Finite Group Databasebeta

← #25086094

Subgroups — #25086094

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#19147503C211yesmaximal, characteristic, complemented
2Q8×#10621883C211yesmaximal, characteristic, complemented
3#19146419C211yesmaximal, characteristic
4#19134214C211yesmaximal, characteristic, complemented
5#19134064C211yesmaximal, characteristic, complemented
6#19134009C211yesmaximal, characteristic, complemented
7#19133994C211yesmaximal, characteristic, complemented
8#19133968C211yesmaximal, characteristic, complemented
9#19133800C211yesmaximal, characteristic, complemented
10#19133760C211yesmaximal, characteristic, complemented
11#19133711C211yesmaximal, characteristic
12#19133672C211yesmaximal, characteristic, complemented
13#19133431C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15D4×SD16×C43C211yesmaximal, characteristic
16Q8×Dic86C2211yescharacteristic, complemented
17#14583606C2211yescharacteristic
18#14583306—21no—
19#14583304C2211yescharacteristic, complemented
20#14583295—21no—
21#14583295C2211yescharacteristic, complemented
22#14583271C2211yescharacteristic
23#14583251C2211yescharacteristic, complemented
24#14583245C2211yescharacteristic
25#14583215—21no—
26#14583208—21no—
27#14583194C2211yescharacteristic, complemented
28#14583189—21no—
29#14583189C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583189C2211yescharacteristic
32#14583181—21no—
33#14583181C2211yescharacteristic, complemented
34#14583177—21no—
35#14583126—21no—
36#14583096C2211yescharacteristic
37#14583050—21no—
38#14583029C2211yescharacteristic, complemented
39Q8×C43⋊C8C2211yescharacteristic, complemented
40#14583000—21no—
41C4×#10621883—21no—
42C4×#10621883C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063246—21no—
45#14582652C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, complemented
48#14582647C2211yescharacteristic, complemented
49#14582645C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52#14582629C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582620C2211yescharacteristic, complemented
56C22×SD16×C43—21no—
57D4×Q8×C43C2211yescharacteristic
58D42×C43C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#465—21no—
61C43×#461C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C43×#450—21no—
64C43×#448—21no—
65C4×SD16×C43C2211yescharacteristic
66C8×D4×C43C2211yescharacteristic
67C2×#10621883—21no—
68C2×#10621883—41no—
69C2×#10621883D411yescharacteristic
70C22×C43⋊C8—21no—
71#13063325—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063324—21no—
75#13063324—41no—
76#13063316—21no—
77#13063304—21no—
78#13063302—41no—
79Q8×Dic43—21no—
80C4×Dic86—21no—
81C4×Dic86C2311yescharacteristic
82D4×Dic43—21no—
83C2×C4⋊Dic43—21no—
84#13063259—21no—
85#13063259—21no—
86#13063258—21no—
87#13063256—21no—
88#13063256—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256D411yescharacteristic
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98Dic43⋊C8—21no—
99#13063249—21no—
100#13063248—21no—
101#13063248—41no—
102#13063248D411yescharacteristic
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111#13063235—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C22×Q8×C43—21no—
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43—21no—
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×SD16×C43—44no—
123C2×SD16×C43D411yescharacteristic
124C22×C8×C43—21no—
125C4⋊Q8×C43—21no—
126C4⋊Q8×C43C2311yescharacteristic
127#127×C43C2311yescharacteristic
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43—41no—
130#121×C43—21no—
131#121×C43—21no—
132#120×C43—41no—
133C4×Q8×C43C2311yescharacteristic
134C4×D4×C43—21no—
135C4×D4×C43C2311yescharacteristic
136C4×D4×C43C2311yescharacteristic
137#106×C43D411yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#102×C43—21no—
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146C2×Q8×C43—21no—
147C2×Q8×C43—41no—
148C2×Q8×C43—42no—
149C2×Q8×C43—81no—
150C2×Q8×C43C2×D411yescharacteristic
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—41no—
155C2×D4×C43—41no—
156C2×D4×C43—42no—
157C2×D4×C43—42no—
158C2×D4×C43—81no—
159C2×D4×C43—81no—
160C2×D4×C43C2×D411yescharacteristic
161C2×D4×C43C2×D411yescharacteristic
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—41no—
165C22×Dic43—41no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—41no—
169C2×Dic86C2×D411yescharacteristic
170SD16×C43—42no—
171SD16×C43—42no—
172SD16×C43—42no—
173SD16×C43—81no—
174SD16×C43SD1614yescomplemented
175C2×C8×C43—21no—
176C2×C8×C43—42no—
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43C2×D411yescharacteristic
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C22⋊C4×C43—21no—
187C22⋊C4×C43—21no—
188C22⋊C4×C43—41no—
189C22⋊C4×C43—41no—
190C42×C43—21no—
191C42×C43C2411yescharacteristic
192C22⋊Dic43—41no—
193#10621883—22no—
194#10621883—81no—
195#10621883—82no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—41no—
201C4⋊Dic43—41no—
202C4⋊Dic43C2×D411yescharacteristic
203Dic43⋊C4—21no—
204Dic43⋊C4—41no—
205Dic43⋊C4—41no—
206C4×Dic43—21no—
207C4×Dic43—41no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—81no—
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—41no—
218C23×C43—82no—
219C23×C43—82no—
220C23×C43—161no—
221Q8×C43—21no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—82no—
225Q8×C43C2×SD1612yes—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—81no—
233D4×C43—82no—
234D4×C43—82no—
235D4×C43C2×SD1612yes—
236D4×C43#13712yes—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—82no—
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—161no—
255Dic86—21no—
256Dic86—21no—
257Dic86—81no—
258Dic86—81no—
259Dic86—161no—
260C8×C43—21no—
261C8×C43—41no—
262C8×C43C2×SD1612yes—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269#19765—431nomaximal, Sylow
270C22×C43—22no—
271C22×C43—22no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—164no—
280C22×C43D4211yescharacteristic
281C4×C43—22no—
282C4×C43—21no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—81no—
287C4×C43C22×SD1611yescharacteristic
288C4×C43C2×#13711yescharacteristic
289C4×C43#57711yescharacteristic
290C4×C43#57711yescharacteristic
291Dic43—41no—
292Dic43—41no—
293Dic43—81no—
294Dic43—81no—
295#3385—431no—
296Q8×SD16—431no—
297#3295—431no—
298D4×SD16D4311yescharacteristic
299#1714—431no—
300#1686—431no—
301#1678—431no—
302#1675—431no—
303#1671—431no—
304#1643—431no—
305#1637—431no—
306#1629—431no—
307#1623—431no—
308#1582—431no—
309SD16⋊C8—431no—
310C2×C43—42no—
311C2×C43—42no—
312C2×C43—161no—
313C2×C43#326611yescharacteristic
314C2×C43D4×SD1611yescharacteristic
315C2×C43#328811yescharacteristic
316C22×SD16—21no—
317Q82—431no—
318#554—431no—
319D4×Q8C2×D4311yescharacteristic
320D42C2×D4311yescharacteristic
321#501—861no—
322#500—431no—
323#498—431no—
324#498—861no—
325#492—431no—
326#492C2×D4311yescharacteristic
327#487—431no—
328#486—431no—
329#481—861no—
330#479—861no—
331#477—431no—
332#476—431no—
333#476—431no—
334#476—431no—
335#476—861no—
336#475—431no—
337#475—861no—
338#474—861no—
339#465—21no—
340#465—861no—
341#461C2×D4311yescharacteristic
342#460—431no—
343#460C2×D4311yescharacteristic
344#450—21no—
345#450—861no—
346#448—21no—
347#446—431no—
348C8×Q8—431no—
349#440—861no—
350C4×SD16—431no—
351C4×SD16—861no—
352C4×SD16C2×D4311yescharacteristic
353C8×D4—431no—
354C8×D4C2×D4311yescharacteristic
355C2×#102—861no—
356#335—431no—
357#334—431no—
358#333—431no—
359#333—431no—
360#332—431no—
361#331—431no—
362Q8⋊C8—431no—
363Q8⋊C8—431no—
364D4⋊C8—431no—
365D4⋊C8—431no—
366#322—431no—
367C43#1976511yescharacteristic, complemented, Sylow
368C22×Q8—21no—
369C22×D4—21no—
370C22×D4—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—44no—
376C2×SD16—431no—
377C2×SD16—861no—
378C2×SD16—1721no—
379C2×SD16C22⋊D4311yescharacteristic
380C22×C8—21no—
381C22×C8—861no—
382C4⋊Q8—21no—
383C4⋊Q8—431no—
384C4⋊Q8—431no—
385C4⋊Q8—861no—
386C4⋊Q8—861no—
387C4⋊Q8—1721no—
388C4⋊Q8C22×D4311yescharacteristic
389#127C22×D4311yescharacteristic
390#125—861no—
391C22⋊Q8—21no—
392C22⋊Q8—41no—
393C22⋊Q8—861no—
394C22⋊Q8—1721no—
395#121—21no—
396#121—21no—
397#120—41no—
398C4×Q8—431no—
399C4×Q8—861no—
400C4×Q8—861no—
401C4×Q8C22×D4311yescharacteristic
402C4×D4—21no—
403C4×D4—861no—
404C4×D4C22×D4311yescharacteristic
405C4×D4C22×D4311yescharacteristic
406C2×C4⋊C4—861no—
407#107—861no—
408#107—861no—
409#107—861no—
410#106—431no—
411#106—861no—
412#106—861no—
413#106—861no—
414#106—861no—
415#106—861no—
416#106—861no—
417#106C22⋊D4311yescharacteristic
418C4⋊C8—431no—
419C4⋊C8—431no—
420C4⋊C8—431no—
421C4⋊C8—861no—
422C4⋊C8—861no—
423C4⋊C8C22×D4311yescharacteristic
424#103—21no—
425#103—431no—
426#103—861no—
427#103—861no—
428#103—1721no—
429#103C22⋊D4311yescharacteristic
430#102—21no—
431#102—431no—
432#102—861no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102C22⋊D4311yescharacteristic
439C22⋊C8—21no—
440C22⋊C8—861no—
441#97—861no—
442C4×C8—431no—
443C4×C8—431no—
444C4×C8—861no—
445C4×C8C22×D4311yescharacteristic
446C24—41no—
447C2×Q8—21no—
448C2×Q8—41no—
449C2×Q8—42no—
450C2×Q8—81no—
451C2×Q8—431no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—1721no—
455C2×Q8C2×C22⋊D4311yescharacteristic
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—81no—
464C2×D4—81no—
465C2×D4D4×D4311yescharacteristic
466C2×D4C2×C22⋊D4311yescharacteristic
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—41no—
470C22×C4—1721no—
471SD16—42no—
472SD16—42no—
473SD16—42no—
474SD16—81no—
475SD16—862no—
476SD16—3441no—
477SD16—3442no—
478SD16#1062188314yescomplemented
479C2×C8—21no—
480C2×C8—42no—
481C2×C8—431no—
482C2×C8—431no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—3441no—
488C2×C8C2×C22⋊D4311yescharacteristic
489C2×C8C2×C22⋊D4311yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—41no—
494C4⋊C4—431no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—1721no—
501C4⋊C4—1721no—
502C4⋊C4—1721no—
503C4⋊C4—1721no—
504C4⋊C4D4×D4311yescharacteristic
505C4⋊C4C2×C22⋊D4311yescharacteristic
506C4⋊C4C2×C22⋊D4311yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—1721no—
512C42—21no—
513C42—861no—
514C42—1721no—
515C42C23×D4311yescharacteristic
516C23—21no—
517C23—21no—
518C23—41no—
519C23—82no—
520C23—82no—
521C23—161no—
522Q8—21no—
523Q8—41no—
524Q8—41no—
525Q8—82no—
526Q8—861no—
527Q8—861no—
528Q8—3441no—
529Q8—3441no—
530Q8—6881no—
531Q8C2×#1062188312yes—
532D4—21no—
533D4—21no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—81no—
539D4—82no—
540D4—82no—
541D4C2×#1062188312yes—
542D4#1306335412yes—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—82no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—6881no—
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4C22×C22⋊D4311yescharacteristic
560C2×C4#1306337011yescharacteristic
561C8—21no—
562C8—41no—
563C8—861no—
564C8—861no—
565C8—1721no—
566C8—1721no—
567C8—1721no—
568C8—1721no—
569C8C2×#1062188312yes—
570C22—22no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—164no—
580C22D4×C22⋊D4311yescharacteristic
581C4—22no—
582C4—21no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—81no—
587C4—3441no—
588C4—3441no—
589C4—1721no—
590C4—1721no—
591C4C22×#1062188311yescharacteristic
592C4C2×#1306335411yescharacteristic
593C4#1458370511yescharacteristic
594C4#1458371011yescharacteristic
595C2—42no—
596C2—42no—
597C2—161no—
598C2#1914610511yescharacteristic
599C2D4×#1062188311yescharacteristic
600C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingD4×SD16×C43C2
socleC22×C43D42
prime radicalD42×C43C22
hypercenterD4×SD16D43
hypocenterC43#19765
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ D4×SD16

Complements

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

NH ≅ G/Ntype
1. #19147503C2semidirect
2. Q8×#10621883C2semidirect
4. #19134214C2semidirect
5. #19134064C2semidirect
6. #19134009C2semidirect
7. #19133994C2semidirect
8. #19133968C2semidirect
9. #19133800C2semidirect
10. #19133760C2semidirect
12. #19133672C2semidirect
13. #19133431C2semidirect
14. SD16⋊(C43⋊C8)C2semidirect
16. Q8×Dic86C22semidirect
19. #14583304C22semidirect
21. #14583295C22semidirect
23. #14583251C22semidirect
27. #14583194C22semidirect
33. #14583181C22semidirect
38. #14583029C22semidirect
39. Q8×C43⋊C8C22semidirect
45. #14582652C22semidirect
46. #14582649C22semidirect
47. #14582647C22semidirect
48. #14582647C22semidirect
49. #14582645C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. #14582629C22semidirect
55. #14582620C22semidirect
174. SD16×C43SD16semidirect
367. C43#19765semidirect
478. SD16#10621883semidirect

Maximal subgroups

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

subgroupindex
#191475032
Q8×#106218832
#191464192
#191342142
#191340642
#191340092
#191339942
#191339682
#191338002
#191337602
#191337112
#191336722
#191334312
SD16⋊(C43⋊C8)2
D4×SD16×C432
#1976543