Finite Group Databasebeta

← D61×#2060 #29708108

Subgroups — D61×#2060 #29708108

Order 15616.

1218 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#544×D61C211yesmaximal, characteristic
2#428×D61C212yesmaximal
3#384×D61C211yesmaximal, characteristic
4#21447165C211yesmaximal, characteristic, complemented
5#21447164C211yesmaximal, characteristic, complemented
6#21447163C212yesmaximal, complemented
7#21447162C212yesmaximal, complemented
8#21447161C211yesmaximal, characteristic, complemented
9#343×D61C211yesmaximal, characteristic
10#339×D61C212yesmaximal
11C61×#2060C211yesmaximal, characteristic, complemented
12C2×M16×D61C2212yes—
13#16840393C2211yescharacteristic
14#16840392—22no—
15#16840391—22no—
16#16840390C2212yes—
17#16840389—22no—
18C4⋊Q8×D61—22no—
19#125×D61—22no—
20C22⋊Q8×D61—22no—
21#117×D61C2212yes—
22C2×C4⋊C4×D61—22no—
23C2×C4⋊C4×D61C2211yescharacteristic
24C2×C4⋊C4×D61C2211yescharacteristic
25C2×C42×D61C2211yescharacteristic
26#16839805C2212yes—
27#16839804C2212yes—
28#16839803—22no—
29#16839802C2212yes—
30#16839801—22no—
31#107×D61—22no—
32#106×D61—22no—
33#16839632C2211yescharacteristic
34#16839631—22no—
35#16839631C2211yescharacteristic
36#16839631C2211yescharacteristic
37#16839531C2211yescharacteristic
38#16839530C2212yes—
39#16839523C2212yes—
40#16839522C2212yes—
41#16839521C2212yes—
42C61×#544C2211yescharacteristic
43C61×#428C2212yes—
44C61×#384C2211yescharacteristic
45C61×#343C2211yescharacteristic
46C61×#339C2212yes—
47C2×Q8×D61—22no—
48C22×C4×D61—21no—
49C22×C4×D61—21no—
50C22×C4×D61D412yes—
51C22×C4×D61C2311yescharacteristic
52C2×#11758194C2312yes—
53C2×#11758189—22no—
54M16×D61—24no—
55M16×D61Q818yescomplemented
56C2×C8×D61—22no—
57#14519777—22no—
58#14519776—24no—
59#14519776—22no—
60#14519776—22no—
61#14519775—24no—
62#14519769—22no—
63#14519768—22no—
64#14519768—22no—
65#14519767—24no—
66#14519767—24no—
67#14519757—22no—
68#14519756—22no—
69#14519755—24no—
70#14519754—24no—
71#14519753—22no—
72#14519736C2312yes—
73#14519735D412yes—
74#14519735D412yes—
75#14519734—22no—
76#14519733—22no—
77C2×C4⋊Dic61—22no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×#11758196—22no—
81C2×#11758196—22no—
82C2×#11758196—21no—
83C2×#11758196D412yes—
84C4⋊C4×D61—22no—
85C4⋊C4×D61—24no—
86C4⋊C4×D61—22no—
87C4⋊C4×D61—22no—
88C4⋊C4×D61—22no—
89C4⋊C4×D61—22no—
90C4⋊C4×D61—48no—
91C4⋊C4×D61D412yes—
92C4⋊C4×D61D412yes—
93C22⋊C4×D61—22no—
94C2×C4×Dic61—21no—
95C2×C4×Dic61C2311yescharacteristic
96C42×D61—22no—
97C42×D61—22no—
98C42×D61Q814yescomplemented
99#14519711—22no—
100#14519710—22no—
101#14519710—22no—
102#14519709—22no—
103#14519708—22no—
104#14519708—22no—
105C2×M16×C61C2312yes—
106C4⋊Q8×C61—22no—
107#125×C61—22no—
108C22⋊Q8×C61—22no—
109#117×C61C2312yes—
110C2×C4⋊C4×C61—22no—
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C42×C61C2311yescharacteristic
114#107×C61—22no—
115#106×C61—22no—
116C23×D61C2×D411yescharacteristic
117C2×Q8×C61—22no—
118C22×C4×C61—21no—
119C22×C4×C61—21no—
120C22×C4×C61C2×D412yes—
121C22×C4×C61C2411yescharacteristic
122C22×Dic61—21no—
123C22×Dic61—21no—
124C22×Dic61C2×D412yes—
125C22×Dic61C2×D411yescharacteristic
126Q8×D61—84no—
127C2×C4×D61—24no—
128C2×C4×D61—24no—
129C2×C4×D61—24no—
130C2×C4×D61—22no—
131C2×C4×D61—22no—
132C2×C4×D61—22no—
133C2×C4×D61—22no—
134C2×C4×D61—44no—
135C2×C4×D61—44no—
136C2×C4×D61—41no—
137C2×C4×D61—41no—
138C2×C4×D61C2×D412yes—
139C2×C4×D61C2×D412yes—
140C2×C4×D61C2×Q814yes—
141C2×C4×D61C2×Q812yes—
142C2×C4×D61#4112yes—
143C2×Dic122—24no—
144C2×Dic122—22no—
145M16×C61—22no—
146M16×C61C2×Q814yescomplemented
147C2×C8×C61—22no—
148C4⋊C4×C61—22no—
149C4⋊C4×C61—24no—
150C4⋊C4×C61—22no—
151C4⋊C4×C61—22no—
152C4⋊C4×C61—44no—
153C4⋊C4×C61C2×D412yes—
154C4⋊C4×C61C2×D412yes—
155C22⋊C4×C61—22no—
156C42×C61—22no—
157C42×C61—21no—
158C42×C61C2×Q812yescomplemented
159C22⋊Dic61—22no—
160#11758198—22no—
161#11758198—22no—
162C4⋊Dic61—22no—
163C4⋊Dic61—24no—
164C4⋊Dic61—22no—
165C4⋊Dic61—22no—
166C4⋊Dic61—44no—
167C4⋊Dic61C2×D412yes—
168C4⋊Dic61C2×D412yes—
169#11758196—24no—
170#11758196—24no—
171#11758196—24no—
172#11758196—24no—
173#11758196—22no—
174#11758196—22no—
175#11758196—44no—
176#11758196—44no—
177#11758196—42no—
178C4×Dic61—22no—
179C4×Dic61—21no—
180C4×Dic61—22no—
181C4×Dic61—22no—
182C4×Dic61—24no—
183C4×Dic61C2×Q812yescomplemented
184#11758194—22no—
185#11758194C2×Q814yescomplemented
186C2×#92418—22no—
187#11758189—28no—
188C8×D61—28no—
189C23×C61C22×D411yescharacteristic
190C22×D61—22no—
191C22×D61—22no—
192C22×D61#12011yescharacteristic
193C22×D61#12011yescharacteristic
194C22×D61C22⋊Q812yes—
195C22×D61C4⋊Q812yes—
196Q8×C61—82no—
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—22no—
201C2×C4×C61—22no—
202C2×C4×C61—22no—
203C2×C4×C61—42no—
204C2×C4×C61—42no—
205C2×C4×C61—41no—
206C2×C4×C61C22×D412yes—
207C2×C4×C61C22×Q812yes—
208C2×C4×C61C22×Q811yescharacteristic
209C2×C4×C61C2×#4111yescharacteristic
210C2×Dic61—22no—
211C2×Dic61—22no—
212C2×Dic61—22no—
213C2×Dic61—22no—
214C2×Dic61—22no—
215C2×Dic61—22no—
216C2×Dic61—42no—
217C2×Dic61—42no—
218C2×Dic61—41no—
219C2×Dic61#12012yes—
220C2×Dic61C22⋊Q812yes—
221C2×Dic61C4⋊Q812yes—
222C4×D61—216no—
223C4×D61—44no—
224C4×D61—44no—
225C4×D61—44no—
226C4×D61—82no—
227C4×D61—82no—
228C4×D61—82no—
229C4×D61C22⋊Q814yes—
230C4×D61C22⋊Q814yes—
231C4×D61C4⋊Q814yes—
232C4×D61C4⋊Q814yes—
233Dic122—82no—
234Dic122—84no—
235C8×C61—24no—
236#92418—24no—
237C2×#2060—611nomaximal, Sylow
238C22×C61—21no—
239C22×C61—21no—
240C22×C61C2×#12011yescharacteristic
241C22×C61C2×C22⋊Q811yescharacteristic
242C22×C61C2×C4⋊Q811yescharacteristic
243C2×D61—21no—
244C2×D61—21no—
245C2×D61—24no—
246C2×D61—24no—
247C2×D61#39512yes—
248C2×D61#39512yes—
249C2×D61#45312yes—
250C2×D61#45612yes—
251C4×C61—24no—
252C4×C61—42no—
253C4×C61—42no—
254C4×C61—42no—
255C4×C61—81no—
256C4×C61C2×C22⋊Q812yes—
257C4×C61C2×C4⋊Q812yes—
258Dic61—24no—
259Dic61—42no—
260Dic61—42no—
261Dic61—42no—
262Dic61—81no—
263Dic61#39514yes—
264C2×#544—611no—
265C2×#428—612no—
266C2×#384—611no—
267#2060—612no—
268#2060—611no—
269#2060—611no—
270#2060—612no—
271#2060—611no—
272#2060D6111yescharacteristic, direct product factor
273C2×#343—611no—
274C2×#339—612no—
275C2×C61—21no—
276C2×C61—21no—
277C2×C61C2×#39511yescharacteristic
278C2×C61C2×#45311yescharacteristic
279C2×C61C2×#45611yescharacteristic
280D61—22no—
281D61#206014yesdirect product factor
282C22×M16—612no—
283#544—612no—
284#544—611no—
285#544—1222no—
286#544—1222no—
287#544—1222no—
288#544C2×D6111yescharacteristic
289C2×C4⋊Q8—1222no—
290C2×#125—1222no—
291C2×C22⋊Q8—1222no—
292C2×#117—612no—
293C22×C4⋊C4—611no—
294C22×C4⋊C4—611no—
295C22×C4⋊C4—1222no—
296C22×C42—611no—
297#428—612no—
298#428—612no—
299#428—612no—
300#428—1222no—
301#428—1222no—
302#428C2×D6112yes—
303C2×#107—1222no—
304C2×#106—1222no—
305#384—611no—
306#384—611no—
307#384—611no—
308#384—1222no—
309#384C2×D6111yescharacteristic
310#343—612no—
311#343—611no—
312#343C2×D6111yescharacteristic
313#339—612no—
314#339—612no—
315#339—612no—
316#339C2×D6112yes—
317C61C2×#206011yescharacteristic, complemented, Sylow
318C22×Q8—1222no—
319C23×C4—611no—
320C23×C4—612no—
321C23×C4—1221no—
322C23×C4—1221no—
323C2×M16—612no—
324C2×M16—618no—
325C2×M16—1222no—
326C2×M16—1224no—
327C2×M16C22×D6112yes—
328C22×C8—1222no—
329C4⋊Q8—22no—
330C4⋊Q8—1222no—
331C4⋊Q8—1222no—
332C4⋊Q8—1224no—
333C4⋊Q8—1224no—
334C4⋊Q8—1222no—
335#125—22no—
336#125—1222no—
337#125—1222no—
338#125—1224no—
339#125—1224no—
340#125—1222no—
341C22⋊Q8—22no—
342C22⋊Q8—1224no—
343C22⋊Q8—1224no—
344C22⋊Q8—1222no—
345C22⋊Q8—1222no—
346C22⋊Q8—1222no—
347#117—612no—
348#117—612no—
349#117—612no—
350#117—1222no—
351#117—1222no—
352#117C22×D6112yes—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—612no—
355C2×C4⋊C4—612no—
356C2×C4⋊C4—612no—
357C2×C4⋊C4—611no—
358C2×C4⋊C4—611no—
359C2×C4⋊C4—1222no—
360C2×C4⋊C4—1222no—
361C2×C4⋊C4—1222no—
362C2×C4⋊C4—1224no—
363C2×C4⋊C4—1222no—
364C2×C4⋊C4—1222no—
365C2×C4⋊C4—1221no—
366C2×C4⋊C4—1222no—
367C2×C4⋊C4—1222no—
368C2×C4⋊C4—1222no—
369C2×C4⋊C4—2448no—
370C2×C4⋊C4C22×D6111yescharacteristic
371C2×C4⋊C4C22×D6111yescharacteristic
372C2×C22⋊C4—1222no—
373C2×C42—611no—
374C2×C42—614no—
375C2×C42—1222no—
376C2×C42—1222no—
377C2×C42—1221no—
378C2×C42C22×D6111yescharacteristic
379#107—22no—
380#107—1222no—
381#107—1222no—
382#107—1222no—
383#106—22no—
384#106—1222no—
385#106—1222no—
386#106—1222no—
387C24—611no—
388C2×Q8—22no—
389C2×Q8—1224no—
390C2×Q8—1222no—
391C2×Q8—4884no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—611no—
395C22×C4—612no—
396C22×C4—612no—
397C22×C4—612no—
398C22×C4—614no—
399C22×C4—612no—
400C22×C4—612no—
401C22×C4—1224no—
402C22×C4—1224no—
403C22×C4—1224no—
404C22×C4—1222no—
405C22×C4—1222no—
406C22×C4—1222no—
407C22×C4—1222no—
408C22×C4—1221no—
409C22×C4—1221no—
410C22×C4—2441no—
411C22×C4—2441no—
412C22×C4—2444no—
413C22×C4—2444no—
414C22×C4D4×D6112yes—
415C22×C4C23×D6111yescharacteristic
416M16—22no—
417M16—614no—
418M16—1228no—
419M16—1222no—
420M16Q8×D6114yescomplemented
421C2×C8—22no—
422C2×C8—1228no—
423C2×C8—1222no—
424C4⋊C4—22no—
425C4⋊C4—24no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—44no—
429C4⋊C4—612no—
430C4⋊C4—612no—
431C4⋊C4—1224no—
432C4⋊C4—1222no—
433C4⋊C4—1222no—
434C4⋊C4—1224no—
435C4⋊C4—1224no—
436C4⋊C4—1224no—
437C4⋊C4—1222no—
438C4⋊C4—1224no—
439C4⋊C4—1222no—
440C4⋊C4—1222no—
441C4⋊C4—2444no—
442C4⋊C4—2442no—
443C4⋊C4—2444no—
444C4⋊C4—2444no—
445C4⋊C4D4×D6112yes—
446C4⋊C4D4×D6112yes—
447C22⋊C4—22no—
448C22⋊C4—1222no—
449C22⋊C4—1222no—
450C22⋊C4—1222no—
451C42—22no—
452C42—21no—
453C42—612no—
454C42—1224no—
455C42—1222no—
456C42—1222no—
457C42—1222no—
458C42—1221no—
459C42Q8×D6112yescomplemented
460C23—611no—
461C23—611no—
462C23—612no—
463C23—612no—
464C23—1222no—
465C23—1222no—
466C23C2×D4×D6111yescharacteristic
467Q8—82no—
468Q8—4882no—
469Q8—4884no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—612no—
480C2×C4—612no—
481C2×C4—612no—
482C2×C4—614no—
483C2×C4—614no—
484C2×C4—614no—
485C2×C4—614no—
486C2×C4—12216no—
487C2×C4—1222no—
488C2×C4—1222no—
489C2×C4—1222no—
490C2×C4—1222no—
491C2×C4—1222no—
492C2×C4—1222no—
493C2×C4—4882no—
494C2×C4—4882no—
495C2×C4—4882no—
496C2×C4—2444no—
497C2×C4—2444no—
498C2×C4—2444no—
499C2×C4—2442no—
500C2×C4—2441no—
501C2×C4—2442no—
502C2×C4C2×D4×D6112yes—
503C2×C4C2×Q8×D6112yes—
504C2×C4C2×Q8×D6111yescharacteristic
505C2×C4#41×D6111yescharacteristic
506C8—24no—
507C8—1224no—
508C22—21no—
509C22—21no—
510C22—612no—
511C22—612no—
512C22—612no—
513C22—612no—
514C22—1224no—
515C22—1224no—
516C22—1221no—
517C22—1221no—
518C22#120×D6111yescharacteristic
519C22C22⋊Q8×D6111yescharacteristic
520C22C4⋊Q8×D6111yescharacteristic
521C4—24no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—81no—
526C4—614no—
527C4—1224no—
528C4—4881no—
529C4—2442no—
530C4—2442no—
531C4—2442no—
532C4C22⋊Q8×D6112yes—
533C4C4⋊Q8×D6112yes—
534C2—21no—
535C2—21no—
536C2—614no—
537C2—1222no—
538C2#395×D6111yescharacteristic
539C2#453×D6111yescharacteristic
540C2#456×D6111yescharacteristic
subgroupG/H
centerC22#120×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2060C2
socleC22×C61C2×#120
prime radicalC23×D61C2×D4
hypercenter#2060D61
hypocenterC61C2×#2060
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2060

Complements

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

NH ≅ G/Ntype
4. #21447165C2semidirect
5. #21447164C2semidirect
6. #21447163C2semidirect
7. #21447162C2semidirect
8. #21447161C2semidirect
11. C61×#2060C2semidirect
55. M16×D61Q8semidirect
98. C42×D61Q8semidirect
146. M16×C61C2×Q8semidirect
158. C42×C61C2×Q8semidirect
183. C4×Dic61C2×Q8semidirect
185. #11758194C2×Q8semidirect
272. #2060D61direct (N × H)
281. D61#2060direct (N × H)
317. C61C2×#2060semidirect
420. M16Q8×D61semidirect
459. C42Q8×D61semidirect

Maximal subgroups

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

subgroupindex
#544×D612
#428×D612
#384×D612
#214471652
#214471642
#214471632
#214471622
#214471612
#343×D612
#339×D612
C61×#20602
C2×#206061