Finite Group Databasebeta

← D61×#2213 #29834389

Subgroups — D61×#2213 #29834389

Order 15616.

790 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#509×D61C212yesmaximal, complemented
2#493×D61C211yesmaximal, characteristic, complemented
3#443×D61C211yesmaximal, characteristic, complemented
4#21447896C211yesmaximal, characteristic, complemented
5#21447895C211yesmaximal, characteristic, complemented
6#21447894C212yesmaximal, complemented
7#21447893C212yesmaximal, complemented
8#21447892C211yesmaximal, characteristic, complemented
9#364×D61C211yesmaximal, characteristic, complemented
10#361×D61C212yesmaximal, complemented
11C61×#2213C211yesmaximal, characteristic, complemented
12#135×D61C2211yescharacteristic
13C2×D8×D61—21no—
14C2×D8×D61C2212yes—
15#131×D61—21no—
16#127×D61—21no—
17#16840200C2212yescomplemented
18#16840199—22no—
19#16840198C2212yescomplemented
20#16840197C2212yescomplemented
21#16840196—22no—
22SD32×D61—22no—
23D16×D61—22no—
24M32×D61C2212yes—
25#16840139C2211yescharacteristic, complemented
26#16840138—21no—
27#16840137—21no—
28#16840137C2212yescomplemented
29#16839880C2211yescharacteristic, complemented
30#16839879C2211yescharacteristic, complemented
31#16839878C2211yescharacteristic, complemented
32#16839877—21no—
33#16839876—21no—
34#108×D61C2211yescharacteristic
35#104×D61—21no—
36C4×C8×D61C2211yescharacteristic
37#16839583C2211yescharacteristic, complemented
38#16839582C2212yescomplemented
39#16839576C2212yescomplemented
40#16839575C2212yescomplemented
41#16839574C2212yescomplemented
42C61×#509C2212yescomplemented
43C61×#493C2211yescharacteristic, complemented
44C61×#443C2211yescharacteristic, complemented
45C61×#364C2211yescharacteristic, complemented
46C61×#361C2212yescomplemented
47#41×D61—21no—
48C2×D4×D61—22no—
49C2×D4×D61—42no—
50#14519800D411yescharacteristic, complemented
51#14519799C2311yescharacteristic
52#14519798—21no—
53#14519797—21no—
54#14519796D411yescharacteristic, complemented
55Q16×D61D411yescharacteristic, complemented
56SD16×D61—21no—
57C2×D488—21no—
58C2×D488C2312yes—
59C2×#11758199—22no—
60C2×#11758199—22no—
61D8×D61—22no—
62D8×D61—22no—
63D8×D61—22no—
64D8×D61—22no—
65D8×D61—41no—
66D8×D61—41no—
67D8×D61—41no—
68D8×D61—41no—
69D8×D61D411yescharacteristic, complemented
70#14519785—21no—
71#14519785—41no—
72#14519784—21no—
73#14519783—21no—
74#14519783—41no—
75M16×D61—21no—
76M16×D61—41no—
77C2×C8×D61—41no—
78C2×C8×D61D411yescharacteristic
79C2×C8×D61C2311yescharacteristic
80#14519774—21no—
81#14519773—22no—
82#14519773—42no—
83C42×D61D411yescharacteristic
84#14519722—22no—
85#14519721—22no—
86#14519720—22no—
87D976—22no—
88#14519718—22no—
89#14519718—22no—
90#14519717C2312yes—
91#14519716—22no—
92C16×D61—22no—
93#14519713C2311yescharacteristic
94#14519712—21no—
95#14519705—21no—
96#14519704—21no—
97#14519703—21no—
98C4×#92418D411yescharacteristic
99C8×Dic61D411yescharacteristic
100C8×Dic61C2311yescharacteristic
101#135×C61C2311yescharacteristic
102C2×D8×C61—21no—
103C2×D8×C61C2312yes—
104#131×C61—21no—
105#127×C61—21no—
106SD32×C61—22no—
107D16×C61—22no—
108M32×C61C2312yes—
109#108×C61C2311yescharacteristic
110#104×C61—21no—
111C4×C8×C61C2311yescharacteristic
112C23×D61—42no—
113#41×C61—21no—
114C2×D4×C61—22no—
115C2×D4×C61—42no—
116C2×C22⋊D61—44no—
117C2×C22⋊D61—42no—
118#11758226—21no—
119Q8×D61—21no—
120#11758224—21no—
121#11758224—41no—
122D4×D61—21no—
123D4×D61—41no—
124D4×D61—42no—
125D4×D61—42no—
126D4×D61—42no—
127D4×D61—42no—
128D4×D61—88no—
129#11758222—21no—
130#11758222—41no—
131C2×D244—22no—
132C2×D244—42no—
133C2×C4×D61—21no—
134C2×C4×D61—41no—
135C2×C4×D61C2×D411yescharacteristic
136Q16×C61C2×D411yescharacteristic, complemented
137SD16×C61—21no—
138D8×C61—22no—
139D8×C61—22no—
140D8×C61—41no—
141D8×C61—41no—
142D8×C61C2×D411yescharacteristic, complemented
143M16×C61—21no—
144M16×C61—41no—
145C2×C8×C61—41no—
146C2×C8×C61C2×D411yescharacteristic
147C2×C8×C61C2411yescharacteristic
148C42×C61C2×D411yescharacteristic
149#11758202—21no—
150#11758201—21no—
151#11758200—21no—
152#11758199—21no—
153#11758199—42no—
154#11758199—42no—
155#11758199—42no—
156#11758199—42no—
157C4×Dic61—21no—
158C4×Dic61C2×D411yescharacteristic
159#11758194—21no—
160#11758194—41no—
161C2×#92418—41no—
162C2×#92418C2×D411yescharacteristic
163C2×#92418C2×D411yescharacteristic
164Dic244C2×D411yescharacteristic, complemented
165D488—22no—
166D488—22no—
167D488—41no—
168D488—41no—
169D488C2×D411yescharacteristic, complemented
170#11758190—21no—
171#11758189—41no—
172#11758189—41no—
173#11758189—41no—
174C8×D61—41no—
175C8×D61—41no—
176C8×D61—41no—
177C8×D61D811yescharacteristic
178C8×D61D811yescharacteristic
179C8×D61D811yescharacteristic
180C8×D61D811yescharacteristic
181C8×D61C2×D411yescharacteristic
182C8×D61C2×D411yescharacteristic
183C8×D61#4111yescharacteristic
184C8×D61#4111yescharacteristic
185C16×C61—22no—
186#11758185—22no—
187C23×C61—42no—
188C22×D61—41no—
189C22×D61—42no—
190C22×D61—88no—
191C22×D61—82no—
192C22×D61—82no—
193C22×D61AGL(1,ℤ/8)11yescharacteristic
194Q8×C61—21no—
195D4×C61—21no—
196D4×C61—41no—
197D4×C61—42no—
198D4×C61—42no—
199D4×C61—84no—
200C2×C4×C61—21no—
201C2×C4×C61—41no—
202C2×C4×C61C22×D411yescharacteristic
203C22⋊D61—41no—
204C22⋊D61—41no—
205C22⋊D61—41no—
206C22⋊D61—88no—
207C22⋊D61—82no—
208C22⋊D61—82no—
209C2×Dic61—21no—
210C2×Dic61—41no—
211C2×Dic61AGL(1,ℤ/8)11yescharacteristic
212D244—21no—
213D244—41no—
214D244—42no—
215D244—42no—
216D244—84no—
217C4×D61—24no—
218C4×D61—41no—
219C4×D61—41no—
220C4×D61—41no—
221C4×D61#12111yescharacteristic
222C4×D61#12111yescharacteristic
223C4×D61C2×D811yescharacteristic
224C4×D61C2×D811yescharacteristic
225Dic122—21no—
226Dic122—41no—
227C8×C61—41no—
228C8×C61C2×D811yescharacteristic
229C8×C61C2×D811yescharacteristic
230C8×C61C22×D411yescharacteristic
231C8×C61C2×#4111yescharacteristic
232#92418—41no—
233#92418#12111yescharacteristic
234#92418#12111yescharacteristic
235#92418C2×D811yescharacteristic
236#92418C2×D811yescharacteristic
237C2×#2213—611nomaximal, Sylow
238C22×C61—41no—
239C22×C61—84no—
240C22×C61—82no—
241C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
242C2×D61—22no—
243C2×D61—41no—
244C2×D61—82no—
245C2×D61—84no—
246C2×D61—82no—
247C2×D61—164no—
248C2×D61—164no—
249C2×D61#45911yescharacteristic
250C2×D61#45911yescharacteristic
251C4×C61—22no—
252C4×C61—41no—
253C4×C61C2×#12111yescharacteristic
254C4×C61C22×D811yescharacteristic
255Dic61—22no—
256Dic61—41no—
257Dic61#45911yescharacteristic
258Dic61#45911yescharacteristic
259C2×#509—612no—
260C2×#493—611no—
261C2×#443—611no—
262#2213—612no—
263#2213—611no—
264#2213—611no—
265#2213—611no—
266#2213—612no—
267#2213D6111yescharacteristic, direct product factor
268C2×#364—611no—
269C2×#361—612no—
270C2×C61—21no—
271C2×C61—81no—
272C2×C61—162no—
273C2×C61C2×#45911yescharacteristic
274D61—21no—
275D61—81no—
276D61—162no—
277D61#221312yesdirect product factor
278C2×#135—611no—
279C22×D8—612no—
280C22×D8—1221no—
281C2×#131—1221no—
282C2×#127—1221no—
283#509—612no—
284#509—612no—
285#509—612no—
286#509—1222no—
287#509—1222no—
288#509C2×D6112yescomplemented
289C2×SD32—1222no—
290C2×D16—1222no—
291C2×M32—612no—
292#493—612no—
293#493—611no—
294#493—1221no—
295#493—1221no—
296#493C2×D6111yescharacteristic, complemented
297#443—611no—
298#443—611no—
299#443—611no—
300#443—1221no—
301#443—1221no—
302#443C2×D6111yescharacteristic, complemented
303C2×#108—611no—
304C2×#104—1221no—
305C2×C4×C8—611no—
306#364—612no—
307#364—611no—
308#364C2×D6111yescharacteristic, complemented
309#361—612no—
310#361—612no—
311#361—612no—
312#361C2×D6112yescomplemented
313C61C2×#221311yescharacteristic, complemented, Sylow
314C2×#41—1221no—
315C22×D4—1222no—
316C22×D4—2442no—
317#135—611no—
318#135—611no—
319#135—611no—
320#135—1221no—
321#135—1221no—
322#135C22×D6111yescharacteristic
323C2×Q16—611no—
324C2×SD16—1221no—
325C2×D8—21no—
326C2×D8—611no—
327C2×D8—612no—
328C2×D8—1222no—
329C2×D8—1222no—
330C2×D8—1222no—
331C2×D8—1222no—
332C2×D8—1222no—
333C2×D8—1222no—
334C2×D8—1221no—
335C2×D8—2441no—
336C2×D8—2441no—
337C2×D8—2441no—
338C2×D8—2441no—
339C2×D8C22×D6112yes—
340#131—21no—
341#131—1221no—
342#131—1221no—
343#131—1221no—
344#131—2441no—
345#131—2441no—
346C2×M16—1221no—
347C2×M16—2441no—
348C22×C8—611no—
349C22×C8—611no—
350C22×C8—2441no—
351#127—21no—
352#127—1222no—
353#127—1221no—
354#127—2442no—
355C2×C42—611no—
356SD32—22no—
357SD32—1222no—
358SD32—1222no—
359SD32—1222no—
360D16—22no—
361D16—1222no—
362D16—1222no—
363D16—1222no—
364M32—612no—
365M32—1222no—
366M32C22×D6112yes—
367C2×C16—1222no—
368#108—611no—
369#108—1221no—
370#108C22×D6111yescharacteristic
371#104—21no—
372#104—1221no—
373#104—1221no—
374#104—1221no—
375C4×C8—611no—
376C4×C8—611no—
377C4×C8—611no—
378C4×C8C22×D6111yescharacteristic
379C24—2442no—
380#41—21no—
381#41—1221no—
382#41—1221no—
383#41—1221no—
384#41—2441no—
385#41—2441no—
386C2×Q8—1221no—
387C2×D4—22no—
388C2×D4—42no—
389C2×D4—1221no—
390C2×D4—1222no—
391C2×D4—4888no—
392C2×D4—2442no—
393C2×D4—2442no—
394C2×D4—2442no—
395C2×D4—2442no—
396C2×D4—2442no—
397C2×D4—2442no—
398C2×D4—2444no—
399C2×D4—2441no—
400C22×C4—611no—
401C22×C4—1221no—
402C22×C4—2441no—
403Q16—611no—
404Q16—1221no—
405Q16D4×D6111yescharacteristic, complemented
406SD16—21no—
407SD16—1221no—
408SD16—1221no—
409SD16—1221no—
410D8—22no—
411D8—22no—
412D8—41no—
413D8—41no—
414D8—611no—
415D8—1221no—
416D8—1222no—
417D8—1222no—
418D8—2442no—
419D8—2442no—
420D8—2442no—
421D8—2442no—
422D8—2441no—
423D8—2441no—
424D8D4×D6111yescharacteristic, complemented
425M16—21no—
426M16—41no—
427M16—1221no—
428M16—2441no—
429M16—2441no—
430M16—2441no—
431M16—2441no—
432C2×C8—41no—
433C2×C8—611no—
434C2×C8—611no—
435C2×C8—611no—
436C2×C8—611no—
437C2×C8—611no—
438C2×C8—611no—
439C2×C8—611no—
440C2×C8—611no—
441C2×C8—611no—
442C2×C8—611no—
443C2×C8—2441no—
444C2×C8—2441no—
445C2×C8—2441no—
446C2×C8—2441no—
447C2×C8D4×D6111yescharacteristic
448C2×C8C23×D6111yescharacteristic
449C42—611no—
450C42—1221no—
451C42D4×D6111yescharacteristic
452C16—22no—
453C16—1222no—
454C23—42no—
455C23—611no—
456C23—4882no—
457C23—4882no—
458C23—4888no—
459C23—2441no—
460C23—2442no—
461Q8—21no—
462Q8—1221no—
463Q8—2441no—
464D4—21no—
465D4—41no—
466D4—42no—
467D4—42no—
468D4—84no—
469D4—1221no—
470D4—4884no—
471D4—4882no—
472D4—4882no—
473D4—4888no—
474D4—2441no—
475D4—2441no—
476D4—2441no—
477D4—2441no—
478D4—2442no—
479D4—2442no—
480C2×C4—21no—
481C2×C4—41no—
482C2×C4—611no—
483C2×C4—611no—
484C2×C4—611no—
485C2×C4—611no—
486C2×C4—611no—
487C2×C4—1224no—
488C2×C4—1221no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4C2×D4×D6111yescharacteristic
494C8—41no—
495C8—611no—
496C8—611no—
497C8—611no—
498C8—611no—
499C8—2441no—
500C8D8×D6111yescharacteristic
501C8D8×D6111yescharacteristic
502C8C2×D4×D6111yescharacteristic
503C8#41×D6111yescharacteristic
504C22—41no—
505C22—84no—
506C22—82no—
507C22—611no—
508C22—611no—
509C22—1222no—
510C22—9764no—
511C22—9764no—
512C22—4884no—
513C22—4882no—
514C22—4882no—
515C22—2441no—
516C22AGL(1,ℤ/8)×D6111yescharacteristic
517C4—22no—
518C4—41no—
519C4—611no—
520C4—611no—
521C4—1222no—
522C4—2441no—
523C4#121×D6111yescharacteristic
524C4C2×D8×D6111yescharacteristic
525C2—21no—
526C2—81no—
527C2—162no—
528C2—612no—
529C2—1221no—
530C2—9762no—
531C2—4881no—
532C2#459×D6111yescharacteristic
subgroupG/H
centerC2#459×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2213C2
socleC2×C61C2×#459
hypercenter#2213D61
hypocenterC61C2×#2213
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2213

Complements

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

NH ≅ G/Ntype
1. #509×D61C2semidirect
2. #493×D61C2semidirect
3. #443×D61C2semidirect
4. #21447896C2semidirect
5. #21447895C2semidirect
6. #21447894C2semidirect
7. #21447893C2semidirect
8. #21447892C2semidirect
9. #364×D61C2semidirect
10. #361×D61C2semidirect
11. C61×#2213C2semidirect
17. #16840200C22semidirect
19. #16840198C22semidirect
20. #16840197C22semidirect
25. #16840139C22semidirect
28. #16840137C22semidirect
29. #16839880C22semidirect
30. #16839879C22semidirect
31. #16839878C22semidirect
37. #16839583C22semidirect
38. #16839582C22semidirect
39. #16839576C22semidirect
40. #16839575C22semidirect
41. #16839574C22semidirect
42. C61×#509C22semidirect
43. C61×#493C22semidirect
44. C61×#443C22semidirect
45. C61×#364C22semidirect
46. C61×#361C22semidirect
50. #14519800D4semidirect
54. #14519796D4semidirect
55. Q16×D61D4semidirect
69. D8×D61D4semidirect
136. Q16×C61C2×D4semidirect
142. D8×C61C2×D4semidirect
164. Dic244C2×D4semidirect
169. D488C2×D4semidirect
267. #2213D61direct (N × H)
277. D61#2213direct (N × H)
288. #509C2×D61semidirect
296. #493C2×D61semidirect
302. #443C2×D61semidirect
308. #364C2×D61semidirect
312. #361C2×D61semidirect
313. C61C2×#2213semidirect
405. Q16D4×D61semidirect
424. D8D4×D61semidirect

Maximal subgroups

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

subgroupindex
#509×D612
#493×D612
#443×D612
#214478962
#214478952
#214478942
#214478932
#214478922
#364×D612
#361×D612
C61×#22132
C2×#221361