Finite Group Databasebeta

← #25086087

Subgroups — #25086087

Order 11008.

668 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#19147504C211yesmaximal, characteristic, complemented
2Q8×#10621883C211yesmaximal, characteristic, complemented
3#19146416C211yesmaximal, characteristic
4D4×#10621884C211yesmaximal, characteristic
5#19134219C211yesmaximal, characteristic, complemented
6#19134070C211yesmaximal, characteristic, complemented
7#19134013C211yesmaximal, characteristic, complemented
8#19133992C211yesmaximal, characteristic, complemented
9#19133969C211yesmaximal, characteristic, complemented
10#19133799C211yesmaximal, characteristic, complemented
11#19133713C211yesmaximal, characteristic
12#19133675C211yesmaximal, characteristic, complemented
13#19133428C211yesmaximal, characteristic, complemented
14#19133410C211yesmaximal, characteristic, complemented
15C43×#1637C211yesmaximal, characteristic, complemented
16C22×#10621884—21no—
17Q8×Dic86C2211yescharacteristic, complemented
18#14583610C2211yescharacteristic
19D4×D172C2211yescharacteristic
20#14583307—21no—
21#14583302C2211yescharacteristic, complemented
22#14583295—21no—
23#14583295C2211yescharacteristic, complemented
24#14583273C2211yescharacteristic
25#14583272C2211yescharacteristic
26#14583247C2211yescharacteristic
27#14583219—21no—
28#14583204—21no—
29#14583190C2211yescharacteristic
30#14583189—21no—
31#14583189C2211yescharacteristic
32#14583181—21no—
33#14583181C2211yescharacteristic, complemented
34#14583178—21no—
35#14583130—21no—
36#14583129—21no—
37#14583101C2211yescharacteristic
38#14583100C2211yescharacteristic
39#14583099C2211yescharacteristic
40#14583051—21no—
41#14583049—21no—
42#14583038—21no—
43#14583026C2211yescharacteristic, complemented
44Q8×C43⋊C8C2211yescharacteristic, complemented
45#14583002—21no—
46C4×#10621884C2211yescharacteristic
47C4×#10621883—21no—
48C4×#10621883C2211yescharacteristic
49D4×C43⋊C8C2211yescharacteristic
50#14582964C2211yescharacteristic
51#102×D43—21no—
52#14582651C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582642C2211yescharacteristic
57#14582631C2211yescharacteristic, complemented
58#14582628C2211yescharacteristic
59#14582621C2211yescharacteristic, complemented
60D4×Q8×C43C2211yescharacteristic
61C43×#487C2211yescharacteristic, complemented
62C43×#477C2211yescharacteristic, complemented
63C43×#476C2211yescharacteristic
64C43×#332C2211yescharacteristic, complemented
65C43×Q8⋊C8C2211yescharacteristic, complemented
66C43×D4⋊C8C2211yescharacteristic
67C22×D172—21no—
68C2×D4×D43—21no—
69C2×#10621873—21no—
70C2×#10621873—41no—
71C2×#10621883D411yescharacteristic
72C2×#10621884—21no—
73C2×#10621884—21no—
74C2×#10621884—21no—
75C2×#10621884—21no—
76C2×#10621884—44no—
77C2×#10621884D411yescharacteristic
78C22×C43⋊C8—21no—
79C2×C8×D43—21no—
80#13063325—21no—
81#13063325C2311yescharacteristic
82#13063324—21no—
83#13063324—41no—
84#13063322C2311yescharacteristic
85#13063316—21no—
86#13063305—21no—
87#13063301—41no—
88#13063300—21no—
89#13063299—21no—
90#13063295—41no—
91Q8×Dic43—21no—
92C4×Dic86—21no—
93C4×Dic86C2311yescharacteristic
94C4×D172C2311yescharacteristic
95#13063287—21no—
96C4⋊C4×D43—21no—
97#13063258—21no—
98#13063258—21no—
99#13063257—21no—
100#13063256—21no—
101#13063256—21no—
102#13063256—21no—
103#13063256—21no—
104#13063256D411yescharacteristic
105#13063256D411yescharacteristic
106C4⋊(C43⋊C8)—21no—
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110#13063249—21no—
111#13063249D411yescharacteristic
112#13063248—21no—
113#13063248D411yescharacteristic
114#13063247—21no—
115#13063247—21no—
116#13063246—21no—
117#13063246D411yescharacteristic
118#13063245—21no—
119#13063245—21no—
120#13063245—21no—
121#13063245D411yescharacteristic
122C22⋊(C43⋊C8)—21no—
123(C2×D43)⋊C8—21no—
124#13063235—21no—
125C4×C43⋊C8—21no—
126C4×C43⋊C8C2311yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C22×Q8×C43—21no—
129C4⋊Q8×C43—21no—
130C4⋊Q8×C43C2311yescharacteristic
131C4⋊Q8×C43C2311yescharacteristic
132C22⋊Q8×C43—21no—
133C22⋊Q8×C43—41no—
134C4×Q8×C43C2311yescharacteristic
135C4×D4×C43—21no—
136C4×D4×C43C2311yescharacteristic
137#107×C43—21no—
138#106×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#103×C43—21no—
142#103×C43—41no—
143#102×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—41no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43—42no—
150C2×Q8×C43—81no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—41no—
155C2×C22⋊D43—41no—
156D4×D43—42no—
157D4×D43—81no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—41no—
162C2×D172—42no—
163C2×D172—81no—
164C2×D172C2×D411yescharacteristic
165C2×C4×D43—21no—
166C2×C4×D43—41no—
167C2×Dic86—21no—
168C2×Dic86—41no—
169C2×Dic86C2×D411yescharacteristic
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43C2×D411yescharacteristic
180C4⋊C4×C43C2×D411yescharacteristic
181C22⋊C4×C43—21no—
182C22⋊C4×C43—41no—
183C42×C43—21no—
184C42×C43C2411yescharacteristic
185#10621884—42no—
186#10621884—42no—
187#10621884—42no—
188#10621884—81no—
189#10621884SD1614yescomplemented
190#10621883—22no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—41no—
193(C2×D43)⋊C4—41no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—41no—
197C4⋊Dic43—41no—
198C4⋊Dic43C2×D411yescharacteristic
199C4⋊Dic43C2×D411yescharacteristic
200Dic43⋊C4—21no—
201Dic43⋊C4—41no—
202Dic43⋊C4—41no—
203C4×Dic43—21no—
204C4×Dic43—41no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—42no—
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212#10621873—81no—
213#10621873—82no—
214C8×D43—81no—
215C23×C43—21no—
216C22×D43—21no—
217C22×D43—41no—
218C22×D43—82no—
219C22×D43—82no—
220C22×D43—161no—
221Q8×C43—21no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—82no—
225Q8×C43—81no—
226Q8×C43C2×SD1612yes—
227D4×C43—21no—
228D4×C43#13712yes—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—82no—
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43H(5,𝔽2)11yescharacteristic
240C22⋊D43—82no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—41no—
245D172—21no—
246D172—41no—
247D172—41no—
248D172—41no—
249D172—41no—
250D172—81no—
251D172—82no—
252D172C2×SD1612yes—
253C4×D43—41no—
254C4×D43—41no—
255C4×D43—161no—
256Dic86—21no—
257Dic86—21no—
258Dic86—81no—
259Dic86—161no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43—41no—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268C43⋊C8C2×SD1612yes—
269#19765—431nomaximal, Sylow
270C22×C43—22no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43D4211yescharacteristic
274C2×D43—22no—
275C2×D43—41no—
276C2×D43—41no—
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—164no—
281C4×C43—22no—
282C4×C43—21no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43C22×SD1611yescharacteristic
288C4×C43C2×#13711yescharacteristic
289C4×C43#57711yescharacteristic
290C4×C43#57711yescharacteristic
291Dic43—41no—
292Dic43—41no—
293Dic43—41no—
294Dic43—81no—
295#3385—431no—
296Q8×SD16—431no—
297#3295—431no—
298D4×SD16—431no—
299#1714—431no—
300#1686—431no—
301#1678—431no—
302#1675—431no—
303#1671—431no—
304#1643—431no—
305#1637D4311yescharacteristic, complemented
306#1629—431no—
307#1623—431no—
308#1582—431no—
309SD16⋊C8—431no—
310C2×C43—42no—
311C2×C43#326611yescharacteristic
312C2×C43D4×SD1611yescharacteristic
313C2×C43#328811yescharacteristic
314D43—42no—
315D43—161no—
316C22×SD16—861no—
317Q82—431no—
318#554—431no—
319D4×Q8C2×D4311yescharacteristic
320D42—431no—
321#501—861no—
322#500—431no—
323#498—431no—
324#498—861no—
325#492—431no—
326#492—431no—
327#487C2×D4311yescharacteristic, complemented
328#486—431no—
329#481—861no—
330#479—861no—
331#477C2×D4311yescharacteristic, complemented
332#476—431no—
333#476—431no—
334#476—861no—
335#476C2×D4311yescharacteristic
336#475—431no—
337#475—861no—
338#474—861no—
339#465—861no—
340#465—861no—
341#461—431no—
342#460—431no—
343#460—431no—
344#450—861no—
345#450—861no—
346#448—861no—
347#446—431no—
348C8×Q8—431no—
349#440—861no—
350C4×SD16—431no—
351C4×SD16—431no—
352C4×SD16—861no—
353C8×D4—431no—
354C8×D4—431no—
355C2×#102—861no—
356#335—431no—
357#334—431no—
358#333—431no—
359#333—431no—
360#332C2×D4311yescharacteristic, complemented
361#331—431no—
362Q8⋊C8—431no—
363Q8⋊C8C2×D4311yescharacteristic, complemented
364D4⋊C8—431no—
365D4⋊C8C2×D4311yescharacteristic
366#322—431no—
367C43#1976511yescharacteristic, complemented, Sylow
368C22×Q8—21no—
369C22×D4—861no—
370C22×D4—861no—
371C2×SD16—431no—
372C2×SD16—431no—
373C2×SD16—861no—
374C2×SD16—861no—
375C2×SD16—861no—
376C2×SD16—861no—
377C2×SD16—861no—
378C2×SD16—1721no—
379C2×SD16—1724no—
380C22×C8—861no—
381C22×C8—861no—
382C4⋊Q8—21no—
383C4⋊Q8—431no—
384C4⋊Q8—861no—
385C4⋊Q8—861no—
386C4⋊Q8—1721no—
387C4⋊Q8C22×D4311yescharacteristic
388C4⋊Q8C22×D4311yescharacteristic
389#127—431no—
390#125—861no—
391C22⋊Q8—21no—
392C22⋊Q8—41no—
393C22⋊Q8—861no—
394C22⋊Q8—1721no—
395#121—861no—
396#121—861no—
397#120—1721no—
398C4×Q8—431no—
399C4×Q8—861no—
400C4×Q8—861no—
401C4×Q8C22×D4311yescharacteristic
402C4×D4—21no—
403C4×D4—431no—
404C4×D4—861no—
405C4×D4C22×D4311yescharacteristic
406C2×C4⋊C4—861no—
407#107—21no—
408#107—861no—
409#107—861no—
410#106—21no—
411#106—431no—
412#106—431no—
413#106—861no—
414#106—861no—
415#106—861no—
416#106—861no—
417#106—861no—
418C4⋊C8—431no—
419C4⋊C8—431no—
420C4⋊C8—861no—
421C4⋊C8—861no—
422C4⋊C8C22×D4311yescharacteristic
423C4⋊C8C22×D4311yescharacteristic
424#103—21no—
425#103—41no—
426#103—431no—
427#103—431no—
428#103—861no—
429#103—861no—
430#102—21no—
431#102—431no—
432#102—431no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439C22⋊C8—861no—
440C22⋊C8—861no—
441#97—861no—
442C4×C8—431no—
443C4×C8—431no—
444C4×C8—861no—
445C4×C8C22×D4311yescharacteristic
446C24—1721no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—41no—
450C2×Q8—42no—
451C2×Q8—81no—
452C2×Q8—431no—
453C2×Q8—861no—
454C2×Q8—1721no—
455C2×Q8D4×D4311yescharacteristic
456C2×D4—431no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—3441no—
461C2×D4—3441no—
462C2×D4—1721no—
463C2×D4—1722no—
464C2×D4—1721no—
465C2×D4—1722no—
466C2×D4D4×D4311yescharacteristic
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—861no—
470C22×C4—1721no—
471SD16—434no—
472SD16—862no—
473SD16—3442no—
474SD16—3441no—
475SD16—3441no—
476SD16—1722no—
477SD16—1722no—
478SD16—1722no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—431no—
483C2×C8—431no—
484C2×C8—431no—
485C2×C8—431no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—3441no—
489C2×C8—1722no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—41no—
496C4⋊C4—431no—
497C4⋊C4—431no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—1721no—
502C4⋊C4—1721no—
503C4⋊C4—1721no—
504C4⋊C4—1721no—
505C4⋊C4D4×D4311yescharacteristic
506C4⋊C4D4×D4311yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—861no—
510C22⋊C4—1721no—
511C22⋊C4—1721no—
512C42—21no—
513C42—861no—
514C42—1721no—
515C42C23×D4311yescharacteristic
516C23—21no—
517C23—861no—
518C23—3442no—
519C23—3442no—
520C23—1721no—
521C23—6881no—
522Q8—21no—
523Q8—41no—
524Q8—41no—
525Q8—82no—
526Q8—81no—
527Q8—861no—
528Q8—861no—
529Q8—3441no—
530Q8—6881no—
531Q8SD16×D4312yes—
532D4—21no—
533D4—432no—
534D4—861no—
535D4—3441no—
536D4—3442no—
537D4—3442no—
538D4—1721no—
539D4—1721no—
540D4—1721no—
541D4—1721no—
542D4#1306335712yes—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—82no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—6881no—
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4C2×D4×D4311yescharacteristic
560C2×C4#1306337011yescharacteristic
561C8—41no—
562C8—41no—
563C8—41no—
564C8—432no—
565C8—861no—
566C8—861no—
567C8—861no—
568C8—1721no—
569C8—1721no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—862no—
574C22—3441no—
575C22—3441no—
576C22—3441no—
577C22—1721no—
578C22—1721no—
579C22—6884no—
580C22#1458353111yescharacteristic
581C4—22no—
582C4—21no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—81no—
587C4—3441no—
588C4—1721no—
589C4—1721no—
590C4—1721no—
591C4C2×SD16×D4311yescharacteristic
592C4C2×#1306335711yescharacteristic
593C4#1458370811yescharacteristic
594C4#1458370911yescharacteristic
595C2—42no—
596C2—1722no—
597C2—6881no—
598C2#1914609811yescharacteristic
599C2#1914628911yescharacteristic
600C2#1914636311yescharacteristic
subgroupG/H
centerC22#14583531
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1637C2
socleC22×C43D42
prime radicalD4×D172C22
hypercenter#1637D43
hypocenterC43#19765
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1637

Complements

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

NH ≅ G/Ntype
1. #19147504C2semidirect
2. Q8×#10621883C2semidirect
5. #19134219C2semidirect
6. #19134070C2semidirect
7. #19134013C2semidirect
8. #19133992C2semidirect
9. #19133969C2semidirect
10. #19133799C2semidirect
12. #19133675C2semidirect
13. #19133428C2semidirect
14. #19133410C2semidirect
15. C43×#1637C2semidirect
17. Q8×Dic86C22semidirect
21. #14583302C22semidirect
23. #14583295C22semidirect
33. #14583181C22semidirect
43. #14583026C22semidirect
44. Q8×C43⋊C8C22semidirect
52. #14582651C22semidirect
53. #14582649C22semidirect
54. #14582648C22semidirect
55. #14582647C22semidirect
57. #14582631C22semidirect
59. #14582621C22semidirect
61. C43×#487C22semidirect
62. C43×#477C22semidirect
64. C43×#332C22semidirect
65. C43×Q8⋊C8C22semidirect
189. #10621884SD16semidirect
305. #1637D43semidirect
327. #487C2×D43semidirect
331. #477C2×D43semidirect
360. #332C2×D43semidirect
363. Q8⋊C8C2×D43semidirect
367. C43#19765semidirect

Maximal subgroups

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

subgroupindex
#191475042
Q8×#106218832
#191464162
D4×#106218842
#191342192
#191340702
#191340132
#191339922
#191339692
#191337992
#191337132
#191336752
#191334282
#191334102
C43×#16372
#1976543