Subgroups — C₃²×C₄³×C₄₃ #72202062

Order 24768.

1548 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄²×C₄₃	C₂	1	7	yes	maximal
2	C₃×C₄³×C₄₃	C₃	1	4	yes	maximal, direct product factor
3	C₂²×C₃²×C₄×C₄₃	C₂²	1	7	yes	—
4	C₃²×C₄²×C₄₃	C₄	1	28	yes	direct product factor
5	C₂×C₃×C₄²×C₄₃	C₂×C₃	1	28	yes	—
6	C₂³×C₃²×C₄₃	C₂³	1	1	yes	characteristic
7	C₂×C₃²×C₄×C₄₃	C₂×C₄	1	42	yes	—
8	C₂²×C₃×C₄×C₄₃	C₂²×C₃	1	28	yes	—
9	C₃×C₄²×C₄₃	C₃×C₄	1	112	yes	direct product factor
10	C₄³×C₄₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₃²×C₄₃	C₂²×C₄	1	7	yes	—
12	C₃²×C₄×C₄₃	C₄²	1	28	yes	direct product factor
13	C₂×C₄²×C₄₃	C₂×C₃²	1	7	yes	—
14	C₂³×C₃×C₄₃	C₂³×C₃	1	4	yes	—
15	C₂×C₃×C₄×C₄₃	C₂×C₃×C₄	1	168	yes	—
16	C₂×C₃²×C₄₃	C₂×C₄²	1	7	yes	—
17	C₂²×C₄×C₄₃	C₂²×C₃²	1	7	yes	—
18	C₄²×C₄₃	C₃²×C₄	1	28	yes	direct product factor
19	C₃²×C₄³	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₃×C₄₃	C₂²×C₃×C₄	1	28	yes	—
21	C₃×C₄×C₄₃	C₃×C₄²	1	112	yes	direct product factor
22	C₃²×C₄₃	C₄³	1	1	yes	characteristic, direct product factor, Hall
23	C₂³×C₄₃	C₂³×C₃²	1	1	yes	characteristic
24	C₂×C₄×C₄₃	C₂×C₃²×C₄	1	42	yes	—
25	C₂×C₃²×C₄²	C₂×C₄₃	1	7	yes	—
26	C₂×C₃×C₄₃	C₂×C₃×C₄²	1	28	yes	—
27	C₃×C₄³	C₃×C₄₃	1	4	yes	direct product factor
28	C₂²×C₄₃	C₂²×C₃²×C₄	1	7	yes	—
29	C₄×C₄₃	C₃²×C₄²	1	28	yes	direct product factor
30	C₂²×C₃²×C₄	C₂²×C₄₃	1	7	yes	—
31	C₃²×C₄²	C₄×C₄₃	1	28	yes	direct product factor
32	C₃×C₄₃	C₃×C₄³	1	4	yes	direct product factor
33	C₂×C₃×C₄²	C₂×C₃×C₄₃	1	28	yes	—
34	C₂×C₄₃	C₂×C₃²×C₄²	1	7	yes	—
35	C₂³×C₃²	C₂³×C₄₃	1	1	yes	characteristic
36	C₂×C₃²×C₄	C₂×C₄×C₄₃	1	42	yes	—
37	C₄³	C₃²×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
38	C₂²×C₃×C₄	C₂²×C₃×C₄₃	1	28	yes	—
39	C₃×C₄²	C₃×C₄×C₄₃	1	112	yes	direct product factor
40	C₄₃	C₃²×C₄³	1	1	yes	characteristic, direct product factor, Sylow
41	C₂²×C₃²	C₂²×C₄×C₄₃	1	7	yes	—
42	C₃²×C₄	C₄²×C₄₃	1	28	yes	direct product factor
43	C₂×C₄²	C₂×C₃²×C₄₃	1	7	yes	—
44	C₂³×C₃	C₂³×C₃×C₄₃	1	4	yes	—
45	C₂×C₃×C₄	C₂×C₃×C₄×C₄₃	1	168	yes	—
46	C₂×C₃²	C₂×C₄²×C₄₃	1	7	yes	—
47	C₂²×C₄	C₂²×C₃²×C₄₃	1	7	yes	—
48	C₄²	C₃²×C₄×C₄₃	1	28	yes	direct product factor
49	C₂²×C₃	C₂²×C₃×C₄×C₄₃	1	28	yes	—
50	C₃×C₄	C₃×C₄²×C₄₃	1	112	yes	direct product factor
51	C₃²	C₄³×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
52	C₂³	C₂³×C₃²×C₄₃	1	1	yes	characteristic
53	C₂×C₄	C₂×C₃²×C₄×C₄₃	1	42	yes	—
54	C₂×C₃	C₂×C₃×C₄²×C₄₃	1	28	yes	—
55	C₂²	C₂²×C₃²×C₄×C₄₃	1	7	yes	—
56	C₄	C₃²×C₄²×C₄₃	1	28	yes	direct product factor
57	C₃	C₃×C₄³×C₄₃	1	4	yes	direct product factor
58	C₂	C₂×C₃²×C₄²×C₄₃	1	7	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³	C₂³×C₃²×C₄₃
socle, prime radical	C₂³×C₃²×C₄₃	C₂³
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₄³×C₄₃	C₃	direct (N × H)
4. C₃²×C₄²×C₄₃	C₄	direct (N × H)
9. C₃×C₄²×C₄₃	C₃×C₄	direct (N × H)
10. C₄³×C₄₃	C₃²	direct (N × H)
12. C₃²×C₄×C₄₃	C₄²	direct (N × H)
18. C₄²×C₄₃	C₃²×C₄	direct (N × H)
19. C₃²×C₄³	C₄₃	direct (N × H)
21. C₃×C₄×C₄₃	C₃×C₄²	direct (N × H)
22. C₃²×C₄₃	C₄³	direct (N × H)
27. C₃×C₄³	C₃×C₄₃	direct (N × H)
29. C₄×C₄₃	C₃²×C₄²	direct (N × H)
31. C₃²×C₄²	C₄×C₄₃	direct (N × H)
32. C₃×C₄₃	C₃×C₄³	direct (N × H)
37. C₄³	C₃²×C₄₃	direct (N × H)
39. C₃×C₄²	C₃×C₄×C₄₃	direct (N × H)
40. C₄₃	C₃²×C₄³	direct (N × H)
42. C₃²×C₄	C₄²×C₄₃	direct (N × H)
48. C₄²	C₃²×C₄×C₄₃	direct (N × H)
50. C₃×C₄	C₃×C₄²×C₄₃	direct (N × H)
51. C₃²	C₄³×C₄₃	direct (N × H)
56. C₄	C₃²×C₄²×C₄₃	direct (N × H)
57. C₃	C₃×C₄³×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×C₄²×C₄₃	2
C₃×C₄³×C₄₃	3
C₃²×C₄³	43

Subgroups — C32×C43×C43 #72202062

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₄³×C₄₃ #72202062