Subgroups — C₂×C₉×C₃₂×C₄₃ #72202049

Order 24768.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₉×C₃₂×C₄₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₃₂×C₄₃	C₃	1	1	yes	maximal, characteristic
4	C₂×C₈×C₉×C₄₃	C₄	1	1	yes	characteristic
5	C₉×C₁₆×C₄₃	C₄	1	1	yes	characteristic
6	C₉×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₁₆×C₄₃	C₂×C₃	1	1	yes	characteristic
8	C₃×C₃₂×C₄₃	C₂×C₃	1	2	yes	—
9	C₂×C₄×C₉×C₄₃	C₈	1	1	yes	characteristic
10	C₈×C₉×C₄₃	C₈	1	1	yes	characteristic
11	C₈×C₉×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×C₈×C₄₃	C₃×C₄	1	1	yes	characteristic
13	C₃×C₁₆×C₄₃	C₃×C₄	1	1	yes	characteristic
14	C₃×C₁₆×C₄₃	C₂²×C₃	1	1	yes	characteristic
15	C₂×C₃₂×C₄₃	C₉	1	1	yes	characteristic, direct product factor, Hall
16	C₂²×C₉×C₄₃	C₁₆	1	1	yes	characteristic
17	C₄×C₉×C₄₃	C₁₆	1	1	yes	characteristic
18	C₄×C₉×C₄₃	C₂×C₈	1	1	yes	characteristic
19	C₂×C₁₆×C₄₃	C₂×C₉	1	1	yes	characteristic
20	C₃₂×C₄₃	C₂×C₉	1	2	yes	direct product factor
21	C₂×C₃×C₄×C₄₃	C₃×C₈	1	1	yes	characteristic
22	C₃×C₈×C₄₃	C₃×C₈	1	1	yes	characteristic
23	C₃×C₈×C₄₃	C₂×C₃×C₄	1	1	yes	characteristic
24	C₂×C₉×C₄₃	C₃₂	1	2	yes	direct product factor
25	C₂×C₉×C₄₃	C₂×C₁₆	1	1	yes	characteristic
26	C₂×C₈×C₄₃	C₄×C₉	1	1	yes	characteristic
27	C₁₆×C₄₃	C₄×C₉	1	1	yes	characteristic
28	C₁₆×C₄₃	C₂²×C₉	1	1	yes	characteristic
29	C₂×C₉×C₃₂	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂²×C₃×C₄₃	C₃×C₁₆	1	1	yes	characteristic
31	C₃×C₄×C₄₃	C₃×C₁₆	1	1	yes	characteristic
32	C₃×C₄×C₄₃	C₂×C₃×C₈	1	1	yes	characteristic
33	C₉×C₄₃	C₂×C₃₂	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₄×C₄₃	C₈×C₉	1	1	yes	characteristic
35	C₈×C₄₃	C₈×C₉	1	1	yes	characteristic
36	C₈×C₄₃	C₂×C₄×C₉	1	1	yes	characteristic
37	C₂×C₉×C₁₆	C₂×C₄₃	1	1	yes	characteristic
38	C₉×C₃₂	C₂×C₄₃	1	2	yes	direct product factor
39	C₂×C₃×C₄₃	C₃×C₃₂	1	2	yes	—
40	C₂×C₃×C₄₃	C₂×C₃×C₁₆	1	1	yes	characteristic
41	C₂×C₃×C₃₂	C₃×C₄₃	1	1	yes	characteristic
42	C₂²×C₄₃	C₉×C₁₆	1	1	yes	characteristic
43	C₄×C₄₃	C₉×C₁₆	1	1	yes	characteristic
44	C₄×C₄₃	C₂×C₈×C₉	1	1	yes	characteristic
45	C₂×C₈×C₉	C₄×C₄₃	1	1	yes	characteristic
46	C₉×C₁₆	C₄×C₄₃	1	1	yes	characteristic
47	C₉×C₁₆	C₂²×C₄₃	1	1	yes	characteristic
48	C₃×C₄₃	C₂×C₃×C₃₂	1	1	yes	characteristic
49	C₂×C₃×C₁₆	C₂×C₃×C₄₃	1	1	yes	characteristic
50	C₃×C₃₂	C₂×C₃×C₄₃	1	2	yes	—
51	C₂×C₄₃	C₉×C₃₂	1	2	yes	direct product factor
52	C₂×C₄₃	C₂×C₉×C₁₆	1	1	yes	characteristic
53	C₂×C₄×C₉	C₈×C₄₃	1	1	yes	characteristic
54	C₈×C₉	C₈×C₄₃	1	1	yes	characteristic
55	C₈×C₉	C₂×C₄×C₄₃	1	1	yes	characteristic
56	C₂×C₃₂	C₉×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×C₃×C₈	C₃×C₄×C₄₃	1	1	yes	characteristic
58	C₃×C₁₆	C₃×C₄×C₄₃	1	1	yes	characteristic
59	C₃×C₁₆	C₂²×C₃×C₄₃	1	1	yes	characteristic
60	C₄₃	C₂×C₉×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
61	C₂²×C₉	C₁₆×C₄₃	1	1	yes	characteristic
62	C₄×C₉	C₁₆×C₄₃	1	1	yes	characteristic
63	C₄×C₉	C₂×C₈×C₄₃	1	1	yes	characteristic
64	C₂×C₁₆	C₂×C₉×C₄₃	1	1	yes	characteristic
65	C₃₂	C₂×C₉×C₄₃	1	2	yes	direct product factor
66	C₂×C₃×C₄	C₃×C₈×C₄₃	1	1	yes	characteristic
67	C₃×C₈	C₃×C₈×C₄₃	1	1	yes	characteristic
68	C₃×C₈	C₂×C₃×C₄×C₄₃	1	1	yes	characteristic
69	C₂×C₉	C₃₂×C₄₃	1	2	yes	direct product factor
70	C₂×C₉	C₂×C₁₆×C₄₃	1	1	yes	characteristic
71	C₂×C₈	C₄×C₉×C₄₃	1	1	yes	characteristic
72	C₁₆	C₄×C₉×C₄₃	1	1	yes	characteristic
73	C₁₆	C₂²×C₉×C₄₃	1	1	yes	characteristic
74	C₂²×C₃	C₃×C₁₆×C₄₃	1	1	yes	characteristic
75	C₃×C₄	C₃×C₁₆×C₄₃	1	1	yes	characteristic
76	C₃×C₄	C₂×C₃×C₈×C₄₃	1	1	yes	characteristic
77	C₉	C₂×C₃₂×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
78	C₂×C₄	C₈×C₉×C₄₃	1	1	yes	characteristic
79	C₈	C₈×C₉×C₄₃	1	1	yes	characteristic
80	C₈	C₂×C₄×C₉×C₄₃	1	1	yes	characteristic
81	C₂×C₃	C₃×C₃₂×C₄₃	1	2	yes	—
82	C₂×C₃	C₂×C₃×C₁₆×C₄₃	1	1	yes	characteristic
83	C₂²	C₉×C₁₆×C₄₃	1	1	yes	characteristic
84	C₄	C₉×C₁₆×C₄₃	1	1	yes	characteristic
85	C₄	C₂×C₈×C₉×C₄₃	1	1	yes	characteristic
86	C₃	C₂×C₃×C₃₂×C₄₃	1	1	yes	characteristic
87	C₂	C₉×C₃₂×C₄₃	1	2	yes	direct product factor
88	C₂	C₂×C₉×C₁₆×C₄₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₁₆	C₂²×C₃×C₄₃
socle, prime radical	C₂²×C₃×C₄₃	C₃×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×C₃₂×C₄₃	C₂	direct (N × H)
15. C₂×C₃₂×C₄₃	C₉	direct (N × H)
20. C₃₂×C₄₃	C₂×C₉	direct (N × H)
24. C₂×C₉×C₄₃	C₃₂	direct (N × H)
29. C₂×C₉×C₃₂	C₄₃	direct (N × H)
33. C₉×C₄₃	C₂×C₃₂	direct (N × H)
38. C₉×C₃₂	C₂×C₄₃	direct (N × H)
51. C₂×C₄₃	C₉×C₃₂	direct (N × H)
56. C₂×C₃₂	C₉×C₄₃	direct (N × H)
60. C₄₃	C₂×C₉×C₃₂	direct (N × H)
65. C₃₂	C₂×C₉×C₄₃	direct (N × H)
69. C₂×C₉	C₃₂×C₄₃	direct (N × H)
77. C₉	C₂×C₃₂×C₄₃	direct (N × H)
87. C₂	C₉×C₃₂×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×C₉×C₁₆×C₄₃	2
C₉×C₃₂×C₄₃	2
C₂×C₃×C₃₂×C₄₃	3
C₂×C₉×C₃₂	43

Subgroups — C2×C9×C32×C43 #72202049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₃₂×C₄₃ #72202049