Subgroups — C₂²×C₉×C₁₁×C₆₁ #37563455

Order 24156.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₁×C₆₁	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₁₁×C₆₁	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₁×C₆₁	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₁×C₆₁	C₂×C₃	1	3	yes	—
5	C₂²×C₁₁×C₆₁	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₂²×C₉×C₆₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₁₁×C₆₁	C₂²×C₃	1	1	yes	characteristic
8	C₂×C₁₁×C₆₁	C₂×C₉	1	3	yes	direct product factor
9	C₂×C₉×C₆₁	C₂×C₁₁	1	3	yes	direct product factor
10	C₂²×C₃×C₆₁	C₃×C₁₁	1	1	yes	characteristic
11	C₁₁×C₆₁	C₂²×C₉	1	1	yes	characteristic, direct product factor, Hall
12	C₉×C₆₁	C₂²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
13	C₂²×C₉×C₁₁	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₆₁	C₂×C₃×C₁₁	1	3	yes	—
15	C₂²×C₆₁	C₉×C₁₁	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₉×C₁₁	C₂×C₆₁	1	3	yes	direct product factor
17	C₃×C₆₁	C₂²×C₃×C₁₁	1	1	yes	characteristic
18	C₂²×C₃×C₁₁	C₃×C₆₁	1	1	yes	characteristic
19	C₂×C₆₁	C₂×C₉×C₁₁	1	3	yes	direct product factor
20	C₉×C₁₁	C₂²×C₆₁	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃×C₁₁	C₂×C₃×C₆₁	1	3	yes	—
22	C₆₁	C₂²×C₉×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
23	C₂²×C₁₁	C₉×C₆₁	1	1	yes	characteristic, direct product factor, Hall
24	C₂²×C₉	C₁₁×C₆₁	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₁₁	C₂²×C₃×C₆₁	1	1	yes	characteristic
26	C₂×C₁₁	C₂×C₉×C₆₁	1	3	yes	direct product factor
27	C₂×C₉	C₂×C₁₁×C₆₁	1	3	yes	direct product factor
28	C₂²×C₃	C₃×C₁₁×C₆₁	1	1	yes	characteristic
29	C₁₁	C₂²×C₉×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₉	C₂²×C₁₁×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₂×C₃×C₁₁×C₆₁	1	3	yes	—
32	C₂²	C₉×C₁₁×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₂²×C₃×C₁₁×C₆₁	1	1	yes	characteristic
34	C₂	C₂×C₉×C₁₁×C₆₁	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂²×C₃×C₁₁×C₆₁
socle, prime radical	C₂²×C₃×C₁₁×C₆₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×C₁₁×C₆₁	C₂	direct (N × H)
3. C₉×C₁₁×C₆₁	C₂²	direct (N × H)
5. C₂²×C₁₁×C₆₁	C₉	direct (N × H)
6. C₂²×C₉×C₆₁	C₁₁	direct (N × H)
8. C₂×C₁₁×C₆₁	C₂×C₉	direct (N × H)
9. C₂×C₉×C₆₁	C₂×C₁₁	direct (N × H)
11. C₁₁×C₆₁	C₂²×C₉	direct (N × H)
12. C₉×C₆₁	C₂²×C₁₁	direct (N × H)
13. C₂²×C₉×C₁₁	C₆₁	direct (N × H)
15. C₂²×C₆₁	C₉×C₁₁	direct (N × H)
16. C₂×C₉×C₁₁	C₂×C₆₁	direct (N × H)
19. C₂×C₆₁	C₂×C₉×C₁₁	direct (N × H)
20. C₉×C₁₁	C₂²×C₆₁	direct (N × H)
22. C₆₁	C₂²×C₉×C₁₁	direct (N × H)
23. C₂²×C₁₁	C₉×C₆₁	direct (N × H)
24. C₂²×C₉	C₁₁×C₆₁	direct (N × H)
26. C₂×C₁₁	C₂×C₉×C₆₁	direct (N × H)
27. C₂×C₉	C₂×C₁₁×C₆₁	direct (N × H)
29. C₁₁	C₂²×C₉×C₆₁	direct (N × H)
30. C₉	C₂²×C₁₁×C₆₁	direct (N × H)
32. C₂²	C₉×C₁₁×C₆₁	direct (N × H)
34. C₂	C₂×C₉×C₁₁×C₆₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×C₁₁×C₆₁	2
C₂²×C₃×C₁₁×C₆₁	3
C₂²×C₉×C₆₁	11
C₂²×C₉×C₁₁	61

Subgroups — C22×C9×C11×C61 #37563455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₉×C₁₁×C₆₁ #37563455