Finite Group Databasebeta

← #25086098

Subgroups — #25086098

Order 11008.

668 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147509C211yesmaximal, characteristic, complemented
2#19147450C211yesmaximal, characteristic, complemented
3#19146419C211yesmaximal, characteristic
4D4×#10621883C211yesmaximal, characteristic
5#19134215C211yesmaximal, characteristic, complemented
6#19134066C211yesmaximal, characteristic, complemented
7#19134010C211yesmaximal, characteristic, complemented
8#19133992C211yesmaximal, characteristic, complemented
9#19133972C211yesmaximal, characteristic, complemented
10#19133804C211yesmaximal, characteristic, complemented
11#19133763C211yesmaximal, characteristic, complemented
12#19133671C211yesmaximal, characteristic, complemented
13#19133428C211yesmaximal, characteristic, complemented
14#19133404C211yesmaximal, characteristic, complemented
15C43×#1629C211yesmaximal, characteristic
16C22×#10621883—21no—
17#14583629C2211yescharacteristic, complemented
18#14583606C2211yescharacteristic
19D4×Dic86C2211yescharacteristic
20#14583306—21no—
21#14583302C2211yescharacteristic, complemented
22#14583296—21no—
23#14583295C2211yescharacteristic, complemented
24#14583271C2211yescharacteristic
25#14583250C2211yescharacteristic, complemented
26#14583245C2211yescharacteristic
27#14583215—21no—
28#14583209—21no—
29#14583195C2211yescharacteristic, complemented
30#14583189C2211yescharacteristic
31#14583187—21no—
32#14583185C2211yescharacteristic, complemented
33#14583183—21no—
34#14583177—21no—
35#14583126—21no—
36#14583126—21no—
37#14583104C2211yescharacteristic
38#14583096C2211yescharacteristic
39#14583096C2211yescharacteristic
40#14583050—21no—
41#14583050—21no—
42#14583037—21no—
43#14583026C2211yescharacteristic, complemented
44#14583023C2211yescharacteristic, complemented
45#14582996—21no—
46#14582990—21no—
47C4×#10621883C2211yescharacteristic
48C4×#10621883C2211yescharacteristic
49D4×C43⋊C8C2211yescharacteristic
50D4×C43⋊C8C2211yescharacteristic
51C2×#13063246—21no—
52#14582651C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582646C2211yescharacteristic, complemented
57#14582631C2211yescharacteristic, complemented
58#14582631C2211yescharacteristic, complemented
59#14582621C2211yescharacteristic, complemented
60D42×C43C2211yescharacteristic
61C43×#492C2211yescharacteristic
62C43×#476C2211yescharacteristic
63C43×#476C2211yescharacteristic
64C43×#331C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×D4⋊C8C2211yescharacteristic
67C22×Dic86—21no—
68C2×#10621883—21no—
69C2×#10621883—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621883—44no—
74C2×#10621883D411yescharacteristic
75C2×#10621883D411yescharacteristic
76C22×C43⋊C8—21no—
77C22×C43⋊C8—21no—
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063324—21no—
81#13063324—21no—
82#13063324—21no—
83#13063323—41no—
84#13063316—21no—
85#13063304—21no—
86#13063304—21no—
87#13063302—41no—
88#13063302—41no—
89C4×Dic86C2311yescharacteristic
90C4×Dic86C2311yescharacteristic
91#13063290—21no—
92#13063290—21no—
93D4×Dic43—21no—
94D4×Dic43—21no—
95C2×C4⋊Dic43—21no—
96#13063259—21no—
97#13063258—21no—
98#13063258—21no—
99#13063257—21no—
100#13063256—21no—
101#13063256—21no—
102#13063256—21no—
103#13063256D411yescharacteristic
104#13063256D411yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109#13063250—21no—
110#13063250—21no—
111#13063250—41no—
112#13063248—21no—
113#13063248D411yescharacteristic
114#13063248D411yescharacteristic
115#13063246—21no—
116#13063246—21no—
117#13063246—21no—
118#13063246—21no—
119#13063246—21no—
120#13063246D411yescharacteristic
121#13063246D411yescharacteristic
122C22⋊(C43⋊C8)—21no—
123C22⋊(C43⋊C8)—21no—
124#13063235—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—
160C22×Dic43—41no—
161C22×Dic43—41no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—42no—
165C2×Dic86—41no—
166C2×Dic86—41no—
167C2×Dic86—81no—
168C2×Dic86C2×D411yescharacteristic
169C2×Dic86C2×D411yescharacteristic
170SD16×C43—82no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—41no—
181C42×C43C2411yescharacteristic
182C22⋊Dic43—41no—
183C22⋊Dic43—41no—
184#10621883—22no—
185#10621883—42no—
186#10621883—42no—
187#10621883—42no—
188#10621883—81no—
189#10621883—81no—
190#10621883SD1614yescomplemented
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—41no—
196C4⋊Dic43C2×D411yescharacteristic
197C4⋊Dic43C2×D411yescharacteristic
198Dic43⋊C4—21no—
199Dic43⋊C4—21no—
200Dic43⋊C4—41no—
201Dic43⋊C4—41no—
202Dic43⋊C4—41no—
203Dic43⋊C4—41no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—41no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—42no—
210C2×C43⋊C8—81no—
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—41no—
218C23×C43—82no—
219C23×C43—82no—
220C23×C43—161no—
221Q8×C43—81no—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—81no—
229D4×C43—82no—
230D4×C43—82no—
231D4×C43C2×SD1612yes—
232D4×C43#13712yes—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—82no—
250C2×Dic43—161no—
251Dic86—21no—
252Dic86—21no—
253Dic86—21no—
254Dic86—41no—
255Dic86—41no—
256Dic86—82no—
257Dic86—81no—
258Dic86—161no—
259Dic86C2×SD1612yes—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43—41no—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268C43⋊C8C2×SD1612yes—
269#19765—431nomaximal, Sylow
270C22×C43—22no—
271C22×C43—22no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—164no—
280C22×C43D4211yescharacteristic
281C4×C43—21no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—81no—
285C4×C43C22×SD1611yescharacteristic
286C4×C43C2×#13711yescharacteristic
287C4×C43#57711yescharacteristic
288C4×C43#57711yescharacteristic
289Dic43—22no—
290Dic43—41no—
291Dic43—41no—
292Dic43—41no—
293Dic43—81no—
294Dic43—81no—
295#3385—431no—
296Q8×SD16—431no—
297#3295—431no—
298D4×SD16—431no—
299#1714—431no—
300#1686—431no—
301#1678—431no—
302#1675—431no—
303#1671—431no—
304#1643—431no—
305#1637—431no—
306#1629D4311yescharacteristic
307#1623—431no—
308#1582—431no—
309SD16⋊C8—431no—
310C2×C43—42no—
311C2×C43—42no—
312C2×C43—161no—
313C2×C43#326611yescharacteristic
314C2×C43D4×SD1611yescharacteristic
315C2×C43#328811yescharacteristic
316C22×SD16—861no—
317Q82—431no—
318#554—431no—
319D4×Q8—431no—
320D42C2×D4311yescharacteristic
321#501—861no—
322#500—431no—
323#498—431no—
324#498—861no—
325#492—431no—
326#492C2×D4311yescharacteristic
327#487—431no—
328#486—431no—
329#481—861no—
330#479—861no—
331#477—431no—
332#476—431no—
333#476—861no—
334#476C2×D4311yescharacteristic
335#476C2×D4311yescharacteristic
336#475—431no—
337#475—861no—
338#474—861no—
339#465—861no—
340#465—861no—
341#461—431no—
342#460—431no—
343#460—431no—
344#450—861no—
345#450—861no—
346#448—861no—
347#446—431no—
348C8×Q8—431no—
349#440—861no—
350C4×SD16—431no—
351C4×SD16—431no—
352C4×SD16—861no—
353C8×D4—431no—
354C8×D4—431no—
355C2×#102—861no—
356#335—431no—
357#334—431no—
358#333—431no—
359#333—431no—
360#332—431no—
361#331C2×D4311yescharacteristic
362Q8⋊C8—431no—
363Q8⋊C8—431no—
364D4⋊C8C2×D4311yescharacteristic
365D4⋊C8C2×D4311yescharacteristic
366#322—431no—
367C43#1976511yescharacteristic, complemented, Sylow
368C22×Q8—861no—
369C22×D4—21no—
370C22×D4—21no—
371C2×SD16—41no—
372C2×SD16—431no—
373C2×SD16—431no—
374C2×SD16—861no—
375C2×SD16—861no—
376C2×SD16—861no—
377C2×SD16—861no—
378C2×SD16—861no—
379C2×SD16—1724no—
380C22×C8—861no—
381C22×C8—861no—
382C4⋊Q8—431no—
383C4⋊Q8—431no—
384C4⋊Q8—861no—
385C4⋊Q8—861no—
386C4⋊Q8—861no—
387C4⋊Q8—1721no—
388C4⋊Q8C22×D4311yescharacteristic
389#127C22×D4311yescharacteristic
390#125—861no—
391C22⋊Q8—861no—
392C22⋊Q8—861no—
393C22⋊Q8—1721no—
394C22⋊Q8—1721no—
395#121—21no—
396#121—21no—
397#120—41no—
398C4×Q8—431no—
399C4×Q8—431no—
400C4×Q8—861no—
401C4×Q8—861no—
402C4×D4—861no—
403C4×D4—861no—
404C4×D4C22×D4311yescharacteristic
405C4×D4C22×D4311yescharacteristic
406C2×C4⋊C4—861no—
407#107—861no—
408#107—861no—
409#107—861no—
410#106—21no—
411#106—21no—
412#106—431no—
413#106—431no—
414#106—861no—
415#106—861no—
416#106—861no—
417#106—861no—
418C4⋊C8—431no—
419C4⋊C8—431no—
420C4⋊C8—861no—
421C4⋊C8—861no—
422C4⋊C8C22×D4311yescharacteristic
423C4⋊C8C22×D4311yescharacteristic
424#103—431no—
425#103—431no—
426#103—861no—
427#103—861no—
428#103—861no—
429#103—1721no—
430#102—21no—
431#102—21no—
432#102—431no—
433#102—431no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439C22⋊C8—861no—
440C22⋊C8—861no—
441#97—861no—
442C4×C8—431no—
443C4×C8—431no—
444C4×C8—861no—
445C4×C8C22×D4311yescharacteristic
446C24—41no—
447C2×Q8—21no—
448C2×Q8—431no—
449C2×Q8—431no—
450C2×Q8—861no—
451C2×Q8—861no—
452C2×Q8—3441no—
453C2×Q8—1721no—
454C2×Q8—1721no—
455C2×Q8—1722no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—81no—
464C2×D4—81no—
465C2×D4D4×D4311yescharacteristic
466C2×D4D4×D4311yescharacteristic
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—1721no—
470C22×C4—1721no—
471SD16—82no—
472SD16—434no—
473SD16—862no—
474SD16—3441no—
475SD16—3441no—
476SD16—1722no—
477SD16—1722no—
478SD16—1722no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—431no—
483C2×C8—431no—
484C2×C8—431no—
485C2×C8—431no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—3441no—
489C2×C8—1722no—
490C4⋊C4—21no—
491C4⋊C4—21no—
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—1721no—
501C4⋊C4—1721no—
502C4⋊C4—1721no—
503C4⋊C4—1721no—
504C4⋊C4—1721no—
505C4⋊C4D4×D4311yescharacteristic
506C4⋊C4D4×D4311yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—41no—
510C22⋊C4—1721no—
511C22⋊C4—1721no—
512C42—861no—
513C42—861no—
514C42—1721no—
515C42C23×D4311yescharacteristic
516C23—21no—
517C23—21no—
518C23—41no—
519C23—82no—
520C23—82no—
521C23—161no—
522Q8—81no—
523Q8—432no—
524Q8—861no—
525Q8—861no—
526Q8—861no—
527Q8—3441no—
528Q8—3442no—
529Q8—1721no—
530Q8—1721no—
531Q8—6881no—
532D4—21no—
533D4—21no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—81no—
539D4—82no—
540D4—82no—
541D4SD16×D4312yes—
542D4#1306335412yes—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—3442no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—6881no—
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4C2×D4×D4311yescharacteristic
560C2×C4#1306337011yescharacteristic
561C8—41no—
562C8—41no—
563C8—41no—
564C8—432no—
565C8—861no—
566C8—861no—
567C8—861no—
568C8—1721no—
569C8—1721no—
570C22—22no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—164no—
580C22#1458353111yescharacteristic
581C4—21no—
582C4—41no—
583C4—41no—
584C4—81no—
585C4—862no—
586C4—3441no—
587C4—3441no—
588C4—1721no—
589C4—1721no—
590C4—1721no—
591C4C2×SD16×D4311yescharacteristic
592C4C2×#1306335411yescharacteristic
593C4#1458370911yescharacteristic
594C4#1458370911yescharacteristic
595C2—42no—
596C2—42no—
597C2—161no—
598C2#1914610911yescharacteristic
599C2#1914628911yescharacteristic
600C2#1914635611yescharacteristic
subgroupG/H
centerC22#14583531
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1629C2
socleC22×C43D42
prime radicalD42×C43C22
hypercenter#1629D43
hypocenterC43#19765
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. #19147509C2semidirect
2. #19147450C2semidirect
5. #19134215C2semidirect
6. #19134066C2semidirect
7. #19134010C2semidirect
8. #19133992C2semidirect
9. #19133972C2semidirect
10. #19133804C2semidirect
11. #19133763C2semidirect
12. #19133671C2semidirect
13. #19133428C2semidirect
14. #19133404C2semidirect
17. #14583629C22semidirect
21. #14583302C22semidirect
23. #14583295C22semidirect
25. #14583250C22semidirect
29. #14583195C22semidirect
32. #14583185C22semidirect
43. #14583026C22semidirect
44. #14583023C22semidirect
52. #14582651C22semidirect
53. #14582649C22semidirect
54. #14582648C22semidirect
55. #14582647C22semidirect
56. #14582646C22semidirect
57. #14582631C22semidirect
58. #14582631C22semidirect
59. #14582621C22semidirect
190. #10621883SD16semidirect
367. C43#19765semidirect

Maximal subgroups

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

subgroupindex
#191475092
#191474502
#191464192
D4×#106218832
#191342152
#191340662
#191340102
#191339922
#191339722
#191338042
#191337632
#191336712
#191334282
#191334042
C43×#16292
#1976543