Finite Group Databasebeta

← C₂×C₃⁴×C₁₅₁ #72201732

Subgroups — C₂×C₃⁴×C₁₅₁ #72201732

Order 24462.

848 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₁₅₁	C₃	1	40	yes	maximal, direct product factor
2	C₃⁴×C₁₅₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃³×C₁₅₁	C₂×C₃	1	40	yes	direct product factor
4	C₂×C₃²×C₁₅₁	C₃²	1	130	yes	direct product factor
5	C₃²×C₁₅₁	C₂×C₃²	1	130	yes	direct product factor
6	C₂×C₃×C₁₅₁	C₃³	1	40	yes	direct product factor
7	C₃×C₁₅₁	C₂×C₃³	1	40	yes	direct product factor
8	C₂×C₁₅₁	C₃⁴	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃⁴	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₅₁	C₂×C₃⁴	1	1	yes	characteristic, direct product factor, Sylow
11	C₃⁴	C₂×C₁₅₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃³	C₃×C₁₅₁	1	40	yes	direct product factor
13	C₃³	C₂×C₃×C₁₅₁	1	40	yes	direct product factor
14	C₂×C₃²	C₃²×C₁₅₁	1	130	yes	direct product factor
15	C₃²	C₂×C₃²×C₁₅₁	1	130	yes	direct product factor
16	C₂×C₃	C₃³×C₁₅₁	1	40	yes	direct product factor
17	C₃	C₂×C₃³×C₁₅₁	1	40	yes	direct product factor
18	C₂	C₃⁴×C₁₅₁	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. C₂×C₃³×C₁₅₁	C₃	direct (N × H)
2. C₃⁴×C₁₅₁	C₂	direct (N × H)
3. C₃³×C₁₅₁	C₂×C₃	direct (N × H)
4. C₂×C₃²×C₁₅₁	C₃²	direct (N × H)
5. C₃²×C₁₅₁	C₂×C₃²	direct (N × H)
6. C₂×C₃×C₁₅₁	C₃³	direct (N × H)
7. C₃×C₁₅₁	C₂×C₃³	direct (N × H)
8. C₂×C₁₅₁	C₃⁴	direct (N × H)
9. C₂×C₃⁴	C₁₅₁	direct (N × H)
10. C₁₅₁	C₂×C₃⁴	direct (N × H)
11. C₃⁴	C₂×C₁₅₁	direct (N × H)
12. C₂×C₃³	C₃×C₁₅₁	direct (N × H)
13. C₃³	C₂×C₃×C₁₅₁	direct (N × H)
14. C₂×C₃²	C₃²×C₁₅₁	direct (N × H)
15. C₃²	C₂×C₃²×C₁₅₁	direct (N × H)
16. C₂×C₃	C₃³×C₁₅₁	direct (N × H)
17. C₃	C₂×C₃³×C₁₅₁	direct (N × H)
18. C₂	C₃⁴×C₁₅₁	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×C₃³×C₁₅₁	3
C₃⁴×C₁₅₁	2
C₂×C₃⁴	151