Subgroups — C₂×C₃²×C₉×C₁₅₁ #72201733

Order 24462.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₁₅₁	C₃	1	1	yes	maximal, characteristic
2	C₂×C₃×C₉×C₁₅₁	C₃	1	12	yes	maximal, direct product factor
3	C₃²×C₉×C₁₅₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃³×C₁₅₁	C₂×C₃	1	1	yes	characteristic
5	C₃×C₉×C₁₅₁	C₂×C₃	1	12	yes	direct product factor
6	C₂×C₃²×C₁₅₁	C₉	1	9	yes	direct product factor
7	C₂×C₃²×C₁₅₁	C₃²	1	4	yes	—
8	C₂×C₉×C₁₅₁	C₃²	1	9	yes	direct product factor
9	C₃²×C₁₅₁	C₂×C₉	1	9	yes	direct product factor
10	C₃²×C₁₅₁	C₂×C₃²	1	4	yes	—
11	C₉×C₁₅₁	C₂×C₃²	1	9	yes	direct product factor
12	C₂×C₃×C₁₅₁	C₃×C₉	1	12	yes	direct product factor
13	C₂×C₃×C₁₅₁	C₃³	1	1	yes	characteristic
14	C₃×C₁₅₁	C₂×C₃×C₉	1	12	yes	direct product factor
15	C₃×C₁₅₁	C₂×C₃³	1	1	yes	characteristic
16	C₂×C₁₅₁	C₃²×C₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃²×C₉	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₁₅₁	C₂×C₃²×C₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₃²×C₉	C₂×C₁₅₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃³	C₃×C₁₅₁	1	1	yes	characteristic
21	C₂×C₃×C₉	C₃×C₁₅₁	1	12	yes	direct product factor
22	C₃³	C₂×C₃×C₁₅₁	1	1	yes	characteristic
23	C₃×C₉	C₂×C₃×C₁₅₁	1	12	yes	direct product factor
24	C₂×C₃²	C₉×C₁₅₁	1	9	yes	direct product factor
25	C₂×C₃²	C₃²×C₁₅₁	1	4	yes	—
26	C₂×C₉	C₃²×C₁₅₁	1	9	yes	direct product factor
27	C₃²	C₂×C₉×C₁₅₁	1	9	yes	direct product factor
28	C₃²	C₂×C₃²×C₁₅₁	1	4	yes	—
29	C₉	C₂×C₃²×C₁₅₁	1	9	yes	direct product factor
30	C₂×C₃	C₃×C₉×C₁₅₁	1	12	yes	direct product factor
31	C₂×C₃	C₃³×C₁₅₁	1	1	yes	characteristic
32	C₃	C₂×C₃×C₉×C₁₅₁	1	12	yes	direct product factor
33	C₃	C₂×C₃³×C₁₅₁	1	1	yes	characteristic
34	C₂	C₃²×C₉×C₁₅₁	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃³×C₁₅₁
socle, prime radical	C₂×C₃³×C₁₅₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₉×C₁₅₁	C₃	direct (N × H)
3. C₃²×C₉×C₁₅₁	C₂	direct (N × H)
5. C₃×C₉×C₁₅₁	C₂×C₃	direct (N × H)
6. C₂×C₃²×C₁₅₁	C₉	direct (N × H)
8. C₂×C₉×C₁₅₁	C₃²	direct (N × H)
9. C₃²×C₁₅₁	C₂×C₉	direct (N × H)
11. C₉×C₁₅₁	C₂×C₃²	direct (N × H)
12. C₂×C₃×C₁₅₁	C₃×C₉	direct (N × H)
14. C₃×C₁₅₁	C₂×C₃×C₉	direct (N × H)
16. C₂×C₁₅₁	C₃²×C₉	direct (N × H)
17. C₂×C₃²×C₉	C₁₅₁	direct (N × H)
18. C₁₅₁	C₂×C₃²×C₉	direct (N × H)
19. C₃²×C₉	C₂×C₁₅₁	direct (N × H)
21. C₂×C₃×C₉	C₃×C₁₅₁	direct (N × H)
23. C₃×C₉	C₂×C₃×C₁₅₁	direct (N × H)
24. C₂×C₃²	C₉×C₁₅₁	direct (N × H)
26. C₂×C₉	C₃²×C₁₅₁	direct (N × H)
27. C₃²	C₂×C₉×C₁₅₁	direct (N × H)
29. C₉	C₂×C₃²×C₁₅₁	direct (N × H)
30. C₂×C₃	C₃×C₉×C₁₅₁	direct (N × H)
32. C₃	C₂×C₃×C₉×C₁₅₁	direct (N × H)
34. C₂	C₃²×C₉×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
C₂×C₃×C₉×C₁₅₁	3
C₃²×C₉×C₁₅₁	2
C₂×C₃²×C₉	151

Subgroups — C2×C32×C9×C151 #72201733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₉×C₁₅₁ #72201733