Finite Group Databasebeta

← D61×#2210 #29834245

Subgroups — D61×#2210 #29834245

Order 15616.

786 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD32×D61C211yesmaximal, characteristic, complemented
2C2×D16×D61C211yesmaximal, characteristic
3#495×D61C211yesmaximal, characteristic, complemented
4C4×D8×D61C211yesmaximal, characteristic, complemented
5#21447877C211yesmaximal, characteristic, complemented
6#21447876C211yesmaximal, characteristic, complemented
7#21447875C211yesmaximal, characteristic, complemented
8#21447874C211yesmaximal, characteristic, complemented
9#21447873C211yesmaximal, characteristic, complemented
10#21447872C211yesmaximal, characteristic, complemented
11#21447871C211yesmaximal, characteristic, complemented
12C4⋊C16×D61C211yesmaximal, characteristic, complemented
13#358×D61C211yesmaximal, characteristic, complemented
14#357×D61C211yesmaximal, characteristic, complemented
15C61×#2210C211yesmaximal, characteristic, complemented
16C2×Q16×D61C2211yescharacteristic
17C2×SD16×D61—21no—
18C2×D8×D61C2211yescharacteristic
19C2×D8×D61C2211yescharacteristic
20#124×D61—21no—
21C4×D4×D61—21no—
22C2×#14519722C2211yescharacteristic, complemented
23C2×#14519721C2211yescharacteristic, complemented
24C2×#14519720C2211yescharacteristic, complemented
25SD32×D61—24no—
26C2×D976C2211yescharacteristic
27C2×#14519718C2211yescharacteristic
28C2×#14519718C2211yescharacteristic
29D16×D61—24no—
30C2×C16×D61C2211yescharacteristic
31C2×C16×D61C2211yescharacteristic
32#16840147C2211yescharacteristic, complemented
33#16840146C2211yescharacteristic, complemented
34#16840145C2211yescharacteristic, complemented
35#16840144—21no—
36#16840143—21no—
37C4×D488C2211yescharacteristic, complemented
38D8×Dic61C2211yescharacteristic, complemented
39#16839844C2211yescharacteristic, complemented
40C4×#11758199—21no—
41#16839842—21no—
42#107×D61C2211yescharacteristic
43#102×D61—21no—
44C4×C8×D61C2211yescharacteristic
45C4⋊#11758185C2211yescharacteristic, complemented
46#16839580C2211yescharacteristic, complemented
47#16839580C2211yescharacteristic, complemented
48#16839567C2211yescharacteristic, complemented
49#16839566C2211yescharacteristic, complemented
50#16839565C2211yescharacteristic, complemented
51#16839564C2211yescharacteristic, complemented
52#16839563C2211yescharacteristic, complemented
53#16839562C2211yescharacteristic, complemented
54C2×SD32×C61C2211yescharacteristic, complemented
55C2×D16×C61C2211yescharacteristic
56C61×#495C2211yescharacteristic, complemented
57C4×D8×C61C2211yescharacteristic, complemented
58C61×C4⋊C16C2211yescharacteristic, complemented
59C61×#358C2211yescharacteristic, complemented
60C61×#357C2211yescharacteristic, complemented
61C2×Q8×D61—21no—
62C2×D4×D61—21no—
63C2×D4×D61—21no—
64C22×C4×D61—41no—
65C2×Dic244C2311yescharacteristic
66C2×#11758202—21no—
67Q16×D61—22no—
68Q16×D61—22no—
69C2×#11758190—21no—
70C2×#11758200—21no—
71C2×#11758201—21no—
72SD16×D61—44no—
73C2×D488C2311yescharacteristic
74C2×D488C2311yescharacteristic
75C2×#11758199—21no—
76C2×#11758199—21no—
77D8×D61—22no—
78D8×D61—22no—
79D8×D61—22no—
80D8×D61D414yes—
81C2×C8×D61D411yescharacteristic
82C2×C8×D61C2311yescharacteristic
83#14519766—21no—
84#14519765—21no—
85#14519764—21no—
86#14519763—41no—
87#14519763—41no—
88C4×D244—21no—
89D4×Dic61—21no—
90#14519739—21no—
91C4×C22⋊D61—41no—
92#14519737—41no—
93C4⋊C4×D61—21no—
94C22⋊C4×D61—41no—
95C22⋊C4×D61—41no—
96C22⋊C4×D61—41no—
97C42×D61D411yescharacteristic
98#14519722—22no—
99#14519721—22no—
100#14519720—22no—
101D976—22no—
102#14519718—22no—
103#14519718—22no—
104C2×#11758185C2311yescharacteristic
105C2×#11758185C2311yescharacteristic
106C16×D61—22no—
107C16×D61—22no—
108#14519711C2311yescharacteristic
109#14519710—21no—
110#14519699—21no—
111#14519698—21no—
112#14519697—21no—
113C4×#92418D411yescharacteristic
114C8×Dic61D411yescharacteristic
115C8×Dic61C2311yescharacteristic
116C2×Q16×C61C2311yescharacteristic
117C2×SD16×C61—21no—
118C2×D8×C61C2311yescharacteristic
119C2×D8×C61C2311yescharacteristic
120#124×C61—21no—
121C4×D4×C61—21no—
122SD32×C61—22no—
123D16×C61—22no—
124C2×C16×C61C2311yescharacteristic
125C2×C16×C61C2311yescharacteristic
126#107×C61C2311yescharacteristic
127#102×C61—21no—
128C4×C8×C61C2311yescharacteristic
129C23×D61—41no—
130C23×D61—41no—
131C2×Q8×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C22×C4×C61—41no—
135C2×C22⋊D61—41no—
136C2×C22⋊D61—41no—
137C22×Dic61—41no—
138Q8×D61—42no—
139Q8×D61—42no—
140D4×D61—24no—
141D4×D61—42no—
142D4×D61—42no—
143D4×D61—42no—
144C2×D244—21no—
145C2×D244—21no—
146C2×C4×D61—41no—
147C2×C4×D61—41no—
148C2×C4×D61—41no—
149C2×C4×D61—41no—
150C2×C4×D61—84no—
151C2×C4×D61D811yescharacteristic
152C2×C4×D61D811yescharacteristic
153C2×C4×D61C2×D411yescharacteristic
154C2×Dic122—21no—
155C2×Dic122—41no—
156Q16×C61—21no—
157Q16×C61—21no—
158SD16×C61—42no—
159D8×C61—21no—
160D8×C61—21no—
161D8×C61—21no—
162D8×C61C2×D412yes—
163C2×C8×C61C2×D411yescharacteristic
164C2×C8×C61C2411yescharacteristic
165C4⋊C4×C61—21no—
166C22⋊C4×C61—41no—
167C22⋊C4×C61—41no—
168C22⋊C4×C61—41no—
169C42×C61C2×D411yescharacteristic
170C22⋊Dic61—41no—
171C22⋊Dic61—41no—
172C22⋊Dic61—41no—
173#11758202—42no—
174#11758201—42no—
175#11758200—42no—
176#11758199—24no—
177#11758199—42no—
178#11758198—41no—
179#11758198—41no—
180#11758198—41no—
181#11758198—41no—
182#11758198—41no—
183#11758198—41no—
184C4⋊Dic61—21no—
185#11758196—41no—
186C4×Dic61D811yescharacteristic
187C4×Dic61D811yescharacteristic
188C4×Dic61C2×D411yescharacteristic
189C2×#92418C2×D411yescharacteristic
190C2×#92418C2×D411yescharacteristic
191Dic244—21no—
192Dic244—21no—
193D488—21no—
194D488—21no—
195D488—21no—
196D488C2×D412yes—
197#11758190—42no—
198C8×D61—22no—
199C8×D61C2×D412yes—
200C8×D61#4112yes—
201C16×C61—21no—
202C16×C61—21no—
203#11758185—21no—
204#11758185—21no—
205C23×C61—41no—
206C23×C61—41no—
207C22×D61—41no—
208C22×D61—44no—
209C22×D61—41no—
210C22×D61—82no—
211C22×D61—82no—
212C22×D61—82no—
213C22×D61—82no—
214C22×D61—82no—
215C22×D61C2×D811yescharacteristic
216Q8×C61—41no—
217Q8×C61—41no—
218D4×C61—22no—
219D4×C61—41no—
220D4×C61—41no—
221D4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—82no—
225C2×C4×C61C2×D811yescharacteristic
226C2×C4×C61C2×D811yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C22⋊D61—44no—
229C22⋊D61—82no—
230C2×Dic61—41no—
231C2×Dic61—41no—
232C2×Dic61—82no—
233C2×Dic61C2×D811yescharacteristic
234C2×Dic61C2×D811yescharacteristic
235C2×Dic61C2×D811yescharacteristic
236D244—22no—
237D244—41no—
238D244—41no—
239D244—41no—
240C4×D61—22no—
241C4×D61—22no—
242C4×D61—82no—
243C4×D61—82no—
244C4×D61—82no—
245C4×D61—82no—
246C4×D61#12112yes—
247C4×D61AGL(1,ℤ/8)12yes—
248Dic122—41no—
249Dic122—41no—
250Dic122—82no—
251C8×C61—21no—
252C8×C61C22×D411yescharacteristic
253C8×C61C2×#4111yescharacteristic
254#92418—21no—
255#92418#12112yes—
256C2×#2210—611nomaximal, Sylow
257C22×C61—42no—
258C22×C61—81no—
259C22×C61—81no—
260C22×C61—81no—
261C22×C61—81no—
262C22×C61—81no—
263C22×C61C22×D811yescharacteristic
264C2×D61—42no—
265C2×D61—81no—
266C2×D61—81no—
267C2×D61—88no—
268C2×D61—81no—
269C2×D61—81no—
270C2×D61—81no—
271C2×D61—164no—
272C2×D61#45912yes—
273C2×D61#50812yes—
274C2×D61#50912yes—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—81no—
278C4×C61—81no—
279C4×C61C2×#12111yescharacteristic
280C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
281Dic61—21no—
282Dic61—21no—
283Dic61—81no—
284Dic61—81no—
285Dic61#45912yes—
286C22×SD32—611no—
287C22×D16—611no—
288C2×#495—611no—
289C2×C4×D8—611no—
290#2210—611no—
291#2210—611no—
292#2210—611no—
293#2210—611no—
294#2210—611no—
295#2210—611no—
296#2210—611no—
297#2210D6111yescharacteristic, direct product factor
298C2×C4⋊C16—611no—
299C2×#358—611no—
300C2×#357—611no—
301C2×C61—82no—
302C2×C61—161no—
303C2×C61C2×#45911yescharacteristic
304C2×C61C2×#50811yescharacteristic
305C2×C61C2×#50911yescharacteristic
306D61—82no—
307D61—161no—
308D61#221014yesdirect product factor
309C22×Q16—611no—
310C22×SD16—1221no—
311C22×D8—611no—
312C22×D8—611no—
313C2×#124—1221no—
314C2×C4×D4—1221no—
315C2×SD32—611no—
316C2×SD32—611no—
317C2×SD32—611no—
318C2×SD32—1224no—
319C2×SD32C2×D6111yescharacteristic, complemented
320C2×D16—611no—
321C2×D16—611no—
322C2×D16—611no—
323C2×D16—1224no—
324C2×D16C2×D6111yescharacteristic
325C22×C16—611no—
326C22×C16—611no—
327#495—611no—
328#495—611no—
329#495—611no—
330#495—1221no—
331#495—1221no—
332#495C2×D6111yescharacteristic, complemented
333C4×D8—611no—
334C4×D8—611no—
335C4×D8—611no—
336C4×D8—1221no—
337C4×D8—1221no—
338C4×D8C2×D6111yescharacteristic, complemented
339C2×#107—611no—
340C2×#102—1221no—
341C2×C4×C8—611no—
342C4⋊C16—611no—
343C4⋊C16—611no—
344C4⋊C16—611no—
345C4⋊C16C2×D6111yescharacteristic, complemented
346#358—611no—
347#358—611no—
348#358—611no—
349#358C2×D6111yescharacteristic, complemented
350#357—611no—
351#357—611no—
352#357—611no—
353#357C2×D6111yescharacteristic, complemented
354C61C2×#221011yescharacteristic, complemented, Sylow
355C22×Q8—1221no—
356C22×D4—1221no—
357C22×D4—1221no—
358C23×C4—2441no—
359C2×Q16—611no—
360C2×Q16—1222no—
361C2×Q16—1222no—
362C2×Q16—1221no—
363C2×Q16C22×D6111yescharacteristic
364C2×SD16—21no—
365C2×SD16—1221no—
366C2×SD16—1221no—
367C2×SD16—1221no—
368C2×SD16—2444no—
369C2×D8—614no—
370C2×D8—611no—
371C2×D8—611no—
372C2×D8—1222no—
373C2×D8—1222no—
374C2×D8—1222no—
375C2×D8—1221no—
376C2×D8—1221no—
377C2×D8C22×D6111yescharacteristic
378C2×D8C22×D6111yescharacteristic
379C22×C8—611no—
380C22×C8—611no—
381#124—21no—
382#124—1221no—
383#124—1221no—
384#124—1221no—
385#124—2441no—
386#124—2441no—
387C4×D4—21no—
388C4×D4—1221no—
389C4×D4—1221no—
390C4×D4—1221no—
391C4×D4—2441no—
392C4×D4—2441no—
393C2×C4⋊C4—1221no—
394C2×C22⋊C4—2441no—
395C2×C22⋊C4—2441no—
396C2×C22⋊C4—2441no—
397C2×C42—611no—
398SD32—22no—
399SD32—1222no—
400SD32—1222no—
401SD32—1222no—
402D16—22no—
403D16—1222no—
404D16—1222no—
405D16—1222no—
406C2×C16—611no—
407C2×C16—611no—
408C2×C16—1222no—
409C2×C16—1222no—
410C2×C16C22×D6111yescharacteristic
411C2×C16C22×D6111yescharacteristic
412#107—611no—
413#107—1221no—
414#107C22×D6111yescharacteristic
415#102—21no—
416#102—1221no—
417#102—1221no—
418#102—1221no—
419C4×C8—611no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8C22×D6111yescharacteristic
423C24—2441no—
424C24—2441no—
425C2×Q8—21no—
426C2×Q8—1221no—
427C2×Q8—2441no—
428C2×Q8—2442no—
429C2×Q8—2442no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—1224no—
433C2×D4—1221no—
434C2×D4—1221no—
435C2×D4—2442no—
436C2×D4—2442no—
437C2×D4—2442no—
438C2×D4—2441no—
439C2×D4—2441no—
440C22×C4—41no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—4884no—
445C22×C4—2441no—
446C22×C4—2441no—
447C22×C4—2441no—
448C22×C4—2441no—
449C22×C4—2441no—
450Q16—21no—
451Q16—21no—
452Q16—1221no—
453Q16—1221no—
454Q16—2442no—
455SD16—42no—
456SD16—2442no—
457SD16—2442no—
458SD16—2442no—
459D8—21no—
460D8—21no—
461D8—21no—
462D8—612no—
463D8—1224no—
464D8—1221no—
465D8—1221no—
466D8—1221no—
467D8—2442no—
468D8D4×D6112yes—
469C2×C8—611no—
470C2×C8—612no—
471C2×C8—612no—
472C2×C8—611no—
473C2×C8—1222no—
474C2×C8D4×D6111yescharacteristic
475C2×C8C23×D6111yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—1221no—
478C4⋊C4—2441no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—2441no—
483C22⋊C4—2441no—
484C22⋊C4—2441no—
485C22⋊C4—2441no—
486C22⋊C4—2441no—
487C22⋊C4—2441no—
488C22⋊C4—2441no—
489C22⋊C4—2441no—
490C22⋊C4—2441no—
491C42—611no—
492C42—611no—
493C42—611no—
494C42D4×D6111yescharacteristic
495C16—21no—
496C16—21no—
497C16—1221no—
498C16—1221no—
499C23—41no—
500C23—41no—
501C23—611no—
502C23—4882no—
503C23—4882no—
504C23—4882no—
505C23—4882no—
506C23—4882no—
507C23—2444no—
508C23—2441no—
509C23—2441no—
510Q8—41no—
511Q8—41no—
512Q8—4882no—
513Q8—2441no—
514Q8—2441no—
515D4—22no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—1222no—
520D4—4882no—
521D4—2444no—
522D4—2441no—
523D4—2441no—
524D4—2441no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—611no—
529C2×C4—612no—
530C2×C4—612no—
531C2×C4—611no—
532C2×C4—611no—
533C2×C4—1222no—
534C2×C4—1222no—
535C2×C4—4882no—
536C2×C4—4882no—
537C2×C4—4882no—
538C2×C4—4882no—
539C2×C4—4882no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4D8×D6111yescharacteristic
543C2×C4D8×D6111yescharacteristic
544C2×C4C2×D4×D6111yescharacteristic
545C8—21no—
546C8—612no—
547C8—1221no—
548C8C2×D4×D6111yescharacteristic
549C8#41×D6111yescharacteristic
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—612no—
557C22—612no—
558C22—612no—
559C22—9764no—
560C22—4888no—
561C22—4881no—
562C22—4881no—
563C22—4881no—
564C22—4881no—
565C22—4881no—
566C22—2442no—
567C22C2×D8×D6111yescharacteristic
568C4—21no—
569C4—21no—
570C4—81no—
571C4—81no—
572C4—612no—
573C4—1221no—
574C4—1221no—
575C4—4881no—
576C4—4881no—
577C4#121×D6111yescharacteristic
578C4AGL(1,ℤ/8)×D6111yescharacteristic
579C2—82no—
580C2—161no—
581C2—614no—
582C2—9761no—
583C2—4882no—
584C2#459×D6111yescharacteristic
585C2#508×D6111yescharacteristic
586C2#509×D6111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2210C2
socleC22×C61C22×D8
prime radicalC2×D16×D61C2
hypercenter#2210D61
hypocenterC61C2×#2210
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2210

Complements

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

NH ≅ G/Ntype
1. C2×SD32×D61C2semidirect
3. #495×D61C2semidirect
4. C4×D8×D61C2semidirect
5. #21447877C2semidirect
6. #21447876C2semidirect
7. #21447875C2semidirect
8. #21447874C2semidirect
9. #21447873C2semidirect
10. #21447872C2semidirect
11. #21447871C2semidirect
12. C4⋊C16×D61C2semidirect
13. #358×D61C2semidirect
14. #357×D61C2semidirect
15. C61×#2210C2semidirect
22. C2×#14519722C22semidirect
23. C2×#14519721C22semidirect
24. C2×#14519720C22semidirect
32. #16840147C22semidirect
33. #16840146C22semidirect
34. #16840145C22semidirect
37. C4×D488C22semidirect
38. D8×Dic61C22semidirect
39. #16839844C22semidirect
45. C4⋊#11758185C22semidirect
46. #16839580C22semidirect
47. #16839580C22semidirect
48. #16839567C22semidirect
49. #16839566C22semidirect
50. #16839565C22semidirect
51. #16839564C22semidirect
52. #16839563C22semidirect
53. #16839562C22semidirect
54. C2×SD32×C61C22semidirect
56. C61×#495C22semidirect
57. C4×D8×C61C22semidirect
58. C61×C4⋊C16C22semidirect
59. C61×#358C22semidirect
60. C61×#357C22semidirect
297. #2210D61direct (N × H)
308. D61#2210direct (N × H)
319. C2×SD32C2×D61semidirect
332. #495C2×D61semidirect
338. C4×D8C2×D61semidirect
345. C4⋊C16C2×D61semidirect
349. #358C2×D61semidirect
353. #357C2×D61semidirect
354. C61C2×#2210semidirect

Maximal subgroups

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

subgroupindex
C2×SD32×D612
C2×D16×D612
#495×D612
C4×D8×D612
#214478772
#214478762
#214478752
#214478742
#214478732
#214478722
#214478712
C4⋊C16×D612
#358×D612
#357×D612
C61×#22102
C2×#221061