Finite Group Databasebeta

← #25080583

Subgroups — #25080583

Order 11008.

630 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144751C211yesmaximal, characteristic, complemented
2#19144740C211yesmaximal, characteristic
3C8×#10621898C211yesmaximal, characteristic, complemented
4#19134050C211yesmaximal, characteristic, complemented
5#19134043C211yesmaximal, characteristic, complemented
6#19134036C211yesmaximal, characteristic, complemented
7#19134029C211yesmaximal, characteristic, complemented
8#19134022C211yesmaximal, characteristic, complemented
9#19134015C211yesmaximal, characteristic, complemented
10#19134008C211yesmaximal, characteristic, complemented
11#19134001C211yesmaximal, characteristic, complemented
12#19133358C211yesmaximal, characteristic, complemented
13#19133305C211yesmaximal, characteristic, complemented
14#19133300C211yesmaximal, characteristic, complemented
15C43×#3131C211yesmaximal, characteristic, complemented
16C4×#10621898C2211yescharacteristic
17#14583237—21no—
18#14583220—21no—
19#14583191C2211yescharacteristic
20#14583186C2211yescharacteristic
21#14583181C2211yescharacteristic
22#14583176C2211yescharacteristic
23#14583106C2211yescharacteristic
24#14583101C2211yescharacteristic
25#14583096C2211yescharacteristic
26#14583091C2211yescharacteristic
27#14583059—21no—
28#14583042—21no—
29C8×Dic86C2211yescharacteristic
30C8×Dic86C2211yescharacteristic
31#14583009—21no—
32#14583004—21no—
33#14582999—21no—
34#14582997—21no—
35C8×D172C2211yescharacteristic
36C8×D172C2211yescharacteristic
37C8×C22⋊D43—21no—
38C8×C22⋊D43—21no—
39#14582956C2211yescharacteristic
40#14582956C2211yescharacteristic
41#14582952C2211yescharacteristic
42#14582950—21no—
43C4×C8×D43—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#532C2211yescharacteristic
58C43×#488—21no—
59C43×#488—21no—
60C43×#487C2211yescharacteristic
61C43×#487C2211yescharacteristic
62C43×#486C2211yescharacteristic
63C43×#486C2211yescharacteristic
64C43×#416—21no—
65C43×#416—21no—
66C2×C4×C8×C43C2211yescharacteristic
67C2×#10621898D411yescharacteristic
68C2×#10621885—21no—
69C2×#10621883—21no—
70C2×#10621884—21no—
71C2×#10621882—21no—
72C2×C8×D43—21no—
73C2×C8×D43—21no—
74C4×Dic86D411yescharacteristic
75C4×Dic86C2311yescharacteristic
76C4×D172D411yescharacteristic
77C4×D172C2311yescharacteristic
78C4×C22⋊D43—21no—
79C4×C22⋊D43—21no—
80#13063284D411yescharacteristic
81#13063282—21no—
82C42×D43—21no—
83#13063258—21no—
84#13063258—21no—
85#13063256—21no—
86#13063256—21no—
87C4⋊(C43⋊C8)C2311yescharacteristic
88C4⋊(C43⋊C8)C2311yescharacteristic
89C4⋊(C43⋊C8)C2311yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93Dic43⋊C8—21no—
94Dic43⋊C8—21no—
95#13063249—21no—
96#13063249—21no—
97#13063248—21no—
98#13063248—21no—
99#13063246—21no—
100#13063246—21no—
101#13063245—21no—
102#13063245—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106(C2×D43)⋊C8—21no—
107(C2×D43)⋊C8—21no—
108#13063236—21no—
109#13063236—21no—
110C4×C43⋊C8—21no—
111C8×Dic43—21no—
112C8×Dic43—21no—
113C2×#41×C43—21no—
114C22×C8×C43D411yescharacteristic
115C22×C8×C43D411yescharacteristic
116C4⋊Q8×C43C2311yescharacteristic
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119#127×C43C2311yescharacteristic
120#125×C43—21no—
121#124×C43—21no—
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43—21no—
124#121×C43—21no—
125#121×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130#117×C43—21no—
131C2×C42×C43C2311yescharacteristic
132#103×C43—21no—
133#103×C43—21no—
134#103×C43—21no—
135#103×C43—21no—
136#102×C43—21no—
137#102×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140C4×C8×C43D411yescharacteristic
141C4×C8×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—42no—
145#41×C43—42no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—41no—
153C22×C4×C43—41no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43#4111yescharacteristic
157C2×C22⋊D43—21no—
158#10621898—22no—
159#10621898—22no—
160C2×D172C2×D411yescharacteristic
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×Dic86C2×D411yescharacteristic
165C2×C8×C43—41no—
166C2×C8×C43—41no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C22⋊C4×C43—41no—
181C22⋊C4×C43—41no—
182C42×C43—41no—
183C42×C43C2×D411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C42×C43#4111yescharacteristic
186C42×C43C2411yescharacteristic
187C22⋊Dic43—21no—
188#10621885—42no—
189#10621884—42no—
190#10621883—42no—
191#10621882—42no—
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—21no—
194C4⋊Dic43C2×D411yescharacteristic
195C4⋊Dic43C2×D411yescharacteristic
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C8×D43—42no—
208C8×D43—42no—
209C23×C43—41no—
210C23×C43#12111yescharacteristic
211C22×D43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—81no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—81no—
222D4×C43—82no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—82no—
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C22⋊D43—24no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242D172—21no—
243D172#13512yes—
244C4×D43—24no—
245C4×D43—42no—
246C4×D43—41no—
247C4×D43—41no—
248Dic86—21no—
249Dic86#13512yes—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260#19278—431nomaximal, Sylow
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43C2×#12111yescharacteristic
268C2×D43—22no—
269C2×D43—41no—
270C2×D43—41no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—81no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43C2×#13511yescharacteristic
279C4×C43C2×#13511yescharacteristic
280C4×C43#57511yescharacteristic
281C4×C43#57511yescharacteristic
282Dic43—22no—
283Dic43—41no—
284Dic43—41no—
285#3131D4311yescharacteristic, complemented
286#3116—431no—
287#3115—431no—
288C8×#41—431no—
289#1684—431no—
290#1683—431no—
291#1682—431no—
292#1681—431no—
293#1680—431no—
294#1679—431no—
295#1678—431no—
296#1677—431no—
297#1568—431no—
298#1554—431no—
299#1553—431no—
300C2×C43—41no—
301C2×C43—161no—
302C2×C43#304011yescharacteristic
303C2×C43#305011yescharacteristic
304C2×C43#306711yescharacteristic
305D43—42no—
306#533C2×D4311yescharacteristic
307#532C2×D4311yescharacteristic
308C4×#41—431no—
309#488—21no—
310#488—21no—
311#487C2×D4311yescharacteristic
312#487C2×D4311yescharacteristic
313#486C2×D4311yescharacteristic
314#486C2×D4311yescharacteristic
315#485—861no—
316#482—861no—
317#477—431no—
318#476—431no—
319#475—431no—
320#474—431no—
321#462—431no—
322#461—431no—
323#460—431no—
324#459—431no—
325#452—861no—
326#449—861no—
327C8×Q8—431no—
328C8×Q8—431no—
329#442—861no—
330#441—861no—
331#440—861no—
332#440—861no—
333C8×D4—431no—
334C8×D4—431no—
335C8×D4—861no—
336C8×D4—861no—
337#432—431no—
338#432—431no—
339#431—431no—
340#431—861no—
341#416—21no—
342#416—21no—
343C2×C4×C8—861no—
344C2×C4×C8C2×D4311yescharacteristic
345#335—431no—
346#335—431no—
347#334—431no—
348#334—431no—
349#333—431no—
350#333—431no—
351#332—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#331—431no—
356#331—431no—
357C43#1927811yescharacteristic, complemented, Sylow
358C2×#41—21no—
359C2×#41—431no—
360C2×Q16—861no—
361C2×SD16—861no—
362C2×SD16—861no—
363C2×D8—861no—
364C22×C8—861no—
365C22×C8—861no—
366C22×C8C22⋊D4311yescharacteristic
367C22×C8C22⋊D4311yescharacteristic
368C4⋊Q8C22×D4311yescharacteristic
369C4⋊Q8C22×D4311yescharacteristic
370C4⋊Q8C22×D4311yescharacteristic
371#127C22×D4311yescharacteristic
372#125—21no—
373#124—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376#121—21no—
377#121—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—431no—
381C4×Q8—431no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—431no—
385C4×D4—431no—
386C4×D4—861no—
387C4×D4—861no—
388#117—21no—
389#117—431no—
390#117—861no—
391C2×C42—861no—
392C2×C42C22×D4311yescharacteristic
393#107—861no—
394#107—861no—
395#106—861no—
396#106—861no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—431no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—861no—
418#102—861no—
419#102—861no—
420#102—861no—
421C22⋊C8—861no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—861no—
427#97—861no—
428C4×C8—861no—
429C4×C8—861no—
430C4×C8—861no—
431C4×C8C22⋊D4311yescharacteristic
432C4×C8C22⋊D4311yescharacteristic
433C4×C8C22×D4311yescharacteristic
434C4×C8C22×D4311yescharacteristic
435#41—42no—
436#41—42no—
437#41—862no—
438#41—862no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—431no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—41no—
447C2×D4—431no—
448C2×D4—861no—
449C22×C4—41no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4D4×D4311yescharacteristic
454C22×C4#1062190011yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456Q16—1722no—
457SD16—1722no—
458SD16—1722no—
459D8—1722no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—1722no—
469C2×C8—1722no—
470C2×C8C2×C22⋊D4311yescharacteristic
471C2×C8C2×C22⋊D4311yescharacteristic
472C2×C8C2×C22⋊D4311yescharacteristic
473C2×C8C2×C22⋊D4311yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—431no—
483C4⋊C4—431no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—861no—
490C22⋊C4—861no—
491C22⋊C4—861no—
492C42—41no—
493C42—861no—
494C42—861no—
495C42—861no—
496C42D4×D4311yescharacteristic
497C42#1062190011yescharacteristic
498C42C2×C22⋊D4311yescharacteristic
499C42C23×D4311yescharacteristic
500C23—41no—
501C23—861no—
502C23#1306329611yescharacteristic
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—81no—
508Q8—432no—
509Q8—861no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—81no—
515D4—82no—
516D4—432no—
517D4—864no—
518D4—861no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—864no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—1722no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4#1306329611yescharacteristic
536C2×C4#1306329611yescharacteristic
537C2×C4#1306329611yescharacteristic
538C2×C4C2×D4×D4311yescharacteristic
539C2×C4C22×C22⋊D4311yescharacteristic
540C2×C4C2×#1062190011yescharacteristic
541C8—21no—
542C8—21no—
543C8—21no—
544C8—21no—
545C8—1721no—
546C8—1721no—
547C8—1721no—
548C8—1721no—
549C8—1721no—
550C8—1721no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—862no—
558C22—1721no—
559C22—1721no—
560C22C2×#1306329611yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—81no—
566C4—81no—
567C4—81no—
568C4—862no—
569C4—1721no—
570C4—1721no—
571C4#135×D4311yescharacteristic
572C4#135×D4311yescharacteristic
573C4#1458369711yescharacteristic
574C4#1458369711yescharacteristic
575C2—41no—
576C2—161no—
577C2—1722no—
578C2#1914408511yescharacteristic
579C2#1914417211yescharacteristic
580C2#1914431111yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3131C2
socleC22×C43C2×#121
prime radical#19144740C2
hypercenter#3131D43
hypocenterC43#19278
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3131

Complements

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

NH ≅ G/Ntype
1. #19144751C2semidirect
3. C8×#10621898C2semidirect
4. #19134050C2semidirect
5. #19134043C2semidirect
6. #19134036C2semidirect
7. #19134029C2semidirect
8. #19134022C2semidirect
9. #19134015C2semidirect
10. #19134008C2semidirect
11. #19134001C2semidirect
12. #19133358C2semidirect
13. #19133305C2semidirect
14. #19133300C2semidirect
15. C43×#3131C2semidirect
285. #3131D43semidirect
357. C43#19278semidirect

Maximal subgroups

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

subgroupindex
#191447512
#191447402
C8×#106218982
#191340502
#191340432
#191340362
#191340292
#191340222
#191340152
#191340082
#191340012
#191333582
#191333052
#191333002
C43×#31312
#1927843