Finite Group Databasebeta

← #25079393

Subgroups — #25079393

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145136C211yesmaximal, characteristic, complemented
2#19144602C211yesmaximal, characteristic
3#476×D43C211yesmaximal, characteristic
4#19143331C211yesmaximal, characteristic
5#19134118C211yesmaximal, characteristic, complemented
6#19134116C211yesmaximal, characteristic, complemented
7#19134092C211yesmaximal, characteristic, complemented
8#19133995C211yesmaximal, characteristic, complemented
9#19133993C211yesmaximal, characteristic, complemented
10#19133969C211yesmaximal, characteristic, complemented
11#19133967C211yesmaximal, characteristic, complemented
12#19133346C211yesmaximal, characteristic, complemented
13#19133284C211yesmaximal, characteristic, complemented
14#19133274C211yesmaximal, characteristic, complemented
15C43×#1691C211yesmaximal, characteristic, complemented
16C2×M16×D43—21no—
17#14583454C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4×D4×D43C2211yescharacteristic
20#14583306—21no—
21#14583306—21no—
22#14583304C2211yescharacteristic, complemented
23#14583302C2211yescharacteristic, complemented
24#14583295C2211yescharacteristic, complemented
25#14583228—21no—
26#14583190C2211yescharacteristic
27#14583190C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583188—21no—
31#14583187—21no—
32#14583186C2211yescharacteristic
33#14583101C2211yescharacteristic
34#14583048—21no—
35SD16×Dic43—21no—
36#14582984—21no—
37#14582977C2211yescharacteristic
38#14582973—21no—
39#14582968—21no—
40C8×D172C2211yescharacteristic
41#14582964C2211yescharacteristic
42#14582951C2211yescharacteristic
43#14582938—21no—
44#14582938—21no—
45#106×D43—21no—
46#14582921C2211yescharacteristic
47C4⋊C8×D43C2211yescharacteristic
48#102×D43—21no—
49#14582861—21no—
50C4×#10621872C2211yescharacteristic
51#14582651C2211yescharacteristic, complemented
52#14582650C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582647C2211yescharacteristic, complemented
57#14582647C2211yescharacteristic, complemented
58#14582647C2211yescharacteristic, complemented
59#14582645C2211yescharacteristic, complemented
60C43×#498C2211yescharacteristic, complemented
61C43×#476C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C43×#436C2211yescharacteristic
64C43×#335C2211yescharacteristic, complemented
65C43×#333C2211yescharacteristic, complemented
66C43×#332C2211yescharacteristic, complemented
67C2×Q8×D43—21no—
68C2×D4×D43D411yescharacteristic
69C22×C4×D43—21no—
70C2×#10621884—21no—
71C2×#10621877—21no—
72C2×#10621872—21no—
73C2×#10621872D411yescharacteristic
74C2×#10621872D411yescharacteristic
75M16×D43—44no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063324—21no—
82#13063324—21no—
83#13063323—21no—
84#13063316—21no—
85#13063305—21no—
86#13063301—21no—
87Q8×Dic43—21no—
88#13063290—21no—
89C4×D172C2311yescharacteristic
90D4×Dic43D411yescharacteristic
91#13063287D411yescharacteristic
92C4×C22⋊D43—21no—
93(C22⋊D43)⋊C4—21no—
94#13063283—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43D411yescharacteristic
98C22⋊C4×D43—21no—
99C42×D43C2311yescharacteristic
100#13063259—21no—
101#13063259—21no—
102#13063258—21no—
103#13063258—21no—
104#13063257—21no—
105#13063257—21no—
106#13063256—21no—
107#13063256—21no—
108#13063256—21no—
109#13063256—21no—
110#13063256—21no—
111C4⋊(C43⋊C8)C2311yescharacteristic
112C4⋊(C43⋊C8)C2311yescharacteristic
113C4⋊(C43⋊C8)C2311yescharacteristic
114Dic43⋊C8—21no—
115Dic43⋊C8—21no—
116#13063249—21no—
117#13063247—21no—
118#13063247—21no—
119#13063246—21no—
120#13063246—21no—
121#13063245—21no—
122C22⋊(C43⋊C8)—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126#13063235D411yescharacteristic
127#13063235D411yescharacteristic
128C4×C43⋊C8C2311yescharacteristic
129C8×Dic43—21no—
130C2×SD16×C43—21no—
131C2×M16×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133C4⋊Q8×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#106×C43—21no—
136#106×C43—21no—
137#106×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#103×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—
152Q8×D43—82no—
153D4×D43—22no—
154D4×D43—41no—
155C2×D172C2×D411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—41no—
162C2×C4×D43C2×D411yescharacteristic
163C2×C4×D43C2×D411yescharacteristic
164C2×C4×D43#4111yescharacteristic
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—41no—
168SD16×C43—42no—
169M16×C43—42no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43C2×D411yescharacteristic
180C22⋊C4×C43—21no—
181C42×C43C2411yescharacteristic
182C22⋊Dic43—21no—
183#10621884—42no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—41no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—41no—
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197C4×Dic43—41no—
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43#4111yescharacteristic
201#10621877—42no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207#10621872—22no—
208#10621872—42no—
209#10621872SD1614yescomplemented
210C8×D43—42no—
211C8×D43—42no—
212C8×D43—42no—
213C23×C43—21no—
214C22×D43—21no—
215C22×D43—42no—
216C22×D43—42no—
217C22×D43—81no—
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#13712yes—
242C4×D43—21no—
243C4×D43—21no—
244C4×D43—41no—
245C4×D43—42no—
246C4×D43—41no—
247C4×D43—41no—
248C4×D43—42no—
249C4×D43—82no—
250C4×D43C2×SD1612yes—
251C4×D43#13712yes—
252Dic86—82no—
253Dic86—81no—
254Dic86—81no—
255C8×C43—21no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43—41no—
259C8×C43C2×SD1612yes—
260C43⋊C8—21no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8C2×SD1612yes—
265#19165—431nomaximal, Sylow
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43C2×#12111yescharacteristic
270C2×D43—21no—
271C2×D43—21no—
272C2×D43—22no—
273C2×D43—41no—
274C2×D43—41no—
275C2×D43—84no—
276C2×D43#46112yes—
277C4×C43—21no—
278C4×C43—41no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43C22×SD1611yescharacteristic
282C4×C43C2×#13711yescharacteristic
283C4×C43C2×#13711yescharacteristic
284C4×C43#57511yescharacteristic
285Dic43—21no—
286Dic43—21no—
287Dic43—41no—
288Dic43—81no—
289Dic43—81no—
290Dic43#46112yes—
291#3165—431no—
292#3101—431no—
293C2×#476—431no—
294D4×M16—431no—
295#1695—431no—
296#1695—431no—
297#1691—431no—
298#1691D4311yescharacteristic, complemented
299#1675—431no—
300#1675—431no—
301#1671—431no—
302#1671—431no—
303#1565—431no—
304#1550—431no—
305#1548—431no—
306C2×C43—81no—
307C2×C43C2×#46111yescharacteristic
308C2×C43#305611yescharacteristic
309C2×C43#306811yescharacteristic
310D43—22no—
311D43—42no—
312C22×M16—861no—
313#533—431no—
314C2×C4⋊Q8—431no—
315C2×C4×D4—431no—
316#501—861no—
317#501—861no—
318#500—431no—
319#500—431no—
320#498—431no—
321#498C2×D4311yescharacteristic, complemented
322#483—861no—
323#476—431no—
324#476—431no—
325#476—431no—
326#476—431no—
327#476—431no—
328#476—861no—
329#476—861no—
330#476C2×D4311yescharacteristic
331#461—431no—
332#461C2×D4311yescharacteristic
333#450—861no—
334C4×SD16—861no—
335C4×SD16—861no—
336#436—431no—
337#436C2×D4311yescharacteristic
338#435—861no—
339#435—861no—
340C8×D4—431no—
341C8×D4—431no—
342#431—431no—
343#428—861no—
344#428—861no—
345C2×#106—861no—
346#423—431no—
347C2×C4⋊C8—431no—
348C2×#102—861no—
349#407—861no—
350C4×M16—431no—
351#335—431no—
352#335C2×D4311yescharacteristic, complemented
353#334—431no—
354#334—431no—
355#333—431no—
356#333—431no—
357#333—431no—
358#333—431no—
359#333—431no—
360#333C2×D4311yescharacteristic, complemented
361#332—431no—
362#332C2×D4311yescharacteristic, complemented
363C43#1916511yescharacteristic, complemented, Sylow
364C22×Q8—861no—
365C22×D4—431no—
366C23×C4—861no—
367C2×SD16—21no—
368C2×SD16—861no—
369C2×M16—21no—
370C2×M16—431no—
371C2×M16—431no—
372C2×M16—861no—
373C2×M16—861no—
374C2×M16—1724no—
375C22×C8—861no—
376C22×C8—861no—
377C22×C8—861no—
378C4⋊Q8—431no—
379C4⋊Q8—431no—
380C4⋊Q8—861no—
381C4⋊Q8—861no—
382C4⋊Q8—861no—
383C4⋊Q8C22×D4311yescharacteristic
384C4⋊Q8C22×D4311yescharacteristic
385#125—861no—
386C22⋊Q8—861no—
387C22⋊Q8—861no—
388C4×Q8—861no—
389C4×Q8—861no—
390C4×D4—431no—
391C4×D4—431no—
392C4×D4—431no—
393C4×D4—861no—
394C4×D4—861no—
395C4×D4C22×D4311yescharacteristic
396#117—861no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C42—431no—
402#107—861no—
403#107—861no—
404#107—861no—
405#107—861no—
406#106—21no—
407#106—21no—
408#106—21no—
409#106—861no—
410#106—861no—
411#106—861no—
412#106—861no—
413#106—861no—
414#106—861no—
415#106—861no—
416C4⋊C8—431no—
417C4⋊C8—431no—
418C4⋊C8—431no—
419C4⋊C8—861no—
420C4⋊C8—861no—
421C4⋊C8C22×D4311yescharacteristic
422C4⋊C8C22×D4311yescharacteristic
423C4⋊C8C22×D4311yescharacteristic
424#103—21no—
425#103—861no—
426#102—21no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431#102—861no—
432C22⋊C8—21no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437#97—431no—
438#97—431no—
439C4×C8—431no—
440C4×C8—861no—
441C4×C8C22×D4311yescharacteristic
442C24—861no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8—3442no—
448C2×Q8—1721no—
449C2×D4—431no—
450C2×D4—861no—
451C2×D4—862no—
452C2×D4—1721no—
453C2×D4D4×D4311yescharacteristic
454C22×C4—21no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—1722no—
463C22×C4—1722no—
464C22×C4—1721no—
465SD16—42no—
466SD16—1722no—
467M16—42no—
468M16—434no—
469M16—862no—
470M16—1722no—
471M16—1722no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—431no—
476C2×C8—431no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—1722no—
481C2×C8—1722no—
482C2×C8—1722no—
483C2×C8D4×D4311yescharacteristic
484C2×C8D4×D4311yescharacteristic
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—431no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—1721no—
496C4⋊C4—1721no—
497C4⋊C4—1721no—
498C4⋊C4—1721no—
499C4⋊C4D4×D4311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—861no—
502C22⋊C4—861no—
503C22⋊C4—861no—
504C22⋊C4—1721no—
505C42—431no—
506C42—431no—
507C42—431no—
508C42—1721no—
509C42C23×D4311yescharacteristic
510C23—21no—
511C23—431no—
512C23—861no—
513C23—3441no—
514C23—1722no—
515C23—1722no—
516Q8—41no—
517Q8—41no—
518Q8—81no—
519Q8—3441no—
520Q8—3441no—
521Q8—3442no—
522D4—21no—
523D4—21no—
524D4—432no—
525D4—861no—
526D4—1722no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—431no—
533C2×C4—432no—
534C2×C4—432no—
535C2×C4—431no—
536C2×C4—431no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—3442no—
541C2×C4—1721no—
542C2×C4—1722no—
543C2×C4—1722no—
544C2×C4—1722no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4C2×D4×D4311yescharacteristic
550C2×C4C2×D4×D4311yescharacteristic
551C2×C4#41×D4311yescharacteristic
552C8—21no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—432no—
557C8—861no—
558C8—1721no—
559C8—1721no—
560C8—1721no—
561C8SD16×D4312yes—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—432no—
566C22—861no—
567C22—861no—
568C22—862no—
569C22—3444no—
570C22—1721no—
571C22—1721no—
572C22#121×D4311yescharacteristic
573C4—21no—
574C4—41no—
575C4—81no—
576C4—81no—
577C4—432no—
578C4—861no—
579C4—861no—
580C4—3441no—
581C4—3441no—
582C4—1721no—
583C4C2×SD16×D4311yescharacteristic
584C4#137×D4311yescharacteristic
585C4#137×D4311yescharacteristic
586C4#1458369511yescharacteristic
587C2—81no—
588C2—862no—
589C2—1722no—
590C2#461×D4311yescharacteristic
591C2#1914422011yescharacteristic
592C2#1914431811yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1691C2
socleC22×C43C2×#121
prime radicalC2×D4×D43D4
hypercenter#1691D43
hypocenterC43#19165
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1691

Complements

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

NH ≅ G/Ntype
1. #19145136C2semidirect
5. #19134118C2semidirect
6. #19134116C2semidirect
7. #19134092C2semidirect
8. #19133995C2semidirect
9. #19133993C2semidirect
10. #19133969C2semidirect
11. #19133967C2semidirect
12. #19133346C2semidirect
13. #19133284C2semidirect
14. #19133274C2semidirect
15. C43×#1691C2semidirect
22. #14583304C22semidirect
23. #14583302C22semidirect
24. #14583295C22semidirect
51. #14582651C22semidirect
52. #14582650C22semidirect
53. #14582649C22semidirect
54. #14582648C22semidirect
55. #14582647C22semidirect
56. #14582647C22semidirect
57. #14582647C22semidirect
58. #14582647C22semidirect
59. #14582645C22semidirect
60. C43×#498C22semidirect
64. C43×#335C22semidirect
65. C43×#333C22semidirect
66. C43×#332C22semidirect
209. #10621872SD16semidirect
298. #1691D43semidirect
321. #498C2×D43semidirect
352. #335C2×D43semidirect
360. #333C2×D43semidirect
362. #332C2×D43semidirect
363. C43#19165semidirect

Maximal subgroups

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

subgroupindex
#191451362
#191446022
#476×D432
#191433312
#191341182
#191341162
#191340922
#191339952
#191339932
#191339692
#191339672
#191333462
#191332842
#191332742
C43×#16912
#1916543