Finite Group Databasebeta

← D43×AGL(1,ℤ/16) #25250034

Subgroups — D43×AGL(1,ℤ/16) #25250034

Order 11008.

710 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#509×D43C211yesmaximal, characteristic
2#444×D43C211yesmaximal, characteristic, complemented
3#442×D43C211yesmaximal, characteristic, complemented
4#19136496C211yesmaximal, characteristic, complemented
5#19136495C211yesmaximal, characteristic, complemented
6#19136494C211yesmaximal, characteristic, complemented
7#19136493C211yesmaximal, characteristic, complemented
8#19136492C211yesmaximal, characteristic, complemented
9#19136491C211yesmaximal, characteristic, complemented
10#19136490C211yesmaximal, characteristic, complemented
11#365×D43C211yesmaximal, characteristic, complemented
12#361×D43C211yesmaximal, characteristic, complemented
13#360×D43C211yesmaximal, characteristic, complemented
14#347×D43C211yesmaximal, characteristic, complemented
15C43×AGL(1,ℤ/16)C211yesmaximal, characteristic, complemented
16#135×D43C2211yescharacteristic
17C2×D8×D43C2211yescharacteristic
18#131×D43—21no—
19C4×D4×D43—21no—
20#14583337C2211yescharacteristic
21#14583336C412yescomplemented
22#14583335C2211yescharacteristic
23#14583334C2211yescharacteristic
24#14583333C412yescomplemented
25SD32×D43C412yescomplemented
26D16×D43C412yescomplemented
27M32×D43C2211yescharacteristic
28M32×D43C2211yescharacteristic
29#14583022C2211yescharacteristic, complemented
30#14583021C2211yescharacteristic, complemented
31#14583020C2211yescharacteristic, complemented
32#14583019—21no—
33#14583018—21no—
34#14583012C2211yescharacteristic, complemented
35#14583011C2211yescharacteristic, complemented
36#14583010C2211yescharacteristic, complemented
37#14583009—21no—
38#14583008—21no—
39#108×D43C2211yescharacteristic
40#106×D43C2211yescharacteristic
41#104×D43—21no—
42#102×D43—21no—
43#97×D43C2211yescharacteristic
44#14582723C2211yescharacteristic, complemented
45#14582722C2211yescharacteristic, complemented
46#14582721C2211yescharacteristic, complemented
47#14582713C2211yescharacteristic, complemented
48#14582712C2211yescharacteristic, complemented
49#14582711C2211yescharacteristic, complemented
50#14582710C2211yescharacteristic, complemented
51#14582709C2211yescharacteristic, complemented
52#14582708C2211yescharacteristic, complemented
53#14582677C2211yescharacteristic, complemented
54#14582676C2211yescharacteristic, complemented
55#14582676C2211yescharacteristic, complemented
56C43×#509C2211yescharacteristic
57C43×#444C2211yescharacteristic, complemented
58C43×#442C2211yescharacteristic, complemented
59C43×#365C2211yescharacteristic, complemented
60C43×#361C2211yescharacteristic, complemented
61C43×#360C2211yescharacteristic, complemented
62C43×#347C2211yescharacteristic, complemented
63#41×D43—21no—
64C2×D4×D43—21no—
65C22×C4×D43—41no—
66#13063348C2×C411yescharacteristic, complemented
67#13063347C2311yescharacteristic
68#13063346—21no—
69#13063345—21no—
70#13063344C2×C411yescharacteristic, complemented
71Q16×D43C2×C411yescharacteristic, complemented
72SD16×D43—21no—
73C2×D344C2311yescharacteristic
74C2×#10621882—21no—
75D8×D43—21no—
76D8×D43—21no—
77D8×D43C2×C412yes—
78D8×D43C2×C412yes—
79D8×D43C2×C411yescharacteristic, complemented
80#13063333—21no—
81#13063333—41no—
82#13063332—21no—
83#13063331—21no—
84#13063331—41no—
85M16×D43—21no—
86M16×D43—41no—
87C2×C8×D43—41no—
88C2×C8×D43D411yescharacteristic
89C2×C8×D43C2311yescharacteristic
90C4×D172—21no—
91D4×Dic43—21no—
92#13063287—21no—
93C4×C22⋊D43—41no—
94(C22⋊D43)⋊C4—41no—
95C4⋊C4×D43—21no—
96C22⋊C4×D43—41no—
97C42×D43D411yescharacteristic
98#13063270C2×C412yescomplemented
99#13063269C2×C412yescomplemented
100#13063268C2×C412yescomplemented
101D688C2×C412yescomplemented
102#13063266C2×C412yescomplemented
103#13063266C2×C412yescomplemented
104#13063265C2311yescharacteristic
105#13063265C2311yescharacteristic
106#13063264—21no—
107#13063264C2×C412yescomplemented
108C16×D43—21no—
109C16×D43C2×C412yescomplemented
110#13063261C2311yescharacteristic
111#13063260—21no—
112#13063257C2311yescharacteristic
113#13063256—21no—
114#13063253—21no—
115#13063252—21no—
116#13063251—21no—
117#13063247—21no—
118#13063246—21no—
119#13063245—21no—
120#13063236D411yescharacteristic
121#13063235D411yescharacteristic
122#13063235C2311yescharacteristic
123#135×C43C2311yescharacteristic
124C2×D8×C43C2311yescharacteristic
125#131×C43—21no—
126C4×D4×C43—21no—
127SD32×C43C2×C412yescomplemented
128D16×C43C2×C412yescomplemented
129M32×C43C2311yescharacteristic
130M32×C43C2311yescharacteristic
131#108×C43C2311yescharacteristic
132#106×C43C2311yescharacteristic
133#104×C43—21no—
134#102×C43—21no—
135#97×C43C2311yescharacteristic
136C23×D43—41no—
137#41×C43—21no—
138C2×D4×C43—21no—
139C22×C4×C43—41no—
140C2×C22⋊D43—41no—
141C22×Dic43—41no—
142#10621902—21no—
143Q8×D43—21no—
144#10621900—21no—
145#10621900—41no—
146D4×D43—22no—
147D4×D43—22no—
148D4×D43—21no—
149D4×D43—41no—
150D4×D43—41no—
151D4×D43—41no—
152#10621898—21no—
153#10621898—41no—
154C2×D172—21no—
155C2×C4×D43—21no—
156C2×C4×D43—41no—
157C2×C4×D43—41no—
158C2×C4×D43—41no—
159C2×C4×D43—41no—
160C2×C4×D43—84no—
161C2×C4×D43C2×D411yescharacteristic
162Q16×C43C22×C411yescharacteristic, complemented
163SD16×C43—21no—
164D8×C43—21no—
165D8×C43C22×C412yes—
166D8×C43C22×C411yescharacteristic, complemented
167M16×C43—21no—
168M16×C43—41no—
169C2×C8×C43—41no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2411yescharacteristic
172C4⋊C4×C43—21no—
173C22⋊C4×C43—41no—
174C42×C43C2×D411yescharacteristic
175C22⋊Dic43—41no—
176#10621885—21no—
177#10621884—21no—
178#10621883—21no—
179#10621882—22no—
180#10621882—22no—
181#10621882—21no—
182(C2×D43)⋊C4—41no—
183(C2×D43)⋊C4—41no—
184C4⋊Dic43—21no—
185Dic43⋊C4—41no—
186C4×Dic43—21no—
187C4×Dic43C2×D411yescharacteristic
188#10621877—21no—
189#10621877—41no—
190C2×C43⋊C8—41no—
191C2×C43⋊C8C2×D411yescharacteristic
192C2×C43⋊C8C2×D411yescharacteristic
193Dic172C22×C411yescharacteristic, complemented
194D344—21no—
195D344C22×C412yes—
196D344C22×C411yescharacteristic, complemented
197#10621873—21no—
198#10621872—41no—
199#10621872—41no—
200#10621872—41no—
201C8×D43—21no—
202C8×D43—21no—
203C8×D43—41no—
204C8×D43—41no—
205C8×D43—41no—
206C8×D43C22×C411yescharacteristic
207C8×D43C22×C411yescharacteristic
208C8×D43#4111yescharacteristic
209C8×D43#4111yescharacteristic
210C16×C43—21no—
211C16×C43C22×C412yescomplemented
212C43⋊C16—21no—
213C43⋊C16C22×C412yescomplemented
214C23×C43—41no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—42no—
218C22×D43—42no—
219C22×D43—82no—
220C22×D43—82no—
221C22×D43AGL(1,ℤ/8)11yescharacteristic
222Q8×C43—21no—
223D4×C43—22no—
224D4×C43—21no—
225D4×C43—41no—
226D4×C43—41no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—82no—
231C2×C4×C43C22×D411yescharacteristic
232C22⋊D43—41no—
233C22⋊D43—41no—
234C22⋊D43—41no—
235C22⋊D43—42no—
236C22⋊D43—42no—
237C2×Dic43—21no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—82no—
241C2×Dic43AGL(1,ℤ/8)11yescharacteristic
242D172—21no—
243D172—22no—
244D172—41no—
245D172—41no—
246C4×D43—42no—
247C4×D43—41no—
248C4×D43—41no—
249C4×D43—41no—
250C4×D43—82no—
251C4×D43—82no—
252C4×D43—82no—
253C4×D43C4×D411yescharacteristic
254C4×D43C4×D411yescharacteristic
255C4×D43AGL(1,ℤ/8)11yescharacteristic
256C4×D43AGL(1,ℤ/8)11yescharacteristic
257Dic86—21no—
258Dic86—41no—
259C8×C43—21no—
260C8×C43—41no—
261C8×C43C23×C411yescharacteristic
262C8×C43C2×#4111yescharacteristic
263C43⋊C8—21no—
264C43⋊C8—41no—
265C43⋊C8C4×D411yescharacteristic
266C43⋊C8C4×D411yescharacteristic
267C2×AGL(1,ℤ/16)—431nomaximal, Sylow
268C22×C43—42no—
269C22×C43—41no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
273C2×D43—22no—
274C2×D43—42no—
275C2×D43—41no—
276C2×D43—84no—
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—82no—
280C2×D43—84no—
281C2×D43#44211yescharacteristic
282C2×D43#44211yescharacteristic
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—81no—
286C4×C43C2×C4×D411yescharacteristic
287C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
288Dic43—41no—
289Dic43—41no—
290Dic43—81no—
291Dic43#44211yescharacteristic
292Dic43#44211yescharacteristic
293C2×#509—431no—
294C2×#444—431no—
295C2×#442—431no—
296AGL(1,ℤ/16)—431no—
297AGL(1,ℤ/16)—431no—
298AGL(1,ℤ/16)—431no—
299AGL(1,ℤ/16)—431no—
300AGL(1,ℤ/16)—431no—
301AGL(1,ℤ/16)—431no—
302AGL(1,ℤ/16)—431no—
303AGL(1,ℤ/16)D4311yescharacteristic, direct product factor
304C2×#365—431no—
305C2×#361—431no—
306C2×#360—431no—
307C2×#347—431no—
308C2×C43—21no—
309C2×C43—82no—
310C2×C43—81no—
311C2×C43C2×#44211yescharacteristic
312D43—21no—
313D43—81no—
314D43—82no—
315D43AGL(1,ℤ/16)12yesdirect product factor
316C2×#135—431no—
317C22×D8—431no—
318C2×#131—861no—
319C2×C4×D4—861no—
320#509—431no—
321#509—431no—
322#509—432no—
323#509—432no—
324#509—431no—
325#509C2×D4311yescharacteristic
326C2×SD32—432no—
327C2×D16—432no—
328C2×M32—431no—
329C2×M32—431no—
330#444—431no—
331#444—431no—
332#444—431no—
333#444—861no—
334#444—861no—
335#444C2×D4311yescharacteristic, complemented
336#442—431no—
337#442—431no—
338#442—431no—
339#442—861no—
340#442—861no—
341#442C2×D4311yescharacteristic, complemented
342C2×#108—431no—
343C2×#106—431no—
344C2×#104—861no—
345C2×#102—861no—
346C2×#97—431no—
347#365—431no—
348#365—431no—
349#365—431no—
350#365C2×D4311yescharacteristic, complemented
351#361—431no—
352#361—431no—
353#361—431no—
354#361C2×D4311yescharacteristic, complemented
355#360—431no—
356#360—431no—
357#360—431no—
358#360C2×D4311yescharacteristic, complemented
359#347—431no—
360#347—431no—
361#347—431no—
362#347C2×D4311yescharacteristic, complemented
363C43C2×AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
364C2×#41—861no—
365C22×D4—861no—
366C23×C4—1721no—
367#135—431no—
368#135—431no—
369#135—431no—
370#135—861no—
371#135—861no—
372#135C22×D4311yescharacteristic
373C2×Q16—431no—
374C2×SD16—861no—
375C2×D8—432no—
376C2×D8—432no—
377C2×D8—431no—
378C2×D8—431no—
379C2×D8—861no—
380C2×D8—861no—
381C2×D8—861no—
382C2×D8C22×D4311yescharacteristic
383#131—21no—
384#131—861no—
385#131—861no—
386#131—861no—
387#131—1721no—
388#131—1721no—
389C2×M16—861no—
390C2×M16—1721no—
391C22×C8—431no—
392C22×C8—431no—
393C22×C8—1721no—
394C4×D4—21no—
395C4×D4—861no—
396C4×D4—861no—
397C4×D4—861no—
398C4×D4—1721no—
399C4×D4—1721no—
400C2×C4⋊C4—861no—
401C2×C22⋊C4—1721no—
402C2×C42—431no—
403SD32—432no—
404SD32—432no—
405SD32—432no—
406SD32C4×D4312yescomplemented
407D16—432no—
408D16—432no—
409D16—432no—
410D16C4×D4312yescomplemented
411M32—431no—
412M32—432no—
413M32—431no—
414M32—861no—
415M32C22×D4311yescharacteristic
416M32C22×D4311yescharacteristic
417C2×C16—432no—
418C2×C16—861no—
419#108—431no—
420#108—861no—
421#108C22×D4311yescharacteristic
422#106—431no—
423#106—861no—
424#106C22×D4311yescharacteristic
425#104—21no—
426#104—861no—
427#104—861no—
428#104—861no—
429#102—21no—
430#102—861no—
431#102—861no—
432#102—861no—
433#97—431no—
434#97—431no—
435#97—431no—
436#97C22×D4311yescharacteristic
437C24—1721no—
438#41—21no—
439#41—861no—
440#41—861no—
441#41—861no—
442#41—1721no—
443#41—1721no—
444C2×Q8—861no—
445C2×D4—21no—
446C2×D4—862no—
447C2×D4—862no—
448C2×D4—861no—
449C2×D4—861no—
450C2×D4—1721no—
451C2×D4—1721no—
452C2×D4—1721no—
453C2×D4—1721no—
454C22×C4—41no—
455C22×C4—431no—
456C22×C4—861no—
457C22×C4—3444no—
458C22×C4—1721no—
459C22×C4—1721no—
460C22×C4—1721no—
461C22×C4—1721no—
462C22×C4—1721no—
463Q16—431no—
464Q16—861no—
465Q16C2×C4×D4311yescharacteristic, complemented
466SD16—21no—
467SD16—861no—
468SD16—861no—
469SD16—861no—
470D8—21no—
471D8—431no—
472D8—432no—
473D8—862no—
474D8—862no—
475D8—861no—
476D8—861no—
477D8C2×C4×D4312yes—
478D8C2×C4×D4311yescharacteristic, complemented
479M16—21no—
480M16—41no—
481M16—861no—
482M16—1721no—
483M16—1721no—
484M16—1721no—
485M16—1721no—
486C2×C8—41no—
487C2×C8—431no—
488C2×C8—431no—
489C2×C8—431no—
490C2×C8—431no—
491C2×C8—431no—
492C2×C8—431no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—1721no—
496C2×C8—1721no—
497C2×C8—1721no—
498C2×C8—1721no—
499C2×C8D4×D4311yescharacteristic
500C2×C8C23×D4311yescharacteristic
501C4⋊C4—21no—
502C4⋊C4—861no—
503C4⋊C4—1721no—
504C22⋊C4—41no—
505C22⋊C4—1721no—
506C22⋊C4—1721no—
507C22⋊C4—1721no—
508C42—431no—
509C42—861no—
510C42D4×D4311yescharacteristic
511C16—21no—
512C16—432no—
513C16—861no—
514C16C2×C4×D4312yescomplemented
515C23—41no—
516C23—431no—
517C23—3442no—
518C23—3442no—
519C23—1721no—
520C23—1722no—
521C23—1722no—
522C23—1721no—
523Q8—21no—
524Q8—861no—
525Q8—1721no—
526D4—22no—
527D4—21no—
528D4—41no—
529D4—41no—
530D4—862no—
531D4—861no—
532D4—1721no—
533D4—1722no—
534D4—1722no—
535D4—1721no—
536D4—1721no—
537D4—1721no—
538D4—1721no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—82no—
543C2×C4—431no—
544C2×C4—431no—
545C2×C4—431no—
546C2×C4—431no—
547C2×C4—431no—
548C2×C4—861no—
549C2×C4—3442no—
550C2×C4—3442no—
551C2×C4—3442no—
552C2×C4—3442no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1722no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4C2×D4×D4311yescharacteristic
560C8—21no—
561C8—41no—
562C8—431no—
563C8—431no—
564C8—861no—
565C8—1721no—
566C8C22×C4×D4311yescharacteristic
567C8#41×D4311yescharacteristic
568C22—41no—
569C22—42no—
570C22—81no—
571C22—81no—
572C22—431no—
573C22—431no—
574C22—862no—
575C22—3441no—
576C22—3441no—
577C22—3444no—
578C22—3442no—
579C22—3444no—
580C22—1721no—
581C22—1722no—
582C22AGL(1,ℤ/8)×D4311yescharacteristic
583C4—41no—
584C4—41no—
585C4—81no—
586C4—431no—
587C4—431no—
588C4—3441no—
589C4—1721no—
590C4—1721no—
591C4C4×D4×D4311yescharacteristic
592C4AGL(1,ℤ/8)×D4311yescharacteristic
593C2—21no—
594C2—82no—
595C2—81no—
596C2—432no—
597C2—861no—
598C2—3442no—
599C2—3441no—
600C2#442×D4311yescharacteristic
subgroupG/H
centerC2#442×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC43×AGL(1,ℤ/16)C2
socleC2×C43C2×#442
prime radical#509×D43C2
cosocleC2×C8×C43C24
hypercenterAGL(1,ℤ/16)D43
hypocenterC43C2×AGL(1,ℤ/16)
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ AGL(1,ℤ/16)

Complements

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

NH ≅ G/Ntype
2. #444×D43C2semidirect
3. #442×D43C2semidirect
4. #19136496C2semidirect
5. #19136495C2semidirect
6. #19136494C2semidirect
7. #19136493C2semidirect
8. #19136492C2semidirect
9. #19136491C2semidirect
10. #19136490C2semidirect
11. #365×D43C2semidirect
12. #361×D43C2semidirect
13. #360×D43C2semidirect
14. #347×D43C2semidirect
15. C43×AGL(1,ℤ/16)C2semidirect
21. #14583336C4semidirect
24. #14583333C4semidirect
25. SD32×D43C4semidirect
26. D16×D43C4semidirect
29. #14583022C22semidirect
30. #14583021C22semidirect
31. #14583020C22semidirect
34. #14583012C22semidirect
35. #14583011C22semidirect
36. #14583010C22semidirect
44. #14582723C22semidirect
45. #14582722C22semidirect
46. #14582721C22semidirect
47. #14582713C22semidirect
48. #14582712C22semidirect
49. #14582711C22semidirect
50. #14582710C22semidirect
51. #14582709C22semidirect
52. #14582708C22semidirect
53. #14582677C22semidirect
54. #14582676C22semidirect
55. #14582676C22semidirect
57. C43×#444C22semidirect
58. C43×#442C22semidirect
59. C43×#365C22semidirect
60. C43×#361C22semidirect
61. C43×#360C22semidirect
62. C43×#347C22semidirect
66. #13063348C2×C4semidirect
70. #13063344C2×C4semidirect
71. Q16×D43C2×C4semidirect
79. D8×D43C2×C4semidirect
98. #13063270C2×C4semidirect
99. #13063269C2×C4semidirect
100. #13063268C2×C4semidirect
101. D688C2×C4semidirect
102. #13063266C2×C4semidirect
103. #13063266C2×C4semidirect
107. #13063264C2×C4semidirect
109. C16×D43C2×C4semidirect
127. SD32×C43C2×C4semidirect
128. D16×C43C2×C4semidirect
162. Q16×C43C22×C4semidirect
166. D8×C43C22×C4semidirect
193. Dic172C22×C4semidirect
196. D344C22×C4semidirect
211. C16×C43C22×C4semidirect
213. C43⋊C16C22×C4semidirect
303. AGL(1,ℤ/16)D43direct (N × H)
315. D43AGL(1,ℤ/16)direct (N × H)
335. #444C2×D43semidirect
341. #442C2×D43semidirect
350. #365C2×D43semidirect
354. #361C2×D43semidirect
358. #360C2×D43semidirect
362. #347C2×D43semidirect
363. C43C2×AGL(1,ℤ/16)semidirect
406. SD32C4×D43semidirect
410. D16C4×D43semidirect
465. Q16C2×C4×D43semidirect
478. D8C2×C4×D43semidirect
514. C16C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
#509×D432
#444×D432
#442×D432
#191364962
#191364952
#191364942
#191364932
#191364922
#191364912
#191364902
#365×D432
#361×D432
#360×D432
#347×D432
C43×AGL(1,ℤ/16)2
C2×AGL(1,ℤ/16)43