Finite Group Databasebeta

← #25081849

Subgroups — #25081849

Order 11008.

650 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145726C211yesmaximal, characteristic, complemented
2#19144685C211yesmaximal, characteristic
3#19144602C211yesmaximal, characteristic, complemented
4#19143616C211yesmaximal, characteristic, complemented
5#19134029C211yesmaximal, characteristic, complemented
6#19134003C211yesmaximal, characteristic, complemented
7#19134002C211yesmaximal, characteristic, complemented
8#19133995C211yesmaximal, characteristic, complemented
9#19133994C211yesmaximal, characteristic, complemented
10#19133969C211yesmaximal, characteristic, complemented
11#19133968C211yesmaximal, characteristic, complemented
12#19133374C211yesmaximal, characteristic, complemented
13#19133302C211yesmaximal, characteristic, complemented
14#19133254C211yesmaximal, characteristic, complemented
15C43×#1681C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583447C2211yescharacteristic
18C4×D4×D43C2211yescharacteristic
19#14583304C2211yescharacteristic, complemented
20#14583295C2211yescharacteristic, complemented
21#14583245C2211yescharacteristic, complemented
22#14583228—21no—
23#14583221—21no—
24#14583221—21no—
25#14583216—21no—
26#14583197—21no—
27#14583197—21no—
28#14583190C2211yescharacteristic
29#14583190C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583189C2211yescharacteristic
32#14583101C2211yescharacteristic
33#14583091C2211yescharacteristic
34#14583048—21no—
35#14583031—21no—
36#14583011—21no—
37#14583008—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#14582647C2211yescharacteristic, complemented
57#14582647C2211yescharacteristic, complemented
58#14582645C2211yescharacteristic, complemented
59#14582643C2211yescharacteristic, complemented
60C43×#486C2211yescharacteristic, complemented
61C43×#461C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic, complemented
65C43×#332C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic, complemented
67C2×#10621900—21no—
68C2×D4×D43D411yescharacteristic
69C22×C4×D43—21no—
70C2×#10621884—21no—
71C2×#10621882—21no—
72C22×C43⋊C8—21no—
73C2×C8×D43—21no—
74C2×C8×D43—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063316—21no—
78#13063312—21no—
79#13063305—21no—
80#13063301—21no—
81#13063296—21no—
82#13063296—21no—
83Q8×Dic43—21no—
84#13063290—21no—
85C4×D172C2311yescharacteristic
86D4×Dic43—21no—
87D4×Dic43—21no—
88D4×Dic43D411yescharacteristic
89#13063287D411yescharacteristic
90C4×C22⋊D43—21no—
91(C22⋊D43)⋊C4—21no—
92#13063283—21no—
93C4⋊C4×D43D411yescharacteristic
94C22⋊C4×D43—21no—
95C42×D43C2311yescharacteristic
96#13063259—21no—
97#13063259—21no—
98#13063257—21no—
99#13063257—21no—
100#13063256—21no—
101#13063256—21no—
102#13063256—21no—
103#13063256—21no—
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8D411yescharacteristic
108Dic43⋊C8D411yescharacteristic
109#13063249—21no—
110#13063247—21no—
111#13063247—21no—
112#13063246—21no—
113#13063246—21no—
114#13063246—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×D8×C43—21no—
131C22×C8×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133#127×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C23×D43—21no—
145C2×Q8×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43C2×D411yescharacteristic
150C22×C4×C43—21no—
151C2×C22⋊D43—21no—
152C2×C22⋊D43—41no—
153C22×Dic43—21no—
154C22×Dic43—41no—
155#10621900—82no—
156D4×D43—22no—
157D4×D43—22no—
158C2×D172C2×D411yescharacteristic
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—81no—
163C2×C4×D43—81no—
164C2×C4×D43C2×D411yescharacteristic
165C2×C4×D43C2×D411yescharacteristic
166C2×C4×D43#4111yescharacteristic
167C2×Dic86—21no—
168C2×Dic86—21no—
169SD16×C43—42no—
170D8×C43—42no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—81no—
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43C2×D411yescharacteristic
180C22⋊C4×C43—21no—
181C42×C43C2411yescharacteristic
182C22⋊Dic43—21no—
183C22⋊Dic43—41no—
184C22⋊Dic43—41no—
185#10621884—42no—
186#10621882—42no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—41no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—41no—
195C4⋊Dic43C2×D411yescharacteristic
196Dic43⋊C4—21no—
197Dic43⋊C4—41no—
198C4×Dic43—41no—
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43C2×D411yescharacteristic
201C4×Dic43#4111yescharacteristic
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—81no—
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C8×D43—81no—
209C8×D43—81no—
210C23×C43—21no—
211C23×C43—41no—
212C22×D43—21no—
213C22×D43—24no—
214C22×D43—81no—
215C22×D43—81no—
216C22×D43#12111yescharacteristic
217Q8×C43—41no—
218Q8×C43—41no—
219D4×C43—21no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—81no—
225D4×C43#13512yes—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C22⋊D43—24no—
234C22⋊D43—82no—
235C2×Dic43—21no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—81no—
239C2×Dic43—82no—
240C2×Dic43#12111yescharacteristic
241C2×Dic43#12111yescharacteristic
242C2×Dic43#12111yescharacteristic
243D172—21no—
244D172#13512yes—
245C4×D43—21no—
246C4×D43—21no—
247C4×D43—21no—
248C4×D43—21no—
249C4×D43—41no—
250C4×D43—41no—
251C4×D43—41no—
252C4×D43—81no—
253C4×D43—81no—
254Dic86—81no—
255Dic86—81no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—41no—
259C8×C43—41no—
260C8×C43—41no—
261C43⋊C8—21no—
262C43⋊C8—21no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266#19394—431nomaximal, Sylow
267C22×C43—22no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43C2×#12111yescharacteristic
274C2×D43—21no—
275C2×D43—21no—
276C2×D43—22no—
277C2×D43—21no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—84no—
281C4×C43—21no—
282C4×C43—41no—
283C4×C43—81no—
284C4×C43C2×#13511yescharacteristic
285C4×C43C2×#13511yescharacteristic
286C4×C43#57711yescharacteristic
287C4×C43#57711yescharacteristic
288Dic43—21no—
289Dic43—21no—
290Dic43—21no—
291Dic43—41no—
292Dic43—81no—
293Dic43—81no—
294#3228—431no—
295#3109—431no—
296#3101—431no—
297#2972—431no—
298#1681—431no—
299#1681D4311yescharacteristic, complemented
300#1677—431no—
301#1677—431no—
302#1675—431no—
303#1675—431no—
304#1671—431no—
305#1671—431no—
306#1572—431no—
307#1554—431no—
308#1543—431no—
309C2×C43—42no—
310C2×C43—161no—
311C2×C43#304211yescharacteristic
312C2×C43#305011yescharacteristic
313C2×C43#306811yescharacteristic
314D43—41no—
315D43—42no—
316#533—431no—
317#532—431no—
318C2×C4×D4—431no—
319#500—431no—
320#498—431no—
321#486—431no—
322#486C2×D4311yescharacteristic, complemented
323#483—861no—
324#482—861no—
325#482—861no—
326#481—861no—
327#478—861no—
328#478—861no—
329#476—431no—
330#476—431no—
331#476—431no—
332#476—431no—
333#461—431no—
334#461C2×D4311yescharacteristic
335#459—431no—
336#459C2×D4311yescharacteristic
337#450—861no—
338#447—861no—
339#442—861no—
340#442—861no—
341C4×SD16—861no—
342C4×SD16—861no—
343C8×D4—431no—
344C8×D4—431no—
345C8×D4—431no—
346C8×D4—861no—
347C8×D4—861no—
348C8×D4C2×D4311yescharacteristic
349#432—431no—
350#431—431no—
351#431—431no—
352#431—431no—
353C2×C22⋊C8—861no—
354C2×C22⋊C8—861no—
355#335—431no—
356#335C2×D4311yescharacteristic, complemented
357#334—431no—
358#334—431no—
359#333—431no—
360#333—431no—
361#333—431no—
362#333—431no—
363#332—431no—
364#332C2×D4311yescharacteristic, complemented
365#331—431no—
366#331C2×D4311yescharacteristic, complemented
367C43#1939411yescharacteristic, complemented, Sylow
368C2×#41—861no—
369C22×D4—431no—
370C23×C4—861no—
371C2×SD16—21no—
372C2×SD16—861no—
373C2×D8—21no—
374C2×D8—861no—
375C22×C8—21no—
376C22×C8—861no—
377C22×C8—861no—
378C22×C8—861no—
379C4⋊Q8—431no—
380C4⋊Q8—431no—
381C4⋊Q8C22×D4311yescharacteristic
382#127C22×D4311yescharacteristic
383#125—861no—
384#124—861no—
385C22⋊Q8—861no—
386C22⋊Q8—861no—
387#121—861no—
388#121—861no—
389C4×Q8—861no—
390C4×Q8—861no—
391C4×D4—431no—
392C4×D4—431no—
393C4×D4—431no—
394C4×D4—861no—
395C4×D4—861no—
396C4×D4—861no—
397C4×D4—861no—
398C4×D4C22×D4311yescharacteristic
399#117—861no—
400C2×C4⋊C4—431no—
401C2×C22⋊C4—861no—
402C2×C42—431no—
403#107—861no—
404#107—861no—
405#106—861no—
406#106—861no—
407#106—861no—
408#106—861no—
409#106—861no—
410#106—861no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8C22×D4311yescharacteristic
417C4⋊C8C22×D4311yescharacteristic
418C4⋊C8C22×D4311yescharacteristic
419#103—21no—
420#103—861no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—861no—
425#102—861no—
426#102—861no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431C22⋊C8—21no—
432C22⋊C8—431no—
433C22⋊C8—431no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439C22⋊C8—861no—
440#97—861no—
441C4×C8—431no—
442C4×C8—861no—
443C4×C8—861no—
444C4×C8C22×D4311yescharacteristic
445C24—861no—
446#41—3442no—
447C2×Q8—21no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—431no—
454C2×D4—861no—
455C2×D4—862no—
456C2×D4—862no—
457C2×D4—1721no—
458C2×D4D4×D4311yescharacteristic
459C22×C4—21no—
460C22×C4—431no—
461C22×C4—431no—
462C22×C4—431no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—3441no—
468C22×C4—3441no—
469C22×C4—1721no—
470SD16—42no—
471SD16—1722no—
472D8—42no—
473D8—1722no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—81no—
478C2×C8—431no—
479C2×C8—431no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—3441no—
484C2×C8—3441no—
485C2×C8—3441no—
486C2×C8D4×D4311yescharacteristic
487C2×C8D4×D4311yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—431no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—1721no—
497C4⋊C4—1721no—
498C4⋊C4D4×D4311yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—861no—
501C22⋊C4—861no—
502C22⋊C4—861no—
503C22⋊C4—1721no—
504C22⋊C4—1721no—
505C22⋊C4—1721no—
506C42—431no—
507C42—431no—
508C42—431no—
509C42—1721no—
510C42C23×D4311yescharacteristic
511C23—21no—
512C23—41no—
513C23—431no—
514C23—864no—
515C23—861no—
516C23—3441no—
517C23—3441no—
518Q8—41no—
519Q8—41no—
520Q8—3441no—
521Q8—3441no—
522D4—21no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—81no—
528D4—432no—
529D4—864no—
530D4—861no—
531D4—3442no—
532D4#1306334412yes—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—431no—
538C2×C4—431no—
539C2×C4—431no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—3441no—
546C2×C4—3441no—
547C2×C4—3442no—
548C2×C4—3441no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4C2×D4×D4311yescharacteristic
555C2×C4C2×D4×D4311yescharacteristic
556C2×C4#41×D4311yescharacteristic
557C8—21no—
558C8—21no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—861no—
563C8—861no—
564C8—1721no—
565C8—1721no—
566C8—1721no—
567C22—22no—
568C22—41no—
569C22—41no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—861no—
574C22—861no—
575C22—861no—
576C22—862no—
577C22—3444no—
578C22—1721no—
579C22—1721no—
580C22#121×D4311yescharacteristic
581C4—21no—
582C4—41no—
583C4—81no—
584C4—861no—
585C4—861no—
586C4—861no—
587C4—3441no—
588C4—3441no—
589C4—1721no—
590C4#135×D4311yescharacteristic
591C4C2×#1306334411yescharacteristic
592C4#1458370611yescharacteristic
593C4#1458370911yescharacteristic
594C2—42no—
595C2—161no—
596C2—1721no—
597C2—1722no—
598C2#1914410511yescharacteristic
599C2#1914417411yescharacteristic
600C2#1914431811yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1681C2
socleC22×C43C2×#121
prime radical#19144685C2
hypercenter#1681D43
hypocenterC43#19394
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1681

Complements

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

NH ≅ G/Ntype
1. #19145726C2semidirect
3. #19144602C2semidirect
4. #19143616C2semidirect
5. #19134029C2semidirect
6. #19134003C2semidirect
7. #19134002C2semidirect
8. #19133995C2semidirect
9. #19133994C2semidirect
10. #19133969C2semidirect
11. #19133968C2semidirect
12. #19133374C2semidirect
13. #19133302C2semidirect
14. #19133254C2semidirect
15. C43×#1681C2semidirect
19. #14583304C22semidirect
20. #14583295C22semidirect
21. #14583245C22semidirect
51. #14582652C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582647C22semidirect
55. #14582647C22semidirect
56. #14582647C22semidirect
57. #14582647C22semidirect
58. #14582645C22semidirect
59. #14582643C22semidirect
60. C43×#486C22semidirect
64. C43×#335C22semidirect
65. C43×#332C22semidirect
66. C43×#331C22semidirect
299. #1681D43semidirect
322. #486C2×D43semidirect
356. #335C2×D43semidirect
364. #332C2×D43semidirect
366. #331C2×D43semidirect
367. C43#19394semidirect

Maximal subgroups

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

subgroupindex
#191457262
#191446852
#191446022
#191436162
#191340292
#191340032
#191340022
#191339952
#191339942
#191339692
#191339682
#191333742
#191333022
#191332542
C43×#16812
#1939443