Finite Group Databasebeta

← #25081742

Subgroups — #25081742

Order 11008.

606 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#19145951C211yesmaximal, characteristic
2#19145624C211yesmaximal, characteristic, complemented
3#19144988C211yesmaximal, characteristic, complemented
4#19143593C211yesmaximal, characteristic, complemented
5#19134162C211yesmaximal, characteristic, complemented
6#19134155C211yesmaximal, characteristic, complemented
7#19134148C211yesmaximal, characteristic, complemented
8#19134141C211yesmaximal, characteristic, complemented
9#19134038C211yesmaximal, characteristic, complemented
10#19134031C211yesmaximal, characteristic, complemented
11#19134024C211yesmaximal, characteristic, complemented
12#19134017C211yesmaximal, characteristic, complemented
13#19133363C211yesmaximal, characteristic, complemented
14#19133266C211yesmaximal, characteristic, complemented
15C43×#1553C211yesmaximal, characteristic, complemented
16C2×#13063325C2211yescharacteristic
17#14583433C2211yescharacteristic
18#14583293—21no—
19#14583268—21no—
20#14583258—21no—
21#14583258—21no—
22#14583249C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583245C2211yescharacteristic
25#14583245C2211yescharacteristic
26#14583199—21no—
27#14583181C2211yescharacteristic
28#14583176C2211yescharacteristic
29#14583150—21no—
30#14583143—21no—
31#14583114—21no—
32#14583110C2211yescharacteristic
33#14583110C2211yescharacteristic
34#14583105C2211yescharacteristic
35#14583105C2211yescharacteristic
36#14583096C2211yescharacteristic
37#14583091C2211yescharacteristic
38#14583057—21no—
39#14583040—21no—
40#14583026C2211yescharacteristic
41#14583023C2211yescharacteristic
42#14582976C2211yescharacteristic
43#14582974—21no—
44#14582973—21no—
45#14582964C2211yescharacteristic
46#14582958—21no—
47#14582923C2211yescharacteristic
48#14582900—21no—
49#14582900—21no—
50#14582853—21no—
51C4×#10621877C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582644C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#532C2211yescharacteristic
61C43×#432C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C22×Dic86—21no—
68C2×Dic172—21no—
69C2×Dic172—21no—
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×#10621883—21no—
73C2×#10621882—21no—
74C2×#10621877—21no—
75C2×#10621877D411yescharacteristic
76C2×#10621877D411yescharacteristic
77C2×#10621872—21no—
78C2×C8×D43—21no—
79#13063325—21no—
80#13063325—21no—
81#13063325—21no—
82#13063325C2311yescharacteristic
83#13063325C2311yescharacteristic
84#13063319—21no—
85#13063317D411yescharacteristic
86#13063313D411yescharacteristic
87#13063308—21no—
88#13063304D411yescharacteristic
89#13063299D411yescharacteristic
90C4×Dic86C2311yescharacteristic
91C4×D172C2311yescharacteristic
92C4×C22⋊D43—21no—
93#13063282—21no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43—21no—
96#13063258—21no—
97#13063256—21no—
98C4⋊(C43⋊C8)—21no—
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103#13063250—21no—
104#13063250—21no—
105#13063250—21no—
106#13063250—21no—
107#13063249—21no—
108#13063249—21no—
109#13063249—21no—
110#13063249—21no—
111#13063248—21no—
112#13063246—21no—
113#13063246—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117#13063246—21no—
118#13063245—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063236D411yescharacteristic
122#13063236D411yescharacteristic
123#13063235—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
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—
156C22×Dic43—41no—
157C2×D172C2×D411yescharacteristic
158C2×C4×D43—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—41no—
162C2×Dic86—81no—
163C2×Dic86—81no—
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—
178#10621883—81no—
179#10621882—81no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—41no—
189C4⋊Dic43—41no—
190C4⋊Dic43C2×D411yescharacteristic
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196C4×Dic43—21no—
197#10621877—41no—
198#10621877—41no—
199#10621877—81no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206Dic172—81no—
207Dic172—81no—
208#10621873—81no—
209#10621873—81no—
210#10621872—42no—
211C8×D43—42no—
212C23×C43—41no—
213C23×C43#12111yescharacteristic
214C22×D43—21no—
215Q8×C43—41no—
216Q8×C43—41no—
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—82no—
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C22⋊D43—81no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—82no—
243D172—21no—
244D172—21no—
245C4×D43—41no—
246C4×D43—41no—
247Dic86—21no—
248Dic86—21no—
249Dic86—41no—
250Dic86—41no—
251Dic86—41no—
252Dic86—41no—
253Dic86—82no—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—41no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264#19383—431nomaximal, Sylow
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43C2×#12111yescharacteristic
272C2×D43—41no—
273C2×D43—41no—
274C2×D43—41no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—81no—
280C4×C43#57511yescharacteristic
281C4×C43#57511yescharacteristic
282C4×C43#57611yescharacteristic
283C4×C43#57711yescharacteristic
284Dic43—41no—
285Dic43—41no—
286Dic43—41no—
287Dic43—81no—
288Dic43—81no—
289#3251—431no—
290#3218—431no—
291#3141—431no—
292#2969—431no—
293#1702—431no—
294#1701—431no—
295#1700—431no—
296#1699—431no—
297#1682—431no—
298#1681—431no—
299#1680—431no—
300#1679—431no—
301#1569—431no—
302#1553D4311yescharacteristic, complemented
303#1546—431no—
304C2×C43—41no—
305C2×C43—161no—
306C2×C43#304011yescharacteristic
307C2×C43#306211yescharacteristic
308C2×C43#306911yescharacteristic
309D43—81no—
310#532C2×D4311yescharacteristic
311C2×C4⋊Q8—431no—
312#529—431no—
313#497—861no—
314#491—861no—
315#489—861no—
316#489—861no—
317#487—431no—
318#487—431no—
319#486—431no—
320#486—431no—
321#478—861no—
322#475—431no—
323#474—431no—
324#469—861no—
325#468—861no—
326#463—861no—
327#462—431no—
328#462—431no—
329#461—431no—
330#461—431no—
331#460—431no—
332#459—431no—
333#451—861no—
334#448—861no—
335#446—431no—
336C8×Q8—431no—
337#436—431no—
338#436—861no—
339#435—861no—
340C8×D4—431no—
341#433—861no—
342#432C2×D4311yescharacteristic
343#431C2×D4311yescharacteristic
344#423—431no—
345#417—861no—
346#417—861no—
347#405—861no—
348C4×M16—431no—
349#335—431no—
350#335—431no—
351#334—431no—
352#334—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#332—431no—
357#332C2×D4311yescharacteristic
358#332C2×D4311yescharacteristic
359#331C2×D4311yescharacteristic
360#331C2×D4311yescharacteristic
361C43#1938311yescharacteristic, complemented, Sylow
362C2×#41—21no—
363C22×Q8—861no—
364C2×Q16—861no—
365C2×Q16—861no—
366C2×SD16—861no—
367C2×SD16—861no—
368C2×SD16—861no—
369C2×D8—861no—
370C2×M16—431no—
371C2×M16—431no—
372C2×M16—861no—
373C2×M16—861no—
374C22×C8—861no—
375C4⋊Q8—431no—
376C4⋊Q8—431no—
377C4⋊Q8—861no—
378C4⋊Q8—861no—
379C4⋊Q8—861no—
380C4⋊Q8C22×D4311yescharacteristic
381#127C22×D4311yescharacteristic
382#126—861no—
383#125—431no—
384#124—21no—
385#124—431no—
386#123—861no—
387C22⋊Q8—431no—
388#121—21no—
389#121—21no—
390#121—431no—
391C4×Q8—431no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—431no—
395C4×D4—861no—
396#117—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C42C22×D4311yescharacteristic
400#107—861no—
401#106—861no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—861no—
405C4⋊C8—861no—
406C4⋊C8—861no—
407C4⋊C8C22×D4311yescharacteristic
408C4⋊C8C22×D4311yescharacteristic
409C4⋊C8C22×D4311yescharacteristic
410C4⋊C8C22×D4311yescharacteristic
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—861no—
420#102—861no—
421#102—861no—
422#102—861no—
423#102—861no—
424#102—861no—
425#102—861no—
426#102—861no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431#97—21no—
432#97—431no—
433#97—431no—
434#97—861no—
435C4×C8—21no—
436C4×C8—431no—
437C4×C8—431no—
438C4×C8—861no—
439#41—42no—
440#41—42no—
441C2×Q8—21no—
442C2×Q8—431no—
443C2×Q8—861no—
444C2×Q8—861no—
445C2×Q8—3441no—
446C2×Q8—3441no—
447C2×Q8—1721no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4—431no—
453C2×D4—861no—
454C22×C4—41no—
455C22×C4—861no—
456C22×C4—1721no—
457C22×C4#1062189811yescharacteristic
458C22×C4D4×D4311yescharacteristic
459C22×C4D4×D4311yescharacteristic
460Q16—3441no—
461Q16—3441no—
462SD16—3441no—
463SD16—3441no—
464SD16—3441no—
465D8—3441no—
466M16—3441no—
467M16—1722no—
468M16—1721no—
469M16—1721no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—431no—
475C2×C8—431no—
476C2×C8—431no—
477C2×C8—431no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—1722no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—431no—
484C4⋊C4—431no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—1721no—
494C4⋊C4—1721no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—861no—
498C22⋊C4—861no—
499C22⋊C4—861no—
500C22⋊C4—861no—
501C22⋊C4—861no—
502C42—861no—
503C42#1062189811yescharacteristic
504C42D4×D4311yescharacteristic
505C42D4×D4311yescharacteristic
506C42C23×D4311yescharacteristic
507C23—41no—
508C23—861no—
509C23#1306329811yescharacteristic
510Q8—41no—
511Q8—41no—
512Q8—861no—
513Q8—861no—
514Q8—3442no—
515Q8—1721no—
516Q8—1721no—
517Q8—1721no—
518Q8—1721no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—81no—
524D4—82no—
525D4—861no—
526D4—861no—
527D4—3441no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—82no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—3442no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4#1306329811yescharacteristic
544C2×C4#1306329811yescharacteristic
545C2×C4#1306329811yescharacteristic
546C2×C4C2×D4×D4311yescharacteristic
547C2×C4C2×D4×D4311yescharacteristic
548C2×C4C2×#1062189811yescharacteristic
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—861no—
554C8—861no—
555C8—861no—
556C8—861no—
557C8—1721no—
558C8—1721no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—1721no—
566C22—1721no—
567C22—1721no—
568C22C2×#1306329811yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—81no—
574C4—3441no—
575C4—3441no—
576C4—1721no—
577C4—1721no—
578C4—1721no—
579C4#1458369511yescharacteristic
580C4#1458369511yescharacteristic
581C4#1458370111yescharacteristic
582C4#1458370611yescharacteristic
583C2—41no—
584C2—161no—
585C2—3441no—
586C2#1914408811yescharacteristic
587C2#1914427811yescharacteristic
588C2#1914433511yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1553C2
socleC22×C43C2×#121
prime radical#19145951C2
hypercenter#1553D43
hypocenterC43#19383
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
2. #19145624C2semidirect
3. #19144988C2semidirect
4. #19143593C2semidirect
5. #19134162C2semidirect
6. #19134155C2semidirect
7. #19134148C2semidirect
8. #19134141C2semidirect
9. #19134038C2semidirect
10. #19134031C2semidirect
11. #19134024C2semidirect
12. #19134017C2semidirect
13. #19133363C2semidirect
14. #19133266C2semidirect
15. C43×#1553C2semidirect
302. #1553D43semidirect
361. C43#19383semidirect

Maximal subgroups

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

subgroupindex
#191459512
#191456242
#191449882
#191435932
#191341622
#191341552
#191341482
#191341412
#191340382
#191340312
#191340242
#191340172
#191333632
#191332662
C43×#15532
#1938343