Finite Group Databasebeta

← #25081866

Subgroups — #25081866

Order 11008.

628 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#19145755C211yesmaximal, characteristic, complemented
2#19144693C211yesmaximal, characteristic
3#19144602C211yesmaximal, characteristic
4#19143616C211yesmaximal, characteristic
5#19134047C211yesmaximal, characteristic, complemented
6#19134046C211yesmaximal, characteristic, complemented
7#19134021C211yesmaximal, characteristic, complemented
8#19134020C211yesmaximal, characteristic, complemented
9#19133981C211yesmaximal, characteristic, complemented
10#19133969C211yesmaximal, characteristic, complemented
11#19133968C211yesmaximal, characteristic, complemented
12#19133374C211yesmaximal, characteristic, complemented
13#19133302C211yesmaximal, characteristic, complemented
14#19133258C211yesmaximal, characteristic, complemented
15C43×#1673C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18C4×D4×D43C2211yescharacteristic
19#14583295C2211yescharacteristic, complemented
20#14583251C2211yescharacteristic, complemented
21#14583250C2211yescharacteristic, complemented
22#14583242—21no—
23#14583242—21no—
24#14583233—21no—
25#14583228—21no—
26#14583205—21no—
27#14583205—21no—
28#14583190C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583180C2211yescharacteristic
31#14583179C2211yescharacteristic
32#14583101C2211yescharacteristic
33#14583101C2211yescharacteristic
34#14583048—21no—
35#14583048—21no—
36#14583002—21no—
37#14583000—21no—
38SD16×Dic43—21no—
39#14582984—21no—
40C8×D172C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42#14582964C2211yescharacteristic
43C8×C22⋊D43—21no—
44(C22⋊D43)⋊C8—21no—
45#14582955C2211yescharacteristic
46#14582951C2211yescharacteristic
47#14582951C2211yescharacteristic
48#14582950C2211yescharacteristic
49C2×(C2×D43)⋊C8—21no—
50C22⋊C8×D43—21no—
51#14582652C2211yescharacteristic, complemented
52#14582649C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582647C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582646C2211yescharacteristic, complemented
57#14582645C2211yescharacteristic, complemented
58#14582645C2211yescharacteristic, complemented
59#14582644C2211yescharacteristic, complemented
60C43×#500C2211yescharacteristic, complemented
61C43×#461C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic, complemented
65C43×#332C2211yescharacteristic, complemented
66C43×#332C2211yescharacteristic, complemented
67C2×D4×D43D411yescharacteristic
68C22×C4×D43—21no—
69C2×#10621884—21no—
70C2×#10621884—21no—
71C22×C43⋊C8—21no—
72C2×C8×D43—21no—
73C2×C8×D43—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063316—21no—
77#13063316—21no—
78#13063305—21no—
79#13063305—21no—
80#13063301—21no—
81#13063301—21no—
82Q8×Dic43—21no—
83Q8×Dic43—21no—
84#13063290—21no—
85#13063290—21no—
86C4×D172C2311yescharacteristic
87D4×Dic43D411yescharacteristic
88#13063287D411yescharacteristic
89C4×C22⋊D43—21no—
90(C22⋊D43)⋊C4—21no—
91#13063283—21no—
92#13063283—21no—
93C4⋊C4×D43D411yescharacteristic
94C22⋊C4×D43—21no—
95C42×D43C2311yescharacteristic
96#13063259—21no—
97#13063258—21no—
98#13063257—21no—
99#13063256—21no—
100#13063256—21no—
101#13063256—21no—
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8D411yescharacteristic
106Dic43⋊C8D411yescharacteristic
107#13063250—21no—
108#13063250—21no—
109#13063249—21no—
110#13063249—21no—
111#13063248—21no—
112#13063248—21no—
113#13063247—21no—
114#13063247—21no—
115#13063246—21no—
116#13063246—21no—
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8D411yescharacteristic
124(C2×D43)⋊C8D411yescharacteristic
125#13063235—21no—
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×SD16×C43—21no—
130C2×SD16×C43—21no—
131C22×C8×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133C4⋊Q8×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#107×C43—21no—
136#107×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C23×D43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×D4×C43C2×D411yescharacteristic
148C22×C4×C43—21no—
149C2×C22⋊D43—21no—
150C22×Dic43—21no—
151D4×D43—22no—
152D4×D43—22no—
153C2×D172C2×D411yescharacteristic
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—81no—
158C2×C4×D43—81no—
159C2×C4×D43C2×D411yescharacteristic
160C2×C4×D43C2×D411yescharacteristic
161C2×C4×D43#4111yescharacteristic
162C2×Dic86—21no—
163C2×Dic86—21no—
164SD16×C43—42no—
165SD16×C43—42no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—81no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43C2×D411yescharacteristic
177C22⋊C4×C43—21no—
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180#10621884—42no—
181#10621884—42no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—41no—
185(C2×D43)⋊C4—41no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—41no—
191C4⋊Dic43—41no—
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196C4×Dic43—41no—
197C4×Dic43—41no—
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43#4111yescharacteristic
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—81no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C8×D43—81no—
208C8×D43—81no—
209C23×C43—21no—
210C22×D43—21no—
211C22×D43—24no—
212C22×D43—81no—
213C22×D43—81no—
214C22×D43#12111yescharacteristic
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219D4×C43—21no—
220D4×C43#13512yes—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C22⋊D43—24no—
230C2×Dic43—21no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—81no—
234C2×Dic43#12111yescharacteristic
235C2×Dic43#12111yescharacteristic
236C2×Dic43#12111yescharacteristic
237D172—21no—
238D172#13512yes—
239C4×D43—21no—
240C4×D43—21no—
241C4×D43—21no—
242C4×D43—21no—
243C4×D43—41no—
244C4×D43—41no—
245C4×D43—41no—
246C4×D43—81no—
247C4×D43—81no—
248Dic86—41no—
249Dic86—41no—
250Dic86—81no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—41no—
254C8×C43—41no—
255C8×C43—41no—
256C43⋊C8—21no—
257C43⋊C8—21no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261#19395—431nomaximal, Sylow
262C22×C43—22no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43C2×#12111yescharacteristic
266C2×D43—21no—
267C2×D43—21no—
268C2×D43—22no—
269C2×D43—21no—
270C2×D43—41no—
271C2×D43—41no—
272C2×D43—84no—
273C4×C43—21no—
274C4×C43—41no—
275C4×C43—81no—
276C4×C43—81no—
277C4×C43C2×#13511yescharacteristic
278C4×C43C2×#13511yescharacteristic
279C4×C43#57711yescharacteristic
280C4×C43#57711yescharacteristic
281Dic43—21no—
282Dic43—21no—
283Dic43—21no—
284Dic43—41no—
285Dic43—81no—
286Dic43—81no—
287#3231—431no—
288#3110—431no—
289#3101—431no—
290#2972—431no—
291#1683—431no—
292#1683—431no—
293#1679—431no—
294#1679—431no—
295#1673—431no—
296#1673D4311yescharacteristic, complemented
297#1671—431no—
298#1671—431no—
299#1572—431no—
300#1554—431no—
301#1544—431no—
302C2×C43—42no—
303C2×C43#304211yescharacteristic
304C2×C43#305011yescharacteristic
305C2×C43#306911yescharacteristic
306D43—41no—
307D43—42no—
308#533—431no—
309#533—431no—
310C2×C4×D4—431no—
311#500C2×D4311yescharacteristic, complemented
312#498—431no—
313#487—431no—
314#487—431no—
315#485—861no—
316#485—861no—
317#484—861no—
318#483—861no—
319#479—861no—
320#479—861no—
321#476—431no—
322#476—431no—
323#474—431no—
324#474—431no—
325#461—431no—
326#461—431no—
327#461C2×D4311yescharacteristic
328#461C2×D4311yescharacteristic
329#450—861no—
330#450—861no—
331#440—861no—
332#440—861no—
333C4×SD16—861no—
334C4×SD16—861no—
335C8×D4—431no—
336C8×D4—431no—
337C8×D4—431no—
338C8×D4—861no—
339C8×D4—861no—
340C8×D4C2×D4311yescharacteristic
341#432—431no—
342#431—431no—
343#431—431no—
344#431—431no—
345C2×C22⋊C8—861no—
346C2×C22⋊C8—861no—
347#335—431no—
348#335C2×D4311yescharacteristic, complemented
349#334—431no—
350#334—431no—
351#333—431no—
352#333—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#332—431no—
357#332C2×D4311yescharacteristic, complemented
358#332C2×D4311yescharacteristic, complemented
359C43#1939511yescharacteristic, complemented, Sylow
360C22×D4—431no—
361C23×C4—861no—
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16—861no—
365C2×SD16—861no—
366C22×C8—21no—
367C22×C8—861no—
368C22×C8—861no—
369C22×C8—861no—
370C4⋊Q8—431no—
371C4⋊Q8—431no—
372C4⋊Q8C22×D4311yescharacteristic
373C4⋊Q8C22×D4311yescharacteristic
374#125—861no—
375#125—861no—
376C22⋊Q8—861no—
377C22⋊Q8—861no—
378C22⋊Q8—861no—
379C22⋊Q8—861no—
380C4×Q8—861no—
381C4×Q8—861no—
382C4×Q8—861no—
383C4×Q8—861no—
384C4×D4—431no—
385C4×D4—431no—
386C4×D4—431no—
387C4×D4—861no—
388C4×D4—861no—
389C4×D4C22×D4311yescharacteristic
390#117—861no—
391#117—861no—
392C2×C4⋊C4—431no—
393C2×C22⋊C4—861no—
394C2×C42—431no—
395#107—21no—
396#107—21no—
397#107—861no—
398#107—861no—
399#106—861no—
400#106—861no—
401#106—861no—
402#106—861no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8C22×D4311yescharacteristic
409C4⋊C8C22×D4311yescharacteristic
410C4⋊C8C22×D4311yescharacteristic
411#103—21no—
412#103—21no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#102—861no—
420#102—861no—
421#102—861no—
422#102—861no—
423C22⋊C8—21no—
424C22⋊C8—431no—
425C22⋊C8—431no—
426C22⋊C8—861no—
427C22⋊C8—861no—
428C22⋊C8—861no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431C22⋊C8—861no—
432#97—861no—
433C4×C8—431no—
434C4×C8—861no—
435C4×C8—861no—
436C4×C8C22×D4311yescharacteristic
437C24—861no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×D4—431no—
443C2×D4—861no—
444C2×D4—862no—
445C2×D4—862no—
446C2×D4D4×D4311yescharacteristic
447C22×C4—21no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—3441no—
456C22×C4—3441no—
457SD16—42no—
458SD16—42no—
459SD16—1722no—
460SD16—1722no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—81no—
465C2×C8—431no—
466C2×C8—431no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—3441no—
471C2×C8—3441no—
472C2×C8—3441no—
473C2×C8D4×D4311yescharacteristic
474C2×C8D4×D4311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—431no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—1721no—
486C4⋊C4—1721no—
487C4⋊C4—1721no—
488C4⋊C4—1721no—
489C4⋊C4D4×D4311yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—861no—
492C22⋊C4—861no—
493C22⋊C4—861no—
494C22⋊C4—1721no—
495C22⋊C4—1721no—
496C42—431no—
497C42—431no—
498C42—431no—
499C42—1721no—
500C42—1721no—
501C42C23×D4311yescharacteristic
502C23—21no—
503C23—431no—
504C23—864no—
505C23—861no—
506C23—3441no—
507C23—3441no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—3441no—
513Q8—1721no—
514Q8—1721no—
515D4—21no—
516D4—432no—
517D4—864no—
518D4—861no—
519D4#1306334412yes—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—431no—
526C2×C4—431no—
527C2×C4—431no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—3441no—
534C2×C4—3441no—
535C2×C4—3441no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4C2×D4×D4311yescharacteristic
542C2×C4C2×D4×D4311yescharacteristic
543C2×C4#41×D4311yescharacteristic
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—861no—
550C8—861no—
551C8—1721no—
552C8—1721no—
553C8—1721no—
554C22—22no—
555C22—41no—
556C22—41no—
557C22—861no—
558C22—861no—
559C22—861no—
560C22—862no—
561C22—3444no—
562C22—1721no—
563C22—1721no—
564C22#121×D4311yescharacteristic
565C4—21no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—861no—
570C4—861no—
571C4—861no—
572C4—3441no—
573C4—3441no—
574C4—1721no—
575C4#135×D4311yescharacteristic
576C4C2×#1306334411yescharacteristic
577C4#1458370511yescharacteristic
578C4#1458370811yescharacteristic
579C2—42no—
580C2—1721no—
581C2—1722no—
582C2#1914410211yescharacteristic
583C2#1914417411yescharacteristic
584C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1673C2
socleC22×C43C2×#121
prime radicalC2×D4×D43D4
hypercenter#1673D43
hypocenterC43#19395
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1673

Complements

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

NH ≅ G/Ntype
1. #19145755C2semidirect
5. #19134047C2semidirect
6. #19134046C2semidirect
7. #19134021C2semidirect
8. #19134020C2semidirect
9. #19133981C2semidirect
10. #19133969C2semidirect
11. #19133968C2semidirect
12. #19133374C2semidirect
13. #19133302C2semidirect
14. #19133258C2semidirect
15. C43×#1673C2semidirect
19. #14583295C22semidirect
20. #14583251C22semidirect
21. #14583250C22semidirect
51. #14582652C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582647C22semidirect
55. #14582647C22semidirect
56. #14582646C22semidirect
57. #14582645C22semidirect
58. #14582645C22semidirect
59. #14582644C22semidirect
60. C43×#500C22semidirect
64. C43×#335C22semidirect
65. C43×#332C22semidirect
66. C43×#332C22semidirect
296. #1673D43semidirect
311. #500C2×D43semidirect
348. #335C2×D43semidirect
357. #332C2×D43semidirect
358. #332C2×D43semidirect
359. C43#19395semidirect

Maximal subgroups

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

subgroupindex
#191457552
#191446932
#191446022
#191436162
#191340472
#191340462
#191340212
#191340202
#191339812
#191339692
#191339682
#191333742
#191333022
#191332582
C43×#16732
#1939543