Finite Group Databasebeta

← #25086232

Subgroups — #25086232

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#19147458C211yesmaximal, characteristic, complemented
2#19146905C211yesmaximal, characteristic, complemented
3#19146422C211yesmaximal, characteristic, complemented
4#19146411C211yesmaximal, characteristic
5#19134246C211yesmaximal, characteristic, complemented
6#19134126C211yesmaximal, characteristic, complemented
7#19134049C211yesmaximal, characteristic, complemented
8#19134037C211yesmaximal, characteristic, complemented
9#19133993C211yesmaximal, characteristic, complemented
10#19133811C211yesmaximal, characteristic, complemented
11#19133749C211yesmaximal, characteristic, complemented
12#19133709C211yesmaximal, characteristic, complemented
13#19133427C211yesmaximal, characteristic, complemented
14#19133410C211yesmaximal, characteristic, complemented
15C43×#1622C211yesmaximal, characteristic, complemented
16#14583609C2211yescharacteristic
17#14583554C2211yescharacteristic
18#14583534C2211yescharacteristic
19#14583302C2211yescharacteristic, complemented
20#14583298—21no—
21#14583251C2211yescharacteristic, complemented
22#14583250C2211yescharacteristic, complemented
23#14583245C2211yescharacteristic
24#14583245C2211yescharacteristic
25#14583229—21no—
26#14583216—21no—
27#14583211—21no—
28#14583199—21no—
29#14583196—21no—
30#14583190C2211yescharacteristic
31#14583189C2211yescharacteristic, complemented
32#14583186C2211yescharacteristic
33#14583186C2211yescharacteristic
34#14583180C2211yescharacteristic
35#14583155—21no—
36#14583132—21no—
37#14583125—21no—
38#14583109C2211yescharacteristic, complemented
39#14583059—21no—
40#14583048—21no—
41#14583031—21no—
42Q8×C43⋊C8C2211yescharacteristic, complemented
43C4×#10621884C2211yescharacteristic
44C4×#10621882—21no—
45C4×#10621882C2211yescharacteristic
46#14582977C2211yescharacteristic, complemented
47#14582964C2211yescharacteristic
48#14582964C2211yescharacteristic
49#14582898—21no—
50#102×D43—21no—
51#102×D43—21no—
52#14582651C2211yescharacteristic, complemented
53#14582651C2211yescharacteristic, complemented
54#14582647C2211yescharacteristic, complemented
55#14582646C2211yescharacteristic, complemented
56#14582643C2211yescharacteristic
57#14582628C2211yescharacteristic
58#14582628C2211yescharacteristic
59#14582621C2211yescharacteristic, complemented
60C43×#554C2211yescharacteristic, complemented
61C43×#492C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C43×#459C2211yescharacteristic
64C43×#333C2211yescharacteristic, complemented
65C43×Q8⋊C8C2211yescharacteristic, complemented
66C43×D4⋊C8C2211yescharacteristic, complemented
67C2×#10621898—21no—
68C2×D4×D43—21no—
69C2×D4×D43—21no—
70C2×#10621885—21no—
71C2×#10621884D411yescharacteristic
72C2×#10621882D411yescharacteristic
73C2×#10621877—21no—
74C2×C8×D43—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—
84#13063296—21no—
85#13063296—21no—
86#13063293—41no—
87C4×D172—21no—
88C4×D172C2311yescharacteristic
89C4×D172C2311yescharacteristic
90C4⋊C4×D43—21no—
91C4⋊C4×D43—21no—
92#13063259—21no—
93#13063258—21no—
94#13063258—21no—
95#13063258D411yescharacteristic
96#13063257—21no—
97#13063256—21no—
98#13063256—21no—
99#13063256—21no—
100#13063256D411yescharacteristic
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104#13063250—41no—
105#13063249D411yescharacteristic
106#13063248—21no—
107#13063248—21no—
108#13063248—21no—
109#13063247—21no—
110#13063247—21no—
111#13063246—21no—
112#13063246—21no—
113#13063246—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246D411yescharacteristic
117#13063245—21no—
118#13063245—21no—
119#13063245D411yescharacteristic
120#13063245D411yescharacteristic
121C22⋊(C43⋊C8)—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8—21no—
124C4×C43⋊C8—21no—
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C2×SD16×C43—21no—
128C2×SD16×C43—41no—
129C2×D8×C43—21no—
130C4⋊Q8×C43C2311yescharacteristic
131#127×C43C2311yescharacteristic
132#125×C43—21no—
133C22⋊Q8×C43—21no—
134C22⋊Q8×C43—41no—
135C4×Q8×C43C2311yescharacteristic
136C4×D4×C43—21no—
137C4×D4×C43C2311yescharacteristic
138C2×C4⋊C4×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#102×C43—21no—
142#102×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C23×D43—41no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43—41no—
153C2×C22⋊D43—41no—
154C2×C22⋊D43—41no—
155C2×C22⋊D43—41no—
156D4×D43—42no—
157D4×D43—42no—
158D4×D43—81no—
159D4×D43—81no—
160#10621898—42no—
161#10621898—81no—
162C2×D172C2×D411yescharacteristic
163C2×D172C2×D411yescharacteristic
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—41no—
167C2×C4×D43—41no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170SD16×C43—81no—
171SD16×C43—82no—
172D8×C43—81no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43—41no—
181C4⋊C4×C43C2×D411yescharacteristic
182C4⋊C4×C43C2×D411yescharacteristic
183C22⋊C4×C43—21no—
184C22⋊C4×C43—41no—
185C42×C43—21no—
186C42×C43C2411yescharacteristic
187C22⋊Dic43—41no—
188C22⋊Dic43—41no—
189#10621885—81no—
190#10621884—22no—
191#10621882—22no—
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—21no—
194(C2×D43)⋊C4—41no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43C2×D411yescharacteristic
200C4⋊Dic43C2×D411yescharacteristic
201Dic43⋊C4—41no—
202Dic43⋊C4—41no—
203Dic43⋊C4—41no—
204#10621877—81no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C8×D43—81no—
212C8×D43—81no—
213C23×C43—21no—
214C23×C43—41no—
215C22×D43—21no—
216C22×D43—21no—
217C22×D43—82no—
218C22×D43—82no—
219C22×D43—161no—
220Q8×C43—21no—
221Q8×C43—21no—
222Q8×C43—81no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—81no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—161no—
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43H(5,𝔽2)11yescharacteristic
240C22⋊D43—82no—
241C22⋊D43—82no—
242C22⋊D43—82no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247D172—21no—
248D172—21no—
249D172#13512yes—
250D172#13712yes—
251C4×D43—41no—
252C4×D43—41no—
253C4×D43—41no—
254C4×D43—41no—
255C4×D43—82no—
256C4×D43—161no—
257Dic86—41no—
258Dic86—41no—
259Dic86—81no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43—41no—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—21no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269#19774—431nomaximal, Sylow
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43D4211yescharacteristic
277C2×D43—22no—
278C2×D43—22no—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—164no—
284C4×C43—21no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43—81no—
289C4×C43C2×#13511yescharacteristic
290C4×C43C2×#13711yescharacteristic
291C4×C43#57611yescharacteristic
292C4×C43#57711yescharacteristic
293Dic43—41no—
294Dic43—41no—
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#1622D4311yescharacteristic, complemented
310#1581—431no—
311SD16⋊C8—431no—
312C2×C43—81no—
313C2×C43—161no—
314C2×C43#326611yescharacteristic
315C2×C43#328011yescharacteristic
316C2×C43#328811yescharacteristic
317D43—42no—
318D43—42no—
319#554—431no—
320#554C2×D4311yescharacteristic, complemented
321#547—431no—
322D42—431no—
323#500—431no—
324#499—861no—
325#492C2×D4311yescharacteristic
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#460C2×D4311yescharacteristic
345#459C2×D4311yescharacteristic
346#452—861no—
347#450—861no—
348#447—861no—
349C8×Q8—431no—
350C4×SD16—431no—
351C4×D8—431no—
352C4×D8—861no—
353#436—431no—
354C8×D4—431no—
355C8×D4—431no—
356#417—861no—
357C2×#102—861no—
358C2×#102—861no—
359#335—431no—
360#335—431no—
361#333—431no—
362#333C2×D4311yescharacteristic, complemented
363#332—431no—
364#331—431no—
365Q8⋊C8C2×D4311yescharacteristic, complemented
366D4⋊C8—431no—
367D4⋊C8—431no—
368D4⋊C8C2×D4311yescharacteristic, complemented
369#322—431no—
370C43#1977411yescharacteristic, complemented, Sylow
371C2×#41—861no—
372C22×D4—861no—
373C22×D4—861no—
374C2×Q16—861no—
375C2×SD16—21no—
376C2×SD16—41no—
377C2×SD16—431no—
378C2×D8—21no—
379C2×D8—431no—
380C2×M16—861no—
381C22×C8—861no—
382C22×C8—861no—
383C4⋊Q8—431no—
384C4⋊Q8—431no—
385C4⋊Q8C22×D4311yescharacteristic
386#127C22×D4311yescharacteristic
387#125—21no—
388#125—861no—
389#123—1721no—
390C22⋊Q8—21no—
391C22⋊Q8—41no—
392C22⋊Q8—861no—
393C22⋊Q8—861no—
394C22⋊Q8—1721no—
395#121—861no—
396#121—861no—
397#121—861no—
398#120—1721no—
399C4×Q8C22×D4311yescharacteristic
400C4×D4—21no—
401C4×D4—431no—
402C4×D4—431no—
403C4×D4—861no—
404C4×D4C22×D4311yescharacteristic
405C2×C4⋊C4—21no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408#107—431no—
409#107—861no—
410#107—861no—
411#107—861no—
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—21no—
428#102—21no—
429#102—431no—
430#102—431no—
431#102—431no—
432#102—861no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441C22⋊C8—861no—
442C22⋊C8—861no—
443C22⋊C8—861no—
444C4×C8—431no—
445C4×C8—431no—
446C4×C8—861no—
447C4×C8C22×D4311yescharacteristic
448C24—1721no—
449#41—3441no—
450#41—1722no—
451C2×Q8—21no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8D4×D4311yescharacteristic
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—431no—
459C2×D4—431no—
460C2×D4—3441no—
461C2×D4—3441no—
462C2×D4—1721no—
463C2×D4—1721no—
464C2×D4—1722no—
465C2×D4—1722no—
466C2×D4—1721no—
467C2×D4D4×D4311yescharacteristic
468C22×C4—21no—
469C22×C4—41no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—1721no—
473C22×C4—1721no—
474Q16—3441no—
475SD16—81no—
476SD16—82no—
477SD16—862no—
478D8—81no—
479D8—862no—
480M16—3441no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—431no—
485C2×C8—431no—
486C2×C8—431no—
487C2×C8—431no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—3441no—
491C2×C8—3441no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—431no—
498C4⋊C4—431no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—1721no—
504C4⋊C4—1721no—
505C4⋊C4—1721no—
506C4⋊C4D4×D4311yescharacteristic
507C4⋊C4D4×D4311yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—41no—
510C22⋊C4—861no—
511C22⋊C4—861no—
512C22⋊C4—1721no—
513C22⋊C4—1721no—
514C22⋊C4—1721no—
515C42—21no—
516C42C23×D4311yescharacteristic
517C23—21no—
518C23—41no—
519C23—861no—
520C23—861no—
521C23—3442no—
522C23—3442no—
523C23—6881no—
524Q8—21no—
525Q8—21no—
526Q8—81no—
527Q8—3441no—
528Q8—1721no—
529Q8—1721no—
530D4—21no—
531D4—21no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—81no—
537D4—432no—
538D4—432no—
539D4—861no—
540D4—861no—
541D4—3442no—
542D4—3442no—
543D4—3442no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—161no—
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—1721no—
560C2×C4—6881no—
561C2×C4C2×D4×D4311yescharacteristic
562C2×C4C2×D4×D4311yescharacteristic
563C2×C4#1306337011yescharacteristic
564C8—41no—
565C8—41no—
566C8—41no—
567C8—861no—
568C8—861no—
569C8—861no—
570C8—861no—
571C8—1721no—
572C8—1721no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—862no—
580C22—862no—
581C22—1721no—
582C22—1721no—
583C22—1721no—
584C22—1721no—
585C22—6884no—
586C22#1458353111yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—81no—
592C4—3441no—
593C4—3441no—
594C4—1721no—
595C4—1721no—
596C4#135×D4311yescharacteristic
597C4#137×D4311yescharacteristic
598C4#1458370311yescharacteristic
599C4#1458370511yescharacteristic
600C2—81no—
601C2—161no—
602C2—1722no—
603C2—1722no—
604C2#1914610811yescharacteristic
605C2#1914627811yescharacteristic
606C2#1914635611yescharacteristic
subgroupG/H
centerC22#14583531
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1622C2
socleC22×C43D42
prime radical#19146411C2
hypercenter#1622D43
hypocenterC43#19774
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1622

Complements

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

NH ≅ G/Ntype
1. #19147458C2semidirect
2. #19146905C2semidirect
3. #19146422C2semidirect
5. #19134246C2semidirect
6. #19134126C2semidirect
7. #19134049C2semidirect
8. #19134037C2semidirect
9. #19133993C2semidirect
10. #19133811C2semidirect
11. #19133749C2semidirect
12. #19133709C2semidirect
13. #19133427C2semidirect
14. #19133410C2semidirect
15. C43×#1622C2semidirect
19. #14583302C22semidirect
21. #14583251C22semidirect
22. #14583250C22semidirect
31. #14583189C22semidirect
38. #14583109C22semidirect
42. Q8×C43⋊C8C22semidirect
46. #14582977C22semidirect
52. #14582651C22semidirect
53. #14582651C22semidirect
54. #14582647C22semidirect
55. #14582646C22semidirect
59. #14582621C22semidirect
60. C43×#554C22semidirect
64. C43×#333C22semidirect
65. C43×Q8⋊C8C22semidirect
66. C43×D4⋊C8C22semidirect
309. #1622D43semidirect
320. #554C2×D43semidirect
362. #333C2×D43semidirect
365. Q8⋊C8C2×D43semidirect
368. D4⋊C8C2×D43semidirect
370. C43#19774semidirect

Maximal subgroups

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

subgroupindex
#191474582
#191469052
#191464222
#191464112
#191342462
#191341262
#191340492
#191340372
#191339932
#191338112
#191337492
#191337092
#191334272
#191334102
C43×#16222
#1977443