Finite Group Databasebeta

← #25080619

Subgroups — #25080619

Order 11008.

658 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145180C211yesmaximal, characteristic, complemented
2#19144393C211yesmaximal, characteristic
3#19144387C211yesmaximal, characteristic
4#436×D43C211yesmaximal, characteristic
5#19134171C211yesmaximal, characteristic, complemented
6#19134170C211yesmaximal, characteristic, complemented
7#19134167C211yesmaximal, characteristic, complemented
8#19134117C211yesmaximal, characteristic, complemented
9#19134116C211yesmaximal, characteristic, complemented
10#19134083C211yesmaximal, characteristic, complemented
11#19134082C211yesmaximal, characteristic, complemented
12#19133349C211yesmaximal, characteristic, complemented
13#19133284C211yesmaximal, characteristic, complemented
14#19133282C211yesmaximal, characteristic, complemented
15C43×#1703C211yesmaximal, characteristic, complemented
16C2×M16×D43—21no—
17#14583454C2211yescharacteristic
18#14583454C2211yescharacteristic
19C4×D4×D43C2211yescharacteristic
20#14583302C2211yescharacteristic, complemented
21#14583278C2211yescharacteristic, complemented
22#14583250C2211yescharacteristic, complemented
23#14583202—21no—
24#14583201—21no—
25#14583198—21no—
26#14583197—21no—
27#14583190C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583186C2211yescharacteristic
30#14583180C2211yescharacteristic
31#14583179C2211yescharacteristic
32#14583176C2211yescharacteristic
33#14583139—21no—
34#14583139—21no—
35#14582991—21no—
36#14582991—21no—
37#14582978C2211yescharacteristic
38#14582977C2211yescharacteristic
39#14582976C2211yescharacteristic
40#14582975—21no—
41#14582974—21no—
42#14582940—21no—
43#14582938—21no—
44#14582921C2211yescharacteristic
45#14582921C2211yescharacteristic
46C4⋊C8×D43C2211yescharacteristic
47#14582902—21no—
48#14582902—21no—
49C22⋊C8×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582650C2211yescharacteristic, complemented
52#14582649C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582647C2211yescharacteristic, complemented
57#14582646C2211yescharacteristic, complemented
58#14582645C2211yescharacteristic, complemented
59#14582644C2211yescharacteristic, complemented
60C43×#487C2211yescharacteristic, complemented
61C43×#476C2211yescharacteristic
62C43×#474C2211yescharacteristic
63C43×#436C2211yescharacteristic
64C43×#334C2211yescharacteristic, complemented
65C43×#333C2211yescharacteristic, complemented
66C43×#332C2211yescharacteristic, complemented
67C2×D4×D43D411yescharacteristic
68C22×C4×D43—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621877—21no—
72C2×#10621872—21no—
73C2×#10621872—21no—
74C2×#10621872—21no—
75C2×#10621872—21no—
76M16×D43—44no—
77C2×C8×D43—21no—
78C2×C8×D43D411yescharacteristic
79C2×C8×D43D411yescharacteristic
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063316—21no—
83#13063316—21no—
84#13063305—21no—
85#13063305—21no—
86#13063301—21no—
87#13063301—21no—
88Q8×Dic43—21no—
89Q8×Dic43—21no—
90#13063290—21no—
91#13063290—21no—
92C4×D172C2311yescharacteristic
93D4×Dic43D411yescharacteristic
94#13063287D411yescharacteristic
95C4×C22⋊D43—21no—
96(C22⋊D43)⋊C4—21no—
97#13063283—21no—
98#13063283—21no—
99C4⋊C4×D43D411yescharacteristic
100C22⋊C4×D43—21no—
101C42×D43C2311yescharacteristic
102#13063259—21no—
103#13063258—21no—
104#13063258—21no—
105#13063258—21no—
106#13063258—21no—
107#13063257—21no—
108#13063256—21no—
109#13063256—21no—
110C4⋊(C43⋊C8)C2311yescharacteristic
111C4⋊(C43⋊C8)C2311yescharacteristic
112C4⋊(C43⋊C8)C2311yescharacteristic
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115Dic43⋊C8—21no—
116#13063250—21no—
117#13063250—21no—
118#13063247—21no—
119#13063247—21no—
120#13063246—21no—
121#13063246—21no—
122#13063245—21no—
123#13063245—21no—
124C22⋊(C43⋊C8)—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C2×M16×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132C4⋊Q8×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#107×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C2×C22⋊D43—21no—
151C22×Dic43—21no—
152D4×D43—22no—
153D4×D43—22no—
154C2×D172C2×D411yescharacteristic
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43C2×D411yescharacteristic
161C2×C4×D43C2×D411yescharacteristic
162C2×C4×D43#4111yescharacteristic
163C2×Dic86—21no—
164C2×Dic86—21no—
165M16×C43—42no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43C2×D411yescharacteristic
176C22⋊C4×C43—21no—
177C42×C43C2411yescharacteristic
178C22⋊Dic43—21no—
179#10621885—42no—
180#10621885—42no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—41no—
184(C2×D43)⋊C4—41no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—41no—
190C4⋊Dic43—41no—
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195C4×Dic43—41no—
196C4×Dic43—41no—
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43#4111yescharacteristic
200#10621877—42no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206#10621872—42no—
207#10621872—42no—
208#10621872—42no—
209#10621872—42no—
210C8×D43—22no—
211C8×D43—41no—
212C8×D43—42no—
213C23×C43—21no—
214C22×D43—21no—
215C22×D43—42no—
216C22×D43—42no—
217C22×D43—42no—
218C22×D43#12111yescharacteristic
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—81no—
222D4×C43—21no—
223D4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C22⋊D43—42no—
233C2×Dic43—21no—
234C2×Dic43—42no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43#12111yescharacteristic
238C2×Dic43#12111yescharacteristic
239C2×Dic43#12111yescharacteristic
240D172—21no—
241D172—21no—
242C4×D43—21no—
243C4×D43—21no—
244C4×D43—41no—
245C4×D43—42no—
246C4×D43—42no—
247C4×D43—41no—
248C4×D43—41no—
249C4×D43#13712yes—
250C4×D43#13712yes—
251Dic86—41no—
252Dic86—41no—
253Dic86—81no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43—41no—
259C43⋊C8—21no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8AGL(1,ℤ/8)12yes—
264#19281—431nomaximal, Sylow
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43C2×#12111yescharacteristic
269C2×D43—21no—
270C2×D43—21no—
271C2×D43—41no—
272C2×D43—41no—
273C2×D43—41no—
274C2×D43—84no—
275C2×D43#47012yes—
276C4×C43—21no—
277C4×C43—41no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
281C4×C43C2×#13711yescharacteristic
282C4×C43C2×#13711yescharacteristic
283C4×C43#57511yescharacteristic
284Dic43—21no—
285Dic43—21no—
286Dic43—41no—
287Dic43—81no—
288Dic43—81no—
289Dic43#47012yes—
290#3170—431no—
291#3077—431no—
292#3077—431no—
293C2×#436—431no—
294#1703—431no—
295#1703—431no—
296#1703—431no—
297#1703D4311yescharacteristic, complemented
298#1695—431no—
299#1695—431no—
300#1689—431no—
301#1689—431no—
302#1566—431no—
303#1550—431no—
304#1550—431no—
305C2×C43—81no—
306C2×C43#303611yescharacteristic
307C2×C43C2×#47011yescharacteristic
308C2×C43#306711yescharacteristic
309D43—22no—
310D43—81no—
311C22×M16—861no—
312#533—431no—
313#533—431no—
314C2×C4×D4—431no—
315#500—431no—
316#494—431no—
317#487—431no—
318#487C2×D4311yescharacteristic, complemented
319#478—861no—
320#478—861no—
321#478—861no—
322#478—861no—
323#476—431no—
324#476—431no—
325#476—431no—
326#476C2×D4311yescharacteristic
327#474—431no—
328#474—431no—
329#474—431no—
330#474C2×D4311yescharacteristic
331#467—861no—
332#467—861no—
333C4×Q16—861no—
334C4×Q16—861no—
335#436—431no—
336#436—431no—
337#436—431no—
338#436—861no—
339#436—861no—
340#436C2×D4311yescharacteristic
341#428—861no—
342#428—861no—
343#423—431no—
344#423—431no—
345C2×C4⋊C8—431no—
346#418—861no—
347#418—861no—
348C2×C22⋊C8—861no—
349C2×C4×C8—431no—
350#334—431no—
351#334—431no—
352#334—431no—
353#334C2×D4311yescharacteristic, complemented
354#333—431no—
355#333—431no—
356#333—431no—
357#333C2×D4311yescharacteristic, complemented
358#332—431no—
359#332—431no—
360#332—431no—
361#332C2×D4311yescharacteristic, complemented
362C43#1928111yescharacteristic, complemented, Sylow
363C22×D4—431no—
364C23×C4—861no—
365C2×Q16—861no—
366C2×Q16—861no—
367C2×M16—21no—
368C2×M16—861no—
369C2×M16—861no—
370C2×M16—861no—
371C2×M16—861no—
372C2×M16—861no—
373C2×M16—1724no—
374C22×C8—431no—
375C22×C8—431no—
376C22×C8—861no—
377C4⋊Q8—431no—
378C4⋊Q8—431no—
379C4⋊Q8C22×D4311yescharacteristic
380C4⋊Q8C22×D4311yescharacteristic
381#125—861no—
382#125—861no—
383C22⋊Q8—861no—
384C22⋊Q8—861no—
385C22⋊Q8—861no—
386C22⋊Q8—861no—
387C4×Q8—861no—
388C4×Q8—861no—
389C4×Q8—861no—
390C4×Q8—861no—
391C4×D4—431no—
392C4×D4—431no—
393C4×D4—431no—
394C4×D4—861no—
395C4×D4—861no—
396C4×D4C22×D4311yescharacteristic
397#117—861no—
398#117—861no—
399C2×C4⋊C4—431no—
400C2×C22⋊C4—861no—
401C2×C42—431no—
402#107—21no—
403#107—861no—
404#107—861no—
405#107—861no—
406#107—861no—
407#107—861no—
408#106—21no—
409#106—861no—
410#106—861no—
411#106—861no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—861no—
416C4⋊C8—861no—
417C4⋊C8—861no—
418C4⋊C8C22×D4311yescharacteristic
419C4⋊C8C22×D4311yescharacteristic
420C4⋊C8C22×D4311yescharacteristic
421#103—21no—
422#103—21no—
423#103—861no—
424#103—861no—
425#102—21no—
426#102—21no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431#102—861no—
432#102—861no—
433C22⋊C8—21no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C4×C8—431no—
438C4×C8—431no—
439C4×C8—431no—
440C4×C8C22×D4311yescharacteristic
441C24—861no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×D4—431no—
447C2×D4—862no—
448C2×D4—862no—
449C2×D4—861no—
450C2×D4D4×D4311yescharacteristic
451C22×C4—21no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—1722no—
460C22×C4—1722no—
461Q16—1722no—
462Q16—1722no—
463M16—42no—
464M16—1722no—
465M16—1722no—
466M16—1722no—
467M16—1722no—
468M16—1722no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—431no—
473C2×C8—431no—
474C2×C8—862no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—1721no—
479C2×C8—1722no—
480C2×C8D4×D4311yescharacteristic
481C2×C8D4×D4311yescharacteristic
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—431no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—1721no—
493C4⋊C4—1721no—
494C4⋊C4—1721no—
495C4⋊C4—1721no—
496C4⋊C4D4×D4311yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—861no—
499C22⋊C4—861no—
500C22⋊C4—861no—
501C22⋊C4—1721no—
502C22⋊C4—1721no—
503C42—431no—
504C42—431no—
505C42—431no—
506C42—1721no—
507C42—1721no—
508C42C23×D4311yescharacteristic
509C23—21no—
510C23—431no—
511C23—861no—
512C23—1722no—
513C23—1722no—
514C23—1722no—
515Q8—41no—
516Q8—41no—
517Q8—81no—
518Q8—3441no—
519Q8—1721no—
520Q8—1721no—
521D4—21no—
522D4—21no—
523D4—861no—
524D4—861no—
525D4—1722no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—431no—
532C2×C4—432no—
533C2×C4—432no—
534C2×C4—431no—
535C2×C4—431no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—1721no—
540C2×C4—1722no—
541C2×C4—1722no—
542C2×C4—1722no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4C2×D4×D4311yescharacteristic
548C2×C4C2×D4×D4311yescharacteristic
549C2×C4#41×D4311yescharacteristic
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—432no—
556C8—861no—
557C8—1721no—
558C8—1721no—
559C8—1721no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—432no—
564C22—861no—
565C22—861no—
566C22—3444no—
567C22—1721no—
568C22—1721no—
569C22—1721no—
570C22#121×D4311yescharacteristic
571C4—21no—
572C4—41no—
573C4—81no—
574C4—81no—
575C4—432no—
576C4—861no—
577C4—861no—
578C4—3441no—
579C4—3441no—
580C4—1721no—
581C4AGL(1,ℤ/8)×D4311yescharacteristic
582C4#137×D4311yescharacteristic
583C4#137×D4311yescharacteristic
584C4#1458369611yescharacteristic
585C2—81no—
586C2—862no—
587C2—3441no—
588C2#1914405711yescharacteristic
589C2#470×D4311yescharacteristic
590C2#1914431011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1703C2
socleC22×C43C2×#121
prime radicalC2×D4×D43D4
hypercenter#1703D43
hypocenterC43#19281
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1703

Complements

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

NH ≅ G/Ntype
1. #19145180C2semidirect
5. #19134171C2semidirect
6. #19134170C2semidirect
7. #19134167C2semidirect
8. #19134117C2semidirect
9. #19134116C2semidirect
10. #19134083C2semidirect
11. #19134082C2semidirect
12. #19133349C2semidirect
13. #19133284C2semidirect
14. #19133282C2semidirect
15. C43×#1703C2semidirect
20. #14583302C22semidirect
21. #14583278C22semidirect
22. #14583250C22semidirect
51. #14582650C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582648C22semidirect
55. #14582647C22semidirect
56. #14582647C22semidirect
57. #14582646C22semidirect
58. #14582645C22semidirect
59. #14582644C22semidirect
60. C43×#487C22semidirect
64. C43×#334C22semidirect
65. C43×#333C22semidirect
66. C43×#332C22semidirect
297. #1703D43semidirect
318. #487C2×D43semidirect
353. #334C2×D43semidirect
357. #333C2×D43semidirect
361. #332C2×D43semidirect
362. C43#19281semidirect

Maximal subgroups

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

subgroupindex
#191451802
#191443932
#191443872
#436×D432
#191341712
#191341702
#191341672
#191341172
#191341162
#191340832
#191340822
#191333492
#191332842
#191332822
C43×#17032
#1928143