Finite Group Databasebeta

← D61×#2220 #29834467

Subgroups — D61×#2220 #29834467

Order 15616.

734 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD32×D61C211yesmaximal, characteristic, complemented
2C2×M32×D61C211yesmaximal, characteristic, complemented
3#467×D61C211yesmaximal, characteristic, complemented
4#466×D61C211yesmaximal, characteristic
5#21447935C211yesmaximal, characteristic, complemented
6#21447934C211yesmaximal, characteristic, complemented
7#21447933C211yesmaximal, characteristic, complemented
8#21447932C211yesmaximal, characteristic, complemented
9#21447931C211yesmaximal, characteristic, complemented
10#21447930C211yesmaximal, characteristic, complemented
11#21447929C211yesmaximal, characteristic, complemented
12#366×D61C211yesmaximal, characteristic, complemented
13#358×D61C211yesmaximal, characteristic, complemented
14#357×D61C211yesmaximal, characteristic, complemented
15C61×#2220C211yesmaximal, characteristic, complemented
16C2×Q16×D61C2211yescharacteristic
17C2×D8×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C22⋊Q8×D61—21no—
20#121×D61—21no—
21C2×#14519722C2211yescharacteristic, complemented
22C2×#14519721C2211yescharacteristic, complemented
23C2×#14519720C2211yescharacteristic, complemented
24SD32×D61—24no—
25C2×#14519717C2211yescharacteristic, complemented
26C2×#14519716C2211yescharacteristic, complemented
27C2×#14519716C2211yescharacteristic, complemented
28M32×D61—24no—
29C2×C16×D61C2211yescharacteristic
30C2×C16×D61C2211yescharacteristic
31#16840004C2211yescharacteristic, complemented
32#16840003C2211yescharacteristic, complemented
33#16840002—21no—
34#16840001—21no—
35#16840000C2211yescharacteristic, complemented
36#16839999C2211yescharacteristic
37#16839998C2211yescharacteristic
38#16839997—21no—
39#16839996—21no—
40#16839995C2211yescharacteristic
41#107×D61C2211yescharacteristic
42#107×D61C2211yescharacteristic
43#103×D61—21no—
44#102×D61—21no—
45#16839588C2211yescharacteristic, complemented
46#16839587C2211yescharacteristic, complemented
47#16839587C2211yescharacteristic, complemented
48#16839567C2211yescharacteristic, complemented
49#16839566C2211yescharacteristic, complemented
50#16839565C2211yescharacteristic, complemented
51#16839564C2211yescharacteristic, complemented
52#16839563C2211yescharacteristic, complemented
53#16839562C2211yescharacteristic, complemented
54C2×SD32×C61C2211yescharacteristic, complemented
55C2×M32×C61C2211yescharacteristic, complemented
56C61×#467C2211yescharacteristic, complemented
57C61×#466C2211yescharacteristic
58C61×#366C2211yescharacteristic, complemented
59C61×#358C2211yescharacteristic, complemented
60C61×#357C2211yescharacteristic, complemented
61C2×Q8×D61—21no—
62C2×D4×D61—21no—
63C2×D4×D61—41no—
64C22×C4×D61D411yescharacteristic
65C2×Dic244C2311yescharacteristic
66C2×#11758202—21no—
67Q16×D61—22no—
68Q16×D61—22no—
69C2×D488C2311yescharacteristic
70C2×#11758199—21no—
71D8×D61—22no—
72D8×D61—22no—
73C22×#92418D411yescharacteristic
74C2×C8×D61—22no—
75C2×C8×D61—22no—
76C2×C8×D61D411yescharacteristic
77C2×C8×D61D411yescharacteristic
78C2×C8×D61C2311yescharacteristic
79C2×C8×D61C2311yescharacteristic
80#14519757—21no—
81#14519756—21no—
82#14519755—41no—
83#14519754—41no—
84#14519753—21no—
85#14519752—21no—
86#14519751—21no—
87#14519750—41no—
88#14519749—41no—
89#14519748—21no—
90C4⋊C4×D61—21no—
91C4⋊C4×D61—21no—
92C4⋊C4×D61—41no—
93C22⋊C4×D61—41no—
94C22⋊C4×D61—41no—
95#14519722—22no—
96#14519721—22no—
97#14519720—22no—
98#14519717—22no—
99#14519716—22no—
100#14519716—22no—
101C2×#11758185C2311yescharacteristic
102C2×#11758185C2311yescharacteristic
103C16×D61—22no—
104C16×D61D414yescomplemented
105#14519711C2311yescharacteristic
106#14519711C2311yescharacteristic
107#14519710—21no—
108#14519710—21no—
109#14519702—21no—
110#14519701—21no—
111#14519700—21no—
112#14519699—21no—
113#14519698—21no—
114#14519697—21no—
115C2×Q16×C61C2311yescharacteristic
116C2×D8×C61C2311yescharacteristic
117C22×C8×C61C2311yescharacteristic
118C22⋊Q8×C61—21no—
119#121×C61—21no—
120SD32×C61—22no—
121M32×C61—22no—
122C2×C16×C61C2311yescharacteristic
123C2×C16×C61C2311yescharacteristic
124#107×C61C2311yescharacteristic
125#107×C61C2311yescharacteristic
126#103×C61—21no—
127#102×C61—21no—
128C23×D61—41no—
129C23×D61D811yescharacteristic
130C2×Q8×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61—41no—
133C22×C4×C61C2×D411yescharacteristic
134C2×C22⋊D61—41no—
135C2×C22⋊D61—41no—
136C2×C22⋊D61—41no—
137C22×Dic61D811yescharacteristic
138Q8×D61—42no—
139Q8×D61—42no—
140D4×D61—42no—
141D4×D61—42no—
142D4×D61—84no—
143C2×D244—21no—
144C2×D244—41no—
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61—41no—
148C2×C4×D61—41no—
149C2×C4×D61—41no—
150C2×C4×D61D811yescharacteristic
151C2×C4×D61D811yescharacteristic
152C2×C4×D61C2×D411yescharacteristic
153C2×C4×D61C2×D411yescharacteristic
154C2×Dic122—21no—
155C2×Dic122—41no—
156Q16×C61—21no—
157Q16×C61—21no—
158D8×C61—21no—
159D8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61C2×D411yescharacteristic
163C2×C8×C61C2411yescharacteristic
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—41no—
167C22⋊C4×C61—41no—
168C22⋊C4×C61—41no—
169C22⋊Dic61—41no—
170C22⋊Dic61—41no—
171#11758202—42no—
172#11758199—42no—
173#11758198—41no—
174#11758198—41no—
175#11758198—41no—
176#11758198—41no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—41no—
180#11758196—41no—
181#11758196—41no—
182#11758196—41no—
183#11758196—41no—
184C2×#92418—22no—
185C2×#92418C2×D411yescharacteristic
186C2×#92418C2×D411yescharacteristic
187Dic244—21no—
188Dic244—21no—
189D488—21no—
190D488—21no—
191C8×D61—22no—
192C8×D61—21no—
193C8×D61—21no—
194C8×D61—22no—
195C8×D61C2×D412yes—
196C8×D61#4112yes—
197C16×C61—21no—
198C16×C61C2×D412yescomplemented
199#11758185—21no—
200#11758185C2×D412yescomplemented
201C23×C61—41no—
202C23×C61C2×D811yescharacteristic
203C22×D61—22no—
204C22×D61—22no—
205C22×D61—22no—
206C22×D61—41no—
207C22×D61—82no—
208C22×D61—82no—
209C22×D61—82no—
210C22×D61C2×D811yescharacteristic
211C22×D61C2×D811yescharacteristic
212Q8×C61—41no—
213Q8×C61—41no—
214D4×C61—41no—
215D4×C61—41no—
216D4×C61—82no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61C2×D811yescharacteristic
223C2×C4×C61C22×D411yescharacteristic
224C22⋊D61—82no—
225C22⋊D61—82no—
226C22⋊D61—82no—
227C2×Dic61—22no—
228C2×Dic61—41no—
229C2×Dic61—41no—
230C2×Dic61—41no—
231C2×Dic61C2×D811yescharacteristic
232C2×Dic61C2×D811yescharacteristic
233D244—41no—
234D244—41no—
235D244—82no—
236C4×D61—22no—
237C4×D61—21no—
238C4×D61—21no—
239C4×D61—22no—
240C4×D61—82no—
241C4×D61—82no—
242C4×D61—82no—
243C4×D61#12112yes—
244C4×D61#13512yes—
245Dic122—41no—
246Dic122—41no—
247Dic122—82no—
248C8×C61—21no—
249C8×C61C22×D411yescharacteristic
250C8×C61C2×#4111yescharacteristic
251#92418—21no—
252#92418#12112yes—
253C2×#2220—611nomaximal, Sylow
254C22×C61—21no—
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—81no—
258C22×C61—81no—
259C22×C61—81no—
260C22×C61C22×D811yescharacteristic
261C2×D61—21no—
262C2×D61—21no—
263C2×D61—21no—
264C2×D61—44no—
265C2×D61—81no—
266C2×D61—81no—
267C2×D61—81no—
268C2×D61—164no—
269C2×D61#46612yes—
270C2×D61#50912yes—
271C2×D61#51012yes—
272C4×C61—21no—
273C4×C61—81no—
274C4×C61—81no—
275C4×C61—81no—
276C4×C61C2×#12111yescharacteristic
277C4×C61C2×#13511yescharacteristic
278Dic61—21no—
279Dic61—81no—
280Dic61—81no—
281Dic61—81no—
282Dic61#46612yes—
283C22×SD32—611no—
284C22×M32—611no—
285C2×#467—611no—
286C2×#466—611no—
287#2220—611no—
288#2220—611no—
289#2220—611no—
290#2220—611no—
291#2220—611no—
292#2220—611no—
293#2220—611no—
294#2220D6111yescharacteristic, direct product factor
295C2×#366—611no—
296C2×#358—611no—
297C2×#357—611no—
298C2×C61—41no—
299C2×C61—161no—
300C2×C61C2×#46611yescharacteristic
301C2×C61C2×#50911yescharacteristic
302C2×C61C2×#51011yescharacteristic
303D61—41no—
304D61—161no—
305D61#222014yesdirect product factor
306C22×Q16—611no—
307C22×D8—611no—
308C23×C8—611no—
309C2×C22⋊Q8—1221no—
310C2×#121—1221no—
311C2×SD32—611no—
312C2×SD32—611no—
313C2×SD32—611no—
314C2×SD32—1224no—
315C2×SD32C2×D6111yescharacteristic, complemented
316C2×M32—611no—
317C2×M32—611no—
318C2×M32—611no—
319C2×M32—1224no—
320C2×M32C2×D6111yescharacteristic, complemented
321C22×C16—611no—
322C22×C16—611no—
323#467—611no—
324#467—611no—
325#467—611no—
326#467—1221no—
327#467—1221no—
328#467C2×D6111yescharacteristic, complemented
329#466—611no—
330#466—611no—
331#466—611no—
332#466—1221no—
333#466—1221no—
334#466C2×D6111yescharacteristic
335C2×#107—611no—
336C2×#107—611no—
337C2×#103—1221no—
338C2×#102—1221no—
339#366—611no—
340#366—611no—
341#366—611no—
342#366C2×D6111yescharacteristic, complemented
343#358—611no—
344#358—611no—
345#358—611no—
346#358C2×D6111yescharacteristic, complemented
347#357—611no—
348#357—611no—
349#357—611no—
350#357C2×D6111yescharacteristic, complemented
351C61C2×#222011yescharacteristic, complemented, Sylow
352C22×Q8—1221no—
353C22×D4—1221no—
354C22×D4—2441no—
355C23×C4—611no—
356C2×Q16—611no—
357C2×Q16—1222no—
358C2×Q16—1222no—
359C2×Q16—1221no—
360C2×Q16C22×D6111yescharacteristic
361C2×D8—611no—
362C2×D8—1222no—
363C2×D8—1222no—
364C2×D8—1221no—
365C2×D8C22×D6111yescharacteristic
366C22×C8—611no—
367C22×C8—611no—
368C22×C8—611no—
369C22×C8—611no—
370C22×C8—611no—
371C22×C8—1222no—
372C22×C8—1222no—
373C22×C8C22×D6111yescharacteristic
374C22⋊Q8—21no—
375C22⋊Q8—1221no—
376C22⋊Q8—1221no—
377C22⋊Q8—1221no—
378C22⋊Q8—2441no—
379C22⋊Q8—2441no—
380#121—21no—
381#121—1221no—
382#121—1221no—
383#121—1221no—
384#121—2441no—
385#121—2441no—
386C2×C4⋊C4—1221no—
387C2×C4⋊C4—1221no—
388C2×C4⋊C4—2441no—
389C2×C22⋊C4—2441no—
390C2×C22⋊C4—2441no—
391SD32—22no—
392SD32—1222no—
393SD32—1222no—
394SD32—1222no—
395M32—22no—
396M32—1222no—
397M32—1222no—
398M32—1222no—
399C2×C16—611no—
400C2×C16—614no—
401C2×C16—611no—
402C2×C16—1222no—
403C2×C16C22×D6111yescharacteristic
404C2×C16C22×D6111yescharacteristic
405#107—611no—
406#107—611no—
407#107—1221no—
408#107—1221no—
409#107C22×D6111yescharacteristic
410#107C22×D6111yescharacteristic
411#103—21no—
412#103—1221no—
413#103—1221no—
414#103—1221no—
415#102—21no—
416#102—1221no—
417#102—1221no—
418#102—1221no—
419C24—611no—
420C24—2441no—
421C2×Q8—21no—
422C2×Q8—1221no—
423C2×Q8—2441no—
424C2×Q8—2442no—
425C2×Q8—2442no—
426C2×D4—21no—
427C2×D4—41no—
428C2×D4—1221no—
429C2×D4—4884no—
430C2×D4—2441no—
431C2×D4—2442no—
432C2×D4—2442no—
433C2×D4—2441no—
434C2×D4—2441no—
435C2×D4—2441no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—1222no—
442C22×C4—1222no—
443C22×C4—2441no—
444C22×C4—2441no—
445C22×C4—2441no—
446C22×C4D4×D6111yescharacteristic
447Q16—21no—
448Q16—21no—
449Q16—1221no—
450Q16—1221no—
451Q16—2442no—
452D8—21no—
453D8—21no—
454D8—1221no—
455D8—1221no—
456D8—2442no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—611no—
460C2×C8—612no—
461C2×C8—612no—
462C2×C8—611no—
463C2×C8—1222no—
464C2×C8—1222no—
465C2×C8—1222no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8D4×D6111yescharacteristic
469C2×C8C23×D6111yescharacteristic
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—41no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—2441no—
476C4⋊C4—2441no—
477C4⋊C4—2441no—
478C4⋊C4—2441no—
479C4⋊C4—2441no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—2441no—
483C22⋊C4—2441no—
484C22⋊C4—2441no—
485C22⋊C4—2441no—
486C22⋊C4—2441no—
487C22⋊C4—2441no—
488C16—21no—
489C16—612no—
490C16—1221no—
491C16D4×D6112yescomplemented
492C23—41no—
493C23—611no—
494C23—611no—
495C23—1222no—
496C23—1222no—
497C23—1222no—
498C23—4882no—
499C23—4882no—
500C23—4882no—
501C23—2441no—
502C23D8×D6111yescharacteristic
503Q8—41no—
504Q8—41no—
505Q8—4882no—
506Q8—2441no—
507Q8—2441no—
508D4—41no—
509D4—41no—
510D4—82no—
511D4—4882no—
512D4—4882no—
513D4—4882no—
514D4—4882no—
515D4—2441no—
516D4—2441no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—611no—
523C2×C4—612no—
524C2×C4—612no—
525C2×C4—611no—
526C2×C4—1222no—
527C2×C4—1222no—
528C2×C4—1222no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—4882no—
532C2×C4—4882no—
533C2×C4—4882no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4D8×D6111yescharacteristic
538C2×C4C2×D4×D6111yescharacteristic
539C8—21no—
540C8—612no—
541C8—1221no—
542C8C2×D4×D6111yescharacteristic
543C8#41×D6111yescharacteristic
544C22—21no—
545C22—21no—
546C22—21no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22—612no—
551C22—612no—
552C22—612no—
553C22—1221no—
554C22—1221no—
555C22—1221no—
556C22—9764no—
557C22—4881no—
558C22—4881no—
559C22—4881no—
560C22—2444no—
561C22C2×D8×D6111yescharacteristic
562C4—21no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—612no—
567C4—1221no—
568C4—4881no—
569C4—4881no—
570C4—4881no—
571C4#121×D6111yescharacteristic
572C4#135×D6111yescharacteristic
573C2—41no—
574C2—161no—
575C2—614no—
576C2—9761no—
577C2—2441no—
578C2#466×D6111yescharacteristic
579C2#509×D6111yescharacteristic
580C2#510×D6111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2220C2
socleC22×C61C22×D8
prime radical#466×D61C2
hypercenter#2220D61
hypocenterC61C2×#2220
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2220

Complements

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

NH ≅ G/Ntype
1. C2×SD32×D61C2semidirect
2. C2×M32×D61C2semidirect
3. #467×D61C2semidirect
5. #21447935C2semidirect
6. #21447934C2semidirect
7. #21447933C2semidirect
8. #21447932C2semidirect
9. #21447931C2semidirect
10. #21447930C2semidirect
11. #21447929C2semidirect
12. #366×D61C2semidirect
13. #358×D61C2semidirect
14. #357×D61C2semidirect
15. C61×#2220C2semidirect
21. C2×#14519722C22semidirect
22. C2×#14519721C22semidirect
23. C2×#14519720C22semidirect
25. C2×#14519717C22semidirect
26. C2×#14519716C22semidirect
27. C2×#14519716C22semidirect
31. #16840004C22semidirect
32. #16840003C22semidirect
35. #16840000C22semidirect
45. #16839588C22semidirect
46. #16839587C22semidirect
47. #16839587C22semidirect
48. #16839567C22semidirect
49. #16839566C22semidirect
50. #16839565C22semidirect
51. #16839564C22semidirect
52. #16839563C22semidirect
53. #16839562C22semidirect
54. C2×SD32×C61C22semidirect
55. C2×M32×C61C22semidirect
56. C61×#467C22semidirect
58. C61×#366C22semidirect
59. C61×#358C22semidirect
60. C61×#357C22semidirect
104. C16×D61D4semidirect
198. C16×C61C2×D4semidirect
200. #11758185C2×D4semidirect
294. #2220D61direct (N × H)
305. D61#2220direct (N × H)
315. C2×SD32C2×D61semidirect
320. C2×M32C2×D61semidirect
328. #467C2×D61semidirect
342. #366C2×D61semidirect
346. #358C2×D61semidirect
350. #357C2×D61semidirect
351. C61C2×#2220semidirect
491. C16D4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×SD32×D612
C2×M32×D612
#467×D612
#466×D612
#214479352
#214479342
#214479332
#214479322
#214479312
#214479302
#214479292
#366×D612
#358×D612
#357×D612
C61×#22202
C2×#222061