Subgroups — C₂×C₆₁×C₃⋊D₃₃ #37563570

Order 24156.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×C₃⋊D₃₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₁×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×D₃₃	—	3	4	no	maximal
4	C₃²×C₁₁×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₆₁×D₃₃	—	3	8	no	—
6	C₂×C₃×C₁₁×C₆₁	D₃	1	4	yes	complemented
7	C₂×D₁₁×C₆₁	—	9	1	no	Hall
8	C₂×C₃⋊D₃×C₆₁	—	11	1	no	maximal, Hall
9	C₃×C₁₁×C₆₁	C₂×D₃	1	4	yes	complemented
10	C₂×C₁₁×C₆₁	C₃⋊D₃	1	1	yes	characteristic, complemented
11	D₁₁×C₆₁	—	9	2	no	—
12	C₂×C₃²×C₆₁	D₁₁	1	1	yes	characteristic, complemented
13	C₃⋊D₃×C₆₁	—	11	2	no	—
14	C₂×D₃×C₆₁	—	33	4	no	—
15	C₁₁×C₆₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₆₁	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃⋊D₃₃	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂×C₃×C₆₁	D₃₃	1	4	yes	complemented
19	D₃×C₆₁	—	33	8	no	—
20	C₂²×C₆₁	—	99	1	no	Hall
21	C₂×C₃²×C₁₁	C₂×C₆₁	1	1	yes	characteristic, complemented
22	C₃⋊D₃₃	C₂×C₆₁	1	2	yes	direct product factor
23	C₃×C₆₁	C₂×D₃₃	1	4	yes	complemented
24	C₂×D₃₃	—	3	4	no	—
25	C₂×C₆₁	—	99	2	no	—
26	C₂×C₆₁	C₃⋊D₃₃	1	1	yes	characteristic, direct product factor
27	C₃²×C₁₁	C₂²×C₆₁	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₁	D₃×C₆₁	1	4	yes	complemented
29	D₃₃	—	3	8	no	—
30	C₆₁	C₂×C₃⋊D₃₃	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×D₁₁	—	9	1	no	Hall
32	C₂×C₃⋊D₃	—	11	1	no	Hall
33	C₃×C₁₁	C₂×D₃×C₆₁	1	4	yes	complemented
34	C₂×C₁₁	C₃⋊D₃×C₆₁	1	1	yes	characteristic, complemented
35	D₁₁	—	9	2	no	—
36	C₂×C₃²	D₁₁×C₆₁	1	1	yes	characteristic, complemented
37	C₃⋊D₃	—	11	2	no	—
38	C₂×D₃	—	33	4	no	—
39	C₁₁	C₂×C₃⋊D₃×C₆₁	1	1	yes	characteristic, complemented, Sylow
40	C₃²	C₂×D₁₁×C₆₁	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	C₆₁×D₃₃	1	4	yes	complemented
42	D₃	—	33	8	no	—
43	C₂²	—	99	1	no	Sylow
44	C₃	C₂×C₆₁×D₃₃	1	4	yes	complemented
45	C₂	—	99	2	no	—
46	C₂	C₆₁×C₃⋊D₃₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₆₁	C₃⋊D₃₃
commutator, cosocle, hypocenter	C₃²×C₁₁	C₂²×C₆₁
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₁×C₆₁	C₂
LCS	G ▷ C₃²×C₁₁
UCS	C₁ ◁ C₂×C₆₁

Complements

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

N	H ≅ G/N	type
1. C₆₁×C₃⋊D₃₃	C₂	direct (N × H)
2. C₂×C₃²×C₁₁×C₆₁	C₂	semidirect
4. C₃²×C₁₁×C₆₁	C₂²	semidirect
6. C₂×C₃×C₁₁×C₆₁	D₃	semidirect
9. C₃×C₁₁×C₆₁	C₂×D₃	semidirect
10. C₂×C₁₁×C₆₁	C₃⋊D₃	semidirect
12. C₂×C₃²×C₆₁	D₁₁	semidirect
15. C₁₁×C₆₁	C₂×C₃⋊D₃	semidirect
16. C₃²×C₆₁	C₂×D₁₁	semidirect
17. C₂×C₃⋊D₃₃	C₆₁	direct (N × H)
18. C₂×C₃×C₆₁	D₃₃	semidirect
21. C₂×C₃²×C₁₁	C₂×C₆₁	semidirect
22. C₃⋊D₃₃	C₂×C₆₁	direct (N × H)
23. C₃×C₆₁	C₂×D₃₃	semidirect
26. C₂×C₆₁	C₃⋊D₃₃	direct (N × H)
27. C₃²×C₁₁	C₂²×C₆₁	semidirect
28. C₂×C₃×C₁₁	D₃×C₆₁	semidirect
30. C₆₁	C₂×C₃⋊D₃₃	direct (N × H)
33. C₃×C₁₁	C₂×D₃×C₆₁	semidirect
34. C₂×C₁₁	C₃⋊D₃×C₆₁	semidirect
36. C₂×C₃²	D₁₁×C₆₁	semidirect
39. C₁₁	C₂×C₃⋊D₃×C₆₁	semidirect
40. C₃²	C₂×D₁₁×C₆₁	semidirect
41. C₂×C₃	C₆₁×D₃₃	semidirect
44. C₃	C₂×C₆₁×D₃₃	semidirect
46. C₂	C₆₁×C₃⋊D₃₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×C₃⋊D₃₃	2
C₂×C₃²×C₁₁×C₆₁	2
C₂×C₆₁×D₃₃	3
C₂×C₃⋊D₃×C₆₁	11
C₂×C₃⋊D₃₃	61

Subgroups — C2×C61×C3⋊D33 #37563570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×C₃⋊D₃₃ #37563570