Finite Group Databasebeta

← D61×#1714 #29667722

Subgroups — D61×#1714 #29667722

Order 15616.

914 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#500×D61C211yesmaximal, characteristic, complemented
2#498×D61C211yesmaximal, characteristic, complemented
3#492×D61C211yesmaximal, characteristic
4#492×D61C211yesmaximal, characteristic
5#487×D61C211yesmaximal, characteristic, complemented
6#486×D61C211yesmaximal, characteristic
7#21445444C211yesmaximal, characteristic, complemented
8#21445443C211yesmaximal, characteristic, complemented
9#21445442C211yesmaximal, characteristic, complemented
10#21445441C211yesmaximal, characteristic, complemented
11#21445440C211yesmaximal, characteristic, complemented
12#21445439C211yesmaximal, characteristic, complemented
13#21445438C211yesmaximal, characteristic, complemented
14#322×D61C211yesmaximal, characteristic, complemented
15C61×#1714C211yesmaximal, characteristic, complemented
16C2×SD16×D61—22no—
17C2×SD16×D61—22no—
18C4⋊Q8×D61C2211yescharacteristic
19C4⋊Q8×D61C2211yescharacteristic
20C4⋊Q8×D61C2211yescharacteristic
21#127×D61C2211yescharacteristic
22#16840167C2211yescharacteristic, complemented
23#16840166—22no—
24#16840165C2211yescharacteristic, complemented
25#16840165C2211yescharacteristic, complemented
26#16840160C2211yescharacteristic, complemented
27#16840159—22no—
28#16840158C2211yescharacteristic, complemented
29#16840158C2211yescharacteristic, complemented
30#16840136C2211yescharacteristic
31#16840136C2211yescharacteristic
32#16840135C2211yescharacteristic
33#16840135C2211yescharacteristic
34#16840134C2211yescharacteristic
35#16840134C2211yescharacteristic
36#16840133—22no—
37#16840133—22no—
38#16840114C2211yescharacteristic, complemented
39#16840113C2211yescharacteristic, complemented
40#16840112C2211yescharacteristic, complemented
41#16840111—22no—
42#16840110C2211yescharacteristic
43#16840109C2211yescharacteristic
44#16840108C2211yescharacteristic
45#16840107—22no—
46#107×D61—22no—
47#106×D61—22no—
48#103×D61—22no—
49#102×D61—22no—
50C4×C8×D61C2211yescharacteristic
51C4×C8×D61C2211yescharacteristic
52C4×C8×D61C2211yescharacteristic
53#16839484C2211yescharacteristic, complemented
54#16839484C2211yescharacteristic, complemented
55#16839483C2211yescharacteristic, complemented
56C61×#500C2211yescharacteristic, complemented
57C61×#498C2211yescharacteristic, complemented
58C61×#492C2211yescharacteristic
59C61×#492C2211yescharacteristic
60C61×#487C2211yescharacteristic, complemented
61C61×#486C2211yescharacteristic
62C61×#322C2211yescharacteristic, complemented
63C2×Q8×D61—21no—
64C2×Q8×D61—21no—
65C2×Q8×D61—21no—
66C2×D4×D61—21no—
67C2×D4×D61—21no—
68C2×D4×D61—21no—
69C2×#11758190—22no—
70C2×#11758190—22no—
71C2×#11758200—22no—
72C2×#11758200—22no—
73C2×#11758201—22no—
74C2×#11758201—22no—
75SD16×D61—48no—
76SD16×D61—48no—
77C2×C8×D61D412yes—
78C2×C8×D61D412yes—
79C2×C8×D61D412yes—
80#14519777C2311yescharacteristic
81#14519777C2311yescharacteristic
82#14519777C2311yescharacteristic
83#14519776—21no—
84#14519776—21no—
85#14519776—21no—
86#14519776—21no—
87#14519776—21no—
88#14519776—21no—
89#14519775—21no—
90#14519775—21no—
91#14519775—21no—
92#14519774C2311yescharacteristic
93#14519773—21no—
94#14519773—21no—
95#14519773—21no—
96C4⋊C4×D61—21no—
97C4⋊C4×D61—21no—
98C4⋊C4×D61—21no—
99C4⋊C4×D61—21no—
100C4⋊C4×D61—21no—
101C4⋊C4×D61—21no—
102C42×D61C2311yescharacteristic
103#14519711—22no—
104#14519710—22no—
105#14519710—22no—
106#14519709—22no—
107#14519708—22no—
108#14519708—22no—
109#14519702—22no—
110#14519701—22no—
111#14519700—22no—
112#14519699—22no—
113#14519698—22no—
114#14519697—22no—
115C4×#92418C2311yescharacteristic
116C4×#92418C2311yescharacteristic
117C4×#92418C2311yescharacteristic
118C8×Dic61D412yes—
119C8×Dic61D412yes—
120C8×Dic61D412yes—
121C2×SD16×C61—22no—
122C2×SD16×C61—22no—
123C4⋊Q8×C61C2311yescharacteristic
124C4⋊Q8×C61C2311yescharacteristic
125C4⋊Q8×C61C2311yescharacteristic
126#127×C61C2311yescharacteristic
127#107×C61—22no—
128#106×C61—22no—
129#103×C61—22no—
130#102×C61—22no—
131C4×C8×C61C2311yescharacteristic
132C4×C8×C61C2311yescharacteristic
133C4×C8×C61C2311yescharacteristic
134C23×D61—41no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C2×C22⋊D61—41no—
142C2×C22⋊D61—41no—
143C2×C22⋊D61—41no—
144Q8×D61—44no—
145Q8×D61—44no—
146Q8×D61—44no—
147D4×D61—44no—
148D4×D61—44no—
149D4×D61—44no—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244—21no—
153C2×C4×D61—41no—
154C2×C4×D61—41no—
155C2×C4×D61—41no—
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61C2×D411yescharacteristic
158C2×C4×D61C2×D411yescharacteristic
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—41no—
163C2×Dic122—41no—
164C2×Dic122—41no—
165SD16×C61—44no—
166SD16×C61—44no—
167C2×C8×C61C2×D412yes—
168C2×C8×C61C2×D412yes—
169C2×C8×C61C2×D412yes—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C42×C61C2411yescharacteristic
177#11758201—44no—
178#11758201—44no—
179#11758200—44no—
180#11758200—44no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187#11758196—41no—
188#11758196—41no—
189#11758196—41no—
190#11758196—41no—
191#11758196—41no—
192#11758196—41no—
193C4×Dic61C2×D411yescharacteristic
194C4×Dic61C2×D411yescharacteristic
195C4×Dic61C2×D411yescharacteristic
196C2×#92418C2×D412yes—
197C2×#92418C2×D412yes—
198C2×#92418C2×D412yes—
199#11758190—44no—
200#11758190—44no—
201C8×D61—24no—
202C8×D61—24no—
203C8×D61SD1618yescomplemented
204C23×C61—41no—
205C22×D61—41no—
206C22×D61—82no—
207C22×D61—82no—
208C22×D61—82no—
209C22×D61#12711yescharacteristic
210Q8×C61—42no—
211Q8×C61—42no—
212Q8×C61—42no—
213D4×C61—42no—
214D4×C61—42no—
215D4×C61—42no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61C22×D411yescharacteristic
220C2×C4×C61C22×D411yescharacteristic
221C2×C4×C61C22×D411yescharacteristic
222C22⋊D61—82no—
223C22⋊D61—82no—
224C22⋊D61—82no—
225C2×Dic61—41no—
226C2×Dic61—41no—
227C2×Dic61—41no—
228C2×Dic61#12711yescharacteristic
229C2×Dic61#12711yescharacteristic
230C2×Dic61#12711yescharacteristic
231D244—42no—
232D244—42no—
233D244—42no—
234C4×D61—82no—
235C4×D61—82no—
236C4×D61—82no—
237C4×D61C2×SD1614yes—
238C4×D61AGL(1,ℤ/8)14yes—
239C4×D61#13714yes—
240Dic122—42no—
241Dic122—42no—
242Dic122—42no—
243Dic122—82no—
244Dic122—82no—
245Dic122—82no—
246C8×C61—22no—
247C8×C61—22no—
248C8×C61C2×SD1614yescomplemented
249#92418—22no—
250#92418—22no—
251#92418C2×SD1614yescomplemented
252C2×#1714—611nomaximal, Sylow
253C22×C61—81no—
254C22×C61—81no—
255C22×C61—81no—
256C22×C61C2×#12711yescharacteristic
257C2×D61—81no—
258C2×D61—81no—
259C2×D61—81no—
260C2×D61—164no—
261C2×D61#49212yes—
262C2×D61#49612yes—
263C2×D61#49712yes—
264C4×C61—81no—
265C4×C61—81no—
266C4×C61—81no—
267C4×C61C22×SD1612yes—
268C4×C61C2×AGL(1,ℤ/8)12yes—
269C4×C61C2×#13712yes—
270Dic61—81no—
271Dic61—81no—
272Dic61—81no—
273Dic61#49212yes—
274Dic61#49612yes—
275Dic61#49712yes—
276C2×#500—611no—
277C2×#498—611no—
278C2×#492—611no—
279C2×#492—611no—
280C2×#487—611no—
281C2×#486—611no—
282#1714—611no—
283#1714—611no—
284#1714—611no—
285#1714—611no—
286#1714—611no—
287#1714—611no—
288#1714—611no—
289#1714D6111yescharacteristic, direct product factor
290C2×#322—611no—
291C2×C61—161no—
292C2×C61C2×#49211yescharacteristic
293C2×C61C2×#49611yescharacteristic
294C2×C61C2×#49711yescharacteristic
295D61—161no—
296D61#171414yesdirect product factor
297C22×SD16—1222no—
298C22×SD16—1222no—
299C2×C4⋊Q8—611no—
300C2×C4⋊Q8—611no—
301C2×C4⋊Q8—611no—
302C2×#127—611no—
303#500—611no—
304#500—611no—
305#500—611no—
306#500—1222no—
307#500C2×D6111yescharacteristic, complemented
308#498—611no—
309#498—611no—
310#498—611no—
311#498—1222no—
312#498C2×D6111yescharacteristic, complemented
313#492—611no—
314#492—611no—
315#492—611no—
316#492—611no—
317#492—611no—
318#492—611no—
319#492—1222no—
320#492—1222no—
321#492C2×D6111yescharacteristic
322#492C2×D6111yescharacteristic
323#487—611no—
324#487—611no—
325#487—611no—
326#487—1222no—
327#487C2×D6111yescharacteristic, complemented
328#486—611no—
329#486—611no—
330#486—611no—
331#486—1222no—
332#486C2×D6111yescharacteristic
333C2×#107—1222no—
334C2×#106—1222no—
335C2×#103—1222no—
336C2×#102—1222no—
337C2×C4×C8—611no—
338C2×C4×C8—611no—
339C2×C4×C8—611no—
340#322—611no—
341#322—611no—
342#322—611no—
343#322C2×D6111yescharacteristic, complemented
344C61C2×#171411yescharacteristic, complemented, Sylow
345C22×Q8—1221no—
346C22×Q8—1221no—
347C22×Q8—1221no—
348C22×D4—1221no—
349C22×D4—1221no—
350C22×D4—1221no—
351C2×SD16—22no—
352C2×SD16—22no—
353C2×SD16—1222no—
354C2×SD16—1222no—
355C2×SD16—1222no—
356C2×SD16—1222no—
357C2×SD16—1222no—
358C2×SD16—1222no—
359C2×SD16—2448no—
360C2×SD16—2448no—
361C22×C8—612no—
362C22×C8—612no—
363C22×C8—612no—
364C4⋊Q8—611no—
365C4⋊Q8—611no—
366C4⋊Q8—611no—
367C4⋊Q8—1221no—
368C4⋊Q8—1221no—
369C4⋊Q8—1221no—
370C4⋊Q8—1221no—
371C4⋊Q8—1221no—
372C4⋊Q8—1221no—
373C4⋊Q8—1221no—
374C4⋊Q8—1221no—
375C4⋊Q8—1221no—
376C4⋊Q8C22×D6111yescharacteristic
377C4⋊Q8C22×D6111yescharacteristic
378C4⋊Q8C22×D6111yescharacteristic
379#127—611no—
380#127—1221no—
381#127—1221no—
382#127—1221no—
383#127C22×D6111yescharacteristic
384C2×C4⋊C4—1221no—
385C2×C4⋊C4—1221no—
386C2×C4⋊C4—1221no—
387C2×C4⋊C4—1221no—
388C2×C4⋊C4—1221no—
389C2×C4⋊C4—1221no—
390C2×C42—611no—
391#107—22no—
392#107—1222no—
393#107—1222no—
394#107—1222no—
395#106—22no—
396#106—1222no—
397#106—1222no—
398#106—1222no—
399#103—22no—
400#103—1222no—
401#103—1222no—
402#103—1222no—
403#102—22no—
404#102—1222no—
405#102—1222no—
406#102—1222no—
407C4×C8—612no—
408C4×C8—612no—
409C4×C8—612no—
410C4×C8—611no—
411C4×C8—611no—
412C4×C8—611no—
413C4×C8C22×D6111yescharacteristic
414C4×C8C22×D6111yescharacteristic
415C4×C8C22×D6111yescharacteristic
416C24—2441no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—1221no—
421C2×Q8—1221no—
422C2×Q8—1221no—
423C2×Q8—2441no—
424C2×Q8—2441no—
425C2×Q8—2441no—
426C2×Q8—2444no—
427C2×Q8—2444no—
428C2×Q8—2444no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—1221no—
433C2×D4—1221no—
434C2×D4—1221no—
435C2×D4—2444no—
436C2×D4—2444no—
437C2×D4—2444no—
438C2×D4—2441no—
439C2×D4—2441no—
440C2×D4—2441no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—2441no—
445C22×C4—2441no—
446C22×C4—2441no—
447SD16—44no—
448SD16—44no—
449SD16—2444no—
450SD16—2444no—
451SD16—2444no—
452SD16—2444no—
453SD16—2444no—
454SD16—2444no—
455C2×C8—612no—
456C2×C8—618no—
457C2×C8—612no—
458C2×C8—612no—
459C2×C8—1224no—
460C2×C8—1224no—
461C2×C8D4×D6112yes—
462C2×C8D4×D6112yes—
463C2×C8D4×D6112yes—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—2441no—
477C4⋊C4—2441no—
478C4⋊C4—2441no—
479C4⋊C4—2441no—
480C4⋊C4—2441no—
481C4⋊C4—2441no—
482C42—611no—
483C42—611no—
484C42—611no—
485C42C23×D6111yescharacteristic
486C23—41no—
487C23—611no—
488C23—4882no—
489C23—4882no—
490C23—4882no—
491C23—2441no—
492Q8—42no—
493Q8—42no—
494Q8—42no—
495Q8—4882no—
496Q8—4882no—
497Q8—4882no—
498Q8—2442no—
499Q8—2442no—
500Q8—2442no—
501D4—42no—
502D4—42no—
503D4—42no—
504D4—4882no—
505D4—4882no—
506D4—4882no—
507D4—2442no—
508D4—2442no—
509D4—2442no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—611no—
514C2×C4—611no—
515C2×C4—611no—
516C2×C4—614no—
517C2×C4—614no—
518C2×C4—614no—
519C2×C4—4882no—
520C2×C4—4882no—
521C2×C4—4882no—
522C2×C4—2441no—
523C2×C4—2441no—
524C2×C4—2441no—
525C2×C4C2×D4×D6111yescharacteristic
526C2×C4C2×D4×D6111yescharacteristic
527C2×C4C2×D4×D6111yescharacteristic
528C8—22no—
529C8—22no—
530C8—614no—
531C8—1222no—
532C8—1222no—
533C8SD16×D6114yescomplemented
534C22—81no—
535C22—81no—
536C22—81no—
537C22—612no—
538C22—612no—
539C22—612no—
540C22—9764no—
541C22—4881no—
542C22—4881no—
543C22—4881no—
544C22#127×D6111yescharacteristic
545C4—81no—
546C4—81no—
547C4—81no—
548C4—612no—
549C4—612no—
550C4—612no—
551C4—4881no—
552C4—4881no—
553C4—4881no—
554C4C2×SD16×D6112yes—
555C4AGL(1,ℤ/8)×D6112yes—
556C4#137×D6112yes—
557C2—161no—
558C2—614no—
559C2—9761no—
560C2#492×D6111yescharacteristic
561C2#496×D6111yescharacteristic
562C2#497×D6111yescharacteristic
subgroupG/H
centerC22#127×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1714C2
socleC22×C61C2×#127
prime radical#127×D61C22
hypercenter#1714D61
hypocenterC61C2×#1714
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1714

Complements

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

NH ≅ G/Ntype
1. #500×D61C2semidirect
2. #498×D61C2semidirect
5. #487×D61C2semidirect
7. #21445444C2semidirect
8. #21445443C2semidirect
9. #21445442C2semidirect
10. #21445441C2semidirect
11. #21445440C2semidirect
12. #21445439C2semidirect
13. #21445438C2semidirect
14. #322×D61C2semidirect
15. C61×#1714C2semidirect
22. #16840167C22semidirect
24. #16840165C22semidirect
25. #16840165C22semidirect
26. #16840160C22semidirect
28. #16840158C22semidirect
29. #16840158C22semidirect
38. #16840114C22semidirect
39. #16840113C22semidirect
40. #16840112C22semidirect
53. #16839484C22semidirect
54. #16839484C22semidirect
55. #16839483C22semidirect
56. C61×#500C22semidirect
57. C61×#498C22semidirect
60. C61×#487C22semidirect
62. C61×#322C22semidirect
203. C8×D61SD16semidirect
248. C8×C61C2×SD16semidirect
251. #92418C2×SD16semidirect
289. #1714D61direct (N × H)
296. D61#1714direct (N × H)
307. #500C2×D61semidirect
312. #498C2×D61semidirect
327. #487C2×D61semidirect
343. #322C2×D61semidirect
344. C61C2×#1714semidirect
533. C8SD16×D61semidirect

Maximal subgroups

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

subgroupindex
#500×D612
#498×D612
#492×D612
#487×D612
#486×D612
#214454442
#214454432
#214454422
#214454412
#214454402
#214454392
#214454382
#322×D612
C61×#17142
C2×#171461