Finite Group Databasebeta

← #25086234

Subgroups — #25086234

Order 11008.

650 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147460C211yesmaximal, characteristic, complemented
2#19146912C211yesmaximal, characteristic, complemented
3#19146420C211yesmaximal, characteristic, complemented
4#19146410C211yesmaximal, characteristic
5#19134248C211yesmaximal, characteristic, complemented
6#19134128C211yesmaximal, characteristic, complemented
7#19134046C211yesmaximal, characteristic, complemented
8#19134040C211yesmaximal, characteristic, complemented
9#19133995C211yesmaximal, characteristic, complemented
10#19133812C211yesmaximal, characteristic, complemented
11#19133749C211yesmaximal, characteristic, complemented
12#19133713C211yesmaximal, characteristic, complemented
13#19133669C211yesmaximal, characteristic, complemented
14#19133409C211yesmaximal, characteristic, complemented
15C43×#1581C211yesmaximal, characteristic, complemented
16#14583606C2211yescharacteristic
17#14583606C2211yescharacteristic, complemented
18#14583554C2211yescharacteristic
19D4×D172C2211yescharacteristic
20#14583304C2211yescharacteristic, complemented
21#14583300—21no—
22#14583272C2211yescharacteristic
23#14583250C2211yescharacteristic, complemented
24#14583250C2211yescharacteristic, complemented
25#14583246C2211yescharacteristic
26#14583246C2211yescharacteristic
27#14583230—21no—
28#14583218—21no—
29#14583214—21no—
30#14583197—21no—
31#14583197—21no—
32#14583190C2211yescharacteristic
33#14583190C2211yescharacteristic
34#14583189C2211yescharacteristic
35#14583189C2211yescharacteristic, complemented
36#14583179C2211yescharacteristic
37#14583157—21no—
38#14583134—21no—
39#14583128—21no—
40#14583110C2211yescharacteristic, complemented
41#14583100C2211yescharacteristic
42#14583094C2211yescharacteristic
43#14583063—21no—
44#14583052—21no—
45#14583031—21no—
46C8×Dic86C2211yescharacteristic, complemented
47C4×#10621873C2211yescharacteristic
48D8×Dic43—21no—
49C8×D172C2211yescharacteristic
50#14582901—21no—
51C2×#13063247—21no—
52#102×D43—21no—
53#14582652C2211yescharacteristic, complemented
54#14582647C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582646C2211yescharacteristic, complemented
57#14582642C2211yescharacteristic
58#14582631C2211yescharacteristic, complemented
59#14582628C2211yescharacteristic
60C4×D8×C43C2211yescharacteristic
61C43×#436C2211yescharacteristic, complemented
62C8×D4×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic, complemented
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic, complemented
66C43×#322C2211yescharacteristic, complemented
67C2×#10621898—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70C2×Dic172—21no—
71C2×#10621873—21no—
72C2×#10621873—41no—
73C2×#10621873D411yescharacteristic
74C2×#10621882—21no—
75C2×C8×D43—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063322C2311yescharacteristic
80#13063316—21no—
81#13063316—21no—
82#13063307—41no—
83#13063304—21no—
84#13063304—21no—
85#13063304—21no—
86#13063302—41no—
87#13063302—41no—
88#13063300—21no—
89#13063299—21no—
90#13063296—21no—
91#13063295—41no—
92C4×Dic86C2311yescharacteristic
93C4×D172C2311yescharacteristic
94D4×Dic43—21no—
95D4×Dic43—21no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43—21no—
98C4⋊C4×D43—21no—
99#13063259—21no—
100#13063259—21no—
101#13063258—21no—
102#13063257—21no—
103#13063257—21no—
104#13063257D411yescharacteristic
105#13063256—21no—
106#13063256—21no—
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110#13063250—21no—
111#13063250—21no—
112#13063250—21no—
113#13063250—41no—
114#13063250D411yescharacteristic
115#13063247—21no—
116#13063247—21no—
117#13063247—21no—
118#13063247—21no—
119#13063247—21no—
120#13063247—21no—
121#13063247—21no—
122#13063247D411yescharacteristic
123#13063246—21no—
124#13063246—21no—
125#13063246—21no—
126#13063245—21no—
127(C2×D43)⋊C8—21no—
128C8×Dic43—21no—
129C2×D8×C43D411yescharacteristic
130C2×M16×C43—21no—
131C22×C8×C43—21no—
132C4×D4×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#107×C43D411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#102×C43D411yescharacteristic
138#102×C43D411yescharacteristic
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C23×D43—41no—
145C2×D4×C43C2×D411yescharacteristic
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C2×C22⋊D43—41no—
150C2×C22⋊D43—41no—
151C22×Dic43—41no—
152C22×Dic43—41no—
153D4×D43—42no—
154D4×D43—81no—
155#10621898—42no—
156#10621898—81no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—41no—
161C2×D172—42no—
162C2×D172—81no—
163C2×D172C2×D411yescharacteristic
164C2×C4×D43—21no—
165C2×C4×D43—41no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86C2×D411yescharacteristic
170D8×C43—22no—
171M16×C43—81no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—81no—
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C4⋊C4×C43C2×D411yescharacteristic
181C4⋊C4×C43C2×D411yescharacteristic
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C42×C43C2411yescharacteristic
185C22⋊Dic43—41no—
186C22⋊Dic43—41no—
187C22⋊Dic43—41no—
188#10621882—81no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—41no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—41no—
198C4⋊Dic43—41no—
199C4⋊Dic43C2×D411yescharacteristic
200C4⋊Dic43C2×D411yescharacteristic
201Dic43⋊C4—21no—
202Dic43⋊C4—41no—
203Dic43⋊C4—41no—
204Dic43⋊C4—41no—
205C4×Dic43—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208Dic172—81no—
209#10621873—22no—
210#10621873—81no—
211#10621873—82no—
212C8×D43—81no—
213C23×C43—21no—
214C23×C43—21no—
215C22×D43—21no—
216C22×D43—41no—
217C22×D43—82no—
218C22×D43—82no—
219C22×D43—161no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43#13712yes—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43H(5,𝔽2)11yescharacteristic
233C22⋊D43—82no—
234C22⋊D43—82no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—161no—
242C2×Dic43—161no—
243D172—21no—
244D172—41no—
245D172—41no—
246D172—41no—
247D172—41no—
248D172—81no—
249D172—82no—
250D172#13512yes—
251C4×D43—41no—
252C4×D43—41no—
253C4×D43—82no—
254Dic86—21no—
255Dic86—21no—
256Dic86—41no—
257Dic86—41no—
258Dic86—81no—
259Dic86—81no—
260C8×C43—21no—
261C8×C43—21no—
262C8×C43—21no—
263C8×C43—21no—
264C8×C43—41no—
265C8×C43—41no—
266C8×C43—41no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269#19774—431nomaximal, Sylow
270C22×C43—22no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43D4211yescharacteristic
277C2×D43—22no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—164no—
284C4×C43—21no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43C2×#13511yescharacteristic
288C4×C43C2×#13711yescharacteristic
289C4×C43#57611yescharacteristic
290C4×C43#57711yescharacteristic
291Dic43—41no—
292Dic43—41no—
293Dic43—41no—
294Dic43—81no—
295Dic43—81no—
296Dic43—81no—
297#3380—431no—
298#3331—431no—
299#3295—431no—
300#3294—431no—
301#1719—431no—
302#1697—431no—
303#1683—431no—
304#1682—431no—
305#1675—431no—
306#1644—431no—
307#1635—431no—
308#1629—431no—
309#1622—431no—
310#1581D4311yescharacteristic, complemented
311SD16⋊C8—431no—
312C2×C43—42no—
313C2×C43—81no—
314C2×C43#326611yescharacteristic
315C2×C43#328011yescharacteristic
316C2×C43#328811yescharacteristic
317D43—42no—
318D43—161no—
319#554—431no—
320#554—431no—
321#547—431no—
322D42—431no—
323#500—431no—
324#499—861no—
325#492—431no—
326#487—431no—
327#487—431no—
328#486—431no—
329#486—431no—
330#483—861no—
331#481—861no—
332#480—861no—
333#478—861no—
334#478—861no—
335#476—431no—
336#476—431no—
337#476—431no—
338#476—431no—
339#474—431no—
340#470—861no—
341#466—861no—
342#465—861no—
343#462—431no—
344#460—431no—
345#459—431no—
346#452—861no—
347#450—861no—
348#447—861no—
349C8×Q8—431no—
350C4×SD16—431no—
351C4×D8—861no—
352C4×D8C2×D4311yescharacteristic
353#436C2×D4311yescharacteristic, complemented
354C8×D4—431no—
355C8×D4C2×D4311yescharacteristic
356#417—861no—
357C2×#102—861no—
358C2×#102—861no—
359#335—431no—
360#335C2×D4311yescharacteristic, complemented
361#333—431no—
362#333—431no—
363#332—431no—
364#331—431no—
365Q8⋊C8—431no—
366D4⋊C8—431no—
367D4⋊C8C2×D4311yescharacteristic
368D4⋊C8C2×D4311yescharacteristic, complemented
369#322C2×D4311yescharacteristic, complemented
370C43#1977411yescharacteristic, complemented, Sylow
371C2×#41—861no—
372C22×D4—861no—
373C22×D4—861no—
374C2×Q16—861no—
375C2×SD16—431no—
376C2×SD16—861no—
377C2×SD16—1721no—
378C2×D8—861no—
379C2×D8D17211yescharacteristic
380C2×M16—21no—
381C22×C8—21no—
382C22×C8—861no—
383C4⋊Q8—431no—
384C4⋊Q8—431no—
385C4⋊Q8—431no—
386#127—431no—
387#125—861no—
388#125—861no—
389#123—1721no—
390C22⋊Q8—861no—
391C22⋊Q8—861no—
392C22⋊Q8—861no—
393C22⋊Q8—1721no—
394C22⋊Q8—1721no—
395#121—861no—
396#121—861no—
397#121—861no—
398#120—1721no—
399C4×Q8—431no—
400C4×D4—431no—
401C4×D4—861no—
402C4×D4—861no—
403C4×D4C22×D4311yescharacteristic
404C4×D4C22×D4311yescharacteristic
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408#107—861no—
409#107—861no—
410#107—861no—
411#107D17211yescharacteristic
412#106—431no—
413#106—861no—
414#106—861no—
415#106—861no—
416#106—861no—
417C4⋊C8—431no—
418C4⋊C8—431no—
419C4⋊C8—861no—
420C4⋊C8C22×D4311yescharacteristic
421C4⋊C8C22×D4311yescharacteristic
422#103—431no—
423#103—861no—
424#103—861no—
425#103—861no—
426#103—1721no—
427#102—431no—
428#102—861no—
429#102—861no—
430#102—861no—
431#102—861no—
432#102—861no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439#102D17211yescharacteristic
440#102D17211yescharacteristic
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8—861no—
444C4×C8—861no—
445C4×C8C22×D4311yescharacteristic
446C4×C8C22×D4311yescharacteristic
447C4×C8C22×D4311yescharacteristic
448C24—1721no—
449#41—3441no—
450#41—1722no—
451C2×Q8—431no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—861no—
455C2×D4—431no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—3441no—
460C2×D4—3441no—
461C2×D4—1721no—
462C2×D4—1722no—
463C2×D4—1721no—
464C2×D4—1721no—
465C2×D4—1722no—
466C2×D4C2×D17211yescharacteristic
467C2×D4C2×D17211yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—861no—
471C22×C4—1721no—
472C22×C4—1721no—
473C22×C4—1721no—
474Q16—3441no—
475SD16—862no—
476SD16—3442no—
477SD16—3441no—
478D8—22no—
479D8—3441no—
480M16—81no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—81no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—3441no—
488C2×C8C2×D17211yescharacteristic
489C2×C8C2×D17211yescharacteristic
490C2×C8D4×D4311yescharacteristic
491C2×C8D4×D4311yescharacteristic
492C4⋊C4—431no—
493C4⋊C4—431no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—1721no—
502C4⋊C4—1721no—
503C4⋊C4—1721no—
504C4⋊C4—1721no—
505C4⋊C4—1721no—
506C4⋊C4C2×D17211yescharacteristic
507C4⋊C4C2×D17211yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—861no—
511C22⋊C4—1721no—
512C22⋊C4—1721no—
513C22⋊C4—1721no—
514C22⋊C4—1721no—
515C42—861no—
516C42C23×D4311yescharacteristic
517C23—21no—
518C23—21no—
519C23—861no—
520C23—3442no—
521C23—3442no—
522C23—1721no—
523C23—6881no—
524Q8—861no—
525Q8—861no—
526Q8—3441no—
527Q8—3441no—
528Q8—1721no—
529Q8—1721no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—432no—
534D4—861no—
535D4—3441no—
536D4—3442no—
537D4—3442no—
538D4—3442no—
539D4—1721no—
540D4—1721no—
541D4—1721no—
542D4—1721no—
543D4#1306335812yes—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—3442no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—6881no—
560C2×C4—6881no—
561C2×C4C2×D4×D4311yescharacteristic
562C2×C4C22×D17211yescharacteristic
563C2×C4#1306337111yescharacteristic
564C8—21no—
565C8—21no—
566C8—21no—
567C8—21no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—1721no—
572C8—1721no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—862no—
580C22—3441no—
581C22—3441no—
582C22—3441no—
583C22—1721no—
584C22—1721no—
585C22—6884no—
586C22D4×D17211yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—3441no—
591C4—3441no—
592C4—3441no—
593C4—1721no—
594C4—1721no—
595C4—1721no—
596C4#135×D4311yescharacteristic
597C4C2×#1306335811yescharacteristic
598C4#1458370011yescharacteristic
599C4#1458371111yescharacteristic
600C2—42no—
601C2—81no—
602C2—1722no—
603C2—6881no—
604C2#1914611011yescharacteristic
605C2#1914628111yescharacteristic
606C2#1914636211yescharacteristic
subgroupG/H
centerC22D4×D172
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1581C2
socleC22×C43D42
prime radical#19146410C2
hypercenter#1581D43
hypocenterC43#19774
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1581

Complements

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

NH ≅ G/Ntype
1. #19147460C2semidirect
2. #19146912C2semidirect
3. #19146420C2semidirect
5. #19134248C2semidirect
6. #19134128C2semidirect
7. #19134046C2semidirect
8. #19134040C2semidirect
9. #19133995C2semidirect
10. #19133812C2semidirect
11. #19133749C2semidirect
12. #19133713C2semidirect
13. #19133669C2semidirect
14. #19133409C2semidirect
15. C43×#1581C2semidirect
17. #14583606C22semidirect
20. #14583304C22semidirect
23. #14583250C22semidirect
24. #14583250C22semidirect
35. #14583189C22semidirect
40. #14583110C22semidirect
46. C8×Dic86C22semidirect
53. #14582652C22semidirect
54. #14582647C22semidirect
55. #14582647C22semidirect
56. #14582646C22semidirect
58. #14582631C22semidirect
61. C43×#436C22semidirect
63. C43×#335C22semidirect
65. C43×D4⋊C8C22semidirect
66. C43×#322C22semidirect
310. #1581D43semidirect
353. #436C2×D43semidirect
360. #335C2×D43semidirect
368. D4⋊C8C2×D43semidirect
369. #322C2×D43semidirect
370. C43#19774semidirect

Maximal subgroups

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

subgroupindex
#191474602
#191469122
#191464202
#191464102
#191342482
#191341282
#191340462
#191340402
#191339952
#191338122
#191337492
#191337132
#191336692
#191334092
C43×#15812
#1977443