Finite Group Databasebeta

← #25086105

Subgroups — #25086105

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#19147490C211yesmaximal, characteristic, complemented
2#19146954C211yesmaximal, characteristic, complemented
3#19146313C211yesmaximal, characteristic
4#19134230C211yesmaximal, characteristic, complemented
5#19134087C211yesmaximal, characteristic, complemented
6#19134015C211yesmaximal, characteristic, complemented
7#19133970C211yesmaximal, characteristic, complemented
8#19133968C211yesmaximal, characteristic, complemented
9#19133877C211yesmaximal, characteristic, complemented
10#19133858C211yesmaximal, characteristic, complemented
11#19133801C211yesmaximal, characteristic, complemented
12#19133746C211yesmaximal, characteristic, complemented
13#19133432C211yesmaximal, characteristic, complemented
14#19133417C211yesmaximal, characteristic, complemented
15C43×#3298C211yesmaximal, characteristic, complemented
16C2×#13063345—21no—
17#14583609C2211yescharacteristic
18#14583554C2211yescharacteristic
19#14583305—21no—
20#14583297C2211yescharacteristic
21#14583295C2211yescharacteristic
22#14583295C2211yescharacteristic
23#14583278C2211yescharacteristic
24#14583251C2211yescharacteristic
25#14583228—21no—
26#14583216—21no—
27#14583199—21no—
28#14583189C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583186—21no—
31#14583184C2211yescharacteristic
32#14583176C2211yescharacteristic
33#14583138—21no—
34#14583125—21no—
35#14583104C2211yescharacteristic
36#14583101C2211yescharacteristic
37#14583061—21no—
38#14583059—21no—
39#14583030C2211yescharacteristic
40#14583009—21no—
41C4×#10621882C2211yescharacteristic
42C8×D172C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic
44#106×D43—21no—
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic
56D4×Q8×C43C2211yescharacteristic
57C43×#547C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#483—21no—
60C43×#475C2211yescharacteristic
61C43×#465—21no—
62C43×#461C2211yescharacteristic
63C43×#448—21no—
64C4×SD16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C2×#103×C43—21no—
67C2×#10621898—21no—
68#13063345—44no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621883—21no—
72C2×#10621884—21no—
73C2×#10621882D411yescharacteristic
74C22×C43⋊C8—21no—
75C2×C8×D43—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063317—21no—
79#13063307—41no—
80#13063304—21no—
81#13063303—41no—
82#13063301—21no—
83#13063296—21no—
84C4×D172—21no—
85C4×D172C2311yescharacteristic
86C4⋊C4×D43—21no—
87C4⋊C4×D43—21no—
88#13063258—21no—
89#13063258D411yescharacteristic
90#13063257—21no—
91#13063257—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256—21no—
96#13063256—21no—
97#13063256—41no—
98C4⋊(C43⋊C8)—21no—
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102#13063249—21no—
103#13063249—21no—
104#13063248—21no—
105#13063248—41no—
106#13063246—21no—
107#13063246—21no—
108#13063246D411yescharacteristic
109#13063245—21no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113#13063236—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C2×#41×C43—21no—
117C22×Q8×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43D411yescharacteristic
120C22×C8×C43—21no—
121C4⋊Q8×C43—21no—
122C4⋊Q8×C43C2311yescharacteristic
123C4⋊Q8×C43C2311yescharacteristic
124#123×C43—41no—
125C22⋊Q8×C43—21no—
126C22⋊Q8×C43—21no—
127C22⋊Q8×C43—41no—
128#121×C43—21no—
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×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140#103×C43—21no—
141#103×C43D411yescharacteristic
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145#41×C43—42no—
146#41×C43—81no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—41no—
150C2×Q8×C43—42no—
151C2×Q8×C43—81no—
152C2×Q8×C43C2×D411yescharacteristic
153C2×D4×C43—41no—
154C2×D4×C43C2×D411yescharacteristic
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—41no—
159C22×C4×C43—41no—
160C2×C22⋊D43—41no—
161#10621898—42no—
162#10621898—81no—
163C2×D172C2×D411yescharacteristic
164C2×C4×D43—21no—
165C2×C4×D43—41no—
166C2×C4×D43—41no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169SD16×C43—41no—
170SD16×C43—81no—
171C2×C8×C43—21no—
172C2×C8×C43—81no—
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—41no—
181C4⋊C4×C43—41no—
182C4⋊C4×C43C2×D411yescharacteristic
183C4⋊C4×C43C2×D411yescharacteristic
184C4⋊C4×C43C2×D411yescharacteristic
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C22⋊C4×C43—41no—
188C22⋊C4×C43—41no—
189C42×C43—21no—
190C42×C43C2411yescharacteristic
191C22⋊Dic43—41no—
192#10621885—42no—
193#10621885—81no—
194#10621884—42no—
195#10621883—42no—
196#10621882SD1614yescomplemented
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—41no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43C2×D411yescharacteristic
204Dic43⋊C4—41no—
205Dic43⋊C4—41no—
206Dic43⋊C4—41no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—42no—
212C2×C43⋊C8C2×D411yescharacteristic
213C2×C43⋊C8C2×D411yescharacteristic
214C8×D43—42no—
215C23×C43—21no—
216C23×C43—21no—
217C22×D43—21no—
218Q8×C43—21no—
219Q8×C43—21no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—82no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—82no—
229D4×C43C2×SD1612yes—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
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—82no—
241C2×C4×C43—82no—
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43H(5,𝔽2)11yescharacteristic
245C22⋊D43—82no—
246C2×Dic43—21no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249D172—21no—
250D172C2×SD1612yes—
251C4×D43—41no—
252C4×D43—41no—
253C4×D43—82no—
254C4×D43—161no—
255Dic86—41no—
256Dic86—41no—
257Dic86—81no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—41no—
261C43⋊C8—21no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8C2×SD1612yes—
267#19766—431nomaximal, Sylow
268C22×C43—22no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43D4211yescharacteristic
275C2×D43—22no—
276C2×D43—41no—
277C2×D43—41no—
278C4×C43—21no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43C22×SD1611yescharacteristic
286C4×C43#57511yescharacteristic
287C4×C43#57711yescharacteristic
288C4×C43#57711yescharacteristic
289Dic43—41no—
290Dic43—81no—
291Dic43—81no—
292#3384—431no—
293#3335—431no—
294#3298D4311yescharacteristic, complemented
295#3283—431no—
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—81no—
309C2×C43#326711yescharacteristic
310C2×C43D4×SD1611yescharacteristic
311C2×C43#328911yescharacteristic
312D43—42no—
313C2×#135—861no—
314#554—431no—
315D4×Q8C2×D4311yescharacteristic
316#547—431no—
317#547C2×D4311yescharacteristic
318#501—861no—
319#498—431no—
320#498—431no—
321#498—431no—
322#494—431no—
323#487—431no—
324#487C2×D4311yescharacteristic
325#483—21no—
326#483—861no—
327#481—861no—
328#478—861no—
329#476—431no—
330#476—431no—
331#476—861no—
332#475—431no—
333#475C2×D4311yescharacteristic
334#474—431no—
335#467—861no—
336#465—21no—
337#465—861no—
338#461—431no—
339#461—431no—
340#461C2×D4311yescharacteristic
341#452—861no—
342#452—861no—
343#448—21no—
344#446—431no—
345#442—861no—
346C4×SD16C2×D4311yescharacteristic
347C4×D8—431no—
348C8×D4—431no—
349C8×D4—431no—
350C8×D4C2×D4311yescharacteristic
351C2×#106—861no—
352C2×#103—21no—
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—861no—
367C22×Q8—21no—
368#135—1724no—
369C2×Q16—861no—
370C2×Q16—861no—
371C2×SD16—21no—
372C2×SD16—861no—
373C2×SD16—861no—
374C2×SD16C22⋊D4311yescharacteristic
375C2×D8—431no—
376C22×C8—21no—
377C22×C8—861no—
378C22×C8—861no—
379C4⋊Q8—21no—
380C4⋊Q8—431no—
381C4⋊Q8—431no—
382C4⋊Q8C22×D4311yescharacteristic
383C4⋊Q8C22×D4311yescharacteristic
384#125—861no—
385#123—41no—
386#123—1721no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—41no—
390C22⋊Q8—861no—
391C22⋊Q8—861no—
392C22⋊Q8—1721no—
393#121—21no—
394#121—861no—
395C4×Q8C22×D4311yescharacteristic
396C4×D4—21no—
397C4×D4—431no—
398C4×D4—861no—
399C4×D4C22×D4311yescharacteristic
400C4×D4C22×D4311yescharacteristic
401C2×C4⋊C4—21no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404#107—431no—
405#107—861no—
406#106—21no—
407#106—861no—
408#106—861no—
409#106—861no—
410#106—861no—
411#106—861no—
412#106—861no—
413#106—861no—
414#106—1721no—
415#106C22⋊D4311yescharacteristic
416C4⋊C8—431no—
417C4⋊C8—431no—
418C4⋊C8—431no—
419C4⋊C8—861no—
420C4⋊C8C22×D4311yescharacteristic
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—861no—
426#103—861no—
427#103—861no—
428#103—1721no—
429#103C22⋊D4311yescharacteristic
430#102—431no—
431#102—431no—
432#102—861no—
433#102—861no—
434#102—861no—
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—81no—
445#41—3441no—
446#41—1722no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—41no—
450C2×Q8—42no—
451C2×Q8—81no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8C2×C22⋊D4311yescharacteristic
455C2×D4—41no—
456C2×D4—431no—
457C2×D4—1721no—
458C2×D4D4×D4311yescharacteristic
459C2×D4C2×C22⋊D4311yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—861no—
465C22×C4—1721no—
466C22×C4—1721no—
467Q16—3441no—
468Q16—1722no—
469SD16—41no—
470SD16—81no—
471SD16—1722no—
472SD16—1722no—
473D8—434no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—431no—
477C2×C8—431no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—1722no—
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—21no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—431no—
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—41no—
507C22⋊C4—41no—
508C22⋊C4—861no—
509C22⋊C4—1721no—
510C22⋊C4—1721no—
511C42—21no—
512C42C23×D4311yescharacteristic
513C23—21no—
514C23—21no—
515C23—861no—
516Q8—21no—
517Q8—21no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—82no—
523Q8—3441no—
524Q8—1721no—
525Q8—1721no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—82no—
530D4—432no—
531D4—861no—
532D4—3442no—
533D4SD16×D4312yes—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4—861no—
547C2×C4—3442no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—6881no—
553C2×C4C2×D4×D4311yescharacteristic
554C2×C4C22×C22⋊D4311yescharacteristic
555C2×C4#1306337011yescharacteristic
556C8—21no—
557C8—21no—
558C8—41no—
559C8—432no—
560C8—861no—
561C8—1721no—
562C8—1721no—
563C8—1721no—
564C8—1721no—
565C22—22no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—862no—
572C22—1721no—
573C22—1721no—
574C22D4×C22⋊D4311yescharacteristic
575C4—21no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—81no—
581C4—81no—
582C4—3441no—
583C4—3441no—
584C4—1721no—
585C4C2×SD16×D4311yescharacteristic
586C4#1458369711yescharacteristic
587C4#1458370511yescharacteristic
588C4#1458371011yescharacteristic
589C2—42no—
590C2—81no—
591C2—1722no—
592C2#1914611611yescharacteristic
593C2SD16×C22⋊D4311yescharacteristic
594C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3298C2
socleC22×C43D42
prime radical#19146313C2
hypercenter#3298D43
hypocenterC43#19766
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3298

Complements

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

NH ≅ G/Ntype
1. #19147490C2semidirect
2. #19146954C2semidirect
4. #19134230C2semidirect
5. #19134087C2semidirect
6. #19134015C2semidirect
7. #19133970C2semidirect
8. #19133968C2semidirect
9. #19133877C2semidirect
10. #19133858C2semidirect
11. #19133801C2semidirect
12. #19133746C2semidirect
13. #19133432C2semidirect
14. #19133417C2semidirect
15. C43×#3298C2semidirect
196. #10621882SD16semidirect
294. #3298D43semidirect
364. C43#19766semidirect

Maximal subgroups

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

subgroupindex
#191474902
#191469542
#191463132
#191342302
#191340872
#191340152
#191339702
#191339682
#191338772
#191338582
#191338012
#191337462
#191334322
#191334172
C43×#32982
#1976643