Finite Group Databasebeta

← D47×AGL(1,ℤ/16) #26369715

Subgroups — D47×AGL(1,ℤ/16) #26369715

Order 12032.

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×D47C211yesmaximal, characteristic
2#444×D47C211yesmaximal, characteristic, complemented
3#442×D47C211yesmaximal, characteristic, complemented
4#20245289C211yesmaximal, characteristic, complemented
5#20245288C211yesmaximal, characteristic, complemented
6#20245287C211yesmaximal, characteristic, complemented
7#20245286C211yesmaximal, characteristic, complemented
8#20245285C211yesmaximal, characteristic, complemented
9#20245284C211yesmaximal, characteristic, complemented
10#20245283C211yesmaximal, characteristic, complemented
11#365×D47C211yesmaximal, characteristic, complemented
12#361×D47C211yesmaximal, characteristic, complemented
13#360×D47C211yesmaximal, characteristic, complemented
14#347×D47C211yesmaximal, characteristic, complemented
15C47×AGL(1,ℤ/16)C211yesmaximal, characteristic, complemented
16#135×D47C2211yescharacteristic
17C2×D8×D47C2211yescharacteristic
18#131×D47—21no—
19C4×D4×D47—21no—
20#15689561C2211yescharacteristic
21#15689560C412yescomplemented
22#15689559C2211yescharacteristic
23#15689558C2211yescharacteristic
24#15689557C412yescomplemented
25SD32×D47C412yescomplemented
26D16×D47C412yescomplemented
27M32×D47C2211yescharacteristic
28M32×D47C2211yescharacteristic
29#15689246C2211yescharacteristic, complemented
30#15689245C2211yescharacteristic, complemented
31#15689244C2211yescharacteristic, complemented
32#15689243—21no—
33#15689242—21no—
34#15689236C2211yescharacteristic, complemented
35#15689235C2211yescharacteristic, complemented
36#15689234C2211yescharacteristic, complemented
37#15689233—21no—
38#15689232—21no—
39#108×D47C2211yescharacteristic
40#106×D47C2211yescharacteristic
41#104×D47—21no—
42#102×D47—21no—
43#97×D47C2211yescharacteristic
44#15688947C2211yescharacteristic, complemented
45#15688946C2211yescharacteristic, complemented
46#15688945C2211yescharacteristic, complemented
47#15688937C2211yescharacteristic, complemented
48#15688936C2211yescharacteristic, complemented
49#15688935C2211yescharacteristic, complemented
50#15688934C2211yescharacteristic, complemented
51#15688933C2211yescharacteristic, complemented
52#15688932C2211yescharacteristic, complemented
53#15688901C2211yescharacteristic, complemented
54#15688900C2211yescharacteristic, complemented
55#15688900C2211yescharacteristic, complemented
56C47×#509C2211yescharacteristic
57C47×#444C2211yescharacteristic, complemented
58C47×#442C2211yescharacteristic, complemented
59C47×#365C2211yescharacteristic, complemented
60C47×#361C2211yescharacteristic, complemented
61C47×#360C2211yescharacteristic, complemented
62C47×#347C2211yescharacteristic, complemented
63#41×D47—21no—
64C2×D4×D47—21no—
65C22×C4×D47—41no—
66#13094047C2×C411yescharacteristic, complemented
67#13094046C2311yescharacteristic
68#13094045—21no—
69#13094044—21no—
70#13094043C2×C411yescharacteristic, complemented
71Q16×D47C2×C411yescharacteristic, complemented
72SD16×D47—21no—
73C2×D376C2311yescharacteristic
74C2×#10625334—21no—
75D8×D47—21no—
76D8×D47—21no—
77D8×D47C2×C412yes—
78D8×D47C2×C412yes—
79D8×D47C2×C411yescharacteristic, complemented
80#13094032—21no—
81#13094032—41no—
82#13094031—21no—
83#13094030—21no—
84#13094030—41no—
85M16×D47—21no—
86M16×D47—41no—
87C2×C8×D47—41no—
88C2×C8×D47D411yescharacteristic
89C2×C8×D47C2311yescharacteristic
90C4×D188—21no—
91D4×Dic47—21no—
92#13093986—21no—
93C4×C22⋊D47—41no—
94(C22⋊D47)⋊C4—41no—
95C4⋊C4×D47—21no—
96C22⋊C4×D47—41no—
97C42×D47D411yescharacteristic
98#13093969C2×C412yescomplemented
99#13093968C2×C412yescomplemented
100#13093967C2×C412yescomplemented
101D752C2×C412yescomplemented
102#13093965C2×C412yescomplemented
103#13093965C2×C412yescomplemented
104#13093964C2311yescharacteristic
105#13093964C2311yescharacteristic
106#13093963—21no—
107#13093963C2×C412yescomplemented
108C16×D47—21no—
109C16×D47C2×C412yescomplemented
110#13093960C2311yescharacteristic
111#13093959—21no—
112#13093956C2311yescharacteristic
113#13093955—21no—
114#13093952—21no—
115#13093951—21no—
116#13093950—21no—
117#13093946—21no—
118#13093945—21no—
119#13093944—21no—
120#13093935D411yescharacteristic
121#13093934D411yescharacteristic
122#13093934C2311yescharacteristic
123#135×C47C2311yescharacteristic
124C2×D8×C47C2311yescharacteristic
125#131×C47—21no—
126C4×D4×C47—21no—
127SD32×C47C2×C412yescomplemented
128D16×C47C2×C412yescomplemented
129M32×C47C2311yescharacteristic
130M32×C47C2311yescharacteristic
131#108×C47C2311yescharacteristic
132#106×C47C2311yescharacteristic
133#104×C47—21no—
134#102×C47—21no—
135#97×C47C2311yescharacteristic
136C23×D47—41no—
137#41×C47—21no—
138C2×D4×C47—21no—
139C22×C4×C47—41no—
140C2×C22⋊D47—41no—
141C22×Dic47—41no—
142#10625354—21no—
143Q8×D47—21no—
144#10625352—21no—
145#10625352—41no—
146D4×D47—22no—
147D4×D47—22no—
148D4×D47—21no—
149D4×D47—41no—
150D4×D47—41no—
151D4×D47—41no—
152#10625350—21no—
153#10625350—41no—
154C2×D188—21no—
155C2×C4×D47—21no—
156C2×C4×D47—41no—
157C2×C4×D47—41no—
158C2×C4×D47—41no—
159C2×C4×D47—41no—
160C2×C4×D47—84no—
161C2×C4×D47C2×D411yescharacteristic
162Q16×C47C22×C411yescharacteristic, complemented
163SD16×C47—21no—
164D8×C47—21no—
165D8×C47C22×C412yes—
166D8×C47C22×C411yescharacteristic, complemented
167M16×C47—21no—
168M16×C47—41no—
169C2×C8×C47—41no—
170C2×C8×C47C2×D411yescharacteristic
171C2×C8×C47C2411yescharacteristic
172C4⋊C4×C47—21no—
173C22⋊C4×C47—41no—
174C42×C47C2×D411yescharacteristic
175C22⋊Dic47—41no—
176#10625337—21no—
177#10625336—21no—
178#10625335—21no—
179#10625334—22no—
180#10625334—22no—
181#10625334—21no—
182(C2×D47)⋊C4—41no—
183(C2×D47)⋊C4—41no—
184C4⋊Dic47—21no—
185Dic47⋊C4—41no—
186C4×Dic47—21no—
187C4×Dic47C2×D411yescharacteristic
188#10625329—21no—
189#10625329—41no—
190C2×C47⋊C8—41no—
191C2×C47⋊C8C2×D411yescharacteristic
192C2×C47⋊C8C2×D411yescharacteristic
193Dic188C22×C411yescharacteristic, complemented
194D376—21no—
195D376C22×C412yes—
196D376C22×C411yescharacteristic, complemented
197#10625325—21no—
198#10625324—41no—
199#10625324—41no—
200#10625324—41no—
201C8×D47—21no—
202C8×D47—21no—
203C8×D47—41no—
204C8×D47—41no—
205C8×D47—41no—
206C8×D47C22×C411yescharacteristic
207C8×D47C22×C411yescharacteristic
208C8×D47#4111yescharacteristic
209C8×D47#4111yescharacteristic
210C16×C47—21no—
211C16×C47C22×C412yescomplemented
212C47⋊C16—21no—
213C47⋊C16C22×C412yescomplemented
214C23×C47—41no—
215C22×D47—41no—
216C22×D47—41no—
217C22×D47—42no—
218C22×D47—42no—
219C22×D47—82no—
220C22×D47—82no—
221C22×D47AGL(1,ℤ/8)11yescharacteristic
222Q8×C47—21no—
223D4×C47—22no—
224D4×C47—21no—
225D4×C47—41no—
226D4×C47—41no—
227C2×C4×C47—21no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—82no—
231C2×C4×C47C22×D411yescharacteristic
232C22⋊D47—41no—
233C22⋊D47—41no—
234C22⋊D47—41no—
235C22⋊D47—42no—
236C22⋊D47—42no—
237C2×Dic47—21no—
238C2×Dic47—41no—
239C2×Dic47—41no—
240C2×Dic47—82no—
241C2×Dic47AGL(1,ℤ/8)11yescharacteristic
242D188—21no—
243D188—22no—
244D188—41no—
245D188—41no—
246C4×D47—42no—
247C4×D47—41no—
248C4×D47—41no—
249C4×D47—41no—
250C4×D47—82no—
251C4×D47—82no—
252C4×D47—82no—
253C4×D47C4×D411yescharacteristic
254C4×D47C4×D411yescharacteristic
255C4×D47AGL(1,ℤ/8)11yescharacteristic
256C4×D47AGL(1,ℤ/8)11yescharacteristic
257Dic94—21no—
258Dic94—41no—
259C8×C47—21no—
260C8×C47—41no—
261C8×C47C23×C411yescharacteristic
262C8×C47C2×#4111yescharacteristic
263C47⋊C8—21no—
264C47⋊C8—41no—
265C47⋊C8C4×D411yescharacteristic
266C47⋊C8C4×D411yescharacteristic
267C2×AGL(1,ℤ/16)—471nomaximal, Sylow
268C22×C47—41no—
269C22×C47—42no—
270C22×C47—81no—
271C22×C47—81no—
272C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
273C2×D47—22no—
274C2×D47—41no—
275C2×D47—42no—
276C2×D47—84no—
277C2×D47—81no—
278C2×D47—81no—
279C2×D47—82no—
280C2×D47—84no—
281C2×D47#44211yescharacteristic
282C2×D47#44211yescharacteristic
283C4×C47—41no—
284C4×C47—41no—
285C4×C47—81no—
286C4×C47C2×C4×D411yescharacteristic
287C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
288Dic47—41no—
289Dic47—41no—
290Dic47—81no—
291Dic47#44211yescharacteristic
292Dic47#44211yescharacteristic
293C2×#509—471no—
294C2×#444—471no—
295C2×#442—471no—
296AGL(1,ℤ/16)—471no—
297AGL(1,ℤ/16)—471no—
298AGL(1,ℤ/16)—471no—
299AGL(1,ℤ/16)—471no—
300AGL(1,ℤ/16)—471no—
301AGL(1,ℤ/16)—471no—
302AGL(1,ℤ/16)—471no—
303AGL(1,ℤ/16)D4711yescharacteristic, direct product factor
304C2×#365—471no—
305C2×#361—471no—
306C2×#360—471no—
307C2×#347—471no—
308C2×C47—21no—
309C2×C47—82no—
310C2×C47—81no—
311C2×C47C2×#44211yescharacteristic
312D47—21no—
313D47—81no—
314D47—82no—
315D47AGL(1,ℤ/16)12yesdirect product factor
316C2×#135—471no—
317C22×D8—471no—
318C2×#131—941no—
319C2×C4×D4—941no—
320#509—471no—
321#509—471no—
322#509—472no—
323#509—472no—
324#509—471no—
325#509C2×D4711yescharacteristic
326C2×SD32—472no—
327C2×D16—472no—
328C2×M32—471no—
329C2×M32—471no—
330#444—471no—
331#444—471no—
332#444—471no—
333#444—941no—
334#444—941no—
335#444C2×D4711yescharacteristic, complemented
336#442—471no—
337#442—471no—
338#442—471no—
339#442—941no—
340#442—941no—
341#442C2×D4711yescharacteristic, complemented
342C2×#108—471no—
343C2×#106—471no—
344C2×#104—941no—
345C2×#102—941no—
346C2×#97—471no—
347#365—471no—
348#365—471no—
349#365—471no—
350#365C2×D4711yescharacteristic, complemented
351#361—471no—
352#361—471no—
353#361—471no—
354#361C2×D4711yescharacteristic, complemented
355#360—471no—
356#360—471no—
357#360—471no—
358#360C2×D4711yescharacteristic, complemented
359#347—471no—
360#347—471no—
361#347—471no—
362#347C2×D4711yescharacteristic, complemented
363C47C2×AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
364C2×#41—941no—
365C22×D4—941no—
366C23×C4—1881no—
367#135—471no—
368#135—471no—
369#135—471no—
370#135—941no—
371#135—941no—
372#135C22×D4711yescharacteristic
373C2×Q16—471no—
374C2×SD16—941no—
375C2×D8—472no—
376C2×D8—472no—
377C2×D8—471no—
378C2×D8—471no—
379C2×D8—941no—
380C2×D8—941no—
381C2×D8—941no—
382C2×D8C22×D4711yescharacteristic
383#131—21no—
384#131—941no—
385#131—941no—
386#131—941no—
387#131—1881no—
388#131—1881no—
389C2×M16—941no—
390C2×M16—1881no—
391C22×C8—471no—
392C22×C8—471no—
393C22×C8—1881no—
394C4×D4—21no—
395C4×D4—941no—
396C4×D4—941no—
397C4×D4—941no—
398C4×D4—1881no—
399C4×D4—1881no—
400C2×C4⋊C4—941no—
401C2×C22⋊C4—1881no—
402C2×C42—471no—
403SD32—472no—
404SD32—472no—
405SD32—472no—
406SD32C4×D4712yescomplemented
407D16—472no—
408D16—472no—
409D16—472no—
410D16C4×D4712yescomplemented
411M32—471no—
412M32—472no—
413M32—471no—
414M32—941no—
415M32C22×D4711yescharacteristic
416M32C22×D4711yescharacteristic
417C2×C16—472no—
418C2×C16—941no—
419#108—471no—
420#108—941no—
421#108C22×D4711yescharacteristic
422#106—471no—
423#106—941no—
424#106C22×D4711yescharacteristic
425#104—21no—
426#104—941no—
427#104—941no—
428#104—941no—
429#102—21no—
430#102—941no—
431#102—941no—
432#102—941no—
433#97—471no—
434#97—471no—
435#97—471no—
436#97C22×D4711yescharacteristic
437C24—1881no—
438#41—21no—
439#41—941no—
440#41—941no—
441#41—941no—
442#41—1881no—
443#41—1881no—
444C2×Q8—941no—
445C2×D4—21no—
446C2×D4—942no—
447C2×D4—942no—
448C2×D4—941no—
449C2×D4—941no—
450C2×D4—1881no—
451C2×D4—1881no—
452C2×D4—1881no—
453C2×D4—1881no—
454C22×C4—41no—
455C22×C4—471no—
456C22×C4—941no—
457C22×C4—3764no—
458C22×C4—1881no—
459C22×C4—1881no—
460C22×C4—1881no—
461C22×C4—1881no—
462C22×C4—1881no—
463Q16—471no—
464Q16—941no—
465Q16C2×C4×D4711yescharacteristic, complemented
466SD16—21no—
467SD16—941no—
468SD16—941no—
469SD16—941no—
470D8—21no—
471D8—472no—
472D8—471no—
473D8—942no—
474D8—942no—
475D8—941no—
476D8—941no—
477D8C2×C4×D4712yes—
478D8C2×C4×D4711yescharacteristic, complemented
479M16—21no—
480M16—41no—
481M16—941no—
482M16—1881no—
483M16—1881no—
484M16—1881no—
485M16—1881no—
486C2×C8—41no—
487C2×C8—471no—
488C2×C8—471no—
489C2×C8—471no—
490C2×C8—471no—
491C2×C8—471no—
492C2×C8—471no—
493C2×C8—941no—
494C2×C8—941no—
495C2×C8—1881no—
496C2×C8—1881no—
497C2×C8—1881no—
498C2×C8—1881no—
499C2×C8D4×D4711yescharacteristic
500C2×C8C23×D4711yescharacteristic
501C4⋊C4—21no—
502C4⋊C4—941no—
503C4⋊C4—1881no—
504C22⋊C4—41no—
505C22⋊C4—1881no—
506C22⋊C4—1881no—
507C22⋊C4—1881no—
508C42—471no—
509C42—941no—
510C42D4×D4711yescharacteristic
511C16—21no—
512C16—472no—
513C16—941no—
514C16C2×C4×D4712yescomplemented
515C23—41no—
516C23—471no—
517C23—3762no—
518C23—3762no—
519C23—1881no—
520C23—1882no—
521C23—1882no—
522C23—1881no—
523Q8—21no—
524Q8—941no—
525Q8—1881no—
526D4—22no—
527D4—21no—
528D4—41no—
529D4—41no—
530D4—942no—
531D4—941no—
532D4—1881no—
533D4—1882no—
534D4—1882no—
535D4—1881no—
536D4—1881no—
537D4—1881no—
538D4—1881no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—82no—
543C2×C4—471no—
544C2×C4—471no—
545C2×C4—471no—
546C2×C4—471no—
547C2×C4—471no—
548C2×C4—941no—
549C2×C4—3762no—
550C2×C4—3762no—
551C2×C4—3762no—
552C2×C4—3762no—
553C2×C4—1881no—
554C2×C4—1881no—
555C2×C4—1882no—
556C2×C4—1881no—
557C2×C4—1881no—
558C2×C4—1881no—
559C2×C4C2×D4×D4711yescharacteristic
560C8—21no—
561C8—41no—
562C8—471no—
563C8—471no—
564C8—941no—
565C8—1881no—
566C8C22×C4×D4711yescharacteristic
567C8#41×D4711yescharacteristic
568C22—41no—
569C22—42no—
570C22—81no—
571C22—81no—
572C22—471no—
573C22—471no—
574C22—942no—
575C22—3761no—
576C22—3761no—
577C22—3764no—
578C22—3762no—
579C22—3764no—
580C22—1881no—
581C22—1882no—
582C22AGL(1,ℤ/8)×D4711yescharacteristic
583C4—41no—
584C4—41no—
585C4—81no—
586C4—471no—
587C4—471no—
588C4—3761no—
589C4—1881no—
590C4—1881no—
591C4C4×D4×D4711yescharacteristic
592C4AGL(1,ℤ/8)×D4711yescharacteristic
593C2—21no—
594C2—82no—
595C2—81no—
596C2—472no—
597C2—941no—
598C2—3762no—
599C2—3761no—
600C2#442×D4711yescharacteristic
subgroupG/H
centerC2#442×D47
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC47×AGL(1,ℤ/16)C2
socleC2×C47C2×#442
prime radical#509×D47C2
cosocleC2×C8×C47C24
hypercenterAGL(1,ℤ/16)D47
hypocenterC47C2×AGL(1,ℤ/16)
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
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×D47C2semidirect
3. #442×D47C2semidirect
4. #20245289C2semidirect
5. #20245288C2semidirect
6. #20245287C2semidirect
7. #20245286C2semidirect
8. #20245285C2semidirect
9. #20245284C2semidirect
10. #20245283C2semidirect
11. #365×D47C2semidirect
12. #361×D47C2semidirect
13. #360×D47C2semidirect
14. #347×D47C2semidirect
15. C47×AGL(1,ℤ/16)C2semidirect
21. #15689560C4semidirect
24. #15689557C4semidirect
25. SD32×D47C4semidirect
26. D16×D47C4semidirect
29. #15689246C22semidirect
30. #15689245C22semidirect
31. #15689244C22semidirect
34. #15689236C22semidirect
35. #15689235C22semidirect
36. #15689234C22semidirect
44. #15688947C22semidirect
45. #15688946C22semidirect
46. #15688945C22semidirect
47. #15688937C22semidirect
48. #15688936C22semidirect
49. #15688935C22semidirect
50. #15688934C22semidirect
51. #15688933C22semidirect
52. #15688932C22semidirect
53. #15688901C22semidirect
54. #15688900C22semidirect
55. #15688900C22semidirect
57. C47×#444C22semidirect
58. C47×#442C22semidirect
59. C47×#365C22semidirect
60. C47×#361C22semidirect
61. C47×#360C22semidirect
62. C47×#347C22semidirect
66. #13094047C2×C4semidirect
70. #13094043C2×C4semidirect
71. Q16×D47C2×C4semidirect
79. D8×D47C2×C4semidirect
98. #13093969C2×C4semidirect
99. #13093968C2×C4semidirect
100. #13093967C2×C4semidirect
101. D752C2×C4semidirect
102. #13093965C2×C4semidirect
103. #13093965C2×C4semidirect
107. #13093963C2×C4semidirect
109. C16×D47C2×C4semidirect
127. SD32×C47C2×C4semidirect
128. D16×C47C2×C4semidirect
162. Q16×C47C22×C4semidirect
166. D8×C47C22×C4semidirect
193. Dic188C22×C4semidirect
196. D376C22×C4semidirect
211. C16×C47C22×C4semidirect
213. C47⋊C16C22×C4semidirect
303. AGL(1,ℤ/16)D47direct (N × H)
315. D47AGL(1,ℤ/16)direct (N × H)
335. #444C2×D47semidirect
341. #442C2×D47semidirect
350. #365C2×D47semidirect
354. #361C2×D47semidirect
358. #360C2×D47semidirect
362. #347C2×D47semidirect
363. C47C2×AGL(1,ℤ/16)semidirect
406. SD32C4×D47semidirect
410. D16C4×D47semidirect
465. Q16C2×C4×D47semidirect
478. D8C2×C4×D47semidirect
514. C16C2×C4×D47semidirect

Maximal subgroups

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

subgroupindex
#509×D472
#444×D472
#442×D472
#202452892
#202452882
#202452872
#202452862
#202452852
#202452842
#202452832
#365×D472
#361×D472
#360×D472
#347×D472
C47×AGL(1,ℤ/16)2
C2×AGL(1,ℤ/16)47