Finite Group Databasebeta

← #25086109

Subgroups — #25086109

Order 11008.

650 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147492C211yesmaximal, characteristic, complemented
2#19146952C211yesmaximal, characteristic, complemented
3#19146454C211yesmaximal, characteristic, complemented
4#19134226C211yesmaximal, characteristic, complemented
5#19134086C211yesmaximal, characteristic, complemented
6#19134020C211yesmaximal, characteristic, complemented
7#19133970C211yesmaximal, characteristic, complemented
8#19133968C211yesmaximal, characteristic, complemented
9#19133879C211yesmaximal, characteristic, complemented
10#19133856C211yesmaximal, characteristic, complemented
11#19133800C211yesmaximal, characteristic, complemented
12#19133746C211yesmaximal, characteristic, complemented
13#19133431C211yesmaximal, characteristic, complemented
14#19133419C211yesmaximal, characteristic, complemented
15C43×#3283C211yesmaximal, characteristic
16#14583606C2211yescharacteristic
17D4×Dic86C2211yescharacteristic
18#14583307—21no—
19#14583297C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583295C2211yescharacteristic
22#14583251C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583229—21no—
25#14583229—21no—
26#14583215—21no—
27#14583201—21no—
28#14583189C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583187—21no—
31#14583181C2211yescharacteristic
32#14583181C2211yescharacteristic
33#14583179C2211yescharacteristic
34#14583126—21no—
35#14583126—21no—
36#14583104C2211yescharacteristic
37#14583037—21no—
38#14583029C2211yescharacteristic
39#14583011—21no—
40C4×#10621883C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43C2×#13063256—21no—
44C2×#13063248—21no—
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51#14582629C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582620C2211yescharacteristic
56C2×#135×C43—21no—
57C43×#547C2211yescharacteristic
58C43×#547C2211yescharacteristic
59C43×#494C2211yescharacteristic
60C43×#467—21no—
61C43×#461C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C43×#452—21no—
64C43×#452—21no—
65C4×D8×C43C2211yescharacteristic
66C8×D4×C43C2211yescharacteristic
67C22×Dic86—21no—
68C2×#10621883—21no—
69C2×#10621883D411yescharacteristic
70C22×C43⋊C8—21no—
71C22×C43⋊C8—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063324—21no—
75#13063316—21no—
76#13063304—21no—
77#13063304—21no—
78#13063302—41no—
79#13063302—41no—
80C4×Dic86C2311yescharacteristic
81D4×Dic43—21no—
82D4×Dic43—21no—
83C2×C4⋊Dic43—21no—
84#13063258—21no—
85#13063257—21no—
86#13063257—21no—
87#13063256—21no—
88#13063256—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256—41no—
94#13063256D411yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98Dic43⋊C8—21no—
99#13063248—21no—
100#13063248—21no—
101#13063248—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248—41no—
105#13063248D411yescharacteristic
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112#13063235—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×#41×C43—21no—
116C2×#41×C43—21no—
117#135×C43—44no—
118C2×Q16×C43—21no—
119C2×Q16×C43—21no—
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×D8×C43D411yescharacteristic
123C22×C8×C43—21no—
124C4⋊Q8×C43C2311yescharacteristic
125C4⋊Q8×C43C2311yescharacteristic
126#123×C43—41no—
127#123×C43—41no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43—21no—
130#121×C43—21no—
131#121×C43—21no—
132C4×D4×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43—21no—
137#107×C43D411yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43—21no—
141#102×C43D411yescharacteristic
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×C43—21no—
151C2×D4×C43—41no—
152C2×D4×C43—41no—
153C2×D4×C43C2×D411yescharacteristic
154C2×D4×C43C2×D411yescharacteristic
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—41no—
160C22×C4×C43—41no—
161C22×Dic43—41no—
162C22×Dic43—41no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—42no—
166C2×Dic86—41no—
167C2×Dic86—81no—
168C2×Dic86C2×D411yescharacteristic
169Q16×C43—42no—
170Q16×C43—81no—
171SD16×C43—42no—
172SD16×C43—42no—
173D8×C43SD1614yescomplemented
174C2×C8×C43—21no—
175C2×C8×C43—42no—
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C22⋊C4×C43—21no—
188C22⋊C4×C43—21no—
189C22⋊C4×C43—21no—
190C22⋊C4×C43—41no—
191C22⋊C4×C43—41no—
192C42×C43C2411yescharacteristic
193C22⋊Dic43—41no—
194C22⋊Dic43—41no—
195#10621883—41no—
196#10621883—81no—
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—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—42no—
212C2×C43⋊C8—81no—
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—41no—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—82no—
227D4×C43—82no—
228D4×C43C2×SD1612yes—
229D4×C43C2×SD1612yes—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
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—82no—
251C2×Dic43—161no—
252Dic86—21no—
253Dic86—21no—
254Dic86—41no—
255Dic86—41no—
256Dic86—82no—
257Dic86—81no—
258C8×C43—21no—
259C8×C43—41no—
260C8×C43C2×SD1612yes—
261C43⋊C8—21no—
262C43⋊C8—21no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267#19766—431nomaximal, Sylow
268C22×C43—22no—
269C22×C43—22no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43D4211yescharacteristic
278C4×C43—21no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43C22×SD1611yescharacteristic
285C4×C43#57511yescharacteristic
286C4×C43#57711yescharacteristic
287C4×C43#57711yescharacteristic
288Dic43—41no—
289Dic43—41no—
290Dic43—81no—
291Dic43—81no—
292#3384—431no—
293#3335—431no—
294#3298—431no—
295#3283D4311yescharacteristic
296#1716—431no—
297#1690—431no—
298#1679—431no—
299#1671—431no—
300#1671—431no—
301#1654—431no—
302#1651—431no—
303#1643—431no—
304#1635—431no—
305#1582—431no—
306#1580—431no—
307C2×C43—42no—
308C2×C43—42no—
309C2×C43—81no—
310C2×C43#326711yescharacteristic
311C2×C43D4×SD1611yescharacteristic
312C2×C43#328911yescharacteristic
313C2×#135—21no—
314#554—431no—
315D4×Q8—431no—
316#547C2×D4311yescharacteristic
317#547C2×D4311yescharacteristic
318#501—861no—
319#498—431no—
320#498—431no—
321#498—431no—
322#494C2×D4311yescharacteristic
323#487—431no—
324#487—431no—
325#483—861no—
326#483—861no—
327#481—861no—
328#478—861no—
329#476—431no—
330#476—431no—
331#476—861no—
332#475—431no—
333#475—431no—
334#474—431no—
335#467—21no—
336#465—861no—
337#465—861no—
338#461—431no—
339#461C2×D4311yescharacteristic
340#461C2×D4311yescharacteristic
341#452—21no—
342#452—21no—
343#448—861no—
344#446—431no—
345#442—861no—
346C4×SD16—431no—
347C4×D8C2×D4311yescharacteristic
348C8×D4—431no—
349C8×D4—431no—
350C8×D4C2×D4311yescharacteristic
351C2×#106—861no—
352C2×#103—861no—
353#334—431no—
354#334—431no—
355#333—431no—
356#332—431no—
357#332—431no—
358#332—431no—
359Q8⋊C8—431no—
360D4⋊C8—431no—
361D4⋊C8—431no—
362D4⋊C8—431no—
363#322—431no—
364C43#1976611yescharacteristic, complemented, Sylow
365C2×#41—21no—
366C2×#41—21no—
367C22×Q8—861no—
368#135—44no—
369C2×Q16—21no—
370C2×Q16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—431no—
374C2×SD16—861no—
375C2×D8C22⋊D4311yescharacteristic
376C22×C8—21no—
377C22×C8—861no—
378C22×C8—861no—
379C4⋊Q8—431no—
380C4⋊Q8—431no—
381C4⋊Q8—861no—
382C4⋊Q8C22×D4311yescharacteristic
383C4⋊Q8C22×D4311yescharacteristic
384#125—861no—
385#123—41no—
386#123—41no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—861no—
390C22⋊Q8—861no—
391C22⋊Q8—1721no—
392C22⋊Q8—1721no—
393#121—21no—
394#121—21no—
395C4×Q8—431no—
396C4×D4—861no—
397C4×D4—861no—
398C4×D4C22×D4311yescharacteristic
399C4×D4C22×D4311yescharacteristic
400C4×D4C22×D4311yescharacteristic
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—861no—
404#107—861no—
405#107C22⋊D4311yescharacteristic
406#106—431no—
407#106—861no—
408#106—861no—
409#106—861no—
410#106—861no—
411#106—861no—
412#106—861no—
413#106—861no—
414#106—861no—
415#106—1721no—
416C4⋊C8—431no—
417C4⋊C8—431no—
418C4⋊C8—431no—
419C4⋊C8—861no—
420C4⋊C8C22×D4311yescharacteristic
421#103—21no—
422#103—21no—
423#103—431no—
424#103—861no—
425#103—861no—
426#103—861no—
427#103—861no—
428#103—861no—
429#103—1721no—
430#102—431no—
431#102—861no—
432#102—861no—
433#102—861no—
434#102C22⋊D4311yescharacteristic
435#102C22⋊D4311yescharacteristic
436C22⋊C8—21no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439#97—861no—
440C4×C8—431no—
441C4×C8—431no—
442C4×C8C22×D4311yescharacteristic
443#41—42no—
444#41—42no—
445#41—81no—
446#41—81no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—431no—
450C2×Q8—861no—
451C2×Q8—861no—
452C2×Q8—3441no—
453C2×Q8—1721no—
454C2×Q8—1722no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4D4×D4311yescharacteristic
458C2×D4C2×C22⋊D4311yescharacteristic
459C2×D4C2×C22⋊D4311yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—1721no—
466C22×C4—1721no—
467Q16—42no—
468Q16—81no—
469SD16—42no—
470SD16—42no—
471SD16—3441no—
472SD16—1721no—
473D8#1062188314yescomplemented
474C2×C8—21no—
475C2×C8—42no—
476C2×C8—431no—
477C2×C8—431no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—3441no—
483C2×C8—1722no—
484C2×C8C2×C22⋊D4311yescharacteristic
485C2×C8C2×C22⋊D4311yescharacteristic
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—431no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—1721no—
499C4⋊C4—1721no—
500C4⋊C4—1721no—
501C4⋊C4D4×D4311yescharacteristic
502C4⋊C4C2×C22⋊D4311yescharacteristic
503C4⋊C4C2×C22⋊D4311yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—1721no—
510C22⋊C4—1721no—
511C42—861no—
512C42C23×D4311yescharacteristic
513C23—21no—
514C23—21no—
515C23—21no—
516Q8—41no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—861no—
521Q8—861no—
522Q8—3441no—
523Q8—3442no—
524Q8—1721no—
525Q8—1721no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—82no—
531D4—82no—
532D4C2×#1062188312yes—
533D4C2×#1062188312yes—
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—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—3442no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—6881no—
553C2×C4C2×D4×D4311yescharacteristic
554C2×C4C22×C22⋊D4311yescharacteristic
555C2×C4#1306337011yescharacteristic
556C8—21no—
557C8—41no—
558C8—861no—
559C8—861no—
560C8—1721no—
561C8—1721no—
562C8—1721no—
563C8—1721no—
564C8C2×#1062188312yes—
565C22—22no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22D4×C22⋊D4311yescharacteristic
575C4—21no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4—3441no—
582C4—3441no—
583C4—1721no—
584C4—1721no—
585C4C22×#1062188311yescharacteristic
586C4#1458369611yescharacteristic
587C4#1458370611yescharacteristic
588C4#1458371011yescharacteristic
589C2—42no—
590C2—42no—
591C2—81no—
592C2#1914612011yescharacteristic
593C2D4×#1062188311yescharacteristic
594C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3283C2
socleC22×C43D42
hypercenter#3283D43
hypocenterC43#19766
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3283

Complements

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

NH ≅ G/Ntype
1. #19147492C2semidirect
2. #19146952C2semidirect
3. #19146454C2semidirect
4. #19134226C2semidirect
5. #19134086C2semidirect
6. #19134020C2semidirect
7. #19133970C2semidirect
8. #19133968C2semidirect
9. #19133879C2semidirect
10. #19133856C2semidirect
11. #19133800C2semidirect
12. #19133746C2semidirect
13. #19133431C2semidirect
14. #19133419C2semidirect
173. D8×C43SD16semidirect
364. C43#19766semidirect
473. D8#10621883semidirect

Maximal subgroups

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

subgroupindex
#191474922
#191469522
#191464542
#191342262
#191340862
#191340202
#191339702
#191339682
#191338792
#191338562
#191338002
#191337462
#191334312
#191334192
C43×#32832
#1976643