Subgroups — C₂×C₃²×C₁₇×C₇₃ #36375239

Order 22338.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇×C₇₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₁₇×C₇₃	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₁₇×C₇₃	C₂×C₃	1	4	yes	direct product factor
4	C₂×C₁₇×C₇₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₃²×C₇₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₇×C₇₃	C₂×C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₇₃	C₂×C₁₇	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₇₃	C₃×C₁₇	1	4	yes	direct product factor
9	C₂×C₃²×C₁₇	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₇₃	C₂×C₃×C₁₇	1	4	yes	direct product factor
11	C₃²×C₁₇	C₂×C₇₃	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₇₃	C₃²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₁₇	C₃×C₇₃	1	4	yes	direct product factor
14	C₇₃	C₂×C₃²×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₁₇	C₂×C₃×C₇₃	1	4	yes	direct product factor
16	C₂×C₁₇	C₃²×C₇₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃²	C₁₇×C₇₃	1	1	yes	characteristic, direct product factor, Hall
18	C₁₇	C₂×C₃²×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₃²	C₂×C₁₇×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	C₃×C₁₇×C₇₃	1	4	yes	direct product factor
21	C₃	C₂×C₃×C₁₇×C₇₃	1	4	yes	direct product factor
22	C₂	C₃²×C₁₇×C₇₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₇×C₇₃	C₂	direct (N × H)
2. C₂×C₃×C₁₇×C₇₃	C₃	direct (N × H)
3. C₃×C₁₇×C₇₃	C₂×C₃	direct (N × H)
4. C₂×C₁₇×C₇₃	C₃²	direct (N × H)
5. C₂×C₃²×C₇₃	C₁₇	direct (N × H)
6. C₁₇×C₇₃	C₂×C₃²	direct (N × H)
7. C₃²×C₇₃	C₂×C₁₇	direct (N × H)
8. C₂×C₃×C₇₃	C₃×C₁₇	direct (N × H)
9. C₂×C₃²×C₁₇	C₇₃	direct (N × H)
10. C₃×C₇₃	C₂×C₃×C₁₇	direct (N × H)
11. C₃²×C₁₇	C₂×C₇₃	direct (N × H)
12. C₂×C₇₃	C₃²×C₁₇	direct (N × H)
13. C₂×C₃×C₁₇	C₃×C₇₃	direct (N × H)
14. C₇₃	C₂×C₃²×C₁₇	direct (N × H)
15. C₃×C₁₇	C₂×C₃×C₇₃	direct (N × H)
16. C₂×C₁₇	C₃²×C₇₃	direct (N × H)
17. C₂×C₃²	C₁₇×C₇₃	direct (N × H)
18. C₁₇	C₂×C₃²×C₇₃	direct (N × H)
19. C₃²	C₂×C₁₇×C₇₃	direct (N × H)
20. C₂×C₃	C₃×C₁₇×C₇₃	direct (N × H)
21. C₃	C₂×C₃×C₁₇×C₇₃	direct (N × H)
22. C₂	C₃²×C₁₇×C₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₇×C₇₃	2
C₂×C₃×C₁₇×C₇₃	3
C₂×C₃²×C₇₃	17
C₂×C₃²×C₁₇	73

Subgroups — C2×C32×C17×C73 #36375239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₁₇×C₇₃ #36375239