Finite Group Databasebeta

← #25086090

Subgroups — #25086090

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#19147505C211yesmaximal, characteristic, complemented
2SD16×Dic86C211yesmaximal, characteristic, complemented
3D4×#10621883C211yesmaximal, characteristic
4#19134216C211yesmaximal, characteristic, complemented
5#19134065C211yesmaximal, characteristic, complemented
6#19134008C211yesmaximal, characteristic, complemented
7#19133992C211yesmaximal, characteristic, complemented
8#19133970C211yesmaximal, characteristic, complemented
9#19133802C211yesmaximal, characteristic, complemented
10#19133759C211yesmaximal, characteristic, complemented
11#19133711C211yesmaximal, characteristic
12#19133672C211yesmaximal, characteristic, complemented
13#19133432C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic, complemented
15C43×#3295C211yesmaximal, characteristic
16C22×#10621883—21no—
17Q8×Dic86C2211yescharacteristic, complemented
18D4×Dic86C2211yescharacteristic
19#14583309—21no—
20#14583302C2211yescharacteristic, complemented
21#14583297C2211yescharacteristic, complemented
22#14583296—21no—
23#14583271C2211yescharacteristic
24#14583271C2211yescharacteristic
25#14583249C2211yescharacteristic, complemented
26#14583203—21no—
27#14583191C2211yescharacteristic, complemented
28#14583189C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583187—21no—
31#14583184C2211yescharacteristic, complemented
32#14583182—21no—
33#14583179—21no—
34#14583126—21no—
35#14583104C2211yescharacteristic
36#14583096C2211yescharacteristic
37#14583050—21no—
38#14583037—21no—
39#14583030C2211yescharacteristic, complemented
40C8×Dic86C2211yescharacteristic, complemented
41#14582999—21no—
42SD16×Dic43—21no—
43C4×#10621883C2211yescharacteristic
44D4×C43⋊C8C2211yescharacteristic
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582647C2211yescharacteristic, complemented
49#14582644C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52#14582629C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic, complemented
56C43×#554C2211yescharacteristic
57D42×C43C2211yescharacteristic
58C43×#486C2211yescharacteristic
59C43×#481—21no—
60C43×#476C2211yescharacteristic
61C43×#465—21no—
62C43×#460C2211yescharacteristic
63C43×#450—21no—
64C4×SD16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C2×#102×C43—21no—
67C22×Dic86—21no—
68C2×#10621883—21no—
69C2×#10621883—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—41no—
73C2×#10621883—44no—
74C2×#10621883D411yescharacteristic
75C22×C43⋊C8—21no—
76#13063325—21no—
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063324—21no—
80#13063324—21no—
81#13063324—41no—
82#13063304—21no—
83#13063302—41no—
84Q8×Dic43—21no—
85C4×Dic86—21no—
86C4×Dic86C2311yescharacteristic
87D4×Dic43—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258—21no—
91#13063257—21no—
92#13063257—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256—21no—
96#13063256D411yescharacteristic
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101Dic43⋊C8—21no—
102#13063249—21no—
103#13063249—41no—
104#13063248—21no—
105#13063248—21no—
106#13063248D411yescharacteristic
107#13063246—21no—
108#13063246—21no—
109#13063246—21no—
110#13063246D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112#13063236—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C8×Dic43—21no—
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43D411yescharacteristic
120C22×C8×C43—21no—
121C4⋊Q8×C43C2311yescharacteristic
122#127×C43C2311yescharacteristic
123#125×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—41no—
126#121×C43—21no—
127#121×C43—21no—
128#120×C43—41no—
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133C2×C4⋊C4×C43—21no—
134#106×C43—21no—
135#106×C43D411yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43D411yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—41no—
152C2×D4×C43—41no—
153C2×D4×C43—42no—
154C2×D4×C43—42no—
155C2×D4×C43—81no—
156C2×D4×C43—81no—
157C2×D4×C43C2×D411yescharacteristic
158C2×D4×C43C2×D411yescharacteristic
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—41no—
162C22×Dic43—41no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—42no—
166C2×Dic86—41no—
167C2×Dic86—41no—
168C2×Dic86—81no—
169C2×Dic86C2×D411yescharacteristic
170SD16×C43—22no—
171SD16×C43—81no—
172C2×C8×C43—21no—
173C2×C8×C43—81no—
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43—41no—
181C4⋊C4×C43C2×D411yescharacteristic
182C4⋊C4×C43C2×D411yescharacteristic
183C4⋊C4×C43C2×D411yescharacteristic
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—41no—
187C22⋊C4×C43—41no—
188C42×C43—21no—
189C42×C43C2411yescharacteristic
190C22⋊Dic43—41no—
191#10621883—42no—
192#10621883—42no—
193#10621883—42no—
194#10621883—81no—
195#10621883—82no—
196#10621883SD1614yescomplemented
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
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—42no—
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—21no—
223Q8×C43—81no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—81no—
231D4×C43—82no—
232D4×C43—82no—
233D4×C43C2×SD1612yes—
234D4×C43#13712yes—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—161no—
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43H(5,𝔽2)11yescharacteristic
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—82no—
253Dic86—21no—
254Dic86—41no—
255Dic86—41no—
256Dic86—82no—
257Dic86—81no—
258Dic86—161no—
259Dic86C2×SD1612yes—
260C8×C43—21no—
261C8×C43—21no—
262C8×C43—41no—
263C43⋊C8—21no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268C43⋊C8C2×SD1612yes—
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—21no—
282C4×C43—41no—
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—22no—
292Dic43—41no—
293Dic43—81no—
294Dic43—81no—
295#3385—431no—
296Q8×SD16—431no—
297#3295D4311yescharacteristic
298D4×SD16—431no—
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—861no—
317Q82—431no—
318#554C2×D4311yescharacteristic
319D4×Q8—431no—
320D42C2×D4311yescharacteristic
321#501—861no—
322#500—431no—
323#498—431no—
324#498—861no—
325#492—431no—
326#492—431no—
327#487—431no—
328#486C2×D4311yescharacteristic
329#481—21no—
330#479—861no—
331#477—431no—
332#476—431no—
333#476—431no—
334#476—861no—
335#476C2×D4311yescharacteristic
336#475—431no—
337#475—861no—
338#474—861no—
339#465—21no—
340#465—861no—
341#461—431no—
342#460—431no—
343#460C2×D4311yescharacteristic
344#450—21no—
345#450—861no—
346#448—861no—
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—21no—
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—861no—
369C22×D4—21no—
370C22×D4—21no—
371C2×SD16—21no—
372C2×SD16—431no—
373C2×SD16—861no—
374C2×SD16—861no—
375C2×SD16—861no—
376C2×SD16—861no—
377C2×SD16—1721no—
378C2×SD16—1724no—
379C2×SD16C22⋊D4311yescharacteristic
380C22×C8—21no—
381C22×C8—861no—
382C4⋊Q8—431no—
383C4⋊Q8—431no—
384C4⋊Q8—861no—
385C4⋊Q8—861no—
386C4⋊Q8—861no—
387C4⋊Q8—1721no—
388C4⋊Q8C22×D4311yescharacteristic
389#127C22×D4311yescharacteristic
390#125—21no—
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—21no—
407#107—861no—
408#107—861no—
409#107—861no—
410#106—21no—
411#106—431no—
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—431no—
425#103—861no—
426#103—861no—
427#103—861no—
428#103—1721no—
429#103C22⋊D4311yescharacteristic
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—431no—
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—431no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×Q8—3441no—
452C2×Q8—1721no—
453C2×Q8—1721no—
454C2×Q8—1722no—
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—22no—
472SD16—81no—
473SD16—434no—
474SD16—3441no—
475SD16—3442no—
476SD16—1722no—
477SD16—1722no—
478SD16—1722no—
479C2×C8—21no—
480C2×C8—81no—
481C2×C8—431no—
482C2×C8—431no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—1722no—
488C2×C8C2×C22⋊D4311yescharacteristic
489C2×C8C2×C22⋊D4311yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—431no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
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—21no—
524Q8—81no—
525Q8—432no—
526Q8—861no—
527Q8—3441no—
528Q8—3442no—
529Q8—1721no—
530Q8—1721no—
531Q8—6881no—
532D4—21no—
533D4—21no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—81no—
539D4—82no—
540D4—82no—
541D4SD16×D4312yes—
542D4#1306335512yes—
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—161no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—3442no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4C22×C22⋊D4311yescharacteristic
560C2×C4#1306337011yescharacteristic
561C8—21no—
562C8—21no—
563C8—41no—
564C8—432no—
565C8—861no—
566C8—1721no—
567C8—1721no—
568C8—1721no—
569C8—1721no—
570C22—22no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—164no—
580C22D4×C22⋊D4311yescharacteristic
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—81no—
587C4—862no—
588C4—3441no—
589C4—3441no—
590C4—1721no—
591C4C2×SD16×D4311yescharacteristic
592C4C2×#1306335511yescharacteristic
593C4#1458370511yescharacteristic
594C4#1458371011yescharacteristic
595C2—42no—
596C2—42no—
597C2—161no—
598C2#1914610111yescharacteristic
599C2SD16×C22⋊D4311yescharacteristic
600C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3295C2
socleC22×C43D42
prime radicalD42×C43C22
hypercenter#3295D43
hypocenterC43#19765
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3295

Complements

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

NH ≅ G/Ntype
1. #19147505C2semidirect
2. SD16×Dic86C2semidirect
4. #19134216C2semidirect
5. #19134065C2semidirect
6. #19134008C2semidirect
7. #19133992C2semidirect
8. #19133970C2semidirect
9. #19133802C2semidirect
10. #19133759C2semidirect
12. #19133672C2semidirect
13. #19133432C2semidirect
14. #19133407C2semidirect
17. Q8×Dic86C22semidirect
20. #14583302C22semidirect
21. #14583297C22semidirect
25. #14583249C22semidirect
27. #14583191C22semidirect
31. #14583184C22semidirect
39. #14583030C22semidirect
40. C8×Dic86C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582648C22semidirect
48. #14582647C22semidirect
49. #14582644C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. #14582629C22semidirect
55. #14582621C22semidirect
196. #10621883SD16semidirect
367. C43#19765semidirect

Maximal subgroups

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

subgroupindex
#191475052
SD16×Dic862
D4×#106218832
#191342162
#191340652
#191340082
#191339922
#191339702
#191338022
#191337592
#191337112
#191336722
#191334322
#191334072
C43×#32952
#1976543