Subgroups — C₂×C₉×C₁₇×C₆₇ #35206142

Order 20502.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₇×C₆₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₁₇×C₆₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₇×C₆₇	C₂×C₃	1	1	yes	characteristic
4	C₂×C₁₇×C₆₇	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₉×C₆₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₇×C₆₇	C₂×C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₉×C₆₇	C₂×C₁₇	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₆₇	C₃×C₁₇	1	1	yes	characteristic
9	C₂×C₉×C₁₇	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₆₇	C₂×C₃×C₁₇	1	1	yes	characteristic
11	C₉×C₁₇	C₂×C₆₇	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₆₇	C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₁₇	C₃×C₆₇	1	1	yes	characteristic
14	C₆₇	C₂×C₉×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₁₇	C₂×C₃×C₆₇	1	1	yes	characteristic
16	C₂×C₁₇	C₉×C₆₇	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₉	C₁₇×C₆₇	1	1	yes	characteristic, direct product factor, Hall
18	C₁₇	C₂×C₉×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₉	C₂×C₁₇×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	C₃×C₁₇×C₆₇	1	1	yes	characteristic
21	C₃	C₂×C₃×C₁₇×C₆₇	1	1	yes	characteristic
22	C₂	C₉×C₁₇×C₆₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₁₇×C₆₇
socle, prime radical	C₂×C₃×C₁₇×C₆₇	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×C₁₇×C₆₇	C₂	direct (N × H)
4. C₂×C₁₇×C₆₇	C₉	direct (N × H)
5. C₂×C₉×C₆₇	C₁₇	direct (N × H)
6. C₁₇×C₆₇	C₂×C₉	direct (N × H)
7. C₉×C₆₇	C₂×C₁₇	direct (N × H)
9. C₂×C₉×C₁₇	C₆₇	direct (N × H)
11. C₉×C₁₇	C₂×C₆₇	direct (N × H)
12. C₂×C₆₇	C₉×C₁₇	direct (N × H)
14. C₆₇	C₂×C₉×C₁₇	direct (N × H)
16. C₂×C₁₇	C₉×C₆₇	direct (N × H)
17. C₂×C₉	C₁₇×C₆₇	direct (N × H)
18. C₁₇	C₂×C₉×C₆₇	direct (N × H)
19. C₉	C₂×C₁₇×C₆₇	direct (N × H)
22. C₂	C₉×C₁₇×C₆₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×C₁₇×C₆₇	2
C₂×C₃×C₁₇×C₆₇	3
C₂×C₉×C₆₇	17
C₂×C₉×C₁₇	67

Subgroups — C2×C9×C17×C67 #35206142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₁₇×C₆₇ #35206142