Finite Group Databasebeta

← D43×#1717 #25084333

Subgroups — D43×#1717 #25084333

Order 11008.

966 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#493×D43C211yesmaximal, characteristic
2#492×D43C211yesmaximal, characteristic, complemented
3#487×D43C211yesmaximal, characteristic, complemented
4#486×D43C211yesmaximal, characteristic, complemented
5#486×D43C211yesmaximal, characteristic, complemented
6#486×D43C211yesmaximal, characteristic, complemented
7#19134237C211yesmaximal, characteristic, complemented
8#19134236C211yesmaximal, characteristic, complemented
9#19134235C211yesmaximal, characteristic, complemented
10#19134234C211yesmaximal, characteristic, complemented
11#19134233C211yesmaximal, characteristic, complemented
12#19134232C211yesmaximal, characteristic, complemented
13#19134231C211yesmaximal, characteristic, complemented
14#322×D43C211yesmaximal, characteristic, complemented
15C43×#1717C211yesmaximal, characteristic, complemented
16C2×SD16×D43—22no—
17C2×D8×D43—22no—
18C4⋊Q8×D43C2211yescharacteristic
19C4⋊Q8×D43C2211yescharacteristic
20#127×D43C2211yescharacteristic
21#127×D43C2211yescharacteristic
22#14583276C2211yescharacteristic
23#14583275C2211yescharacteristic
24#14583275C2211yescharacteristic
25#14583274—22no—
26#14583273C2211yescharacteristic, complemented
27#14583272C2211yescharacteristic, complemented
28#14583271C2211yescharacteristic, complemented
29#14583270—22no—
30#14583251C2211yescharacteristic, complemented
31#14583250C2211yescharacteristic, complemented
32#14583249C2211yescharacteristic, complemented
33#14583248—22no—
34#14583247C2211yescharacteristic, complemented
35#14583247C2211yescharacteristic, complemented
36#14583247C2211yescharacteristic, complemented
37#14583246C2211yescharacteristic, complemented
38#14583246C2211yescharacteristic, complemented
39#14583246C2211yescharacteristic, complemented
40#14583245C2211yescharacteristic, complemented
41#14583245C2211yescharacteristic, complemented
42#14583245C2211yescharacteristic, complemented
43#14583244—22no—
44#14583244—22no—
45#14583244—22no—
46#103×D43—22no—
47#102×D43—22no—
48#102×D43—22no—
49#102×D43—22no—
50C4×C8×D43C2211yescharacteristic
51C4×C8×D43C2211yescharacteristic
52C4×C8×D43C2211yescharacteristic
53#14582621C2211yescharacteristic, complemented
54#14582621C2211yescharacteristic, complemented
55#14582620C2211yescharacteristic, complemented
56C43×#493C2211yescharacteristic
57C43×#492C2211yescharacteristic, complemented
58C43×#487C2211yescharacteristic, complemented
59C43×#486C2211yescharacteristic, complemented
60C43×#486C2211yescharacteristic, complemented
61C43×#486C2211yescharacteristic, complemented
62C43×#322C2211yescharacteristic, complemented
63C2×Q8×D43—21no—
64C2×Q8×D43—21no—
65C2×D4×D43—21no—
66C2×D4×D43—21no—
67C2×D4×D43—21no—
68C2×D4×D43—21no—
69C2×D4×D43—21no—
70C2×D4×D43—21no—
71C2×#10621873—22no—
72C2×#10621883—22no—
73C2×#10621884—22no—
74SD16×D43—48no—
75C2×D344—22no—
76C2×#10621882—22no—
77C2×#10621882—22no—
78D8×D43—48no—
79C2×C8×D43D412yes—
80C2×C8×D43D412yes—
81C2×C8×D43D412yes—
82#13063325C2311yescharacteristic
83#13063325C2311yescharacteristic
84#13063324—21no—
85#13063324—21no—
86#13063324—21no—
87#13063324—21no—
88#13063323—21no—
89#13063323—21no—
90#13063322C2311yescharacteristic
91#13063322C2311yescharacteristic
92#13063321—21no—
93#13063321—21no—
94#13063321—21no—
95#13063321—21no—
96#13063321—21no—
97#13063321—21no—
98C4⋊C4×D43—21no—
99C4⋊C4×D43—21no—
100C4⋊C4×D43—21no—
101C4⋊C4×D43—21no—
102C42×D43C2311yescharacteristic
103#13063250—22no—
104#13063249—22no—
105#13063248—22no—
106#13063247—22no—
107#13063247—22no—
108#13063247—22no—
109#13063246—22no—
110#13063246—22no—
111#13063246—22no—
112#13063245—22no—
113#13063245—22no—
114#13063245—22no—
115C4×C43⋊C8C2311yescharacteristic
116C4×C43⋊C8C2311yescharacteristic
117C4×C43⋊C8C2311yescharacteristic
118C8×Dic43D412yes—
119C8×Dic43D412yes—
120C8×Dic43D412yes—
121C2×SD16×C43—22no—
122C2×D8×C43—22no—
123C4⋊Q8×C43C2311yescharacteristic
124C4⋊Q8×C43C2311yescharacteristic
125#127×C43C2311yescharacteristic
126#127×C43C2311yescharacteristic
127#103×C43—22no—
128#102×C43—22no—
129#102×C43—22no—
130#102×C43—22no—
131C4×C8×C43C2311yescharacteristic
132C4×C8×C43C2311yescharacteristic
133C4×C8×C43C2311yescharacteristic
134C23×D43—41no—
135C23×D43—41no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×C22⋊D43—41no—
145C2×C22⋊D43—41no—
146C2×C22⋊D43—41no—
147C2×C22⋊D43—41no—
148C2×C22⋊D43—41no—
149C2×C22⋊D43—41no—
150Q8×D43—44no—
151Q8×D43—44no—
152D4×D43—44no—
153D4×D43—44no—
154D4×D43—44no—
155D4×D43—44no—
156D4×D43—44no—
157D4×D43—44no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×C4×D43—41no—
165C2×C4×D43—41no—
166C2×C4×D43C2×D411yescharacteristic
167C2×C4×D43C2×D411yescharacteristic
168C2×C4×D43C2×D411yescharacteristic
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—41no—
172C2×Dic86—41no—
173SD16×C43—44no—
174D8×C43—44no—
175C2×C8×C43C2×D412yes—
176C2×C8×C43C2×D412yes—
177C2×C8×C43C2×D412yes—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C42×C43C2411yescharacteristic
183#10621884—44no—
184#10621883—44no—
185#10621882—44no—
186#10621882—44no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195C4×Dic43C2×D411yescharacteristic
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43C2×D411yescharacteristic
198C2×C43⋊C8C2×D412yes—
199C2×C43⋊C8C2×D412yes—
200C2×C43⋊C8C2×D412yes—
201D344—44no—
202#10621873—44no—
203C8×D43—24no—
204C8×D43—24no—
205C8×D43—24no—
206C23×C43—41no—
207C23×C43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—82no—
211C22×D43—82no—
212C22×D43—82no—
213C22×D43—82no—
214C22×D43—82no—
215C22×D43—82no—
216C22×D43#12711yescharacteristic
217Q8×C43—42no—
218Q8×C43—42no—
219D4×C43—42no—
220D4×C43—42no—
221D4×C43—42no—
222D4×C43—42no—
223D4×C43—42no—
224D4×C43—42no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C22⋊D43—82no—
231C22⋊D43—82no—
232C22⋊D43—82no—
233C22⋊D43—82no—
234C22⋊D43—82no—
235C22⋊D43—82no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43#12711yescharacteristic
239C2×Dic43#12711yescharacteristic
240C2×Dic43#12711yescharacteristic
241D172—42no—
242D172—42no—
243D172—42no—
244D172—42no—
245D172—42no—
246D172—42no—
247C4×D43—82no—
248C4×D43—82no—
249C4×D43#13514yes—
250C4×D43AGL(1,ℤ/8)14yes—
251C4×D43AGL(1,ℤ/8)14yes—
252Dic86—42no—
253Dic86—42no—
254Dic86—82no—
255Dic86—82no—
256C8×C43—22no—
257C8×C43—22no—
258C8×C43—22no—
259C43⋊C8—22no—
260C43⋊C8—22no—
261C43⋊C8—22no—
262C2×#1717—431nomaximal, Sylow
263C22×C43—81no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43C2×#12711yescharacteristic
270C2×D43—81no—
271C2×D43—81no—
272C2×D43—81no—
273C2×D43—81no—
274C2×D43—81no—
275C2×D43—81no—
276C2×D43—164no—
277C2×D43—164no—
278C2×D43#49512yes—
279C2×D43#49612yes—
280C2×D43#49612yes—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43C2×#13512yes—
284C4×C43C2×AGL(1,ℤ/8)12yes—
285C4×C43C2×AGL(1,ℤ/8)12yes—
286Dic43—81no—
287Dic43—81no—
288Dic43#49512yes—
289Dic43#49612yes—
290Dic43#49612yes—
291C2×#493—431no—
292C2×#492—431no—
293C2×#487—431no—
294C2×#486—431no—
295C2×#486—431no—
296C2×#486—431no—
297#1717—431no—
298#1717—431no—
299#1717—431no—
300#1717—431no—
301#1717—431no—
302#1717—431no—
303#1717—431no—
304#1717D4311yescharacteristic, direct product factor
305C2×#322—431no—
306C2×C43—161no—
307C2×C43—161no—
308C2×C43C2×#49511yescharacteristic
309C2×C43C2×#49611yescharacteristic
310C2×C43C2×#49611yescharacteristic
311D43—161no—
312D43—161no—
313D43#171714yesdirect product factor
314C22×SD16—862no—
315C22×D8—862no—
316C2×C4⋊Q8—431no—
317C2×C4⋊Q8—431no—
318C2×#127—431no—
319C2×#127—431no—
320#493—431no—
321#493—431no—
322#493—431no—
323#493—862no—
324#493C2×D4311yescharacteristic
325#492—431no—
326#492—431no—
327#492—431no—
328#492—862no—
329#492C2×D4311yescharacteristic, complemented
330#487—431no—
331#487—431no—
332#487—431no—
333#487—862no—
334#487C2×D4311yescharacteristic, complemented
335#486—431no—
336#486—431no—
337#486—431no—
338#486—431no—
339#486—431no—
340#486—431no—
341#486—431no—
342#486—431no—
343#486—431no—
344#486—862no—
345#486—862no—
346#486—862no—
347#486C2×D4311yescharacteristic, complemented
348#486C2×D4311yescharacteristic, complemented
349#486C2×D4311yescharacteristic, complemented
350C2×#103—862no—
351C2×#102—862no—
352C2×#102—862no—
353C2×#102—862no—
354C2×C4×C8—431no—
355C2×C4×C8—431no—
356C2×C4×C8—431no—
357#322—431no—
358#322—431no—
359#322—431no—
360#322C2×D4311yescharacteristic, complemented
361C43C2×#171711yescharacteristic, complemented, Sylow
362C22×Q8—861no—
363C22×Q8—861no—
364C22×D4—861no—
365C22×D4—861no—
366C22×D4—861no—
367C22×D4—861no—
368C22×D4—861no—
369C22×D4—861no—
370C2×SD16—22no—
371C2×SD16—862no—
372C2×SD16—862no—
373C2×SD16—862no—
374C2×SD16—1728no—
375C2×D8—22no—
376C2×D8—862no—
377C2×D8—862no—
378C2×D8—862no—
379C2×D8—1728no—
380C22×C8—432no—
381C22×C8—432no—
382C22×C8—432no—
383C4⋊Q8—431no—
384C4⋊Q8—431no—
385C4⋊Q8—861no—
386C4⋊Q8—861no—
387C4⋊Q8—861no—
388C4⋊Q8—861no—
389C4⋊Q8—861no—
390C4⋊Q8—861no—
391C4⋊Q8C22×D4311yescharacteristic
392C4⋊Q8C22×D4311yescharacteristic
393#127—431no—
394#127—431no—
395#127—861no—
396#127—861no—
397#127—861no—
398#127—861no—
399#127—861no—
400#127—861no—
401#127C22×D4311yescharacteristic
402#127C22×D4311yescharacteristic
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C42—431no—
408#103—22no—
409#103—862no—
410#103—862no—
411#103—862no—
412#102—22no—
413#102—22no—
414#102—22no—
415#102—862no—
416#102—862no—
417#102—862no—
418#102—862no—
419#102—862no—
420#102—862no—
421#102—862no—
422#102—862no—
423#102—862no—
424C4×C8—432no—
425C4×C8—432no—
426C4×C8—432no—
427C4×C8—431no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8C22×D4311yescharacteristic
431C4×C8C22×D4311yescharacteristic
432C4×C8C22×D4311yescharacteristic
433C24—1721no—
434C24—1721no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8—1721no—
440C2×Q8—1721no—
441C2×Q8—1724no—
442C2×Q8—1724no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—861no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4—1724no—
456C2×D4—1724no—
457C2×D4—1724no—
458C2×D4—1724no—
459C2×D4—1724no—
460C2×D4—1724no—
461C2×D4—1721no—
462C2×D4—1721no—
463C2×D4—1721no—
464C2×D4—1721no—
465C2×D4—1721no—
466C2×D4—1721no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—1721no—
471C22×C4—1721no—
472SD16—44no—
473SD16—1724no—
474SD16—1724no—
475SD16—1724no—
476D8—44no—
477D8—1724no—
478D8—1724no—
479D8—1724no—
480C2×C8—432no—
481C2×C8—432no—
482C2×C8—432no—
483C2×C8—864no—
484C2×C8—864no—
485C2×C8—864no—
486C2×C8D4×D4312yes—
487C2×C8D4×D4312yes—
488C2×C8D4×D4312yes—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—1721no—
498C4⋊C4—1721no—
499C4⋊C4—1721no—
500C4⋊C4—1721no—
501C42—431no—
502C42—431no—
503C42—431no—
504C42C23×D4311yescharacteristic
505C23—41no—
506C23—41no—
507C23—431no—
508C23—3442no—
509C23—3442no—
510C23—3442no—
511C23—3442no—
512C23—3442no—
513C23—3442no—
514C23—1721no—
515C23—1721no—
516Q8—42no—
517Q8—42no—
518Q8—3442no—
519Q8—3442no—
520Q8—1722no—
521Q8—1722no—
522D4—42no—
523D4—42no—
524D4—42no—
525D4—42no—
526D4—42no—
527D4—42no—
528D4—3442no—
529D4—3442no—
530D4—3442no—
531D4—3442no—
532D4—3442no—
533D4—3442no—
534D4—1722no—
535D4—1722no—
536D4—1722no—
537D4—1722no—
538D4—1722no—
539D4—1722no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—431no—
543C2×C4—431no—
544C2×C4—431no—
545C2×C4—434no—
546C2×C4—434no—
547C2×C4—434no—
548C2×C4—3442no—
549C2×C4—3442no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4C2×D4×D4311yescharacteristic
553C2×C4C2×D4×D4311yescharacteristic
554C2×C4C2×D4×D4311yescharacteristic
555C8—22no—
556C8—22no—
557C8—22no—
558C8—862no—
559C8—862no—
560C8—862no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—432no—
568C22—432no—
569C22—432no—
570C22—3441no—
571C22—3441no—
572C22—3441no—
573C22—3441no—
574C22—3441no—
575C22—3441no—
576C22—6884no—
577C22—6884no—
578C22#127×D4311yescharacteristic
579C4—81no—
580C4—81no—
581C4—432no—
582C4—432no—
583C4—432no—
584C4—3441no—
585C4—3441no—
586C4#135×D4312yes—
587C4AGL(1,ℤ/8)×D4312yes—
588C4AGL(1,ℤ/8)×D4312yes—
589C2—161no—
590C2—161no—
591C2—434no—
592C2—6881no—
593C2—6881no—
594C2#495×D4311yescharacteristic
595C2#496×D4311yescharacteristic
596C2#496×D4311yescharacteristic
subgroupG/H
centerC22#127×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1717C2
socleC22×C43C2×#127
prime radical#493×D43C2
hypercenter#1717D43
hypocenterC43C2×#1717
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1717

Complements

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

NH ≅ G/Ntype
2. #492×D43C2semidirect
3. #487×D43C2semidirect
4. #486×D43C2semidirect
5. #486×D43C2semidirect
6. #486×D43C2semidirect
7. #19134237C2semidirect
8. #19134236C2semidirect
9. #19134235C2semidirect
10. #19134234C2semidirect
11. #19134233C2semidirect
12. #19134232C2semidirect
13. #19134231C2semidirect
14. #322×D43C2semidirect
15. C43×#1717C2semidirect
26. #14583273C22semidirect
27. #14583272C22semidirect
28. #14583271C22semidirect
30. #14583251C22semidirect
31. #14583250C22semidirect
32. #14583249C22semidirect
34. #14583247C22semidirect
35. #14583247C22semidirect
36. #14583247C22semidirect
37. #14583246C22semidirect
38. #14583246C22semidirect
39. #14583246C22semidirect
40. #14583245C22semidirect
41. #14583245C22semidirect
42. #14583245C22semidirect
53. #14582621C22semidirect
54. #14582621C22semidirect
55. #14582620C22semidirect
57. C43×#492C22semidirect
58. C43×#487C22semidirect
59. C43×#486C22semidirect
60. C43×#486C22semidirect
61. C43×#486C22semidirect
62. C43×#322C22semidirect
304. #1717D43direct (N × H)
313. D43#1717direct (N × H)
329. #492C2×D43semidirect
334. #487C2×D43semidirect
347. #486C2×D43semidirect
348. #486C2×D43semidirect
349. #486C2×D43semidirect
360. #322C2×D43semidirect
361. C43C2×#1717semidirect

Maximal subgroups

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

subgroupindex
#493×D432
#492×D432
#487×D432
#486×D432
#191342372
#191342362
#191342352
#191342342
#191342332
#191342322
#191342312
#322×D432
C43×#17172
C2×#171743