Finite Group Databasebeta

← #25086703

Subgroups — #25086703

Order 11008.

676 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147460C211yesmaximal, characteristic, complemented
2#19146952C211yesmaximal, characteristic, complemented
3#19146419C211yesmaximal, characteristic, complemented
4#19134214C211yesmaximal, characteristic, complemented
5#19134118C211yesmaximal, characteristic, complemented
6#19134002C211yesmaximal, characteristic, complemented
7#19133968C211yesmaximal, characteristic, complemented
8#19133940C211yesmaximal, characteristic, complemented
9#19133800C211yesmaximal, characteristic, complemented
10#19133746C211yesmaximal, characteristic, complemented
11#19133711C211yesmaximal, characteristic, complemented
12#19133665C211yesmaximal, characteristic, complemented
13#19133436C211yesmaximal, characteristic, complemented
14#19133419C211yesmaximal, characteristic, complemented
15C43×#3272C211yesmaximal, characteristic
16#14583606C2211yescharacteristic
17#14583606C2211yescharacteristic, complemented
18#14583304C2211yescharacteristic, complemented
19#14583300—21no—
20#14583295C2211yescharacteristic, complemented
21#14583271C2211yescharacteristic
22#14583251C2211yescharacteristic, complemented
23#14583245C2211yescharacteristic
24#14583229—21no—
25#14583215—21no—
26#14583215—21no—
27#14583197—21no—
28#14583197—21no—
29#14583189C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583189C2211yescharacteristic
32#14583189C2211yescharacteristic, complemented
33#14583181C2211yescharacteristic, complemented
34#14583126—21no—
35#14583126—21no—
36#14583096C2211yescharacteristic
37#14583050—21no—
38C8×Dic86C2211yescharacteristic, complemented
39C4×#10621883C2211yescharacteristic
40D8×Dic43—21no—
41D4×C43⋊C8C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic, complemented
43C2×#13063256—21no—
44C2×#13063246—21no—
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, complemented
48#14582647C2211yescharacteristic, complemented
49#14582645C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic
51#14582629C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic, complemented
55#14582620C2211yescharacteristic, complemented
56C2×AGL(1,ℤ/8)×C43—21no—
57C43×#547C2211yescharacteristic
58D42×C43C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#468—21no—
61C43×#461C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#450—21no—
64C43×#449—21no—
65C4×D8×C43C2211yescharacteristic
66C43×#436C2211yescharacteristic
67C2×#10621883—21no—
68C2×#10621883—41no—
69C2×#10621883D411yescharacteristic
70C22×C43⋊C8—21no—
71C22×C43⋊C8—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063316—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—
84C2×C4⋊Dic43—21no—
85#13063259—21no—
86#13063259—21no—
87#13063256—21no—
88#13063256—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256D411yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98Dic43⋊C8—21no—
99#13063248—21no—
100#13063248—41no—
101#13063248D411yescharacteristic
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×#41×C43—21no—
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118AGL(1,ℤ/8)×C43—44no—
119C2×SD16×C43—21no—
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×D8×C43—21no—
123C2×D8×C43D411yescharacteristic
124C2×M16×C43—21no—
125C4⋊Q8×C43C2311yescharacteristic
126#127×C43C2311yescharacteristic
127#123×C43—41no—
128C22⋊Q8×C43—21no—
129#121×C43—21no—
130#121×C43—21no—
131#121×C43—21no—
132#120×C43—41no—
133C4×D4×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136C2×C4⋊C4×C43—21no—
137#107×C43D411yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#102×C43—21no—
141#102×C43D411yescharacteristic
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146#41×C43—42no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—41no—
153C2×D4×C43—41no—
154C2×D4×C43—41no—
155C2×D4×C43—42no—
156C2×D4×C43—42no—
157C2×D4×C43—81no—
158C2×D4×C43—81no—
159C2×D4×C43C2×D411yescharacteristic
160C2×D4×C43C2×D411yescharacteristic
161C2×D4×C43C2×D411yescharacteristic
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—41no—
166C22×Dic43—41no—
167C22×Dic43—41no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86C2×D411yescharacteristic
171SD16×C43—42no—
172SD16×C43—42no—
173SD16×C43—81no—
174D8×C43—42no—
175D8×C43SD1614yescomplemented
176M16×C43—42no—
177C2×C8×C43—21no—
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43C2×D411yescharacteristic
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C22⋊C4×C43—21no—
187C22⋊C4×C43—21no—
188C22⋊C4×C43—21no—
189C22⋊C4×C43—41no—
190C22⋊C4×C43—41no—
191C42×C43C2411yescharacteristic
192C22⋊Dic43—41no—
193C22⋊Dic43—41no—
194#10621883—41no—
195#10621883—81no—
196#10621883—82no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—41no—
202C4⋊Dic43—41no—
203C4⋊Dic43C2×D411yescharacteristic
204Dic43⋊C4—21no—
205Dic43⋊C4—41no—
206Dic43⋊C4—41no—
207C4×Dic43—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—42no—
213C2×C43⋊C8—81no—
214C2×C43⋊C8C2×D411yescharacteristic
215C2×C43⋊C8C2×D411yescharacteristic
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—41no—
220C23×C43—82no—
221C23×C43—82no—
222C23×C43—161no—
223Q8×C43—41no—
224Q8×C43—41no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—81no—
234D4×C43—82no—
235D4×C43—82no—
236D4×C43—82no—
237D4×C43C2×SD1612yes—
238D4×C43C2×SD1612yes—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—82no—
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43H(5,𝔽2)11yescharacteristic
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—161no—
258C2×Dic43—161no—
259Dic86—21no—
260Dic86—21no—
261Dic86—81no—
262Dic86—81no—
263C8×C43—21no—
264C8×C43—41no—
265C8×C43C2×SD1612yes—
266C43⋊C8—21no—
267C43⋊C8—21no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272#19806—431nomaximal, Sylow
273C22×C43—22no—
274C22×C43—22no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—164no—
286C22×C43D4211yescharacteristic
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—81no—
292C4×C43C22×SD1611yescharacteristic
293C4×C43#57511yescharacteristic
294C4×C43#57711yescharacteristic
295C4×C43#57711yescharacteristic
296Dic43—41no—
297Dic43—41no—
298Dic43—81no—
299Dic43—81no—
300#3380—431no—
301#3335—431no—
302#3295—431no—
303#3272D4311yescharacteristic
304#1714—431no—
305#1695—431no—
306#1677—431no—
307#1671—431no—
308#1666—431no—
309#1643—431no—
310#1635—431no—
311#1629—431no—
312#1622—431no—
313#1583—431no—
314#1580—431no—
315C2×C43—42no—
316C2×C43—42no—
317C2×C43—81no—
318C2×C43—161no—
319C2×C43#326711yescharacteristic
320C2×C43D4×SD1611yescharacteristic
321C2×C43#328811yescharacteristic
322C2×AGL(1,ℤ/8)—21no—
323#554—431no—
324#554—431no—
325#547C2×D4311yescharacteristic
326D42C2×D4311yescharacteristic
327#500—431no—
328#499—861no—
329#498—431no—
330#492—431no—
331#492C2×D4311yescharacteristic
332#487—431no—
333#486—431no—
334#483—861no—
335#481—861no—
336#481—861no—
337#478—861no—
338#478—861no—
339#476—431no—
340#476—431no—
341#476—431no—
342#476—431no—
343#475—431no—
344#468—21no—
345#465—861no—
346#465—861no—
347#461C2×D4311yescharacteristic
348#460—431no—
349#459C2×D4311yescharacteristic
350#450—21no—
351#450—861no—
352#449—21no—
353C8×Q8—431no—
354C4×SD16—431no—
355C4×D8—861no—
356C4×D8C2×D4311yescharacteristic
357#436C2×D4311yescharacteristic
358C8×D4—431no—
359C8×D4—431no—
360C2×#106—861no—
361C2×#102—861no—
362#334—431no—
363#334—431no—
364#333—431no—
365#333—431no—
366#332—431no—
367#331—431no—
368Q8⋊C8—431no—
369D4⋊C8—431no—
370D4⋊C8—431no—
371D4⋊C8—431no—
372#322—431no—
373C43#1980611yescharacteristic, complemented, Sylow
374C2×#41—21no—
375C22×D4—21no—
376C22×D4—21no—
377AGL(1,ℤ/8)—44no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—431no—
382C2×SD16—861no—
383C2×SD16—1721no—
384C2×D8—21no—
385C2×D8C22⋊D4311yescharacteristic
386C2×M16—21no—
387C22×C8—861no—
388C22×C8—861no—
389C4⋊Q8—431no—
390C4⋊Q8—431no—
391C4⋊Q8C22×D4311yescharacteristic
392#127C22×D4311yescharacteristic
393#125—861no—
394#125—861no—
395#123—41no—
396C22⋊Q8—21no—
397C22⋊Q8—861no—
398C22⋊Q8—861no—
399C22⋊Q8—1721no—
400C22⋊Q8—1721no—
401#121—21no—
402#121—21no—
403#121—21no—
404#120—41no—
405C4×Q8—431no—
406C4×D4—861no—
407C4×D4—861no—
408C4×D4C22×D4311yescharacteristic
409C4×D4C22×D4311yescharacteristic
410C4×D4C22×D4311yescharacteristic
411C2×C4⋊C4—21no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414#107—861no—
415#107—861no—
416#107C22⋊D4311yescharacteristic
417#106—431no—
418#106—861no—
419#106—861no—
420#106—861no—
421#106—861no—
422#106—861no—
423#106—861no—
424#106—861no—
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8—861no—
429C4⋊C8C22×D4311yescharacteristic
430#103—21no—
431#103—431no—
432#103—861no—
433#103—1721no—
434#102—21no—
435#102—431no—
436#102—861no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441#102—861no—
442#102—861no—
443#102C22⋊D4311yescharacteristic
444#102C22⋊D4311yescharacteristic
445C22⋊C8—21no—
446C22⋊C8—861no—
447C22⋊C8—861no—
448C4×C8—431no—
449C4×C8—431no—
450C4×C8—861no—
451C4×C8C22×D4311yescharacteristic
452C24—41no—
453#41—42no—
454#41—81no—
455C2×Q8—21no—
456C2×Q8—431no—
457C2×Q8—861no—
458C2×Q8—861no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—41no—
467C2×D4—81no—
468C2×D4—81no—
469C2×D4D4×D4311yescharacteristic
470C2×D4C2×C22⋊D4311yescharacteristic
471C2×D4C2×C22⋊D4311yescharacteristic
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—41no—
476C22×C4—1721no—
477C22×C4—1721no—
478SD16—42no—
479SD16—42no—
480SD16—81no—
481SD16—3441no—
482SD16—3442no—
483SD16—1721no—
484D8—42no—
485D8#1062188314yescomplemented
486M16—42no—
487C2×C8—21no—
488C2×C8—431no—
489C2×C8—431no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—3441no—
495C2×C8—1722no—
496C2×C8C2×C22⋊D4311yescharacteristic
497C2×C8C2×C22⋊D4311yescharacteristic
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—41no—
501C4⋊C4—431no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—1721no—
508C4⋊C4—1721no—
509C4⋊C4—1721no—
510C4⋊C4—1721no—
511C4⋊C4D4×D4311yescharacteristic
512C4⋊C4C2×C22⋊D4311yescharacteristic
513C4⋊C4C2×C22⋊D4311yescharacteristic
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—1721no—
520C22⋊C4—1721no—
521C42—861no—
522C42C23×D4311yescharacteristic
523C23—21no—
524C23—21no—
525C23—21no—
526C23—41no—
527C23—82no—
528C23—82no—
529C23—161no—
530Q8—41no—
531Q8—41no—
532Q8—861no—
533Q8—861no—
534Q8—3441no—
535Q8—3441no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—81no—
545D4—82no—
546D4—82no—
547D4—82no—
548D4C2×#1062188312yes—
549D4C2×#1062188312yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—82no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—6881no—
566C2×C4—6881no—
567C2×C4C2×D4×D4311yescharacteristic
568C2×C4C22×C22⋊D4311yescharacteristic
569C2×C4#1306337011yescharacteristic
570C8—21no—
571C8—41no—
572C8—861no—
573C8—861no—
574C8—1721no—
575C8—1721no—
576C8—1721no—
577C8—1721no—
578C8C2×#1062188312yes—
579C22—22no—
580C22—22no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—164no—
592C22D4×C22⋊D4311yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—81no—
598C4—3441no—
599C4—3441no—
600C4—1721no—
601C4—1721no—
602C4C22×#1062188311yescharacteristic
603C4#1458369511yescharacteristic
604C4#1458370911yescharacteristic
605C4#1458371011yescharacteristic
606C2—42no—
607C2—42no—
608C2—81no—
609C2—161no—
610C2#1914611411yescharacteristic
611C2D4×#1062188311yescharacteristic
612C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3272C2
socleC22×C43D42
hypercenter#3272D43
hypocenterC43#19806
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3272

Complements

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

NH ≅ G/Ntype
1. #19147460C2semidirect
2. #19146952C2semidirect
3. #19146419C2semidirect
4. #19134214C2semidirect
5. #19134118C2semidirect
6. #19134002C2semidirect
7. #19133968C2semidirect
8. #19133940C2semidirect
9. #19133800C2semidirect
10. #19133746C2semidirect
11. #19133711C2semidirect
12. #19133665C2semidirect
13. #19133436C2semidirect
14. #19133419C2semidirect
17. #14583606C22semidirect
18. #14583304C22semidirect
20. #14583295C22semidirect
22. #14583251C22semidirect
32. #14583189C22semidirect
33. #14583181C22semidirect
38. C8×Dic86C22semidirect
42. D4×C43⋊C8C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582647C22semidirect
48. #14582647C22semidirect
49. #14582645C22semidirect
51. #14582629C22semidirect
54. D4⋊(C43⋊C8)C22semidirect
55. #14582620C22semidirect
175. D8×C43SD16semidirect
373. C43#19806semidirect
485. D8#10621883semidirect

Maximal subgroups

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

subgroupindex
#191474602
#191469522
#191464192
#191342142
#191341182
#191340022
#191339682
#191339402
#191338002
#191337462
#191337112
#191336652
#191334362
#191334192
C43×#32722
#1980643