Finite Group Databasebeta

← #25082043

Subgroups — #25082043

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145546C211yesmaximal, characteristic, complemented
2#19144743C211yesmaximal, characteristic
3#19144668C211yesmaximal, characteristic, complemented
4#19143702C211yesmaximal, characteristic, complemented
5#19134038C211yesmaximal, characteristic, complemented
6#19134030C211yesmaximal, characteristic, complemented
7#19134026C211yesmaximal, characteristic, complemented
8#19134018C211yesmaximal, characteristic, complemented
9#19133964C211yesmaximal, characteristic, complemented
10#19133958C211yesmaximal, characteristic, complemented
11#19133940C211yesmaximal, characteristic, complemented
12#19133372C211yesmaximal, characteristic, complemented
13#19133294C211yesmaximal, characteristic, complemented
14#19133241C211yesmaximal, characteristic, complemented
15C43×#1665C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583447C2211yescharacteristic
18C4×#10621900C2211yescharacteristic
19#14583278C2211yescharacteristic
20#14583250C2211yescharacteristic
21#14583245C2211yescharacteristic
22#14583242—21no—
23#14583222—21no—
24#14583185C2211yescharacteristic
25#14583181C2211yescharacteristic
26#14583179C2211yescharacteristic
27#14583119—21no—
28#14583119—21no—
29#14583110C2211yescharacteristic
30#14583104C2211yescharacteristic
31#14583096C2211yescharacteristic
32#14583062—21no—
33#14583058—21no—
34#14583058—21no—
35#14583041—21no—
36C8×Dic86C2211yescharacteristic
37#14583023C2211yescharacteristic
38#14583011—21no—
39#14582996—21no—
40#14582993—21no—
41#14582990—21no—
42D4×C43⋊C8C2211yescharacteristic
43C8×C22⋊D43—21no—
44(C22⋊D43)⋊C8—21no—
45#14582955C2211yescharacteristic
46#14582951C2211yescharacteristic
47#14582950C2211yescharacteristic
48#14582949—21no—
49C2×Dic43⋊C8—21no—
50C4⋊C8×D43C2211yescharacteristic
51#14582651C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582650C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582645C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582643C2211yescharacteristic
60C43×#492C2211yescharacteristic
61C43×#474C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621900—21no—
68C2×#10621900D411yescharacteristic
69C2×Dic172—21no—
70C2×#10621885—21no—
71C2×#10621885—21no—
72C2×#10621883—21no—
73C2×#10621883—21no—
74C22×C43⋊C8—21no—
75C2×C8×D43—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063316—21no—
79#13063312—21no—
80#13063305—21no—
81#13063301—21no—
82#13063296—21no—
83#13063296—21no—
84Q8×Dic43—21no—
85C4×Dic86C2311yescharacteristic
86#13063290—21no—
87#13063290D411yescharacteristic
88D4×Dic43—21no—
89D4×Dic43—21no—
90D4×Dic43D411yescharacteristic
91C4×C22⋊D43—21no—
92(C22⋊D43)⋊C4—21no—
93#13063283—21no—
94#13063283D411yescharacteristic
95#13063281—21no—
96C2×C4×Dic43—21no—
97C42×D43C2311yescharacteristic
98#13063258—21no—
99#13063257—21no—
100#13063256—21no—
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8D411yescharacteristic
108Dic43⋊C8D411yescharacteristic
109#13063250—21no—
110#13063250—21no—
111#13063250—21no—
112#13063250—21no—
113#13063248—21no—
114#13063248—21no—
115#13063246—21no—
116#13063246—21no—
117#13063246—21no—
118#13063246—21no—
119C22⋊(C43⋊C8)—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8D411yescharacteristic
123(C2×D43)⋊C8D411yescharacteristic
124#13063235—21no—
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×SD16×C43—21no—
130C2×SD16×C43—21no—
131C2×D8×C43—21no—
132C22×C8×C43—21no—
133C4⋊Q8×C43C2311yescharacteristic
134#127×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136#107×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C2×C22⋊D43—21no—
151C2×C22⋊D43—41no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—41no—
155#10621900—22no—
156#10621900—22no—
157#10621900—81no—
158#10621900—81no—
159C2×C4×D43C2×D411yescharacteristic
160C2×C4×D43C2×D411yescharacteristic
161C2×C4×D43#4111yescharacteristic
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86C2×D411yescharacteristic
165SD16×C43—81no—
166SD16×C43—81no—
167D8×C43—42no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—81no—
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43C2×D411yescharacteristic
177C22⋊C4×C43—21no—
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180C22⋊Dic43—41no—
181C22⋊Dic43—41no—
182#10621885—81no—
183#10621885—81no—
184#10621883—42no—
185#10621883—42no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—41no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—41no—
193C4⋊Dic43C2×D411yescharacteristic
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196Dic43⋊C4—41no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—41no—
201C4×Dic43C2×D411yescharacteristic
202C4×Dic43C2×D411yescharacteristic
203C4×Dic43#4111yescharacteristic
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—81no—
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210Dic172—42no—
211C8×D43—81no—
212C23×C43—21no—
213C23×C43—41no—
214C22×D43#12111yescharacteristic
215Q8×C43—41no—
216Q8×C43—41no—
217D4×C43—21no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—81no—
223D4×C43#13512yes—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C22⋊D43—24no—
232C22⋊D43—82no—
233C2×Dic43—24no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—81no—
239C2×Dic43—82no—
240C2×Dic43#12111yescharacteristic
241C2×Dic43#12111yescharacteristic
242C2×Dic43#12111yescharacteristic
243C4×D43—21no—
244C4×D43—21no—
245C4×D43—21no—
246C4×D43—21no—
247C4×D43—41no—
248Dic86—21no—
249Dic86—41no—
250Dic86—41no—
251Dic86—41no—
252Dic86—41no—
253Dic86#13512yes—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43—41no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264#19413—431nomaximal, Sylow
265C22×C43—22no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43C2×#12111yescharacteristic
272C2×D43—21no—
273C2×D43—21no—
274C2×D43—21no—
275C4×C43—21no—
276C4×C43—41no—
277C4×C43—81no—
278C4×C43C2×#13511yescharacteristic
279C4×C43C2×#13511yescharacteristic
280C4×C43#57611yescharacteristic
281C4×C43#57711yescharacteristic
282Dic43—21no—
283Dic43—22no—
284Dic43—21no—
285Dic43—21no—
286Dic43—41no—
287Dic43—81no—
288Dic43—81no—
289#3210—431no—
290#3115—431no—
291#3107—431no—
292#2988—431no—
293#1682—431no—
294#1681—431no—
295#1680—431no—
296#1679—431no—
297#1670—431no—
298#1669—431no—
299#1666—431no—
300#1665D4311yescharacteristic, complemented
301#1572—431no—
302#1552—431no—
303#1540—431no—
304C2×C43—42no—
305C2×C43—161no—
306C2×C43#304511yescharacteristic
307C2×C43#305011yescharacteristic
308C2×C43#306911yescharacteristic
309D43—41no—
310#533—431no—
311#532—431no—
312C4×#41—431no—
313#494—431no—
314#492C2×D4311yescharacteristic
315#487—431no—
316#486—431no—
317#485—861no—
318#482—861no—
319#475—431no—
320#475—431no—
321#474—431no—
322#474C2×D4311yescharacteristic
323#464—861no—
324#464—861no—
325#462—431no—
326#461—431no—
327#460—431no—
328#459C2×D4311yescharacteristic
329#452—861no—
330#452—861no—
331#452—861no—
332#449—861no—
333C8×Q8—431no—
334C8×Q8—431no—
335#442—861no—
336#440—861no—
337C4×Q16—861no—
338C4×SD16—861no—
339C8×D4—431no—
340C8×D4—861no—
341C8×D4—861no—
342C8×D4C2×D4311yescharacteristic
343#432—431no—
344#431—431no—
345#431—431no—
346#431—861no—
347C2×C4⋊C8—431no—
348C2×C4⋊C8—861no—
349#335—431no—
350#335—431no—
351#334—431no—
352#334C2×D4311yescharacteristic
353#332—431no—
354#332—431no—
355#332—431no—
356#332—431no—
357#332—431no—
358#332C2×D4311yescharacteristic
359#331—431no—
360#331C2×D4311yescharacteristic
361C43#1941311yescharacteristic, complemented, Sylow
362C2×#41—431no—
363C2×#41—861no—
364C2×Q16—861no—
365C2×Q16—861no—
366C2×Q16—861no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×D8—21no—
372C22×C8—21no—
373C22×C8—861no—
374C22×C8—861no—
375C4⋊Q8—431no—
376C4⋊Q8—431no—
377C4⋊Q8C22×D4311yescharacteristic
378#127C22×D4311yescharacteristic
379#125—861no—
380#124—861no—
381C22⋊Q8—861no—
382C22⋊Q8—861no—
383#121—861no—
384#121—861no—
385C4×Q8—431no—
386C4×Q8—431no—
387C4×Q8—861no—
388C4×Q8—861no—
389C4×D4—431no—
390C4×D4—861no—
391C4×D4—861no—
392C4×D4—861no—
393C4×D4—861no—
394C4×D4C22×D4311yescharacteristic
395#117—431no—
396#117—861no—
397#117—861no—
398C2×C42—431no—
399C2×C42—861no—
400#107—21no—
401#107—861no—
402#106—861no—
403#106—861no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8—861no—
412C4⋊C8C22×D4311yescharacteristic
413C4⋊C8C22×D4311yescharacteristic
414C4⋊C8C22×D4311yescharacteristic
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—861no—
420#103—861no—
421#102—21no—
422#102—21no—
423#102—861no—
424#102—861no—
425#102—861no—
426#102—861no—
427C22⋊C8—21no—
428C22⋊C8—431no—
429C22⋊C8—431no—
430C22⋊C8—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433#97—861no—
434C4×C8—431no—
435C4×C8—861no—
436C4×C8—861no—
437C4×C8—861no—
438C4×C8C22×D4311yescharacteristic
439#41—862no—
440#41—862no—
441#41—3441no—
442#41—3441no—
443C2×Q8—21no—
444C2×Q8—431no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—861no—
451C2×D4—1721no—
452C2×D4D4×D4311yescharacteristic
453C22×C4—21no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—1721no—
460Q16—3441no—
461Q16—3441no—
462Q16—1722no—
463SD16—81no—
464SD16—81no—
465SD16—1722no—
466SD16—1722no—
467D8—42no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—81no—
472C2×C8—431no—
473C2×C8—431no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—3441no—
478C2×C8—3441no—
479C2×C8D4×D4311yescharacteristic
480C2×C8D4×D4311yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—431no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—1721no—
491C4⋊C4—1721no—
492C4⋊C4D4×D4311yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—861no—
495C22⋊C4—861no—
496C22⋊C4—1721no—
497C22⋊C4—1721no—
498C22⋊C4—1721no—
499C42—431no—
500C42—431no—
501C42—431no—
502C42—861no—
503C42—861no—
504C42—861no—
505C42—1721no—
506C42C23×D4311yescharacteristic
507C23—21no—
508C23—41no—
509C23—431no—
510Q8—41no—
511Q8—41no—
512Q8—432no—
513Q8—861no—
514Q8—1721no—
515Q8—1721no—
516Q8—1721no—
517Q8—1721no—
518D4—21no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—81no—
524D4—864no—
525D4—3442no—
526D4#1306334612yes—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—431no—
532C2×C4—431no—
533C2×C4—431no—
534C2×C4—864no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—3442no—
542C2×C4—3441no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4C2×D4×D4311yescharacteristic
547C2×C4C2×D4×D4311yescharacteristic
548C2×C4#41×D4311yescharacteristic
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—861no—
555C8—861no—
556C8—1721no—
557C8—1721no—
558C8—1721no—
559C22—22no—
560C22—41no—
561C22—41no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—861no—
566C22—861no—
567C22—861no—
568C22#121×D4311yescharacteristic
569C4—21no—
570C4—41no—
571C4—81no—
572C4—861no—
573C4—861no—
574C4—861no—
575C4—862no—
576C4—3441no—
577C4—3441no—
578C4—1721no—
579C4#135×D4311yescharacteristic
580C4C2×#1306334611yescharacteristic
581C4#1458370011yescharacteristic
582C4#1458370911yescharacteristic
583C2—42no—
584C2—161no—
585C2—1721no—
586C2#1914412911yescharacteristic
587C2#1914417111yescharacteristic
588C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1665C2
socleC22×C43C2×#121
prime radical#19144743C2
hypercenter#1665D43
hypocenterC43#19413
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1665

Complements

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

NH ≅ G/Ntype
1. #19145546C2semidirect
3. #19144668C2semidirect
4. #19143702C2semidirect
5. #19134038C2semidirect
6. #19134030C2semidirect
7. #19134026C2semidirect
8. #19134018C2semidirect
9. #19133964C2semidirect
10. #19133958C2semidirect
11. #19133940C2semidirect
12. #19133372C2semidirect
13. #19133294C2semidirect
14. #19133241C2semidirect
15. C43×#1665C2semidirect
300. #1665D43semidirect
361. C43#19413semidirect

Maximal subgroups

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

subgroupindex
#191455462
#191447432
#191446682
#191437022
#191340382
#191340302
#191340262
#191340182
#191339642
#191339582
#191339402
#191333722
#191332942
#191332412
C43×#16652
#1941343