Finite Group Databasebeta

← #25080311

Subgroups — #25080311

Order 11008.

624 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#19145915C211yesmaximal, characteristic, complemented
2#19145571C211yesmaximal, characteristic, complemented
3#19143599C211yesmaximal, characteristic, complemented
4#19134160C211yesmaximal, characteristic, complemented
5#19134132C211yesmaximal, characteristic, complemented
6#19134091C211yesmaximal, characteristic, complemented
7#19134071C211yesmaximal, characteristic, complemented
8#19134029C211yesmaximal, characteristic, complemented
9#19134001C211yesmaximal, characteristic, complemented
10#19133974C211yesmaximal, characteristic, complemented
11#19133952C211yesmaximal, characteristic, complemented
12#19133347C211yesmaximal, characteristic, complemented
13#19133257C211yesmaximal, characteristic, complemented
14#19133244C211yesmaximal, characteristic, complemented
15C43×#3184C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583281—21no—
18#14583253—21no—
19#14583199—21no—
20#14583191C2211yescharacteristic
21#14583186C2211yescharacteristic
22#14583133—21no—
23#14583126—21no—
24#14583114—21no—
25#14583106C2211yescharacteristic
26#14583101C2211yescharacteristic
27#14583096C2211yescharacteristic
28#14583096C2211yescharacteristic
29#14583091C2211yescharacteristic
30#14583091C2211yescharacteristic
31#14583061—21no—
32#14583044—21no—
33#14583029C2211yescharacteristic
34C8×Dic86C2211yescharacteristic
35#14582978C2211yescharacteristic
36#14582975—21no—
37#14582968—21no—
38C8×D172C2211yescharacteristic
39#14582961—21no—
40#14582952C2211yescharacteristic
41#14582952C2211yescharacteristic
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43#14582856—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582643C2211yescharacteristic
53#14582643C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C43×#532C2211yescharacteristic
58C43×#498C2211yescharacteristic
59C43×#493C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#486C2211yescharacteristic
62C43×#469—21no—
63C43×#469—21no—
64C43×#442—21no—
65C43×#442—21no—
66C4×M16×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621883—21no—
69C2×#10621883—21no—
70C2×#10621884—21no—
71C2×#10621882—21no—
72C2×#10621882—21no—
73C2×#10621872—21no—
74C22×C43⋊C8—21no—
75C2×C8×D43—21no—
76#13063319—21no—
77#13063317D411yescharacteristic
78#13063313D411yescharacteristic
79#13063308—21no—
80#13063304D411yescharacteristic
81#13063299D411yescharacteristic
82C4×Dic86C2311yescharacteristic
83C4×D172C2311yescharacteristic
84C4×C22⋊D43—21no—
85#13063282—21no—
86#13063258—21no—
87#13063256—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)C2311yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95Dic43⋊C8—21no—
96Dic43⋊C8—21no—
97#13063249—21no—
98#13063249—21no—
99#13063248—21no—
100#13063246—21no—
101#13063246—21no—
102#13063246—21no—
103#13063246—21no—
104#13063245—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)—21no—
107(C2×D43)⋊C8—21no—
108(C2×D43)⋊C8—21no—
109#13063235—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8—21no—
112C8×Dic43—21no—
113C2×#41×C43—21no—
114C2×#41×C43—21no—
115C2×D8×C43—21no—
116C2×D8×C43—21no—
117C2×M16×C43D411yescharacteristic
118C2×M16×C43D411yescharacteristic
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#127×C43C2311yescharacteristic
122#127×C43C2311yescharacteristic
123#124×C43—21no—
124#124×C43—21no—
125#121×C43—21no—
126#121×C43—21no—
127#121×C43—21no—
128#121×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#106×C43—21no—
135#106×C43—21no—
136#102×C43—21no—
137#102×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140#97×C43D411yescharacteristic
141#97×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—81no—
145#41×C43—81no—
146#41×C43—82no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C22×C4×C43—41no—
158C22×C4×C43—41no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43#4111yescharacteristic
162C2×C22⋊D43—21no—
163C2×D172C2×D411yescharacteristic
164C2×C4×D43—21no—
165C2×Dic86C2×D411yescharacteristic
166D8×C43—42no—
167D8×C43—42no—
168M16×C43—22no—
169M16×C43—41no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C22⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C22⋊C4×C43—41no—
181C22⋊C4×C43—41no—
182C42×C43C2×D411yescharacteristic
183C42×C43C2×D411yescharacteristic
184C42×C43#4111yescharacteristic
185C42×C43C2411yescharacteristic
186C22⋊Dic43—21no—
187#10621885—81no—
188#10621884—81no—
189#10621883—81no—
190#10621883—81no—
191#10621882—81no—
192#10621882—81no—
193(C2×D43)⋊C4—21no—
194(C2×D43)⋊C4—21no—
195(C2×D43)⋊C4—21no—
196(C2×D43)⋊C4—21no—
197C4⋊Dic43C2×D411yescharacteristic
198C4⋊Dic43C2×D411yescharacteristic
199Dic43⋊C4—21no—
200Dic43⋊C4—21no—
201Dic43⋊C4—21no—
202Dic43⋊C4—21no—
203C4×Dic43—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—81no—
211#10621872—42no—
212C8×D43—42no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43#12111yescharacteristic
216C22×D43—21no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—81no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—81no—
229D4×C43—81no—
230D4×C43—82no—
231D4×C43—82no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—82no—
240C2×C4×C43—82no—
241C2×C4×C43#12111yescharacteristic
242C2×C4×C43#12111yescharacteristic
243C2×C4×C43#12111yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C22⋊D43—81no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251D172—21no—
252D172—21no—
253C4×D43—41no—
254C4×D43—41no—
255Dic86—21no—
256Dic86—21no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43#13512yes—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267#19250—431nomaximal, Sylow
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43C2×#12111yescharacteristic
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—41no—
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43C2×#13511yescharacteristic
288C4×C43#57511yescharacteristic
289C4×C43#57611yescharacteristic
290C4×C43#57711yescharacteristic
291Dic43—41no—
292Dic43—41no—
293Dic43—41no—
294#3247—431no—
295#3212—431no—
296#3184D4311yescharacteristic, complemented
297#2969—431no—
298#1702—431no—
299#1698—431no—
300#1691—431no—
301#1687—431no—
302#1681—431no—
303#1677—431no—
304#1672—431no—
305#1668—431no—
306#1565—431no—
307#1543—431no—
308#1540—431no—
309C2×C43—41no—
310C2×C43—161no—
311C2×C43—161no—
312C2×C43#303511yescharacteristic
313C2×C43#306211yescharacteristic
314C2×C43#306811yescharacteristic
315D43—81no—
316#532C2×D4311yescharacteristic
317#532C2×D4311yescharacteristic
318#529—431no—
319#498C2×D4311yescharacteristic
320#495—861no—
321#493C2×D4311yescharacteristic
322#488—861no—
323#486C2×D4311yescharacteristic
324#486C2×D4311yescharacteristic
325#478—861no—
326#477—431no—
327#476—431no—
328#469—21no—
329#469—21no—
330#466—861no—
331#465—861no—
332#463—861no—
333#462—431no—
334#461—431no—
335#460—431no—
336#460—431no—
337#459—431no—
338#459—431no—
339#452—861no—
340#449—861no—
341#446—431no—
342C8×Q8—431no—
343#442—21no—
344#442—21no—
345#436—431no—
346#436—861no—
347#435—861no—
348C8×D4—431no—
349#433—861no—
350#431—431no—
351#431—431no—
352C2×C4⋊C8—431no—
353#405—861no—
354C4×M16C2×D4311yescharacteristic
355#335—431no—
356#335—431no—
357#334—431no—
358#334—431no—
359#333—431no—
360#333—431no—
361#332—431no—
362#332—431no—
363#331—431no—
364#331—431no—
365#331—431no—
366#331—431no—
367C43#1925011yescharacteristic, complemented, Sylow
368C2×#41—21no—
369C2×#41—21no—
370C2×Q16—861no—
371C2×SD16—861no—
372C2×SD16—861no—
373C2×SD16—861no—
374C2×D8—21no—
375C2×D8—21no—
376C2×D8—861no—
377C2×D8—861no—
378C2×M16—861no—
379C2×M16C22⋊D4311yescharacteristic
380C2×M16C22⋊D4311yescharacteristic
381C22×C8—861no—
382C22×C8—861no—
383C4⋊Q8C22×D4311yescharacteristic
384C4⋊Q8C22×D4311yescharacteristic
385#127C22×D4311yescharacteristic
386#127C22×D4311yescharacteristic
387#126—861no—
388#125—431no—
389#124—21no—
390#124—21no—
391#124—431no—
392#123—861no—
393C22⋊Q8—431no—
394#121—21no—
395#121—21no—
396#121—21no—
397#121—21no—
398#121—431no—
399C4×Q8—431no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—431no—
405C4×D4—861no—
406#117—861no—
407C2×C42C22×D4311yescharacteristic
408#107—861no—
409#106—21no—
410#106—21no—
411#106—861no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—431no—
417C4⋊C8—431no—
418C4⋊C8—861no—
419C4⋊C8—861no—
420C4⋊C8—861no—
421#103—861no—
422#103—861no—
423#103—861no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—861no—
429#102—861no—
430#102—861no—
431#102—861no—
432#102—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437#97—861no—
438#97C22⋊D4311yescharacteristic
439#97C22⋊D4311yescharacteristic
440C4×C8—861no—
441C4×C8—861no—
442C4×C8—861no—
443C4×C8C22×D4311yescharacteristic
444C4×C8C22×D4311yescharacteristic
445#41—81no—
446#41—81no—
447#41—82no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—431no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—431no—
460C2×D4—861no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—861no—
464C22×C4D4×D4311yescharacteristic
465C22×C4#1062190011yescharacteristic
466C22×C4C2×C22⋊D4311yescharacteristic
467Q16—3441no—
468SD16—3441no—
469SD16—3441no—
470SD16—3441no—
471D8—42no—
472D8—42no—
473D8—3441no—
474D8—3441no—
475M16—22no—
476M16—41no—
477M16—1722no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—3441no—
485C2×C8—1722no—
486C2×C8C2×C22⋊D4311yescharacteristic
487C2×C8C2×C22⋊D4311yescharacteristic
488C2×C8C2×C22⋊D4311yescharacteristic
489C2×C8C2×C22⋊D4311yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—431no—
495C4⋊C4—431no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—861no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C22⋊C4—861no—
508C22⋊C4—861no—
509C42—861no—
510C42D4×D4311yescharacteristic
511C42#1062190011yescharacteristic
512C42C2×C22⋊D4311yescharacteristic
513C42C23×D4311yescharacteristic
514C23—41no—
515C23—41no—
516C23—861no—
517C23#1306329611yescharacteristic
518Q8—41no—
519Q8—41no—
520Q8—81no—
521Q8—861no—
522Q8—861no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—81no—
532D4—81no—
533D4—82no—
534D4—82no—
535D4—861no—
536D4—861no—
537D4—3441no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4#1306329611yescharacteristic
553C2×C4#1306329611yescharacteristic
554C2×C4#1306329611yescharacteristic
555C2×C4C2×D4×D4311yescharacteristic
556C2×C4C22×C22⋊D4311yescharacteristic
557C2×C4C2×#1062190011yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—1721no—
562C8—1721no—
563C8—1721no—
564C8—1721no—
565C8—1721no—
566C8—1721no—
567C8#1306334512yes—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—1721no—
578C22—1721no—
579C22—1721no—
580C22C2×#1306329611yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—81no—
586C4—81no—
587C4—1721no—
588C4—1721no—
589C4—1721no—
590C4C2×#1306334511yescharacteristic
591C4#1458369711yescharacteristic
592C4#1458370311yescharacteristic
593C4#1458370911yescharacteristic
594C2—41no—
595C2—161no—
596C2—161no—
597C2—3441no—
598C2#1914404411yescharacteristic
599C2#1914426911yescharacteristic
600C2#1914431911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3184C2
socleC22×C43C2×#121
hypercenter#3184D43
hypocenterC43#19250
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3184

Complements

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

NH ≅ G/Ntype
1. #19145915C2semidirect
2. #19145571C2semidirect
3. #19143599C2semidirect
4. #19134160C2semidirect
5. #19134132C2semidirect
6. #19134091C2semidirect
7. #19134071C2semidirect
8. #19134029C2semidirect
9. #19134001C2semidirect
10. #19133974C2semidirect
11. #19133952C2semidirect
12. #19133347C2semidirect
13. #19133257C2semidirect
14. #19133244C2semidirect
15. C43×#3184C2semidirect
296. #3184D43semidirect
367. C43#19250semidirect

Maximal subgroups

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

subgroupindex
#191459152
#191455712
#191435992
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