Finite Group Databasebeta

← #25080587

Subgroups — #25080587

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#19144917C211yesmaximal, characteristic, complemented
2#19144758C211yesmaximal, characteristic, complemented
3#19144740C211yesmaximal, characteristic
4#19143551C211yesmaximal, characteristic, complemented
5#19134052C211yesmaximal, characteristic, complemented
6#19134045C211yesmaximal, characteristic, complemented
7#19134038C211yesmaximal, characteristic, complemented
8#19134031C211yesmaximal, characteristic, complemented
9#19134024C211yesmaximal, characteristic, complemented
10#19134017C211yesmaximal, characteristic, complemented
11#19134010C211yesmaximal, characteristic, complemented
12#19134003C211yesmaximal, characteristic, complemented
13#19133356C211yesmaximal, characteristic, complemented
14#19133303C211yesmaximal, characteristic, complemented
15C43×#1553C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17C4×#10621898C2211yescharacteristic
18#14583253—21no—
19#14583253—21no—
20#14583249C2211yescharacteristic
21#14583249C2211yescharacteristic
22#14583245C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583241—21no—
25#14583220—21no—
26#14583195C2211yescharacteristic
27#14583190C2211yescharacteristic
28#14583181C2211yescharacteristic
29#14583176C2211yescharacteristic
30#14583110C2211yescharacteristic
31#14583105C2211yescharacteristic
32#14583096C2211yescharacteristic
33#14583091C2211yescharacteristic
34#14583063—21no—
35#14583042—21no—
36#14583023C2211yescharacteristic
37#14583023C2211yescharacteristic
38#14583009—21no—
39#14583007—21no—
40#14583001—21no—
41#14582999—21no—
42#14582964C2211yescharacteristic
43#14582964C2211yescharacteristic
44(C22⋊D43)⋊C8—21no—
45(C22⋊D43)⋊C8—21no—
46#14582956C2211yescharacteristic
47#14582950—21no—
48#14582895—21no—
49#14582895—21no—
50C2×C4×C43⋊C8C2211yescharacteristic
51C4×C8×D43—21no—
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#532C2211yescharacteristic
61C43×#432C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621898D411yescharacteristic
68C2×Dic172—21no—
69C2×#10621873—21no—
70C2×#10621883—21no—
71C2×#10621882—21no—
72C22×C43⋊C8D411yescharacteristic
73C22×C43⋊C8D411yescharacteristic
74C2×C8×D43—21no—
75C2×C8×D43—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063317—21no—
79#13063304—21no—
80#13063304—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83C4×Dic86D411yescharacteristic
84C4×Dic86C2311yescharacteristic
85C4×D172D411yescharacteristic
86C4×D172C2311yescharacteristic
87C4×C22⋊D43—21no—
88C4×C22⋊D43—21no—
89#13063284—21no—
90#13063284D411yescharacteristic
91#13063282—21no—
92C42×D43—21no—
93#13063259—21no—
94#13063258—21no—
95#13063257—21no—
96#13063256—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101#13063250—21no—
102#13063250—21no—
103#13063250—21no—
104#13063249—21no—
105#13063249—21no—
106#13063249—21no—
107#13063249—21no—
108#13063248—21no—
109#13063247—21no—
110#13063246—21no—
111#13063246—21no—
112#13063246—21no—
113#13063246—21no—
114#13063246—21no—
115#13063246—21no—
116#13063245—21no—
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120#13063236—21no—
121C4×C43⋊C8D411yescharacteristic
122C4×C43⋊C8D411yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C2×#41×C43—21no—
128C4⋊Q8×C43C2311yescharacteristic
129#127×C43C2311yescharacteristic
130#124×C43—21no—
131#121×C43—21no—
132#121×C43—21no—
133C4×D4×C43—21no—
134C4×D4×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142#97×C43—21no—
143C4×C8×C43—21no—
144#41×C43—42no—
145#41×C43—42no—
146C2×Q8×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—41no—
151C22×C4×C43—41no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C2×C22⋊D43—21no—
156#10621898—22no—
157#10621898—22no—
158C2×D172C2×D411yescharacteristic
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86C2×D411yescharacteristic
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C22⋊C4×C43—41no—
172C22⋊C4×C43—41no—
173C42×C43C2×D411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43#4111yescharacteristic
176C42×C43C2411yescharacteristic
177C22⋊Dic43—21no—
178C22⋊Dic43—41no—
179#10621883—42no—
180#10621882—42no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43C2×D411yescharacteristic
188C4⋊Dic43C2×D411yescharacteristic
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—41no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—41no—
200C2×C43⋊C8—41no—
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205Dic172—42no—
206#10621873—42no—
207C8×D43—42no—
208C8×D43—42no—
209C23×C43—41no—
210C23×C43#12111yescharacteristic
211C22×D43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214D4×C43—41no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—81no—
219D4×C43—82no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—82no—
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C22⋊D43—24no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239D172—21no—
240D172#13512yes—
241C4×D43—24no—
242C4×D43—42no—
243C4×D43—41no—
244C4×D43—41no—
245Dic86—21no—
246Dic86—41no—
247Dic86—41no—
248Dic86—81no—
249Dic86#13512yes—
250C8×C43—41no—
251C8×C43—41no—
252C8×C43—41no—
253C8×C43—41no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—21no—
257C43⋊C8—21no—
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×C43C2×#13511yescharacteristic
277C4×C43C2×#13511yescharacteristic
278C4×C43#57511yescharacteristic
279C4×C43#57511yescharacteristic
280Dic43—22no—
281Dic43—41no—
282Dic43—41no—
283Dic43—81no—
284Dic43—81no—
285#3131—431no—
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#1553D4311yescharacteristic, complemented
300C2×C43—41no—
301C2×C43—161no—
302C2×C43#304011yescharacteristic
303C2×C43#305011yescharacteristic
304C2×C43#306711yescharacteristic
305D43—42no—
306#533—431no—
307#532C2×D4311yescharacteristic
308C4×#41—431no—
309#488—861no—
310#488—861no—
311#487—431no—
312#487—431no—
313#486—431no—
314#486—431no—
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#432C2×D4311yescharacteristic
339#431—861no—
340#431C2×D4311yescharacteristic
341#416—861no—
342#416—861no—
343C2×C4×C8—431no—
344C2×C4×C8—861no—
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#332C2×D4311yescharacteristic
354#332C2×D4311yescharacteristic
355#331C2×D4311yescharacteristic
356#331C2×D4311yescharacteristic
357C43#1927811yescharacteristic, complemented, Sylow
358C2×#41—21no—
359C2×#41—431no—
360C2×Q16—861no—
361C2×SD16—861no—
362C2×SD16—861no—
363C2×D8—861no—
364C22×C8—431no—
365C22×C8—431no—
366C22×C8—861no—
367C22×C8—861no—
368C4⋊Q8—431no—
369C4⋊Q8—431no—
370C4⋊Q8C22×D4311yescharacteristic
371#127C22×D4311yescharacteristic
372#125—861no—
373#124—21no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376#121—21no—
377#121—21no—
378C4×Q8—431no—
379C4×Q8—431no—
380C4×Q8—861no—
381C4×Q8—861no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—431no—
385C4×D4—431no—
386C4×D4—861no—
387C4×D4—861no—
388#117—431no—
389#117—861no—
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—861no—
400C4⋊C8—861no—
401C4⋊C8C22×D4311yescharacteristic
402C4⋊C8C22×D4311yescharacteristic
403C4⋊C8C22×D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420#102—861no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—21no—
427#97—861no—
428C4×C8—21no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—431no—
433C4×C8—861no—
434C4×C8—861no—
435#41—42no—
436#41—42no—
437#41—862no—
438#41—862no—
439C2×Q8—21no—
440C2×Q8—431no—
441C2×Q8—861no—
442C2×Q8—861no—
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×C4#1062189811yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4D4×D4311yescharacteristic
456Q16—1722no—
457SD16—1722no—
458SD16—1722no—
459D8—1722no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—431no—
465C2×C8—431no—
466C2×C8—431no—
467C2×C8—431no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—1722no—
471C2×C8—1722no—
472C2×C8—1721no—
473C2×C8—1721no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—431no—
477C4⋊C4—431no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—1721no—
485C4⋊C4—1721no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—861no—
489C22⋊C4—861no—
490C22⋊C4—861no—
491C22⋊C4—1721no—
492C42—861no—
493C42—861no—
494C42—861no—
495C42—1721no—
496C42#1062189811yescharacteristic
497C42D4×D4311yescharacteristic
498C42D4×D4311yescharacteristic
499C42C23×D4311yescharacteristic
500C23—41no—
501C23—861no—
502C23#1306329811yescharacteristic
503Q8—41no—
504Q8—41no—
505Q8—432no—
506Q8—861no—
507Q8—3441no—
508Q8—1721no—
509Q8—1721no—
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—82no—
526C2×C4—864no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—1722no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4#1306329811yescharacteristic
536C2×C4#1306329811yescharacteristic
537C2×C4#1306329811yescharacteristic
538C2×C4C2×D4×D4311yescharacteristic
539C2×C4C2×D4×D4311yescharacteristic
540C2×C4C2×#1062189811yescharacteristic
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—861no—
546C8—861no—
547C8—861no—
548C8—861no—
549C8—1721no—
550C8—1721no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—862no—
558C22—1721no—
559C22—1721no—
560C22C2×#1306329811yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—81no—
566C4—862no—
567C4—3441no—
568C4—3441no—
569C4—1721no—
570C4—1721no—
571C4#135×D4311yescharacteristic
572C4#135×D4311yescharacteristic
573C4#1458369511yescharacteristic
574C4#1458369511yescharacteristic
575C2—41no—
576C2—161no—
577C2—1722no—
578C2#1914408811yescharacteristic
579C2#1914417511yescharacteristic
580C2#1914431411yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1553C2
socleC22×C43C2×#121
prime radical#19144740C2
hypercenter#1553D43
hypocenterC43#19278
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1553

Complements

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

NH ≅ G/Ntype
1. #19144917C2semidirect
2. #19144758C2semidirect
4. #19143551C2semidirect
5. #19134052C2semidirect
6. #19134045C2semidirect
7. #19134038C2semidirect
8. #19134031C2semidirect
9. #19134024C2semidirect
10. #19134017C2semidirect
11. #19134010C2semidirect
12. #19134003C2semidirect
13. #19133356C2semidirect
14. #19133303C2semidirect
15. C43×#1553C2semidirect
299. #1553D43semidirect
357. C43#19278semidirect

Maximal subgroups

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

subgroupindex
#191449172
#191447582
#191447402
#191435512
#191340522
#191340452
#191340382
#191340312
#191340242
#191340172
#191340102
#191340032
#191333562
#191333032
C43×#15532
#1927843