Subgroups — C₂×C₃×C₄×C₁₇×C₆₁ #72202136

Order 24888.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₇×C₆₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂²×C₃×C₁₇×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×C₁₇×C₆₁	C₂	1	2	yes	maximal, direct product factor
4	C₂×C₃×C₁₇×C₆₁	C₄	1	2	yes	direct product factor
5	C₂×C₃×C₁₇×C₆₁	C₂²	1	1	yes	characteristic
6	C₂²×C₁₇×C₆₁	C₂×C₃	1	1	yes	characteristic
7	C₄×C₁₇×C₆₁	C₂×C₃	1	2	yes	direct product factor
8	C₃×C₁₇×C₆₁	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₁₇×C₆₁	C₃×C₄	1	2	yes	direct product factor
10	C₂×C₁₇×C₆₁	C₂²×C₃	1	1	yes	characteristic
11	C₂×C₃×C₄×C₆₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₇×C₆₁	C₂×C₃×C₄	1	1	yes	characteristic, direct product factor, Hall
13	C₂²×C₃×C₆₁	C₂×C₁₇	1	1	yes	characteristic
14	C₃×C₄×C₆₁	C₂×C₁₇	1	2	yes	direct product factor
15	C₂×C₄×C₆₁	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃×C₄×C₁₇	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₆₁	C₄×C₁₇	1	2	yes	direct product factor
18	C₂×C₃×C₆₁	C₂²×C₁₇	1	1	yes	characteristic
19	C₂²×C₆₁	C₂×C₃×C₁₇	1	1	yes	characteristic
20	C₄×C₆₁	C₂×C₃×C₁₇	1	2	yes	direct product factor
21	C₂²×C₃×C₁₇	C₂×C₆₁	1	1	yes	characteristic
22	C₃×C₄×C₁₇	C₂×C₆₁	1	2	yes	direct product factor
23	C₃×C₆₁	C₂×C₄×C₁₇	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₄×C₁₇	C₃×C₆₁	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₆₁	C₃×C₄×C₁₇	1	2	yes	direct product factor
26	C₂×C₆₁	C₂²×C₃×C₁₇	1	1	yes	characteristic
27	C₂×C₃×C₁₇	C₄×C₆₁	1	2	yes	direct product factor
28	C₂×C₃×C₁₇	C₂²×C₆₁	1	1	yes	characteristic
29	C₂²×C₁₇	C₂×C₃×C₆₁	1	1	yes	characteristic
30	C₄×C₁₇	C₂×C₃×C₆₁	1	2	yes	direct product factor
31	C₆₁	C₂×C₃×C₄×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
32	C₃×C₁₇	C₂×C₄×C₆₁	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₁₇	C₃×C₄×C₆₁	1	2	yes	direct product factor
34	C₂×C₁₇	C₂²×C₃×C₆₁	1	1	yes	characteristic
35	C₂×C₃×C₄	C₁₇×C₆₁	1	1	yes	characteristic, direct product factor, Hall
36	C₁₇	C₂×C₃×C₄×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
37	C₂²×C₃	C₂×C₁₇×C₆₁	1	1	yes	characteristic
38	C₃×C₄	C₂×C₁₇×C₆₁	1	2	yes	direct product factor
39	C₂×C₄	C₃×C₁₇×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃	C₄×C₁₇×C₆₁	1	2	yes	direct product factor
41	C₂×C₃	C₂²×C₁₇×C₆₁	1	1	yes	characteristic
42	C₂²	C₂×C₃×C₁₇×C₆₁	1	1	yes	characteristic
43	C₄	C₂×C₃×C₁₇×C₆₁	1	2	yes	direct product factor
44	C₃	C₂×C₄×C₁₇×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	C₃×C₄×C₁₇×C₆₁	1	2	yes	direct product factor
46	C₂	C₂²×C₃×C₁₇×C₆₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃×C₁₇×C₆₁
socle, prime radical	C₂²×C₃×C₁₇×C₆₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₁₇×C₆₁	C₃	direct (N × H)
3. C₃×C₄×C₁₇×C₆₁	C₂	direct (N × H)
4. C₂×C₃×C₁₇×C₆₁	C₄	direct (N × H)
7. C₄×C₁₇×C₆₁	C₂×C₃	direct (N × H)
8. C₃×C₁₇×C₆₁	C₂×C₄	direct (N × H)
9. C₂×C₁₇×C₆₁	C₃×C₄	direct (N × H)
11. C₂×C₃×C₄×C₆₁	C₁₇	direct (N × H)
12. C₁₇×C₆₁	C₂×C₃×C₄	direct (N × H)
14. C₃×C₄×C₆₁	C₂×C₁₇	direct (N × H)
15. C₂×C₄×C₆₁	C₃×C₁₇	direct (N × H)
16. C₂×C₃×C₄×C₁₇	C₆₁	direct (N × H)
17. C₂×C₃×C₆₁	C₄×C₁₇	direct (N × H)
20. C₄×C₆₁	C₂×C₃×C₁₇	direct (N × H)
22. C₃×C₄×C₁₇	C₂×C₆₁	direct (N × H)
23. C₃×C₆₁	C₂×C₄×C₁₇	direct (N × H)
24. C₂×C₄×C₁₇	C₃×C₆₁	direct (N × H)
25. C₂×C₆₁	C₃×C₄×C₁₇	direct (N × H)
27. C₂×C₃×C₁₇	C₄×C₆₁	direct (N × H)
30. C₄×C₁₇	C₂×C₃×C₆₁	direct (N × H)
31. C₆₁	C₂×C₃×C₄×C₁₇	direct (N × H)
32. C₃×C₁₇	C₂×C₄×C₆₁	direct (N × H)
33. C₂×C₁₇	C₃×C₄×C₆₁	direct (N × H)
35. C₂×C₃×C₄	C₁₇×C₆₁	direct (N × H)
36. C₁₇	C₂×C₃×C₄×C₆₁	direct (N × H)
38. C₃×C₄	C₂×C₁₇×C₆₁	direct (N × H)
39. C₂×C₄	C₃×C₁₇×C₆₁	direct (N × H)
40. C₂×C₃	C₄×C₁₇×C₆₁	direct (N × H)
43. C₄	C₂×C₃×C₁₇×C₆₁	direct (N × H)
44. C₃	C₂×C₄×C₁₇×C₆₁	direct (N × H)
45. C₂	C₃×C₄×C₁₇×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×C₄×C₁₇×C₆₁	3
C₂²×C₃×C₁₇×C₆₁	2
C₃×C₄×C₁₇×C₆₁	2
C₂×C₃×C₄×C₆₁	17
C₂×C₃×C₄×C₁₇	61

Subgroups — C2×C3×C4×C17×C61 #72202136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄×C₁₇×C₆₁ #72202136