Finite Group Databasebeta

← #25086707

Subgroups — #25086707

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#19147461C211yesmaximal, characteristic, complemented
2#19146949C211yesmaximal, characteristic, complemented
3#19146419C211yesmaximal, characteristic, complemented
4#19146191C211yesmaximal, characteristic
5#19134215C211yesmaximal, characteristic, complemented
6#19134116C211yesmaximal, characteristic, complemented
7#19134003C211yesmaximal, characteristic, complemented
8#19133972C211yesmaximal, characteristic, complemented
9#19133942C211yesmaximal, characteristic, complemented
10#19133804C211yesmaximal, characteristic, complemented
11#19133749C211yesmaximal, characteristic, complemented
12#19133664C211yesmaximal, characteristic, complemented
13#19133441C211yesmaximal, characteristic, complemented
14#19133416C211yesmaximal, characteristic, complemented
15C43×#1629C211yesmaximal, characteristic, complemented
16C2×#13063351—21no—
17#14583610C2211yescharacteristic, complemented
18#14583606C2211yescharacteristic
19#14583554C2211yescharacteristic
20#14583302C2211yescharacteristic, complemented
21#14583299—21no—
22#14583295C2211yescharacteristic, complemented
23#14583271C2211yescharacteristic
24#14583250C2211yescharacteristic, complemented
25#14583245C2211yescharacteristic
26#14583231—21no—
27#14583216—21no—
28#14583215—21no—
29#14583201—21no—
30#14583198—21no—
31#14583190C2211yescharacteristic, complemented
32#14583189C2211yescharacteristic
33#14583185C2211yescharacteristic, complemented
34#14583143—21no—
35#14583127—21no—
36#14583126—21no—
37#14583104C2211yescharacteristic
38#14583096C2211yescharacteristic
39#14583091C2211yescharacteristic
40#14583050—21no—
41#14583050—21no—
42#14583042—21no—
43#14583023C2211yescharacteristic, complemented
44C4×#10621883C2211yescharacteristic
45C4×#10621882C2211yescharacteristic
46#14582979—21no—
47#14582977C2211yescharacteristic
48D4×C43⋊C8C2211yescharacteristic
49#14582964C2211yescharacteristic, complemented
50#106×D43—21no—
51C2×#13063246—21no—
52#14582649C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582646C2211yescharacteristic, complemented
57#14582631C2211yescharacteristic, complemented
58#14582628C2211yescharacteristic, complemented
59#14582621C2211yescharacteristic, complemented
60D42×C43C2211yescharacteristic
61C43×#492C2211yescharacteristic
62C43×#476C2211yescharacteristic
63C43×#476C2211yescharacteristic
64C43×#331C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×D4⋊C8C2211yescharacteristic
67C2×#10621898—21no—
68#13063351—44no—
69C2×#10621883—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621883D411yescharacteristic
74C2×#10621882—21no—
75C2×#10621882D411yescharacteristic
76C2×#10621877—21no—
77C22×C43⋊C8—21no—
78C2×C8×D43—21no—
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063316—21no—
82#13063316—21no—
83#13063307—41no—
84#13063305—21no—
85#13063304—21no—
86#13063304—21no—
87#13063302—41no—
88#13063301—41no—
89#13063296—21no—
90C4×Dic86C2311yescharacteristic
91C4×D172C2311yescharacteristic
92D4×Dic43—21no—
93#13063287—21no—
94C2×C4⋊Dic43—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97#13063258—21no—
98#13063258—21no—
99#13063258D411yescharacteristic
100#13063257—21no—
101#13063257—21no—
102#13063256—21no—
103#13063256—21no—
104#13063256—21no—
105#13063256D411yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108Dic43⋊C8—21no—
109#13063250—21no—
110#13063250—41no—
111#13063248—21no—
112#13063248D411yescharacteristic
113#13063247—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117#13063246—21no—
118#13063246—21no—
119#13063246D411yescharacteristic
120#13063246D411yescharacteristic
121#13063245D411yescharacteristic
122C22⋊(C43⋊C8)—21no—
123C22⋊(C43⋊C8)—21no—
124(C2×D43)⋊C8—21no—
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C22×D4×C43—21no—
129C22×D4×C43—21no—
130C2×SD16×C43—41no—
131C4⋊Q8×C43C2311yescharacteristic
132#127×C43C2311yescharacteristic
133#121×C43—21no—
134#121×C43—21no—
135#120×C43—41no—
136C4×D4×C43C2311yescharacteristic
137C4×D4×C43C2311yescharacteristic
138#106×C43—21no—
139#106×C43—21no—
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142#102×C43—21no—
143#102×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146C2×Q8×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—41no—
151C2×D4×C43—41no—
152C2×D4×C43—42no—
153C2×D4×C43—42no—
154C2×D4×C43—81no—
155C2×D4×C43—81no—
156C2×D4×C43C2×D411yescharacteristic
157C2×D4×C43C2×D411yescharacteristic
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C2×C22⋊D43—41no—
161C22×Dic43—41no—
162#10621898—42no—
163#10621898—81no—
164C2×D172C2×D411yescharacteristic
165C2×C4×D43—21no—
166C2×C4×D43—41no—
167C2×C4×D43—41no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86C2×D411yescharacteristic
171SD16×C43—82no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43C2×D411yescharacteristic
178C4⋊C4×C43C2×D411yescharacteristic
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—41no—
182C42×C43C2411yescharacteristic
183C22⋊Dic43—41no—
184C22⋊Dic43—41no—
185#10621883—41no—
186#10621883—42no—
187#10621883—42no—
188#10621883—81no—
189#10621883—81no—
190#10621882—42no—
191#10621882SD1614yescomplemented
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—41no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—41no—
199C4⋊Dic43—41no—
200C4⋊Dic43C2×D411yescharacteristic
201C4⋊Dic43C2×D411yescharacteristic
202Dic43⋊C4—21no—
203Dic43⋊C4—41no—
204Dic43⋊C4—41no—
205Dic43⋊C4—41no—
206C4×Dic43—21no—
207#10621877—42no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—81no—
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215C8×D43—42no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—41no—
219C23×C43—82no—
220C23×C43—82no—
221C23×C43—161no—
222C22×D43—21no—
223Q8×C43—81no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—81no—
232D4×C43—82no—
233D4×C43—82no—
234D4×C43C2×SD1612yes—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43H(5,𝔽2)11yescharacteristic
245C22⋊D43—82no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—161no—
252D172—21no—
253D172C2×SD1612yes—
254C4×D43—41no—
255C4×D43—41no—
256C4×D43—82no—
257C4×D43—161no—
258Dic86—21no—
259Dic86—21no—
260Dic86—41no—
261Dic86—41no—
262Dic86—81no—
263C8×C43—41no—
264C8×C43—41no—
265C8×C43—41no—
266C43⋊C8—21no—
267C43⋊C8—21no—
268C43⋊C8—21no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271C43⋊C8C2×SD1612yes—
272#19806—431nomaximal, Sylow
273C22×C43—22no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—164no—
283C22×C43D4211yescharacteristic
284C2×D43—22no—
285C2×D43—41no—
286C2×D43—41no—
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—81no—
291C4×C43C22×SD1611yescharacteristic
292C4×C43#57511yescharacteristic
293C4×C43#57711yescharacteristic
294C4×C43#57711yescharacteristic
295Dic43—41no—
296Dic43—41no—
297Dic43—41no—
298Dic43—81no—
299Dic43—81no—
300#3380—431no—
301#3335—431no—
302#3295—431no—
303#3272—431no—
304#1714—431no—
305#1695—431no—
306#1677—431no—
307#1671—431no—
308#1666—431no—
309#1643—431no—
310#1635—431no—
311#1629D4311yescharacteristic, complemented
312#1622—431no—
313#1583—431no—
314#1580—431no—
315C2×C43—42no—
316C2×C43—81no—
317C2×C43—161no—
318C2×C43#326711yescharacteristic
319C2×C43D4×SD1611yescharacteristic
320C2×C43#328811yescharacteristic
321D43—42no—
322C2×AGL(1,ℤ/8)—861no—
323#554—431no—
324#554—431no—
325#547—431no—
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#476C2×D4311yescharacteristic
342#476C2×D4311yescharacteristic
343#475—431no—
344#468—861no—
345#465—861no—
346#465—861no—
347#461—431no—
348#460—431no—
349#459—431no—
350#450—861no—
351#450—861no—
352#449—861no—
353C8×Q8—431no—
354C4×SD16—431no—
355C4×D8—431no—
356C4×D8—861no—
357#436—431no—
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#331C2×D4311yescharacteristic
368Q8⋊C8—431no—
369D4⋊C8—431no—
370D4⋊C8C2×D4311yescharacteristic
371D4⋊C8C2×D4311yescharacteristic
372#322—431no—
373C43#1980611yescharacteristic, complemented, Sylow
374C2×#41—861no—
375C22×D4—21no—
376C22×D4—21no—
377AGL(1,ℤ/8)—1724no—
378C2×SD16—41no—
379C2×SD16—431no—
380C2×SD16—861no—
381C2×SD16—861no—
382C2×SD16—861no—
383C2×SD16—861no—
384C2×D8—431no—
385C2×D8—861no—
386C2×M16—861no—
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—1721no—
396C22⋊Q8—861no—
397C22⋊Q8—861no—
398C22⋊Q8—861no—
399C22⋊Q8—1721no—
400C22⋊Q8—1721no—
401#121—21no—
402#121—21no—
403#121—861no—
404#120—41no—
405C4×Q8—431no—
406C4×D4—431no—
407C4×D4—861no—
408C4×D4—861no—
409C4×D4C22×D4311yescharacteristic
410C4×D4C22×D4311yescharacteristic
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414#107—431no—
415#107—861no—
416#107—861no—
417#106—21no—
418#106—21no—
419#106—431no—
420#106—861no—
421#106—861no—
422#106—861no—
423#106—861no—
424#106—861no—
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8—861no—
428C4⋊C8C22×D4311yescharacteristic
429C4⋊C8C22×D4311yescharacteristic
430#103—431no—
431#103—861no—
432#103—861no—
433#103—1721no—
434#102—21no—
435#102—21no—
436#102—431no—
437#102—431no—
438#102—431no—
439#102—861no—
440#102—861no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—861no—
445C22⋊C8—861no—
446C22⋊C8—861no—
447C22⋊C8—861no—
448C4×C8—431no—
449C4×C8—431no—
450C4×C8—861no—
451C4×C8C22×D4311yescharacteristic
452C24—41no—
453#41—3441no—
454#41—1722no—
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—81no—
467C2×D4—81no—
468C2×D4—431no—
469C2×D4—1721no—
470C2×D4D4×D4311yescharacteristic
471C2×D4D4×D4311yescharacteristic
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—861no—
475C22×C4—1721no—
476C22×C4—1721no—
477C22×C4—1721no—
478SD16—82no—
479SD16—3441no—
480SD16—3441no—
481SD16—1722no—
482SD16—1721no—
483SD16—1722no—
484D8—434no—
485D8—1722no—
486M16—1722no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—431no—
491C2×C8—431no—
492C2×C8—431no—
493C2×C8—431no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—3441no—
497C2×C8—1722no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—431no—
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⋊C4—1721no—
512C4⋊C4D4×D4311yescharacteristic
513C4⋊C4D4×D4311yescharacteristic
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—41no—
517C22⋊C4—861no—
518C22⋊C4—1721no—
519C22⋊C4—1721no—
520C22⋊C4—1721no—
521C42—861no—
522C42C23×D4311yescharacteristic
523C23—21no—
524C23—21no—
525C23—41no—
526C23—82no—
527C23—82no—
528C23—161no—
529C23—861no—
530Q8—81no—
531Q8—861no—
532Q8—861no—
533Q8—3441no—
534Q8—1721no—
535Q8—1721no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—81no—
544D4—82no—
545D4—82no—
546D4—432no—
547D4—861no—
548D4—3442no—
549D4SD16×D4312yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—3442no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—6881no—
566C2×C4—6881no—
567C2×C4C2×D4×D4311yescharacteristic
568C2×C4C2×D4×D4311yescharacteristic
569C2×C4#1306337011yescharacteristic
570C8—41no—
571C8—41no—
572C8—41no—
573C8—432no—
574C8—861no—
575C8—861no—
576C8—861no—
577C8—1721no—
578C8—1721no—
579C22—22no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—164no—
589C22—862no—
590C22—1721no—
591C22—1721no—
592C22#1458353111yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—81no—
597C4—3441no—
598C4—3441no—
599C4—1721no—
600C4—1721no—
601C4—1721no—
602C4C2×SD16×D4311yescharacteristic
603C4#1458369511yescharacteristic
604C4#1458370511yescharacteristic
605C4#1458370911yescharacteristic
606C2—42no—
607C2—81no—
608C2—161no—
609C2—1722no—
610C2#1914611811yescharacteristic
611C2#1914628911yescharacteristic
612C2#1914635611yescharacteristic
subgroupG/H
centerC22#14583531
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1629C2
socleC22×C43D42
prime radical#19146191C2
hypercenter#1629D43
hypocenterC43#19806
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1629

Complements

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

NH ≅ G/Ntype
1. #19147461C2semidirect
2. #19146949C2semidirect
3. #19146419C2semidirect
5. #19134215C2semidirect
6. #19134116C2semidirect
7. #19134003C2semidirect
8. #19133972C2semidirect
9. #19133942C2semidirect
10. #19133804C2semidirect
11. #19133749C2semidirect
12. #19133664C2semidirect
13. #19133441C2semidirect
14. #19133416C2semidirect
15. C43×#1629C2semidirect
17. #14583610C22semidirect
20. #14583302C22semidirect
22. #14583295C22semidirect
24. #14583250C22semidirect
31. #14583190C22semidirect
33. #14583185C22semidirect
43. #14583023C22semidirect
49. #14582964C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582648C22semidirect
55. #14582647C22semidirect
56. #14582646C22semidirect
57. #14582631C22semidirect
58. #14582628C22semidirect
59. #14582621C22semidirect
191. #10621882SD16semidirect
311. #1629D43semidirect
373. C43#19806semidirect

Maximal subgroups

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

subgroupindex
#191474612
#191469492
#191464192
#191461912
#191342152
#191341162
#191340032
#191339722
#191339422
#191338042
#191337492
#191336642
#191334412
#191334162
C43×#16292
#1980643