Finite Group Databasebeta

← D43×#1703 #25079166

Subgroups — D43×#1703 #25079166

Order 11008.

694 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#487×D43C211yesmaximal, characteristic, complemented
2#476×D43C211yesmaximal, characteristic
3#474×D43C211yesmaximal, characteristic
4#436×D43C211yesmaximal, characteristic
5#19134173C211yesmaximal, characteristic, complemented
6#19134172C211yesmaximal, characteristic, complemented
7#19134171C211yesmaximal, characteristic, complemented
8#19134170C211yesmaximal, characteristic, complemented
9#19134169C211yesmaximal, characteristic, complemented
10#19134168C211yesmaximal, characteristic, complemented
11#19134167C211yesmaximal, characteristic, complemented
12#334×D43C211yesmaximal, characteristic, complemented
13#333×D43C211yesmaximal, characteristic, complemented
14#332×D43C211yesmaximal, characteristic, complemented
15C43×#1703C211yesmaximal, characteristic, complemented
16C2×M16×D43—21no—
17C4⋊Q8×D43C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4×D4×D43C2211yescharacteristic
20#14583251C2211yescharacteristic, complemented
21#14583250C2211yescharacteristic, complemented
22#14583249C2211yescharacteristic, complemented
23#14583248—21no—
24#14583248—21no—
25#14583190C2211yescharacteristic
26#14583189C2211yescharacteristic
27#14583188—21no—
28#14583187—21no—
29#14583186C2211yescharacteristic
30#14583180C2211yescharacteristic
31#14583179C2211yescharacteristic
32#14583178—21no—
33#14583177—21no—
34#14583176C2211yescharacteristic
35#14582978C2211yescharacteristic
36#14582977C2211yescharacteristic
37#14582976C2211yescharacteristic
38#14582975—21no—
39#14582974—21no—
40#107×D43—21no—
41#106×D43—21no—
42C4⋊C8×D43C2211yescharacteristic
43C4⋊C8×D43C2211yescharacteristic
44C4⋊C8×D43C2211yescharacteristic
45#103×D43—21no—
46#103×D43—21no—
47#102×D43—21no—
48#102×D43—21no—
49C22⋊C8×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582650C2211yescharacteristic, complemented
52#14582649C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582647C2211yescharacteristic, complemented
57#14582646C2211yescharacteristic, complemented
58#14582645C2211yescharacteristic, complemented
59#14582644C2211yescharacteristic, complemented
60C43×#487C2211yescharacteristic, complemented
61C43×#476C2211yescharacteristic
62C43×#474C2211yescharacteristic
63C43×#436C2211yescharacteristic
64C43×#334C2211yescharacteristic, complemented
65C43×#333C2211yescharacteristic, complemented
66C43×#332C2211yescharacteristic, complemented
67C2×Q8×D43—21no—
68C2×Q8×D43—21no—
69C2×D4×D43D411yescharacteristic
70C22×C4×D43—21no—
71C2×#10621877—21no—
72C2×#10621872—21no—
73C2×#10621872—21no—
74M16×D43—44no—
75C2×C8×D43—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78C2×C8×D43D411yescharacteristic
79C2×C8×D43D411yescharacteristic
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063324—21no—
83#13063324—21no—
84#13063324—21no—
85#13063324—21no—
86#13063323—21no—
87#13063323—21no—
88C4×D172C2311yescharacteristic
89D4×Dic43D411yescharacteristic
90#13063287D411yescharacteristic
91C4×C22⋊D43—21no—
92(C22⋊D43)⋊C4—21no—
93C4⋊C4×D43—21no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43D411yescharacteristic
98C22⋊C4×D43—21no—
99C42×D43C2311yescharacteristic
100#13063259—21no—
101#13063258—21no—
102#13063258—21no—
103#13063257—21no—
104#13063256—21no—
105#13063256—21no—
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112#13063250—21no—
113#13063250—21no—
114#13063249—21no—
115#13063249—21no—
116#13063248—21no—
117#13063248—21no—
118#13063247—21no—
119#13063247—21no—
120#13063246—21no—
121#13063246—21no—
122#13063245—21no—
123#13063245—21no—
124C22⋊(C43⋊C8)—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C2×M16×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132C4⋊Q8×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#107×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C2×C22⋊D43—21no—
151C22×Dic43—21no—
152Q8×D43—42no—
153Q8×D43—42no—
154Q8×D43—82no—
155D4×D43—22no—
156D4×D43—22no—
157C2×D172C2×D411yescharacteristic
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—42no—
162C2×C4×D43—42no—
163C2×C4×D43—41no—
164C2×C4×D43—41no—
165C2×C4×D43C2×D411yescharacteristic
166C2×C4×D43C2×D411yescharacteristic
167C2×C4×D43#4111yescharacteristic
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—41no—
171C2×Dic86—41no—
172M16×C43—42no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43C2×D411yescharacteristic
183C22⋊C4×C43—21no—
184C42×C43C2411yescharacteristic
185C22⋊Dic43—21no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43#4111yescharacteristic
201#10621877—42no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207#10621872—42no—
208#10621872—42no—
209C8×D43—22no—
210C8×D43—22no—
211C8×D43—42no—
212C8×D43—42no—
213C8×D43—42no—
214C23×C43—21no—
215C22×D43—21no—
216C22×D43—42no—
217C22×D43—42no—
218C22×D43—42no—
219C22×D43#12111yescharacteristic
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—81no—
223D4×C43—21no—
224D4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C22⋊D43—42no—
234C2×Dic43—21no—
235C2×Dic43—42no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43#12111yescharacteristic
239C2×Dic43#12111yescharacteristic
240C2×Dic43#12111yescharacteristic
241D172—21no—
242D172—21no—
243C4×D43—22no—
244C4×D43—42no—
245C4×D43—41no—
246C4×D43—41no—
247C4×D43—42no—
248C4×D43—82no—
249C4×D43—82no—
250C4×D43#13512yes—
251C4×D43AGL(1,ℤ/8)12yes—
252C4×D43#13712yes—
253C4×D43#13712yes—
254Dic86—41no—
255Dic86—41no—
256Dic86—82no—
257Dic86—82no—
258Dic86—81no—
259C8×C43—21no—
260C8×C43—21no—
261C8×C43—41no—
262C8×C43—41no—
263C8×C43—41no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269C2×#1703—431nomaximal, Sylow
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43C2×#12111yescharacteristic
274C2×D43—41no—
275C2×D43—41no—
276C2×D43—41no—
277C2×D43—84no—
278C2×D43#46312yes—
279C2×D43#47012yes—
280C2×D43#47112yes—
281C4×C43—21no—
282C4×C43—41no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43C2×#13511yescharacteristic
286C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
287C4×C43C2×#13711yescharacteristic
288C4×C43C2×#13711yescharacteristic
289Dic43—21no—
290Dic43—41no—
291Dic43—81no—
292Dic43—81no—
293Dic43#46312yes—
294Dic43#47012yes—
295C2×#487—431no—
296C2×#476—431no—
297C2×#474—431no—
298C2×#436—431no—
299#1703—431no—
300#1703—431no—
301#1703—431no—
302#1703—431no—
303#1703—431no—
304#1703—431no—
305#1703—431no—
306#1703D4311yescharacteristic, direct product factor
307C2×#334—431no—
308C2×#333—431no—
309C2×#332—431no—
310C2×C43—81no—
311C2×C43C2×#46311yescharacteristic
312C2×C43C2×#47011yescharacteristic
313C2×C43C2×#47111yescharacteristic
314D43—81no—
315D43#170314yesdirect product factor
316C22×M16—861no—
317C2×C4⋊Q8—431no—
318C2×C4⋊Q8—431no—
319C2×C4×D4—431no—
320#487—431no—
321#487—431no—
322#487—431no—
323#487—861no—
324#487—861no—
325#487C2×D4311yescharacteristic, complemented
326#476—431no—
327#476—431no—
328#476—431no—
329#476—861no—
330#476—861no—
331#476C2×D4311yescharacteristic
332#474—431no—
333#474—431no—
334#474—431no—
335#474—861no—
336#474—861no—
337#474C2×D4311yescharacteristic
338#436—431no—
339#436—431no—
340#436—431no—
341#436—861no—
342#436—861no—
343#436C2×D4311yescharacteristic
344C2×#107—861no—
345C2×#106—861no—
346C2×C4⋊C8—431no—
347C2×C4⋊C8—431no—
348C2×C4⋊C8—431no—
349C2×#103—861no—
350C2×#103—861no—
351C2×#102—861no—
352C2×#102—861no—
353C2×C22⋊C8—861no—
354C2×C4×C8—431no—
355#334—431no—
356#334—431no—
357#334—431no—
358#334C2×D4311yescharacteristic, complemented
359#333—431no—
360#333—431no—
361#333—431no—
362#333C2×D4311yescharacteristic, complemented
363#332—431no—
364#332—431no—
365#332—431no—
366#332C2×D4311yescharacteristic, complemented
367C43C2×#170311yescharacteristic, complemented, Sylow
368C22×Q8—861no—
369C22×Q8—861no—
370C22×D4—431no—
371C23×C4—861no—
372C2×M16—21no—
373C2×M16—861no—
374C2×M16—861no—
375C2×M16—861no—
376C2×M16—1724no—
377C22×C8—431no—
378C22×C8—431no—
379C22×C8—861no—
380C22×C8—861no—
381C22×C8—861no—
382C4⋊Q8—431no—
383C4⋊Q8—431no—
384C4⋊Q8—861no—
385C4⋊Q8—861no—
386C4⋊Q8—861no—
387C4⋊Q8—861no—
388C4⋊Q8—861no—
389C4⋊Q8—861no—
390C4⋊Q8C22×D4311yescharacteristic
391C4⋊Q8C22×D4311yescharacteristic
392C4×D4—431no—
393C4×D4—431no—
394C4×D4—431no—
395C4×D4—861no—
396C4×D4—861no—
397C4×D4C22×D4311yescharacteristic
398C2×C4⋊C4—431no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C42—431no—
405#107—21no—
406#107—861no—
407#107—861no—
408#107—861no—
409#106—21no—
410#106—861no—
411#106—861no—
412#106—861no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—861no—
417C4⋊C8—861no—
418C4⋊C8—861no—
419C4⋊C8C22×D4311yescharacteristic
420C4⋊C8C22×D4311yescharacteristic
421C4⋊C8C22×D4311yescharacteristic
422#103—21no—
423#103—21no—
424#103—861no—
425#103—861no—
426#103—861no—
427#103—861no—
428#103—861no—
429#103—861no—
430#102—21no—
431#102—21no—
432#102—861no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438C22⋊C8—21no—
439C22⋊C8—861no—
440C22⋊C8—861no—
441C22⋊C8—861no—
442C4×C8—431no—
443C4×C8—431no—
444C4×C8—431no—
445C4×C8C22×D4311yescharacteristic
446C24—861no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×Q8—3442no—
452C2×Q8—1721no—
453C2×Q8—1721no—
454C2×Q8—1722no—
455C2×Q8—1722no—
456C2×D4—431no—
457C2×D4—862no—
458C2×D4—862no—
459C2×D4—861no—
460C2×D4D4×D4311yescharacteristic
461C22×C4—21no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—1722no—
470C22×C4—1722no—
471C22×C4—1721no—
472C22×C4—1721no—
473M16—42no—
474M16—1722no—
475M16—1722no—
476M16—1722no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—862no—
483C2×C8—862no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—1722no—
488C2×C8—1722no—
489C2×C8—1722no—
490C2×C8D4×D4311yescharacteristic
491C2×C8D4×D4311yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—431no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—1721no—
503C4⋊C4—1721no—
504C4⋊C4—1721no—
505C4⋊C4—1721no—
506C4⋊C4D4×D4311yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—861no—
509C22⋊C4—861no—
510C22⋊C4—861no—
511C42—431no—
512C42—431no—
513C42—431no—
514C42C23×D4311yescharacteristic
515C23—21no—
516C23—431no—
517C23—861no—
518C23—1722no—
519C23—1722no—
520C23—1722no—
521Q8—41no—
522Q8—41no—
523Q8—81no—
524Q8—3441no—
525Q8—3442no—
526Q8—3442no—
527Q8—1721no—
528Q8—1721no—
529D4—21no—
530D4—21no—
531D4—861no—
532D4—861no—
533D4—1722no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—431no—
540C2×C4—431no—
541C2×C4—432no—
542C2×C4—432no—
543C2×C4—432no—
544C2×C4—432no—
545C2×C4—431no—
546C2×C4—862no—
547C2×C4—861no—
548C2×C4—3442no—
549C2×C4—3442no—
550C2×C4—1722no—
551C2×C4—1722no—
552C2×C4—1722no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4C2×D4×D4311yescharacteristic
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4#41×D4311yescharacteristic
560C8—21no—
561C8—21no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—861no—
566C8—861no—
567C8—1721no—
568C8—1721no—
569C8—1721no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—432no—
574C22—432no—
575C22—432no—
576C22—3444no—
577C22—1721no—
578C22—1721no—
579C22—1721no—
580C22#121×D4311yescharacteristic
581C4—21no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—432no—
586C4—432no—
587C4—861no—
588C4—3441no—
589C4—3441no—
590C4—1721no—
591C4#135×D4311yescharacteristic
592C4AGL(1,ℤ/8)×D4311yescharacteristic
593C4#137×D4311yescharacteristic
594C4#137×D4311yescharacteristic
595C2—81no—
596C2—434no—
597C2—3441no—
598C2#463×D4311yescharacteristic
599C2#470×D4311yescharacteristic
600C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1703C2
socleC22×C43C2×#121
prime radicalC2×D4×D43D4
hypercenter#1703D43
hypocenterC43C2×#1703
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1703

Complements

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

NH ≅ G/Ntype
1. #487×D43C2semidirect
5. #19134173C2semidirect
6. #19134172C2semidirect
7. #19134171C2semidirect
8. #19134170C2semidirect
9. #19134169C2semidirect
10. #19134168C2semidirect
11. #19134167C2semidirect
12. #334×D43C2semidirect
13. #333×D43C2semidirect
14. #332×D43C2semidirect
15. C43×#1703C2semidirect
20. #14583251C22semidirect
21. #14583250C22semidirect
22. #14583249C22semidirect
51. #14582650C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582648C22semidirect
55. #14582647C22semidirect
56. #14582647C22semidirect
57. #14582646C22semidirect
58. #14582645C22semidirect
59. #14582644C22semidirect
60. C43×#487C22semidirect
64. C43×#334C22semidirect
65. C43×#333C22semidirect
66. C43×#332C22semidirect
306. #1703D43direct (N × H)
315. D43#1703direct (N × H)
325. #487C2×D43semidirect
358. #334C2×D43semidirect
362. #333C2×D43semidirect
366. #332C2×D43semidirect
367. C43C2×#1703semidirect

Maximal subgroups

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

subgroupindex
#487×D432
#476×D432
#474×D432
#436×D432
#191341732
#191341722
#191341712
#191341702
#191341692
#191341682
#191341672
#334×D432
#333×D432
#332×D432
C43×#17032
C2×#170343