4—861no—
511D4—1721no—
512D4—1721no—
513D4—1721no—
514D4—1721no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—431no—
520C2×C4—431no—
521C2×C4—431no—
522C2×C4—431no—
523C2×C4—431no—
524C2×C4—861no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1722no—
528C2×C4—1722no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4C2×D4×D4311yescharacteristic
534C8—21no—
535C8—41no—
536C8—431no—
537C8—431no—
538C8—861no—
539C8—1721no—
540C8C22×C4×D4311yescharacteristic
541C8#41×D4311yescharacteristic
542C22—41no—
543C22—431no—
544C22—431no—
545C22—1721no—
546C22—1721no—
547C22—6881no—
548C22AGL(1,ℤ/8)×D4311yescharacteristic
549C4—41no—
550C4—41no—
551C4—42no—
552C4—81no—
553C4—431no—
554C4—431no—
555C4—3441no—
556C4—1721no—
557C4—1721no—
558C4—1722no—
559C4C4×D4×D4311yescharacteristic
560C4AGL(1,ℤ/8)×D4311yescharacteristic
561C2—21no—
562C2—81no—
563C2—861no—
564C2—861no—
565C2—3441no—
566C2#442×D4311yescharacteristic
subgroupG/H
centerC2#442×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC43×#2180C2
socleC2×C43C2×#442
prime radical#135×D43C22
cosocleC2×C8×C43C24
hypercenter#2180D43
hypocenterC43#33470
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
3. #19143460C2semidirect
4. #19136489C2semidirect
5. #19136488C2semidirect
6. #19136487C2semidirect
7. #19136486C2semidirect
8. #19136485C2semidirect
9. #19136484C2semidirect
10. #19136483C2semidirect
11. #19136366C2semidirect
12. #362×D43C2semidirect
14. #19136198C2semidirect
15. C43×#2180C2semidirect
21. #14583341C4semidirect
24. #14583338C4semidirect
25. Q32×D43C4semidirect
26. SD32×D43C4semidirect
34. #14583007C22semidirect
35. #14583006C22semidirect
36. #14583005C22semidirect
44. #14582723C22semidirect
45. #14582722C22semidirect
46. #14582721C22semidirect
47. #14582716C22semidirect
48. #14582715C22semidirect
49. #14582714C22semidirect
53. #14582677C22semidirect
54. #14582676C22semidirect
55. #14582676C22semidirect
58. C43×#441C22semidirect
59. C43×#365C22semidirect
60. C43×#362C22semidirect
62. C43×#347C22semidirect
288. #2180D43semidirect
322. #441C2×D43semidirect
333. #365C2×D43semidirect
337. #362C2×D43semidirect
345. #347C2×D43semidirect
346. C43#33470semidirect

Maximal subgroups

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

subgroupindex
#510×D432
#191435092
#191434602
#191364892
#191364882
#191364872
#191364862
#191364852
#191364842
#191364832
#191363662
#362×D432
#191363292
#191361982
C43×#21802
#3347043