Finite Group Databasebeta

← D61⋊AGL(1,ℤ/16) #30624322

Subgroups — D61⋊AGL(1,ℤ/16) #30624322

Order 15616.

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
1D61⋊#444C211yesmaximal, characteristic, complemented
2C2×#16840803C211yesmaximal, characteristic, complemented
3#21462231C212yesmaximal, complemented
4#21462230C212yesmaximal, complemented
5#21462229C212yesmaximal, complemented
6#21462228C212yesmaximal, complemented
7D61⋊#365C211yesmaximal, characteristic, complemented
8D61⋊#361C211yesmaximal, characteristic, complemented
9D61⋊#360C211yesmaximal, characteristic, complemented
10#21462034C211yesmaximal, characteristic, complemented
11#509×D61C211yesmaximal, characteristic
12D61⋊#131—21no—
13C2×D4×#6923—21no—
14D61⋊M32C2211yescharacteristic
15#16840809C2211yescharacteristic, complemented
16#16840809C2211yescharacteristic, complemented
17#16840808C2211yescharacteristic, complemented
18#16840808C2211yescharacteristic, complemented
19#16840807—21no—
20#16840807—21no—
21#16840803—21no—
22#16840803—21no—
23#16840803C2212yescomplemented
24#16840803C2212yescomplemented
25D61⋊#108C2211yescharacteristic
26C2×#14519845C2211yescharacteristic
27D61⋊#104—21no—
28C2×#14519839—21no—
29C2×#14519831C2211yescharacteristic
30#16840687C2212yescomplemented
31#16840686C2212yescomplemented
32#16840680C2212yescomplemented
33#16840680C2212yescomplemented
34#16840679C2212yescomplemented
35#16840678C2212yescomplemented
36#16840653C2212yescomplemented
37#16840652C2212yescomplemented
38#135×D61C2211yescharacteristic
39C2×D8×D61C2211yescharacteristic
40#16840200C411yescharacteristic, complemented
41#16840199C2212yes—
42#16840198C411yescharacteristic, complemented
43#16840197C411yescharacteristic, complemented
44#16840196C2212yes—
45SD32×D61C412yescomplemented
46D16×D61C412yescomplemented
47M32×D61C2211yescharacteristic
48C61×#509C411yescharacteristic, complemented
49C23×#6923—41no—
50#14519865—21no—
51#14519865—21no—
52#14519864—21no—
53#14519864—21no—
54#14519864—41no—
55#14519864—41no—
56D61⋊M16—21no—
57D61⋊M16—41no—
58C2×D61⋊C8—41no—
59C2×D61⋊C8D411yescharacteristic
60D4×#6923—22no—
61D4×#6923—22no—
62D4×#6923—41no—
63D4×#6923—41no—
64C2×C4⋊#6923—21no—
65C2×C22⋊#6923—41no—
66C2×C4×#6923D411yescharacteristic
67#14519852C2312yes—
68#14519851—21no—
69D61⋊C16—21no—
70#14519848—21no—
71#14519847C2311yescharacteristic
72#14519847C2311yescharacteristic
73#14519845—21no—
74#14519845C2312yes—
75#14519842—21no—
76#14519842—21no—
77#14519841—21no—
78#14519841—21no—
79#14519839—22no—
80#14519839—22no—
81#14519831D411yescharacteristic
82#14519831D411yescharacteristic
83#14519831C2311yescharacteristic
84#14519831C2311yescharacteristic
85#41×D61—21no—
86C2×D4×D61—21no—
87#14519800C2311yescharacteristic
88#14519799C2×C411yescharacteristic, complemented
89#14519798—21no—
90#14519797—21no—
91#14519796C2311yescharacteristic
92Q16×D61C2×C411yescharacteristic, complemented
93SD16×D61—21no—
94C2×D488C2×C411yescharacteristic
95C2×#11758199—21no—
96D8×D61—21no—
97D8×D61—21no—
98D8×D61C2×C412yes—
99D8×D61C2×C411yescharacteristic, complemented
100D8×D61C2312yes—
101C2×C8×D61C2311yescharacteristic
102#14519722C2×C412yescomplemented
103#14519721C2×C412yescomplemented
104#14519720C2×C412yescomplemented
105D976C2×C412yescomplemented
106#14519718C2×C412yescomplemented
107#14519718C2×C412yescomplemented
108#14519717C2×C411yescharacteristic, complemented
109#14519716C2312yes—
110C16×D61C2×C412yescomplemented
111#135×C61C2×C411yescharacteristic, complemented
112C2×D8×C61C2×C411yescharacteristic
113SD32×C61C2×C412yescomplemented
114D16×C61C2×C412yescomplemented
115M32×C61C2×C411yescharacteristic, complemented
116C23×D61—41no—
117C22×#6923—21no—
118C22×#6923—42no—
119C22×#6923—42no—
120C22×#6923—41no—
121C22×#6923—84no—
122#41×C61—21no—
123C2×D4×C61—21no—
124C2×C22⋊D61—41no—
125#11758226—21no—
126Q8×D61—21no—
127#11758224—21no—
128#11758224—41no—
129D4×D61—22no—
130D4×D61—21no—
131D4×D61—22no—
132D4×D61—41no—
133D4×D61—41no—
134D4×D61—41no—
135#11758222—21no—
136#11758222—41no—
137C2×D244—21no—
138C2×C4×D61—41no—
139C2×C4×D61C2×D411yescharacteristic
140C22⋊#6923—42no—
141C22⋊#6923—42no—
142#11758217—41no—
143#11758217—41no—
144#11758217—41no—
145C2×#92420—21no—
146C2×#92420—41no—
147C2×#92420—41no—
148C4⋊#6923—22no—
149C4⋊#6923—41no—
150C4×#6923—21no—
151C4×#6923C2×D411yescharacteristic
152C4×#6923C2×D411yescharacteristic
153#11758213—21no—
154#11758213—21no—
155#11758213—41no—
156#11758213—41no—
157D61⋊C8—21no—
158D61⋊C8—41no—
159D61⋊C8—41no—
160D61⋊C8—41no—
161D61⋊C8C2×D411yescharacteristic
162D61⋊C8C2×D411yescharacteristic
163Q16×C61C22×C411yescharacteristic, complemented
164SD16×C61—21no—
165D8×C61—21no—
166D8×C61C22×C412yes—
167D8×C61C22×C411yescharacteristic, complemented
168C2×C8×C61C22×C411yescharacteristic
169#11758202—21no—
170#11758201—21no—
171#11758200—21no—
172#11758199—22no—
173#11758199—21no—
174#11758199—22no—
175C2×#92418#4111yescharacteristic
176Dic244C22×C411yescharacteristic, complemented
177D488—21no—
178D488C22×C412yes—
179D488C22×C411yescharacteristic, complemented
180#11758190—21no—
181C8×D61C22×C411yescharacteristic
182C8×D61C2×D411yescharacteristic
183C8×D61#4111yescharacteristic
184C8×D61C2411yescharacteristic
185#11758187—22no—
186C16×C61C22×C412yescomplemented
187#11758185C22×C412yescomplemented
188C23×C61—41no—
189C22×D61—41no—
190C22×D61—42no—
191C22×D61—41no—
192C22×D61—42no—
193C22×D61—82no—
194C22×D61—82no—
195C22×D61AGL(1,ℤ/8)11yescharacteristic
196C2×#6923—21no—
197C2×#6923—21no—
198C2×#6923—42no—
199C2×#6923—42no—
200C2×#6923—84no—
201C2×#6923—84no—
202C2×#6923—82no—
203Q8×C61—21no—
204D4×C61—22no—
205D4×C61—21no—
206D4×C61—41no—
207D4×C61—41no—
208C2×C4×C61—41no—
209C2×C4×C61C4×D411yescharacteristic
210C22⋊D61—41no—
211C22⋊D61—41no—
212C22⋊D61—42no—
213C22⋊D61—41no—
214C22⋊D61—42no—
215C2×Dic61—41no—
216C2×Dic61AGL(1,ℤ/8)11yescharacteristic
217D244—21no—
218D244—22no—
219D244—41no—
220D244—41no—
221C4×D61—41no—
222C4×D61—41no—
223C4×D61—41no—
224C4×D61C4×D411yescharacteristic
225C4×D61AGL(1,ℤ/8)11yescharacteristic
226C4×D61AGL(1,ℤ/8)11yescharacteristic
227C4×D61C22×D411yescharacteristic
228Dic122—21no—
229Dic122—41no—
230#92420—21no—
231#92420—21no—
232#92420—41no—
233#92420—41no—
234C8×C61C4×D411yescharacteristic
235C8×C61C23×C411yescharacteristic
236#92418C4×D411yescharacteristic
237#92418C2×#4111yescharacteristic
238C2×AGL(1,ℤ/16)—611nomaximal, Sylow
239C22×C61—41no—
240C22×C61—42no—
241C22×C61—82no—
242C22×C61#44211yescharacteristic
243C2×D61—22no—
244C2×D61—41no—
245C2×D61—42no—
246C2×D61—82no—
247C2×D61—82no—
248C2×D61—82no—
249C2×D61—82no—
250C2×D61—84no—
251C2×D61#44211yescharacteristic
252C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
253#6923—41no—
254#6923—41no—
255#6923—82no—
256C4×C61—41no—
257C4×C61#44211yescharacteristic
258C4×C61C2×C4×D411yescharacteristic
259Dic61—41no—
260Dic61#44211yescharacteristic
261Dic61C2×AGL(1,ℤ/8)11yescharacteristic
262C2×#509—611no—
263C2×#444—611no—
264C2×#442—611no—
265AGL(1,ℤ/16)—612no—
266AGL(1,ℤ/16)—612no—
267AGL(1,ℤ/16)—612no—
268AGL(1,ℤ/16)—612no—
269C2×#365—611no—
270C2×#361—611no—
271C2×#360—611no—
272C2×#347—611no—
273C2×C61—21no—
274C2×C61—82no—
275C2×C61—81no—
276C2×C61C2×#44211yescharacteristic
277D61—21no—
278D61—81no—
279D61—82no—
280D61AGL(1,ℤ/16)12yescomplemented
281C2×#135—611no—
282C22×D8—611no—
283C2×#131—1221no—
284C2×C4×D4—1221no—
285#509—611no—
286#509—611no—
287#509—612no—
288#509—612no—
289#509—611no—
290#509#692311yescharacteristic, complemented
291C2×SD32—612no—
292C2×D16—612no—
293C2×M32—611no—
294C2×M32—611no—
295#444—611no—
296#444—611no—
297#444—611no—
298#444—611no—
299#444—1221no—
300#444—1221no—
301#442—612no—
302#442—612no—
303#442—1221no—
304#442—1221no—
305C2×#108—611no—
306C2×#106—611no—
307C2×#104—1221no—
308C2×#102—1221no—
309C2×#97—611no—
310#365—612no—
311#365—612no—
312#361—612no—
313#361—612no—
314#360—612no—
315#360—612no—
316#347—612no—
317#347—612no—
318C61C2×AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
319C2×#41—1221no—
320C22×D4—1221no—
321C23×C4—2441no—
322#135—611no—
323#135—611no—
324#135—611no—
325#135—1221no—
326#135—1221no—
327#135C2×#692311yescharacteristic, complemented
328C2×Q16—611no—
329C2×SD16—1221no—
330C2×D8—612no—
331C2×D8—612no—
332C2×D8—611no—
333C2×D8—611no—
334C2×D8—1221no—
335C2×D8—1221no—
336C2×D8—1221no—
337C2×D8C2×#692311yescharacteristic
338#131—1221no—
339#131—1221no—
340#131—1221no—
341#131—1221no—
342#131—2441no—
343#131—2441no—
344C2×M16—1221no—
345C2×M16—2441no—
346C22×C8—611no—
347C22×C8—611no—
348C22×C8—2441no—
349C4×D4—1222no—
350C4×D4—1222no—
351C4×D4—2441no—
352C4×D4—2441no—
353C2×C4⋊C4—1221no—
354C2×C22⋊C4—2441no—
355C2×C42—611no—
356SD32—612no—
357SD32—612no—
358SD32—612no—
359SD32C2×#692312yescomplemented
360D16—612no—
361D16—612no—
362D16—612no—
363D16C2×#692312yescomplemented
364M32—611no—
365M32—612no—
366M32—612no—
367M32—1221no—
368M32C2×#692311yescharacteristic, complemented
369C2×C16—612no—
370C2×C16—1221no—
371#108—611no—
372#108—611no—
373#108—1221no—
374#106—612no—
375#106—1221no—
376#104—1221no—
377#104—1221no—
378#104—1221no—
379#104—1221no—
380#102—1222no—
381#102—1222no—
382#97—611no—
383#97—611no—
384#97—611no—
385#97—611no—
386C24—2441no—
387#41—21no—
388#41—1221no—
389#41—1221no—
390#41—1221no—
391#41—2441no—
392#41—2441no—
393C2×Q8—1221no—
394C2×D4—21no—
395C2×D4—1222no—
396C2×D4—1222no—
397C2×D4—1221no—
398C2×D4—1221no—
399C2×D4—2441no—
400C2×D4—2441no—
401C2×D4—2441no—
402C2×D4—2441no—
403C22×C4—611no—
404C22×C4—1221no—
405C22×C4—4884no—
406C22×C4—2441no—
407C22×C4—2442no—
408C22×C4—2442no—
409C22×C4—2441no—
410Q16—611no—
411Q16—1221no—
412Q16C22×#692311yescharacteristic, complemented
413SD16—21no—
414SD16—1221no—
415SD16—1221no—
416SD16—1221no—
417D8—21no—
418D8—611no—
419D8—612no—
420D8—1222no—
421D8—1222no—
422D8—1221no—
423D8—1221no—
424D8C22×#692312yes—
425D8C22×#692311yescharacteristic, complemented
426M16—1221no—
427M16—1221no—
428M16—2441no—
429M16—2441no—
430M16—2441no—
431M16—2441no—
432M16—2441no—
433C2×C8—611no—
434C2×C8—611no—
435C2×C8—611no—
436C2×C8—611no—
437C2×C8—611no—
438C2×C8—611no—
439C2×C8—611no—
440C2×C8—1221no—
441C2×C8—1221no—
442C2×C8—2441no—
443C2×C8—2441no—
444C2×C8—2441no—
445C2×C8—2441no—
446C2×C8—2441no—
447C2×C8C22×#692311yescharacteristic
448C4⋊C4—1222no—
449C4⋊C4—2441no—
450C22⋊C4—2442no—
451C22⋊C4—2442no—
452C42—611no—
453C42—611no—
454C42—1221no—
455C16—612no—
456C16—1222no—
457C16C22×#692312yescomplemented
458C23—41no—
459C23—611no—
460C23—4882no—
461C23—4882no—
462C23—2442no—
463C23—2441no—
464C23—2442no—
465C23—2441no—
466Q8—21no—
467Q8—1221no—
468Q8—2441no—
469D4—22no—
470D4—21no—
471D4—41no—
472D4—41no—
473D4—1222no—
474D4—1221no—
475D4—2441no—
476D4—2442no—
477D4—2442no—
478D4—2441no—
479D4—2441no—
480D4—2441no—
481D4—2441no—
482C2×C4—41no—
483C2×C4—611no—
484C2×C4—611no—
485C2×C4—611no—
486C2×C4—611no—
487C2×C4—611no—
488C2×C4—1221no—
489C2×C4—1221no—
490C2×C4—4882no—
491C2×C4—4884no—
492C2×C4—4884no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4—2441no—
496C2×C4—2442no—
497C2×C4—2442no—
498C2×C4—2441no—
499C2×C4D4×#692311yescharacteristic
500C8—611no—
501C8—611no—
502C8—1221no—
503C8—1221no—
504C8—2441no—
505C8—2441no—
506C8D4×#692311yescharacteristic
507C8C23×#692311yescharacteristic
508C22—41no—
509C22—42no—
510C22—82no—
511C22—611no—
512C22—611no—
513C22—1222no—
514C22—4882no—
515C22—4884no—
516C22—4882no—
517C22—4882no—
518C22—4882no—
519C22—2441no—
520C22—2442no—
521C22#1684080311yescharacteristic
522C4—41no—
523C4—611no—
524C4—611no—
525C4—4882no—
526C4—2441no—
527C4—2441no—
528C4—2441no—
529C4#1684080311yescharacteristic
530C4C2×D4×#692311yescharacteristic
531C2—21no—
532C2—82no—
533C2—81no—
534C2—612no—
535C2—1221no—
536C2—4882no—
537C2—4881no—
538C2C2×#1684080311yescharacteristic
subgroupG/H
centerC2C2×#16840803
commutatorC8×C61C23×C4
FrattiniC8C23×#6923
FittingC61×#509C4
socleC2×C61C2×#442
prime radical#509×D61C2
cosocleC8×D61C24
hypercenter#509#6923
hypocenterC61C2×AGL(1,ℤ/16)
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. D61⋊#444C2semidirect
2. C2×#16840803C2semidirect
3. #21462231C2semidirect
4. #21462230C2semidirect
5. #21462229C2semidirect
6. #21462228C2semidirect
7. D61⋊#365C2semidirect
8. D61⋊#361C2semidirect
9. D61⋊#360C2semidirect
10. #21462034C2semidirect
15. #16840809C22semidirect
16. #16840809C22semidirect
17. #16840808C22semidirect
18. #16840808C22semidirect
23. #16840803C22semidirect
24. #16840803C22semidirect
30. #16840687C22semidirect
31. #16840686C22semidirect
32. #16840680C22semidirect
33. #16840680C22semidirect
34. #16840679C22semidirect
35. #16840678C22semidirect
36. #16840653C22semidirect
37. #16840652C22semidirect
40. #16840200C4semidirect
42. #16840198C4semidirect
43. #16840197C4semidirect
45. SD32×D61C4semidirect
46. D16×D61C4semidirect
48. C61×#509C4semidirect
88. #14519799C2×C4semidirect
92. Q16×D61C2×C4semidirect
99. D8×D61C2×C4semidirect
102. #14519722C2×C4semidirect
103. #14519721C2×C4semidirect
104. #14519720C2×C4semidirect
105. D976C2×C4semidirect
106. #14519718C2×C4semidirect
107. #14519718C2×C4semidirect
108. #14519717C2×C4semidirect
110. C16×D61C2×C4semidirect
111. #135×C61C2×C4semidirect
113. SD32×C61C2×C4semidirect
114. D16×C61C2×C4semidirect
115. M32×C61C2×C4semidirect
163. Q16×C61C22×C4semidirect
167. D8×C61C22×C4semidirect
176. Dic244C22×C4semidirect
179. D488C22×C4semidirect
186. C16×C61C22×C4semidirect
187. #11758185C22×C4semidirect
280. D61AGL(1,ℤ/16)semidirect
290. #509#6923semidirect
318. C61C2×AGL(1,ℤ/16)semidirect
327. #135C2×#6923semidirect
359. SD32C2×#6923semidirect
363. D16C2×#6923semidirect
368. M32C2×#6923semidirect
412. Q16C22×#6923semidirect
425. D8C22×#6923semidirect
457. C16C22×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4442
C2×#168408032
#214622312
#214622302
#214622292
#214622282
D61⋊#3652
D61⋊#3612
D61⋊#3602
#214620342
#509×D612
C2×AGL(1,ℤ/16)61