Finite Group Databasebeta

← D13⋊AGL(1,ℤ/16) #16807228

Subgroups — D13⋊AGL(1,ℤ/16) #16807228

Order 3328.

710 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13⋊#444C211yesmaximal, characteristic, complemented
2C2×#11719102C211yesmaximal, characteristic, complemented
3#13131248C212yesmaximal, complemented
4#13131247C212yesmaximal, complemented
5#13131246C212yesmaximal, complemented
6#13131245C212yesmaximal, complemented
7D13⋊#365C211yesmaximal, characteristic, complemented
8D13⋊#361C211yesmaximal, characteristic, complemented
9D13⋊#360C211yesmaximal, characteristic, complemented
10#13131051C211yesmaximal, characteristic, complemented
11D13×#509C211yesmaximal, characteristic
12D13⋊#131—21no—
13C2×D4×#261—21no—
14D13×#135C2211yescharacteristic
15C2×D8×D13C2211yescharacteristic
16D13⋊#104—21no—
17C2×#88115—21no—
18#11719112C2211yescharacteristic, complemented
19#11719112C2211yescharacteristic, complemented
20#11719108—21no—
21#11719108—21no—
22#11719104C2211yescharacteristic, complemented
23#11719104C2211yescharacteristic, complemented
24#11719102—21no—
25#11719102—21no—
26#11719102C2212yescomplemented
27#11719102C2212yescomplemented
28D13⋊#108C2211yescharacteristic
29C2×#88101C2211yescharacteristic
30C2×#88100C2211yescharacteristic
31D13⋊M32C2211yescharacteristic
32C13×#509C411yescharacteristic, complemented
33#11718854C411yescharacteristic, complemented
34#11718808C411yescharacteristic, complemented
35#11718575C2212yes—
36D13×SD32C412yescomplemented
37#11718572C2212yes—
38D13×D16C412yescomplemented
39#11718569C411yescharacteristic, complemented
40D13×M32C2211yescharacteristic
41#11718279C2212yescomplemented
42#11718278C2212yescomplemented
43#11718278C2212yescomplemented
44#11718275C2212yescomplemented
45#11718220C2212yescomplemented
46#11718219C2212yescomplemented
47#11718218C2212yescomplemented
48#11718217C2212yescomplemented
49C23×#261—41no—
50#41×D13—21no—
51C2×D4×D13—21no—
52C2×C22⋊#261—41no—
53#88240—21no—
54#88240—21no—
55D4×#261—22no—
56D4×#261—22no—
57D4×#261—41no—
58D4×#261—41no—
59#88238—21no—
60#88238—21no—
61#88238—41no—
62#88238—41no—
63C2×C4⋊#261—21no—
64C2×C4×#261D411yescharacteristic
65D13⋊M16—21no—
66D13⋊M16—41no—
67C2×D13⋊C8—41no—
68C2×D13⋊C8D411yescharacteristic
69C13×#135C2×C411yescharacteristic, complemented
70C2×C13×D8C2×C411yescharacteristic
71#88204—21no—
72C2×#6104—21no—
73#88173C2311yescharacteristic
74Q16×D13C2×C411yescharacteristic, complemented
75#88170—21no—
76SD16×D13—21no—
77#88166C2311yescharacteristic
78D8×D13—21no—
79D8×D13—21no—
80D8×D13C2×C412yes—
81D8×D13C2×C411yescharacteristic, complemented
82D8×D13C2312yes—
83#88158C2×C411yescharacteristic, complemented
84C2×D104C2×C411yescharacteristic
85C2×C8×D13C2311yescharacteristic
86#88118—21no—
87#88118—21no—
88#88116—21no—
89#88116—21no—
90#88115—22no—
91#88115—22no—
92#88106—21no—
93#88104—21no—
94#88103C2311yescharacteristic
95#88103C2311yescharacteristic
96#88101—21no—
97#88101C2312yes—
98#88100D411yescharacteristic
99#88100D411yescharacteristic
100#88100C2311yescharacteristic
101#88100C2311yescharacteristic
102#88098C2312yes—
103D13⋊C16—21no—
104C13×SD32C2×C412yescomplemented
105C13×D16C2×C412yescomplemented
106C13×M32C2×C411yescharacteristic, complemented
107#88068C2×C412yescomplemented
108#88067C2×C412yescomplemented
109#88066C2×C412yescomplemented
110#88066C2×C412yescomplemented
111#88052C2×C411yescharacteristic, complemented
112#88040C2×C412yescomplemented
113D208C2×C412yescomplemented
114#88038C2312yes—
115C16×D13C2×C412yescomplemented
116C2×AGL(1,ℤ/16)—131nomaximal, Sylow
117C23×D13—41no—
118C22×#261—21no—
119C22×#261—42no—
120C22×#261—42no—
121C22×#261—41no—
122C22×#261—84no—
123C13×#41—21no—
124C2×D4×C13—21no—
125C2×C22⋊D13—41no—
126#6131—21no—
127Q8×D13—21no—
128#6129—21no—
129#6129—41no—
130D4×D13—22no—
131D4×D13—21no—
132D4×D13—22no—
133D4×D13—41no—
134D4×D13—41no—
135D4×D13—41no—
136#6127—21no—
137#6127—41no—
138C2×D52—21no—
139C2×C4×D13—41no—
140C2×C4×D13C2×D411yescharacteristic
141C22⋊#261—42no—
142C22⋊#261—42no—
143#6122—41no—
144#6122—41no—
145#6122—41no—
146C2×#1057—21no—
147C2×#1057—41no—
148C2×#1057—41no—
149C4⋊#261—22no—
150C4⋊#261—41no—
151C4×#261—21no—
152C4×#261C2×D411yescharacteristic
153C4×#261C2×D411yescharacteristic
154#6118—21no—
155#6118—21no—
156#6118—41no—
157#6118—41no—
158D13⋊C8—21no—
159D13⋊C8—41no—
160D13⋊C8—41no—
161D13⋊C8—41no—
162D13⋊C8C2×D411yescharacteristic
163D13⋊C8C2×D411yescharacteristic
164C13×Q16C22×C411yescharacteristic, complemented
165C13×SD16—21no—
166C13×D8—21no—
167C13×D8C22×C412yes—
168C13×D8C22×C411yescharacteristic, complemented
169C2×C8×C13C22×C411yescharacteristic
170#6107—21no—
171#6106—21no—
172#6105—21no—
173#6104—22no—
174#6104—21no—
175#6104—22no—
176C2×#1055#4111yescharacteristic
177Dic52C22×C411yescharacteristic, complemented
178D104—21no—
179D104C22×C412yes—
180D104C22×C411yescharacteristic, complemented
181#6095—21no—
182C8×D13C22×C411yescharacteristic
183C8×D13C2×D411yescharacteristic
184C8×D13#4111yescharacteristic
185C8×D13C2411yescharacteristic
186#6092—22no—
187C13×C16C22×C412yescomplemented
188#6090C22×C412yescomplemented
189C2×#509—131no—
190C2×#444—131no—
191C2×#442—131no—
192AGL(1,ℤ/16)—132no—
193AGL(1,ℤ/16)—132no—
194AGL(1,ℤ/16)—132no—
195AGL(1,ℤ/16)—132no—
196C2×#365—131no—
197C2×#361—131no—
198C2×#360—131no—
199C2×#347—131no—
200C23×C13—41no—
201C22×D13—41no—
202C22×D13—42no—
203C22×D13—41no—
204C22×D13—42no—
205C22×D13—82no—
206C22×D13—82no—
207C22×D13AGL(1,ℤ/8)11yescharacteristic
208C2×#261—21no—
209C2×#261—21no—
210C2×#261—42no—
211C2×#261—42no—
212C2×#261—84no—
213C2×#261—84no—
214C2×#261—82no—
215Q8×C13—21no—
216D4×C13—22no—
217D4×C13—21no—
218D4×C13—41no—
219D4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13C4×D411yescharacteristic
222C22⋊D13—41no—
223C22⋊D13—41no—
224C22⋊D13—42no—
225C22⋊D13—41no—
226C22⋊D13—42no—
227C2×Dic13—41no—
228C2×Dic13AGL(1,ℤ/8)11yescharacteristic
229D52—21no—
230D52—22no—
231D52—41no—
232D52—41no—
233C4×D13—41no—
234C4×D13—41no—
235C4×D13—41no—
236C4×D13C4×D411yescharacteristic
237C4×D13AGL(1,ℤ/8)11yescharacteristic
238C4×D13AGL(1,ℤ/8)11yescharacteristic
239C4×D13C22×D411yescharacteristic
240Dic26—21no—
241Dic26—41no—
242#1057—21no—
243#1057—21no—
244#1057—41no—
245#1057—41no—
246C8×C13C4×D411yescharacteristic
247C8×C13C23×C411yescharacteristic
248#1055C4×D411yescharacteristic
249#1055C2×#4111yescharacteristic
250C2×#135—131no—
251C22×D8—131no—
252C2×#131—261no—
253C2×C4×D4—261no—
254#509—131no—
255#509—131no—
256#509—132no—
257#509—132no—
258#509—131no—
259#509#26111yescharacteristic, complemented
260C2×SD32—132no—
261C2×D16—132no—
262C2×M32—131no—
263C2×M32—131no—
264#444—131no—
265#444—131no—
266#444—131no—
267#444—131no—
268#444—261no—
269#444—261no—
270#442—132no—
271#442—132no—
272#442—261no—
273#442—261no—
274C2×#108—131no—
275C2×#106—131no—
276C2×#104—261no—
277C2×#102—261no—
278C2×#97—131no—
279#365—132no—
280#365—132no—
281#361—132no—
282#361—132no—
283#360—132no—
284#360—132no—
285#347—132no—
286#347—132no—
287C22×C13—41no—
288C22×C13—42no—
289C22×C13—82no—
290C22×C13#44211yescharacteristic
291C2×D13—22no—
292C2×D13—41no—
293C2×D13—42no—
294C2×D13—82no—
295C2×D13—82no—
296C2×D13—82no—
297C2×D13—82no—
298C2×D13—84no—
299C2×D13#44211yescharacteristic
300C2×D13C2×AGL(1,ℤ/8)11yescharacteristic
301#261—41no—
302#261—41no—
303#261—82no—
304C4×C13—41no—
305C4×C13#44211yescharacteristic
306C4×C13C2×C4×D411yescharacteristic
307Dic13—41no—
308Dic13#44211yescharacteristic
309Dic13C2×AGL(1,ℤ/8)11yescharacteristic
310C2×#41—261no—
311C22×D4—261no—
312C23×C4—521no—
313#135—131no—
314#135—131no—
315#135—131no—
316#135—261no—
317#135—261no—
318#135C2×#26111yescharacteristic, complemented
319C2×Q16—131no—
320C2×SD16—261no—
321C2×D8—132no—
322C2×D8—132no—
323C2×D8—131no—
324C2×D8—131no—
325C2×D8—261no—
326C2×D8—261no—
327C2×D8—261no—
328C2×D8C2×#26111yescharacteristic
329#131—261no—
330#131—261no—
331#131—261no—
332#131—261no—
333#131—521no—
334#131—521no—
335C2×M16—261no—
336C2×M16—521no—
337C22×C8—131no—
338C22×C8—131no—
339C22×C8—521no—
340C4×D4—262no—
341C4×D4—262no—
342C4×D4—521no—
343C4×D4—521no—
344C2×C4⋊C4—261no—
345C2×C22⋊C4—521no—
346C2×C42—131no—
347SD32—132no—
348SD32—132no—
349SD32—132no—
350SD32C2×#26112yescomplemented
351D16—132no—
352D16—132no—
353D16—132no—
354D16C2×#26112yescomplemented
355M32—131no—
356M32—132no—
357M32—132no—
358M32—261no—
359M32C2×#26111yescharacteristic, complemented
360C2×C16—132no—
361C2×C16—261no—
362#108—131no—
363#108—131no—
364#108—261no—
365#106—132no—
366#106—261no—
367#104—261no—
368#104—261no—
369#104—261no—
370#104—261no—
371#102—262no—
372#102—262no—
373#97—131no—
374#97—131no—
375#97—131no—
376#97—131no—
377C2×C13—21no—
378C2×C13—82no—
379C2×C13—81no—
380C2×C13C2×#44211yescharacteristic
381D13—21no—
382D13—81no—
383D13—82no—
384D13AGL(1,ℤ/16)12yescomplemented
385C24—521no—
386#41—21no—
387#41—261no—
388#41—261no—
389#41—261no—
390#41—521no—
391#41—521no—
392C2×Q8—261no—
393C2×D4—21no—
394C2×D4—262no—
395C2×D4—262no—
396C2×D4—261no—
397C2×D4—261no—
398C2×D4—521no—
399C2×D4—521no—
400C2×D4—521no—
401C2×D4—521no—
402C22×C4—131no—
403C22×C4—261no—
404C22×C4—521no—
405C22×C4—522no—
406C22×C4—522no—
407C22×C4—521no—
408C22×C4—1044no—
409Q16—131no—
410Q16—261no—
411Q16C22×#26111yescharacteristic, complemented
412SD16—21no—
413SD16—261no—
414SD16—261no—
415SD16—261no—
416D8—21no—
417D8—131no—
418D8—132no—
419D8—262no—
420D8—262no—
421D8—261no—
422D8—261no—
423D8C22×#26112yes—
424D8C22×#26111yescharacteristic, complemented
425M16—261no—
426M16—261no—
427M16—521no—
428M16—521no—
429M16—521no—
430M16—521no—
431M16—521no—
432C2×C8—131no—
433C2×C8—131no—
434C2×C8—131no—
435C2×C8—131no—
436C2×C8—131no—
437C2×C8—131no—
438C2×C8—131no—
439C2×C8—261no—
440C2×C8—261no—
441C2×C8—521no—
442C2×C8—521no—
443C2×C8—521no—
444C2×C8—521no—
445C2×C8—521no—
446C2×C8C22×#26111yescharacteristic
447C4⋊C4—262no—
448C4⋊C4—521no—
449C22⋊C4—522no—
450C22⋊C4—522no—
451C42—131no—
452C42—131no—
453C42—261no—
454C16—132no—
455C16—262no—
456C16C22×#26112yescomplemented
457C13C2×AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
458C23—41no—
459C23—131no—
460C23—522no—
461C23—521no—
462C23—522no—
463C23—521no—
464C23—1042no—
465C23—1042no—
466Q8—21no—
467Q8—261no—
468Q8—521no—
469D4—22no—
470D4—21no—
471D4—41no—
472D4—41no—
473D4—262no—
474D4—261no—
475D4—521no—
476D4—522no—
477D4—522no—
478D4—521no—
479D4—521no—
480D4—521no—
481D4—521no—
482C2×C4—41no—
483C2×C4—131no—
484C2×C4—131no—
485C2×C4—131no—
486C2×C4—131no—
487C2×C4—131no—
488C2×C4—261no—
489C2×C4—261no—
490C2×C4—521no—
491C2×C4—521no—
492C2×C4—521no—
493C2×C4—522no—
494C2×C4—521no—
495C2×C4—522no—
496C2×C4—1044no—
497C2×C4—1044no—
498C2×C4—1042no—
499C2×C4D4×#26111yescharacteristic
500C8—131no—
501C8—131no—
502C8—261no—
503C8—261no—
504C8—521no—
505C8—521no—
506C8D4×#26111yescharacteristic
507C8C23×#26111yescharacteristic
508C22—41no—
509C22—42no—
510C22—82no—
511C22—131no—
512C22—131no—
513C22—262no—
514C22—521no—
515C22—522no—
516C22—1042no—
517C22—1042no—
518C22—1044no—
519C22—1042no—
520C22—1042no—
521C22#1171910211yescharacteristic
522C4—41no—
523C4—131no—
524C4—131no—
525C4—521no—
526C4—521no—
527C4—521no—
528C4—1042no—
529C4#1171910211yescharacteristic
530C4C2×D4×#26111yescharacteristic
531C2—21no—
532C2—82no—
533C2—81no—
534C2—132no—
535C2—261no—
536C2—1042no—
537C2—1041no—
538C2C2×#1171910211yescharacteristic
subgroupG/H
centerC2C2×#11719102
commutatorC8×C13C23×C4
FrattiniC8C23×#261
FittingC13×#509C4
socleC2×C13C2×#442
prime radicalD13×#509C2
cosocleC8×D13C24
hypercenter#509#261
hypocenterC13C2×AGL(1,ℤ/16)
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. D13⋊#444C2semidirect
2. C2×#11719102C2semidirect
3. #13131248C2semidirect
4. #13131247C2semidirect
5. #13131246C2semidirect
6. #13131245C2semidirect
7. D13⋊#365C2semidirect
8. D13⋊#361C2semidirect
9. D13⋊#360C2semidirect
10. #13131051C2semidirect
18. #11719112C22semidirect
19. #11719112C22semidirect
22. #11719104C22semidirect
23. #11719104C22semidirect
26. #11719102C22semidirect
27. #11719102C22semidirect
32. C13×#509C4semidirect
33. #11718854C4semidirect
34. #11718808C4semidirect
36. D13×SD32C4semidirect
38. D13×D16C4semidirect
39. #11718569C4semidirect
41. #11718279C22semidirect
42. #11718278C22semidirect
43. #11718278C22semidirect
44. #11718275C22semidirect
45. #11718220C22semidirect
46. #11718219C22semidirect
47. #11718218C22semidirect
48. #11718217C22semidirect
69. C13×#135C2×C4semidirect
74. Q16×D13C2×C4semidirect
81. D8×D13C2×C4semidirect
83. #88158C2×C4semidirect
104. C13×SD32C2×C4semidirect
105. C13×D16C2×C4semidirect
106. C13×M32C2×C4semidirect
107. #88068C2×C4semidirect
108. #88067C2×C4semidirect
109. #88066C2×C4semidirect
110. #88066C2×C4semidirect
111. #88052C2×C4semidirect
112. #88040C2×C4semidirect
113. D208C2×C4semidirect
115. C16×D13C2×C4semidirect
164. C13×Q16C22×C4semidirect
168. C13×D8C22×C4semidirect
177. Dic52C22×C4semidirect
180. D104C22×C4semidirect
187. C13×C16C22×C4semidirect
188. #6090C22×C4semidirect
259. #509#261semidirect
318. #135C2×#261semidirect
350. SD32C2×#261semidirect
354. D16C2×#261semidirect
359. M32C2×#261semidirect
384. D13AGL(1,ℤ/16)semidirect
411. Q16C22×#261semidirect
424. D8C22×#261semidirect
456. C16C22×#261semidirect
457. C13C2×AGL(1,ℤ/16)semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4442
C2×#117191022
#131312482
#131312472
#131312462
#131312452
D13⋊#3652
D13⋊#3612
D13⋊#3602
#131310512
D13×#5092
C2×AGL(1,ℤ/16)13