Subgroups — C₂²×C₃²×C₉×C₄₃ #72192145

Order 13932.

500 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₉×C₄₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃³×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₂²×C₃×C₉×C₄₃	C₃	1	12	yes	maximal, direct product factor
4	C₂×C₃³×C₄₃	C₂×C₃	1	3	yes	—
5	C₂×C₃×C₉×C₄₃	C₂×C₃	1	36	yes	direct product factor
6	C₃²×C₉×C₄₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
7	C₂²×C₃²×C₄₃	C₉	1	9	yes	direct product factor
8	C₂²×C₃²×C₄₃	C₃²	1	4	yes	—
9	C₂²×C₉×C₄₃	C₃²	1	9	yes	direct product factor
10	C₃³×C₄₃	C₂²×C₃	1	1	yes	characteristic
11	C₃×C₉×C₄₃	C₂²×C₃	1	12	yes	direct product factor
12	C₂×C₃²×C₄₃	C₂×C₉	1	27	yes	direct product factor
13	C₂×C₃²×C₄₃	C₂×C₃²	1	12	yes	—
14	C₂×C₉×C₄₃	C₂×C₃²	1	27	yes	direct product factor
15	C₂²×C₃×C₄₃	C₃×C₉	1	12	yes	direct product factor
16	C₂²×C₃×C₄₃	C₃³	1	1	yes	characteristic
17	C₃²×C₄₃	C₂²×C₉	1	9	yes	direct product factor
18	C₃²×C₄₃	C₂²×C₃²	1	4	yes	—
19	C₉×C₄₃	C₂²×C₃²	1	9	yes	direct product factor
20	C₂²×C₃²×C₉	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₃×C₄₃	C₂×C₃×C₉	1	36	yes	direct product factor
22	C₂×C₃×C₄₃	C₂×C₃³	1	3	yes	—
23	C₂²×C₄₃	C₃²×C₉	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₃²×C₉	C₂×C₄₃	1	3	yes	direct product factor
25	C₃×C₄₃	C₂²×C₃×C₉	1	12	yes	direct product factor
26	C₃×C₄₃	C₂²×C₃³	1	1	yes	characteristic
27	C₂²×C₃³	C₃×C₄₃	1	1	yes	characteristic
28	C₂²×C₃×C₉	C₃×C₄₃	1	12	yes	direct product factor
29	C₂×C₄₃	C₂×C₃²×C₉	1	3	yes	direct product factor
30	C₃²×C₉	C₂²×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃³	C₂×C₃×C₄₃	1	3	yes	—
32	C₂×C₃×C₉	C₂×C₃×C₄₃	1	36	yes	direct product factor
33	C₄₃	C₂²×C₃²×C₉	1	1	yes	characteristic, direct product factor, Sylow
34	C₂²×C₃²	C₉×C₄₃	1	9	yes	direct product factor
35	C₂²×C₃²	C₃²×C₄₃	1	4	yes	—
36	C₂²×C₉	C₃²×C₄₃	1	9	yes	direct product factor
37	C₃³	C₂²×C₃×C₄₃	1	1	yes	characteristic
38	C₃×C₉	C₂²×C₃×C₄₃	1	12	yes	direct product factor
39	C₂×C₃²	C₂×C₉×C₄₃	1	27	yes	direct product factor
40	C₂×C₃²	C₂×C₃²×C₄₃	1	12	yes	—
41	C₂×C₉	C₂×C₃²×C₄₃	1	27	yes	direct product factor
42	C₂²×C₃	C₃×C₉×C₄₃	1	12	yes	direct product factor
43	C₂²×C₃	C₃³×C₄₃	1	1	yes	characteristic
44	C₃²	C₂²×C₉×C₄₃	1	9	yes	direct product factor
45	C₃²	C₂²×C₃²×C₄₃	1	4	yes	—
46	C₉	C₂²×C₃²×C₄₃	1	9	yes	direct product factor
47	C₂×C₃	C₂×C₃×C₉×C₄₃	1	36	yes	direct product factor
48	C₂×C₃	C₂×C₃³×C₄₃	1	3	yes	—
49	C₂²	C₃²×C₉×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
50	C₃	C₂²×C₃×C₉×C₄₃	1	12	yes	direct product factor
51	C₃	C₂²×C₃³×C₄₃	1	1	yes	characteristic
52	C₂	C₂×C₃²×C₉×C₄₃	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂²×C₃³×C₄₃
socle, prime radical	C₂²×C₃³×C₄₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₉×C₄₃	C₂	direct (N × H)
3. C₂²×C₃×C₉×C₄₃	C₃	direct (N × H)
5. C₂×C₃×C₉×C₄₃	C₂×C₃	direct (N × H)
6. C₃²×C₉×C₄₃	C₂²	direct (N × H)
7. C₂²×C₃²×C₄₃	C₉	direct (N × H)
9. C₂²×C₉×C₄₃	C₃²	direct (N × H)
11. C₃×C₉×C₄₃	C₂²×C₃	direct (N × H)
12. C₂×C₃²×C₄₃	C₂×C₉	direct (N × H)
14. C₂×C₉×C₄₃	C₂×C₃²	direct (N × H)
15. C₂²×C₃×C₄₃	C₃×C₉	direct (N × H)
17. C₃²×C₄₃	C₂²×C₉	direct (N × H)
19. C₉×C₄₃	C₂²×C₃²	direct (N × H)
20. C₂²×C₃²×C₉	C₄₃	direct (N × H)
21. C₂×C₃×C₄₃	C₂×C₃×C₉	direct (N × H)
23. C₂²×C₄₃	C₃²×C₉	direct (N × H)
24. C₂×C₃²×C₉	C₂×C₄₃	direct (N × H)
25. C₃×C₄₃	C₂²×C₃×C₉	direct (N × H)
28. C₂²×C₃×C₉	C₃×C₄₃	direct (N × H)
29. C₂×C₄₃	C₂×C₃²×C₉	direct (N × H)
30. C₃²×C₉	C₂²×C₄₃	direct (N × H)
32. C₂×C₃×C₉	C₂×C₃×C₄₃	direct (N × H)
33. C₄₃	C₂²×C₃²×C₉	direct (N × H)
34. C₂²×C₃²	C₉×C₄₃	direct (N × H)
36. C₂²×C₉	C₃²×C₄₃	direct (N × H)
38. C₃×C₉	C₂²×C₃×C₄₃	direct (N × H)
39. C₂×C₃²	C₂×C₉×C₄₃	direct (N × H)
41. C₂×C₉	C₂×C₃²×C₄₃	direct (N × H)
42. C₂²×C₃	C₃×C₉×C₄₃	direct (N × H)
44. C₃²	C₂²×C₉×C₄₃	direct (N × H)
46. C₉	C₂²×C₃²×C₄₃	direct (N × H)
47. C₂×C₃	C₂×C₃×C₉×C₄₃	direct (N × H)
49. C₂²	C₃²×C₉×C₄₃	direct (N × H)
50. C₃	C₂²×C₃×C₉×C₄₃	direct (N × H)
52. C₂	C₂×C₃²×C₉×C₄₃	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×C₃²×C₉×C₄₃	2
C₂²×C₃³×C₄₃	3
C₂²×C₃×C₉×C₄₃	3
C₂²×C₃²×C₉	43

Subgroups — C22×C32×C9×C43 #72192145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃²×C₉×C₄₃ #72192145