Subgroups — C₂²×C₄²×C₉×C₄₃ #72202063

Order 24768.

1494 conjugacy classes of subgroups.

The subgroup lattice has 108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₉×C₄₃	C₂	1	3	yes	maximal
2	C₂×C₄²×C₉×C₄₃	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₃×C₄²×C₄₃	C₃	1	1	yes	maximal, characteristic
4	C₂⁴×C₉×C₄₃	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₉×C₄₃	C₄	1	24	yes	direct product factor
6	C₂²×C₄×C₉×C₄₃	C₂²	1	18	yes	—
7	C₄²×C₉×C₄₃	C₂²	1	16	yes	direct product factor
8	C₂³×C₃×C₄×C₄₃	C₂×C₃	1	3	yes	—
9	C₂×C₃×C₄²×C₄₃	C₂×C₃	1	12	yes	—
10	C₂³×C₉×C₄₃	C₂×C₄	1	12	yes	—
11	C₂³×C₉×C₄₃	C₂³	1	3	yes	—
12	C₂×C₄×C₉×C₄₃	C₂×C₄	1	72	yes	direct product factor
13	C₂×C₄×C₉×C₄₃	C₂³	1	12	yes	—
14	C₂⁴×C₃×C₄₃	C₂²×C₃	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₄₃	C₃×C₄	1	24	yes	—
16	C₂²×C₃×C₄×C₄₃	C₂²×C₃	1	18	yes	—
17	C₃×C₄²×C₄₃	C₂²×C₃	1	16	yes	—
18	C₂²×C₄²×C₄₃	C₉	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₉×C₄₃	C₄²	1	16	yes	direct product factor
20	C₂²×C₉×C₄₃	C₂²×C₄	1	18	yes	—
21	C₂²×C₉×C₄₃	C₂⁴	1	1	yes	characteristic
22	C₄×C₉×C₄₃	C₂²×C₄	1	24	yes	direct product factor
23	C₂³×C₄×C₄₃	C₂×C₉	1	3	yes	—
24	C₂×C₄²×C₄₃	C₂×C₉	1	12	yes	direct product factor
25	C₂³×C₃×C₄₃	C₂×C₃×C₄	1	12	yes	—
26	C₂³×C₃×C₄₃	C₂³×C₃	1	3	yes	—
27	C₂×C₃×C₄×C₄₃	C₂×C₃×C₄	1	72	yes	—
28	C₂×C₃×C₄×C₄₃	C₂³×C₃	1	12	yes	—
29	C₂×C₉×C₄₃	C₂×C₄²	1	12	yes	direct product factor
30	C₂×C₉×C₄₃	C₂³×C₄	1	3	yes	—
31	C₂⁴×C₄₃	C₂²×C₉	1	1	yes	characteristic
32	C₂²×C₄×C₄₃	C₄×C₉	1	24	yes	direct product factor
33	C₂²×C₄×C₄₃	C₂²×C₉	1	18	yes	—
34	C₄²×C₄₃	C₂²×C₉	1	16	yes	direct product factor
35	C₂²×C₄²×C₉	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
36	C₂²×C₃×C₄₃	C₃×C₄²	1	16	yes	—
37	C₂²×C₃×C₄₃	C₂²×C₃×C₄	1	18	yes	—
38	C₂²×C₃×C₄₃	C₂⁴×C₃	1	1	yes	characteristic
39	C₃×C₄×C₄₃	C₂²×C₃×C₄	1	24	yes	—
40	C₉×C₄₃	C₂²×C₄²	1	1	yes	characteristic, direct product factor, Hall
41	C₂³×C₄₃	C₂×C₄×C₉	1	12	yes	—
42	C₂³×C₄₃	C₂³×C₉	1	3	yes	—
43	C₂×C₄×C₄₃	C₂×C₄×C₉	1	72	yes	direct product factor
44	C₂×C₄×C₄₃	C₂³×C₉	1	12	yes	—
45	C₂³×C₄×C₉	C₂×C₄₃	1	3	yes	—
46	C₂×C₄²×C₉	C₂×C₄₃	1	12	yes	direct product factor
47	C₂×C₃×C₄₃	C₂×C₃×C₄²	1	12	yes	—
48	C₂×C₃×C₄₃	C₂³×C₃×C₄	1	3	yes	—
49	C₂²×C₃×C₄²	C₃×C₄₃	1	1	yes	characteristic
50	C₂²×C₄₃	C₄²×C₉	1	16	yes	direct product factor
51	C₂²×C₄₃	C₂²×C₄×C₉	1	18	yes	—
52	C₂²×C₄₃	C₂⁴×C₉	1	1	yes	characteristic
53	C₄×C₄₃	C₂²×C₄×C₉	1	24	yes	direct product factor
54	C₂⁴×C₉	C₂²×C₄₃	1	1	yes	characteristic
55	C₂²×C₄×C₉	C₄×C₄₃	1	24	yes	direct product factor
56	C₂²×C₄×C₉	C₂²×C₄₃	1	18	yes	—
57	C₄²×C₉	C₂²×C₄₃	1	16	yes	direct product factor
58	C₃×C₄₃	C₂²×C₃×C₄²	1	1	yes	characteristic
59	C₂³×C₃×C₄	C₂×C₃×C₄₃	1	3	yes	—
60	C₂×C₃×C₄²	C₂×C₃×C₄₃	1	12	yes	—
61	C₂×C₄₃	C₂×C₄²×C₉	1	12	yes	direct product factor
62	C₂×C₄₃	C₂³×C₄×C₉	1	3	yes	—
63	C₂³×C₉	C₂×C₄×C₄₃	1	12	yes	—
64	C₂³×C₉	C₂³×C₄₃	1	3	yes	—
65	C₂×C₄×C₉	C₂×C₄×C₄₃	1	72	yes	direct product factor
66	C₂×C₄×C₉	C₂³×C₄₃	1	12	yes	—
67	C₂²×C₄²	C₉×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
68	C₂⁴×C₃	C₂²×C₃×C₄₃	1	1	yes	characteristic
69	C₂²×C₃×C₄	C₃×C₄×C₄₃	1	24	yes	—
70	C₂²×C₃×C₄	C₂²×C₃×C₄₃	1	18	yes	—
71	C₃×C₄²	C₂²×C₃×C₄₃	1	16	yes	—
72	C₄₃	C₂²×C₄²×C₉	1	1	yes	characteristic, direct product factor, Sylow
73	C₂²×C₉	C₄²×C₄₃	1	16	yes	direct product factor
74	C₂²×C₉	C₂²×C₄×C₄₃	1	18	yes	—
75	C₂²×C₉	C₂⁴×C₄₃	1	1	yes	characteristic
76	C₄×C₉	C₂²×C₄×C₄₃	1	24	yes	direct product factor
77	C₂³×C₄	C₂×C₉×C₄₃	1	3	yes	—
78	C₂×C₄²	C₂×C₉×C₄₃	1	12	yes	direct product factor
79	C₂³×C₃	C₂×C₃×C₄×C₄₃	1	12	yes	—
80	C₂³×C₃	C₂³×C₃×C₄₃	1	3	yes	—
81	C₂×C₃×C₄	C₂×C₃×C₄×C₄₃	1	72	yes	—
82	C₂×C₃×C₄	C₂³×C₃×C₄₃	1	12	yes	—
83	C₂×C₉	C₂×C₄²×C₄₃	1	12	yes	direct product factor
84	C₂×C₉	C₂³×C₄×C₄₃	1	3	yes	—
85	C₂⁴	C₂²×C₉×C₄₃	1	1	yes	characteristic
86	C₂²×C₄	C₄×C₉×C₄₃	1	24	yes	direct product factor
87	C₂²×C₄	C₂²×C₉×C₄₃	1	18	yes	—
88	C₄²	C₂²×C₉×C₄₃	1	16	yes	direct product factor
89	C₂²×C₃	C₃×C₄²×C₄₃	1	16	yes	—
90	C₂²×C₃	C₂²×C₃×C₄×C₄₃	1	18	yes	—
91	C₂²×C₃	C₂⁴×C₃×C₄₃	1	1	yes	characteristic
92	C₃×C₄	C₂²×C₃×C₄×C₄₃	1	24	yes	—
93	C₉	C₂²×C₄²×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
94	C₂³	C₂×C₄×C₉×C₄₃	1	12	yes	—
95	C₂³	C₂³×C₉×C₄₃	1	3	yes	—
96	C₂×C₄	C₂×C₄×C₉×C₄₃	1	72	yes	direct product factor
97	C₂×C₄	C₂³×C₉×C₄₃	1	12	yes	—
98	C₂×C₃	C₂×C₃×C₄²×C₄₃	1	12	yes	—
99	C₂×C₃	C₂³×C₃×C₄×C₄₃	1	3	yes	—
100	C₂²	C₄²×C₉×C₄₃	1	16	yes	direct product factor
101	C₂²	C₂²×C₄×C₉×C₄₃	1	18	yes	—
102	C₂²	C₂⁴×C₉×C₄₃	1	1	yes	characteristic
103	C₄	C₂²×C₄×C₉×C₄₃	1	24	yes	direct product factor
104	C₃	C₂²×C₃×C₄²×C₄₃	1	1	yes	characteristic
105	C₂	C₂×C₄²×C₉×C₄₃	1	12	yes	direct product factor
106	C₂	C₂³×C₄×C₉×C₄₃	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃	C₂⁴×C₃×C₄₃
socle, prime radical	C₂⁴×C₃×C₄₃	C₂²×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×C₄²×C₉×C₄₃	C₂	direct (N × H)
5. C₂²×C₄×C₉×C₄₃	C₄	direct (N × H)
7. C₄²×C₉×C₄₃	C₂²	direct (N × H)
12. C₂×C₄×C₉×C₄₃	C₂×C₄	direct (N × H)
18. C₂²×C₄²×C₄₃	C₉	direct (N × H)
19. C₂²×C₉×C₄₃	C₄²	direct (N × H)
22. C₄×C₉×C₄₃	C₂²×C₄	direct (N × H)
24. C₂×C₄²×C₄₃	C₂×C₉	direct (N × H)
29. C₂×C₉×C₄₃	C₂×C₄²	direct (N × H)
32. C₂²×C₄×C₄₃	C₄×C₉	direct (N × H)
34. C₄²×C₄₃	C₂²×C₉	direct (N × H)
35. C₂²×C₄²×C₉	C₄₃	direct (N × H)
40. C₉×C₄₃	C₂²×C₄²	direct (N × H)
43. C₂×C₄×C₄₃	C₂×C₄×C₉	direct (N × H)
46. C₂×C₄²×C₉	C₂×C₄₃	direct (N × H)
50. C₂²×C₄₃	C₄²×C₉	direct (N × H)
53. C₄×C₄₃	C₂²×C₄×C₉	direct (N × H)
55. C₂²×C₄×C₉	C₄×C₄₃	direct (N × H)
57. C₄²×C₉	C₂²×C₄₃	direct (N × H)
61. C₂×C₄₃	C₂×C₄²×C₉	direct (N × H)
65. C₂×C₄×C₉	C₂×C₄×C₄₃	direct (N × H)
67. C₂²×C₄²	C₉×C₄₃	direct (N × H)
72. C₄₃	C₂²×C₄²×C₉	direct (N × H)
73. C₂²×C₉	C₄²×C₄₃	direct (N × H)
76. C₄×C₉	C₂²×C₄×C₄₃	direct (N × H)
78. C₂×C₄²	C₂×C₉×C₄₃	direct (N × H)
83. C₂×C₉	C₂×C₄²×C₄₃	direct (N × H)
86. C₂²×C₄	C₄×C₉×C₄₃	direct (N × H)
88. C₄²	C₂²×C₉×C₄₃	direct (N × H)
93. C₉	C₂²×C₄²×C₄₃	direct (N × H)
96. C₂×C₄	C₂×C₄×C₉×C₄₃	direct (N × H)
100. C₂²	C₄²×C₉×C₄₃	direct (N × H)
103. C₄	C₂²×C₄×C₉×C₄₃	direct (N × H)
105. C₂	C₂×C₄²×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
C₂³×C₄×C₉×C₄₃	2
C₂×C₄²×C₉×C₄₃	2
C₂²×C₃×C₄²×C₄₃	3
C₂²×C₄²×C₉	43

Subgroups — C22×C42×C9×C43 #72202063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄²×C₉×C₄₃ #72202063