Subgroups — C₂⁴×C₉×C₁₃² #72201650

Order 24336.

3216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₉×C₁₃²	C₂	1	15	yes	maximal, direct product factor
2	C₂⁴×C₃×C₁₃²	C₃	1	1	yes	maximal, characteristic
3	C₂³×C₃×C₁₃²	C₂×C₃	1	15	yes	—
4	C₂⁴×C₁₃²	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₂²×C₉×C₁₃²	C₂²	1	35	yes	direct product factor
6	C₂×C₉×C₁₃²	C₂³	1	15	yes	direct product factor
7	C₂²×C₃×C₁₃²	C₂²×C₃	1	35	yes	—
8	C₂⁴×C₉×C₁₃	C₁₃	1	14	yes	maximal, direct product factor
9	C₉×C₁₃²	C₂⁴	1	1	yes	characteristic, direct product factor, Hall
10	C₂³×C₁₃²	C₂×C₉	1	15	yes	direct product factor
11	C₂×C₃×C₁₃²	C₂³×C₃	1	15	yes	—
12	C₂³×C₉×C₁₃	C₂×C₁₃	1	210	yes	direct product factor
13	C₂²×C₁₃²	C₂²×C₉	1	35	yes	direct product factor
14	C₂⁴×C₃×C₁₃	C₃×C₁₃	1	14	yes	—
15	C₃×C₁₃²	C₂⁴×C₃	1	1	yes	characteristic
16	C₂²×C₉×C₁₃	C₂²×C₁₃	1	490	yes	direct product factor
17	C₂×C₁₃²	C₂³×C₉	1	15	yes	direct product factor
18	C₂³×C₃×C₁₃	C₂×C₃×C₁₃	1	210	yes	—
19	C₂×C₉×C₁₃	C₂³×C₁₃	1	210	yes	direct product factor
20	C₂⁴×C₁₃	C₉×C₁₃	1	14	yes	direct product factor
21	C₁₃²	C₂⁴×C₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂²×C₃×C₁₃	C₂²×C₃×C₁₃	1	490	yes	—
23	C₂⁴×C₉	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
24	C₉×C₁₃	C₂⁴×C₁₃	1	14	yes	direct product factor
25	C₂³×C₁₃	C₂×C₉×C₁₃	1	210	yes	direct product factor
26	C₂×C₃×C₁₃	C₂³×C₃×C₁₃	1	210	yes	—
27	C₂³×C₉	C₂×C₁₃²	1	15	yes	direct product factor
28	C₂²×C₁₃	C₂²×C₉×C₁₃	1	490	yes	direct product factor
29	C₂⁴×C₃	C₃×C₁₃²	1	1	yes	characteristic
30	C₃×C₁₃	C₂⁴×C₃×C₁₃	1	14	yes	—
31	C₂²×C₉	C₂²×C₁₃²	1	35	yes	direct product factor
32	C₂×C₁₃	C₂³×C₉×C₁₃	1	210	yes	direct product factor
33	C₂³×C₃	C₂×C₃×C₁₃²	1	15	yes	—
34	C₂×C₉	C₂³×C₁₃²	1	15	yes	direct product factor
35	C₂⁴	C₉×C₁₃²	1	1	yes	characteristic, direct product factor, Sylow
36	C₁₃	C₂⁴×C₉×C₁₃	1	14	yes	direct product factor
37	C₂²×C₃	C₂²×C₃×C₁₃²	1	35	yes	—
38	C₉	C₂⁴×C₁₃²	1	1	yes	characteristic, direct product factor, Sylow
39	C₂³	C₂×C₉×C₁₃²	1	15	yes	direct product factor
40	C₂×C₃	C₂³×C₃×C₁₃²	1	15	yes	—
41	C₂²	C₂²×C₉×C₁₃²	1	35	yes	direct product factor
42	C₃	C₂⁴×C₃×C₁₃²	1	1	yes	characteristic
43	C₂	C₂³×C₉×C₁₃²	1	15	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂⁴×C₃×C₁₃²
socle, prime radical	C₂⁴×C₃×C₁₃²	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₉×C₁₃²	C₂	direct (N × H)
4. C₂⁴×C₁₃²	C₉	direct (N × H)
5. C₂²×C₉×C₁₃²	C₂²	direct (N × H)
6. C₂×C₉×C₁₃²	C₂³	direct (N × H)
8. C₂⁴×C₉×C₁₃	C₁₃	direct (N × H)
9. C₉×C₁₃²	C₂⁴	direct (N × H)
10. C₂³×C₁₃²	C₂×C₉	direct (N × H)
12. C₂³×C₉×C₁₃	C₂×C₁₃	direct (N × H)
13. C₂²×C₁₃²	C₂²×C₉	direct (N × H)
16. C₂²×C₉×C₁₃	C₂²×C₁₃	direct (N × H)
17. C₂×C₁₃²	C₂³×C₉	direct (N × H)
19. C₂×C₉×C₁₃	C₂³×C₁₃	direct (N × H)
20. C₂⁴×C₁₃	C₉×C₁₃	direct (N × H)
21. C₁₃²	C₂⁴×C₉	direct (N × H)
23. C₂⁴×C₉	C₁₃²	direct (N × H)
24. C₉×C₁₃	C₂⁴×C₁₃	direct (N × H)
25. C₂³×C₁₃	C₂×C₉×C₁₃	direct (N × H)
27. C₂³×C₉	C₂×C₁₃²	direct (N × H)
28. C₂²×C₁₃	C₂²×C₉×C₁₃	direct (N × H)
31. C₂²×C₉	C₂²×C₁₃²	direct (N × H)
32. C₂×C₁₃	C₂³×C₉×C₁₃	direct (N × H)
34. C₂×C₉	C₂³×C₁₃²	direct (N × H)
35. C₂⁴	C₉×C₁₃²	direct (N × H)
36. C₁₃	C₂⁴×C₉×C₁₃	direct (N × H)
38. C₉	C₂⁴×C₁₃²	direct (N × H)
39. C₂³	C₂×C₉×C₁₃²	direct (N × H)
41. C₂²	C₂²×C₉×C₁₃²	direct (N × H)
43. C₂	C₂³×C₉×C₁₃²	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₉×C₁₃²	2
C₂⁴×C₃×C₁₃²	3
C₂⁴×C₉×C₁₃	13

Subgroups — C24×C9×C132 #72201650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₉×C₁₃² #72201650