Finite Group Databasebeta

← #25086748

Subgroups — #25086748

Order 11008.

632 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q16×Dic86C211yesmaximal, characteristic, complemented
2Q8×#10621883C211yesmaximal, characteristic, complemented
3#19147262C211yesmaximal, characteristic
4#19134214C211yesmaximal, characteristic, complemented
5#19134118C211yesmaximal, characteristic, complemented
6#19134009C211yesmaximal, characteristic, complemented
7#19133975C211yesmaximal, characteristic, complemented
8#19133940C211yesmaximal, characteristic, complemented
9#19133814C211yesmaximal, characteristic, complemented
10#19133760C211yesmaximal, characteristic, complemented
11#19133722C211yesmaximal, characteristic
12#19133672C211yesmaximal, characteristic, complemented
13#19133436C211yesmaximal, characteristic, complemented
14#19133414C211yesmaximal, characteristic, complemented
15C43×#3278C211yesmaximal, characteristic
16Q8×Dic86C2211yescharacteristic
17Q8×Dic86C2211yescharacteristic
18#14583304C2211yescharacteristic
19#14583303—21no—
20#14583295—21no—
21#14583295C2211yescharacteristic
22#14583271C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583245—21no—
25#14583245C2211yescharacteristic
26#14583194C2211yescharacteristic
27#14583194C2211yescharacteristic
28#14583192—21no—
29#14583192—21no—
30#14583189—21no—
31#14583189—21no—
32#14583189C2211yescharacteristic
33#14583189C2211yescharacteristic
34#14583181—21no—
35#14583181C2211yescharacteristic
36#14583096—21no—
37#14583096C2211yescharacteristic
38Q8×C43⋊C8C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40C8×Dic86C2211yescharacteristic
41Q16×Dic43—21no—
42C4×#10621883—21no—
43C4×#10621883—21no—
44C4×#10621883C2211yescharacteristic
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582620C2211yescharacteristic
56C2×#137×C43—21no—
57C43×#550C2211yescharacteristic
58D4×Q8×C43C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#468—21no—
61C43×#462C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C43×#452—21no—
64C43×#448—21no—
65C4×Q16×C43C2211yescharacteristic
66C43×#436C2211yescharacteristic
67C2×#10621883—21no—
68C2×#10621883—41no—
69C2×#10621883D411yescharacteristic
70#13063325—21no—
71#13063325—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063324—21no—
75#13063324—21no—
76#13063324—41no—
77#13063324—41no—
78Q8×Dic43—21no—
79Q8×Dic43—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86C2311yescharacteristic
83#13063259—21no—
84#13063259—21no—
85#13063258—21no—
86#13063258—21no—
87#13063256—21no—
88#13063256—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256D411yescharacteristic
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98Dic43⋊C8—21no—
99#13063249—21no—
100#13063249—21no—
101#13063248—21no—
102#13063248—41no—
103#13063248D411yescharacteristic
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246D411yescharacteristic
110C4×C43⋊C8—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×#41×C43—21no—
116C22×Q8×C43—21no—
117#137×C43—44no—
118C2×Q16×C43—21no—
119C2×Q16×C43D411yescharacteristic
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×SD16×C43—21no—
123C2×M16×C43—21no—
124C4⋊Q8×C43—21no—
125C4⋊Q8×C43C2311yescharacteristic
126#127×C43—21no—
127#127×C43C2311yescharacteristic
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43—41no—
130#121×C43—21no—
131#121×C43—41no—
132C4×Q8×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134C4×D4×C43—21no—
135C4×D4×C43—21no—
136C4×D4×C43C2311yescharacteristic
137#107×C43D411yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#103×C43D411yescharacteristic
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145#41×C43—42no—
146#41×C43—81no—
147C2×Q8×C43—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43—42no—
150C2×Q8×C43—81no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×Q8×C43C2×D411yescharacteristic
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43C2×D411yescharacteristic
159C22×C4×C43—21no—
160C22×C4×C43—41no—
161C22×C4×C43—41no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—41no—
165C2×Dic86—41no—
166C2×Dic86C2×D411yescharacteristic
167Q16×C43—42no—
168Q16×C43SD1614yescomplemented
169SD16×C43—42no—
170SD16×C43—42no—
171SD16×C43—81no—
172M16×C43—42no—
173C2×C8×C43—21no—
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C4⋊C4×C43—21no—
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—41no—
186C22⋊C4×C43—41no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43C2411yescharacteristic
190#10621883—22no—
191#10621883—42no—
192#10621883—82no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—41no—
198C4⋊Dic43—41no—
199C4⋊Dic43C2×D411yescharacteristic
200Dic43⋊C4—21no—
201Dic43⋊C4—41no—
202Dic43⋊C4—41no—
203C4×Dic43—21no—
204C4×Dic43—41no—
205C4×Dic43—41no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212C23×C43—21no—
213C23×C43—41no—
214Q8×C43—21no—
215Q8×C43—21no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—82no—
219Q8×C43C2×SD1612yes—
220Q8×C43C2×SD1612yes—
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—161no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—82no—
239C2×C4×C43—82no—
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247Dic86—21no—
248Dic86—81no—
249Dic86—81no—
250Dic86—161no—
251Dic86—161no—
252Dic86#13712yescomplemented
253C8×C43—21no—
254C8×C43—41no—
255C8×C43C2×SD1612yes—
256C43⋊C8—21no—
257C43⋊C8—21no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262#19809—431nomaximal, Sylow
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43D4211yescharacteristic
270C4×C43—22no—
271C4×C43—22no—
272C4×C43—21no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—81no—
277C4×C43C22×SD1611yescharacteristic
278C4×C43C2×#13711yescharacteristic
279C4×C43#57711yescharacteristic
280C4×C43#57811yescharacteristic
281Dic43—22no—
282Dic43—41no—
283Dic43—81no—
284Dic43—81no—
285Q8×Q16—431no—
286Q8×SD16—431no—
287#3362—431no—
288#3278D4311yescharacteristic
289#1714—431no—
290#1695—431no—
291#1678—431no—
292#1672—431no—
293#1666—431no—
294#1645—431no—
295#1637—431no—
296#1631—431no—
297#1623—431no—
298#1583—431no—
299#1579—431no—
300C2×C43—81no—
301C2×C43—161no—
302C2×C43#327011yescharacteristic
303C2×C43D4×SD1611yescharacteristic
304C2×C43#328811yescharacteristic
305C2×#137—21no—
306Q82—431no—
307Q82—431no—
308#550C2×D4311yescharacteristic
309D4×Q8C2×D4311yescharacteristic
310#500—431no—
311#500—861no—
312#498—431no—
313#498—861no—
314#492—431no—
315#492C2×D4311yescharacteristic
316#487—431no—
317#486—431no—
318#486—861no—
319#477—431no—
320#477—431no—
321#477—861no—
322#477—861no—
323#476—431no—
324#476—431no—
325#476—861no—
326#476—861no—
327#475—431no—
328#475—861no—
329#468—21no—
330#462C2×D4311yescharacteristic
331#460—431no—
332#460—861no—
333#460C2×D4311yescharacteristic
334#452—21no—
335#448—21no—
336C8×Q8—431no—
337C8×Q8—431no—
338C8×Q8—431no—
339C4×Q16—861no—
340C4×Q16C2×D4311yescharacteristic
341C4×SD16—431no—
342C4×SD16—861no—
343C4×SD16—861no—
344#436C2×D4311yescharacteristic
345#334—431no—
346#334—431no—
347#333—431no—
348#333—431no—
349#332—431no—
350#331—431no—
351Q8⋊C8—431no—
352Q8⋊C8—431no—
353Q8⋊C8—431no—
354D4⋊C8—431no—
355#322—431no—
356C43#1980911yescharacteristic, complemented, Sylow
357C2×#41—21no—
358C22×Q8—21no—
359#137—44no—
360C2×Q16—21no—
361C2×Q16C22⋊D4311yescharacteristic
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—431no—
366C2×SD16—861no—
367C2×SD16—1721no—
368C2×M16—21no—
369C4⋊Q8—21no—
370C4⋊Q8—431no—
371C4⋊Q8—431no—
372C4⋊Q8—861no—
373C4⋊Q8—861no—
374C4⋊Q8—861no—
375C4⋊Q8—861no—
376C4⋊Q8—1721no—
377C4⋊Q8—1721no—
378C4⋊Q8C22×D4311yescharacteristic
379#127—21no—
380#127C22×D4311yescharacteristic
381C22⋊Q8—21no—
382C22⋊Q8—41no—
383#121—21no—
384#121—41no—
385C4×Q8—431no—
386C4×Q8—861no—
387C4×Q8—861no—
388C4×Q8—861no—
389C4×Q8—861no—
390C4×Q8C22×D4311yescharacteristic
391C4×Q8C22×D4311yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4C22×D4311yescharacteristic
395#107—861no—
396#107—861no—
397#107—861no—
398#107—861no—
399#107C22⋊D4311yescharacteristic
400#106—431no—
401#106—861no—
402#106—861no—
403#106—861no—
404#106—861no—
405#106—861no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8—861no—
412C4⋊C8C22×D4311yescharacteristic
413#103—21no—
414#103—431no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—1721no—
419#103C22⋊D4311yescharacteristic
420#103C22⋊D4311yescharacteristic
421#102—21no—
422#102—431no—
423#102—861no—
424#102—861no—
425#102—861no—
426#102—861no—
427#102—861no—
428C22⋊C8—21no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—861no—
432C4×C8—861no—
433C4×C8—861no—
434C4×C8C22×D4311yescharacteristic
435#41—42no—
436#41—81no—
437C2×Q8—21no—
438C2×Q8—41no—
439C2×Q8—42no—
440C2×Q8—81no—
441C2×Q8—431no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×Q8—1721no—
445C2×Q8—1721no—
446C2×Q8C2×C22⋊D4311yescharacteristic
447C2×Q8C2×C22⋊D4311yescharacteristic
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4D4×D4311yescharacteristic
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—41no—
457Q16—42no—
458Q16#1062188314yescomplemented
459SD16—42no—
460SD16—42no—
461SD16—81no—
462SD16—862no—
463SD16—3442no—
464SD16—1722no—
465M16—42no—
466C2×C8—21no—
467C2×C8—431no—
468C2×C8—431no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8C2×C22⋊D4311yescharacteristic
474C2×C8C2×C22⋊D4311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—41no—
480C4⋊C4—431no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—1721no—
487C4⋊C4—1721no—
488C4⋊C4—1721no—
489C4⋊C4—1721no—
490C4⋊C4D4×D4311yescharacteristic
491C4⋊C4C2×C22⋊D4311yescharacteristic
492C4⋊C4C2×C22⋊D4311yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C42—21no—
497C42—21no—
498C42—861no—
499C42—1721no—
500C42—1721no—
501C42C23×D4311yescharacteristic
502C23—21no—
503C23—41no—
504Q8—21no—
505Q8—21no—
506Q8—41no—
507Q8—41no—
508Q8—82no—
509Q8—432no—
510Q8—861no—
511Q8—3441no—
512Q8—3441no—
513Q8—6881no—
514Q8—6881no—
515Q8C2×#1062188312yes—
516Q8C2×#1062188312yes—
517D4—21no—
518D4—21no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—82no—
524D4—81no—
525D4—161no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—82no—
535C2×C4—82no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4C2×D4×D4311yescharacteristic
541C2×C4C22×C22⋊D4311yescharacteristic
542C2×C4#1306337011yescharacteristic
543C8—21no—
544C8—41no—
545C8—861no—
546C8—861no—
547C8—1721no—
548C8—1721no—
549C8—1721no—
550C8—1721no—
551C8C2×#1062188312yes—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22D4×C22⋊D4311yescharacteristic
559C4—22no—
560C4—22no—
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—81no—
566C4—862no—
567C4—3441no—
568C4—3441no—
569C4—1721no—
570C4C22×#1062188311yescharacteristic
571C4#137×D4311yescharacteristic
572C4#1458371011yescharacteristic
573C4#1458371511yescharacteristic
574C2—81no—
575C2—161no—
576C2#1914615911yescharacteristic
577C2D4×#1062188311yescharacteristic
578C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3278C2
socleC22×C43D42
prime radicalC43×#550C22
hypercenter#3278D43
hypocenterC43#19809
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3278

Complements

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

NH ≅ G/Ntype
1. Q16×Dic86C2semidirect
2. Q8×#10621883C2semidirect
4. #19134214C2semidirect
5. #19134118C2semidirect
6. #19134009C2semidirect
7. #19133975C2semidirect
8. #19133940C2semidirect
9. #19133814C2semidirect
10. #19133760C2semidirect
12. #19133672C2semidirect
13. #19133436C2semidirect
14. #19133414C2semidirect
168. Q16×C43SD16semidirect
252. Dic86#137semidirect
356. C43#19809semidirect
458. Q16#10621883semidirect

Maximal subgroups

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

subgroupindex
Q16×Dic862
Q8×#106218832
#191472622
#191342142
#191341182
#191340092
#191339752
#191339402
#191338142
#191337602
#191337222
#191336722
#191334362
#191334142
C43×#32782
#1980943