Finite Group Databasebeta

← #25086139

Subgroups — #25086139

Order 11008.

642 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#19147503C211yesmaximal, characteristic, complemented
2#19147262C211yesmaximal, characteristic, complemented
3#19146952C211yesmaximal, characteristic, complemented
4#19134214C211yesmaximal, characteristic, complemented
5#19134064C211yesmaximal, characteristic, complemented
6#19134002C211yesmaximal, characteristic, complemented
7#19133994C211yesmaximal, characteristic, complemented
8#19133975C211yesmaximal, characteristic, complemented
9#19133814C211yesmaximal, characteristic, complemented
10#19133746C211yesmaximal, characteristic, complemented
11#19133722C211yesmaximal, characteristic, complemented
12#19133665C211yesmaximal, characteristic, complemented
13#19133431C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C43×#3284C211yesmaximal, characteristic
16Q8×Dic86C2211yescharacteristic
17#14583606C2211yescharacteristic
18#14583306—21no—
19#14583304C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583271C2211yescharacteristic
22#14583251C2211yescharacteristic
23#14583245—21no—
24#14583245C2211yescharacteristic
25#14583229—21no—
26#14583215—21no—
27#14583208—21no—
28#14583194C2211yescharacteristic
29#14583189—21no—
30#14583189C2211yescharacteristic
31#14583189C2211yescharacteristic
32#14583189C2211yescharacteristic
33#14583181C2211yescharacteristic
34#14583177—21no—
35#14583126—21no—
36#14583096—21no—
37#14583096C2211yescharacteristic
38#14583029C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40#14583000—21no—
41C4×#10621883—21no—
42C4×#10621883C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063256—21no—
45#14582652C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52#14582629C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582620C2211yescharacteristic
56C2×#135×C43—21no—
57C43×#550C2211yescharacteristic
58C43×#547C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#465—21no—
61C43×#462C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#452—21no—
64C43×#449—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
115C2×#41×C43—21no—
116C2×#41×C43—21no—
117#135×C43—44no—
118C2×Q16×C43—21no—
119C2×SD16×C43—21no—
120C2×SD16×C43—21no—
121C2×SD16×C43D411yescharacteristic
122C2×D8×C43—21no—
123C22×C8×C43—21no—
124C4⋊Q8×C43C2311yescharacteristic
125#127×C43—21no—
126#127×C43C2311yescharacteristic
127#123×C43—41no—
128C22⋊Q8×C43—21no—
129#121×C43—21no—
130#121×C43—21no—
131#121×C43—41no—
132C4×Q8×C43C2311yescharacteristic
133C4×D4×C43—21no—
134C4×D4×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136C2×C4⋊C4×C43—21no—
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
145#41×C43—42no—
146#41×C43—42no—
147#41×C43—81no—
148#41×C43—81no—
149C2×Q8×C43—21no—
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—41no—
157C2×D4×C43C2×D411yescharacteristic
158C2×D4×C43C2×D411yescharacteristic
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—41no—
162C22×C4×C43—41no—
163C22×Dic43—41no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—41no—
167C2×Dic86C2×D411yescharacteristic
168Q16×C43—42no—
169SD16×C43—42no—
170SD16×C43—81no—
171SD16×C43SD1614yescomplemented
172D8×C43—42no—
173C2×C8×C43—21no—
174C2×C8×C43—42no—
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
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—41no—
192#10621883—42no—
193#10621883—82no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—41no—
199C4⋊Dic43—41no—
200C4⋊Dic43C2×D411yescharacteristic
201Dic43⋊C4—21no—
202Dic43⋊C4—41no—
203Dic43⋊C4—41no—
204C4×Dic43—21no—
205C4×Dic43—41no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—42no—
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—41no—
216Q8×C43—21no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43C2×SD1612yes—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—82no—
228D4×C43—81no—
229D4×C43—82no—
230D4×C43—161no—
231D4×C43C2×SD1612yes—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—82no—
242C2×C4×C43—82no—
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—161no—
251Dic86—21no—
252Dic86—21no—
253Dic86—81no—
254Dic86—81no—
255Dic86—161no—
256C8×C43—21no—
257C8×C43—41no—
258C8×C43C2×SD1612yes—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265#19768—431nomaximal, Sylow
266C22×C43—22no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43D4211yescharacteristic
276C4×C43—22no—
277C4×C43—21no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—81no—
282C4×C43C22×SD1611yescharacteristic
283C4×C43#57511yescharacteristic
284C4×C43#57711yescharacteristic
285C4×C43#57811yescharacteristic
286Dic43—41no—
287Dic43—41no—
288Dic43—81no—
289Dic43—81no—
290#3385—431no—
291#3362—431no—
292#3335—431no—
293#3284D4311yescharacteristic
294#1714—431no—
295#1686—431no—
296#1677—431no—
297#1675—431no—
298#1672—431no—
299#1645—431no—
300#1635—431no—
301#1631—431no—
302#1622—431no—
303#1582—431no—
304SD16⋊C8—431no—
305C2×C43—42no—
306C2×C43—81no—
307C2×C43—161no—
308C2×C43#326911yescharacteristic
309C2×C43D4×SD1611yescharacteristic
310C2×C43#328811yescharacteristic
311C2×#135—21no—
312Q82—431no—
313#554—431no—
314#550C2×D4311yescharacteristic
315#547C2×D4311yescharacteristic
316#501—861no—
317#500—431no—
318#498—431no—
319#492—431no—
320#492C2×D4311yescharacteristic
321#487—431no—
322#486—431no—
323#486—861no—
324#483—861no—
325#481—861no—
326#479—861no—
327#477—431no—
328#476—431no—
329#476—431no—
330#476—431no—
331#476—861no—
332#475—431no—
333#474—861no—
334#465—21no—
335#465—861no—
336#462C2×D4311yescharacteristic
337#460—431no—
338#460—861no—
339#459C2×D4311yescharacteristic
340#452—21no—
341#449—21no—
342#446—431no—
343C8×Q8—431no—
344#440—861no—
345C4×SD16—431no—
346C4×SD16—861no—
347C4×SD16C2×D4311yescharacteristic
348C8×D4—431no—
349C8×D4C2×D4311yescharacteristic
350C2×#106—861no—
351#335—431no—
352#334—431no—
353#333—431no—
354#333—431no—
355#332—431no—
356#331—431no—
357Q8⋊C8—431no—
358Q8⋊C8—431no—
359D4⋊C8—431no—
360D4⋊C8—431no—
361#322—431no—
362C43#1976811yescharacteristic, complemented, Sylow
363C2×#41—21no—
364C2×#41—21no—
365#135—44no—
366C2×Q16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—431no—
370C2×SD16—861no—
371C2×SD16—1721no—
372C2×SD16C22⋊D4311yescharacteristic
373C2×D8—21no—
374C22×C8—21no—
375C22×C8—861no—
376C4⋊Q8—431no—
377C4⋊Q8—431no—
378C4⋊Q8—861no—
379C4⋊Q8—861no—
380C4⋊Q8—1721no—
381C4⋊Q8C22×D4311yescharacteristic
382#127—21no—
383#127C22×D4311yescharacteristic
384#125—861no—
385#123—41no—
386C22⋊Q8—21no—
387C22⋊Q8—861no—
388C22⋊Q8—1721no—
389#121—21no—
390#121—21no—
391#121—41no—
392C4×Q8—431no—
393C4×Q8—861no—
394C4×Q8—861no—
395C4×Q8C22×D4311yescharacteristic
396C4×D4—21no—
397C4×D4—861no—
398C4×D4C22×D4311yescharacteristic
399C4×D4C22×D4311yescharacteristic
400C2×C4⋊C4—21no—
401C2×C4⋊C4—861no—
402#107—861no—
403#107—861no—
404#107—861no—
405#106—431no—
406#106—861no—
407#106—861no—
408#106—861no—
409#106—861no—
410#106—861no—
411#106—861no—
412#106C22⋊D4311yescharacteristic
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—861no—
417C4⋊C8—861no—
418C4⋊C8C22×D4311yescharacteristic
419#103—21no—
420#103—431no—
421#103—861no—
422#103—861no—
423#103—1721no—
424#103C22⋊D4311yescharacteristic
425#102—21no—
426#102—431no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431#102—861no—
432#102—861no—
433#102C22⋊D4311yescharacteristic
434C22⋊C8—21no—
435C22⋊C8—861no—
436#97—861no—
437C4×C8—431no—
438C4×C8—431no—
439C4×C8—861no—
440C4×C8C22×D4311yescharacteristic
441#41—42no—
442#41—42no—
443#41—81no—
444#41—81no—
445C2×Q8—21no—
446C2×Q8—431no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—1721no—
450C2×Q8C2×C22⋊D4311yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4D4×D4311yescharacteristic
458C2×D4C2×C22⋊D4311yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—1721no—
464Q16—42no—
465SD16—42no—
466SD16—81no—
467SD16—3442no—
468SD16—1721no—
469SD16—1722no—
470SD16#1062188314yescomplemented
471D8—42no—
472C2×C8—21no—
473C2×C8—42no—
474C2×C8—431no—
475C2×C8—431no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—1722no—
481C2×C8C2×C22⋊D4311yescharacteristic
482C2×C8C2×C22⋊D4311yescharacteristic
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—431no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—1721no—
494C4⋊C4—1721no—
495C4⋊C4—1721no—
496C4⋊C4—1721no—
497C4⋊C4D4×D4311yescharacteristic
498C4⋊C4C2×C22⋊D4311yescharacteristic
499C4⋊C4C2×C22⋊D4311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—1721no—
505C42—21no—
506C42—861no—
507C42—1721no—
508C42C23×D4311yescharacteristic
509C23—21no—
510C23—21no—
511C23—41no—
512Q8—21no—
513Q8—41no—
514Q8—41no—
515Q8—861no—
516Q8—861no—
517Q8—3441no—
518Q8—3441no—
519Q8—6881no—
520Q8C2×#1062188312yes—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—82no—
529D4—81no—
530D4—82no—
531D4—161no—
532D4C2×#1062188312yes—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—6881no—
549C2×C4C2×D4×D4311yescharacteristic
550C2×C4C22×C22⋊D4311yescharacteristic
551C2×C4#1306337011yescharacteristic
552C8—21no—
553C8—41no—
554C8—861no—
555C8—861no—
556C8—1721no—
557C8—1721no—
558C8—1721no—
559C8—1721no—
560C8C2×#1062188312yes—
561C22—22no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22D4×C22⋊D4311yescharacteristic
571C4—22no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—3441no—
578C4—3441no—
579C4—1721no—
580C4—1721no—
581C4C22×#1062188311yescharacteristic
582C4#1458369611yescharacteristic
583C4#1458371011yescharacteristic
584C4#1458371311yescharacteristic
585C2—42no—
586C2—81no—
587C2—161no—
588C2#1914615011yescharacteristic
589C2D4×#1062188311yescharacteristic
590C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3284C2
socleC22×C43D42
hypercenter#3284D43
hypocenterC43#19768
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3284

Complements

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

NH ≅ G/Ntype
1. #19147503C2semidirect
2. #19147262C2semidirect
3. #19146952C2semidirect
4. #19134214C2semidirect
5. #19134064C2semidirect
6. #19134002C2semidirect
7. #19133994C2semidirect
8. #19133975C2semidirect
9. #19133814C2semidirect
10. #19133746C2semidirect
11. #19133722C2semidirect
12. #19133665C2semidirect
13. #19133431C2semidirect
14. SD16⋊(C43⋊C8)C2semidirect
171. SD16×C43SD16semidirect
362. C43#19768semidirect
470. SD16#10621883semidirect

Maximal subgroups

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

subgroupindex
#191475032
#191472622
#191469522
#191342142
#191340642
#191340022
#191339942
#191339752
#191338142
#191337462
#191337222
#191336652
#191334312
SD16⋊(C43⋊C8)2
C43×#32842
#1976843