Subgroups — C₂⁴×C₁₆×C₈₉ #36440468

Order 22784.

2590 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₈×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₁₆×C₈₉	C₂	1	30	yes	maximal, direct product factor
3	C₂⁴×C₄×C₈₉	C₄	1	1	yes	characteristic
4	C₂³×C₈×C₈₉	C₄	1	15	yes	—
5	C₂³×C₈×C₈₉	C₂²	1	15	yes	—
6	C₂²×C₁₆×C₈₉	C₂²	1	140	yes	direct product factor
7	C₂⁵×C₈₉	C₈	1	1	yes	characteristic
8	C₂³×C₄×C₈₉	C₈	1	15	yes	—
9	C₂³×C₄×C₈₉	C₂×C₄	1	15	yes	—
10	C₂²×C₈×C₈₉	C₂×C₄	1	105	yes	—
11	C₂²×C₈×C₈₉	C₂³	1	35	yes	—
12	C₂×C₁₆×C₈₉	C₂³	1	120	yes	direct product factor
13	C₂⁴×C₈₉	C₁₆	1	16	yes	direct product factor
14	C₂⁴×C₈₉	C₂×C₈	1	15	yes	—
15	C₂²×C₄×C₈₉	C₂×C₈	1	105	yes	—
16	C₂²×C₄×C₈₉	C₂²×C₄	1	35	yes	—
17	C₂×C₈×C₈₉	C₂²×C₄	1	105	yes	—
18	C₂×C₈×C₈₉	C₂⁴	1	15	yes	—
19	C₁₆×C₈₉	C₂⁴	1	16	yes	direct product factor
20	C₂³×C₈₉	C₂×C₁₆	1	120	yes	direct product factor
21	C₂³×C₈₉	C₂²×C₈	1	35	yes	—
22	C₂×C₄×C₈₉	C₂²×C₈	1	105	yes	—
23	C₂×C₄×C₈₉	C₂³×C₄	1	15	yes	—
24	C₈×C₈₉	C₂³×C₄	1	15	yes	—
25	C₈×C₈₉	C₂⁵	1	1	yes	characteristic
26	C₂²×C₈₉	C₂²×C₁₆	1	140	yes	direct product factor
27	C₂²×C₈₉	C₂³×C₈	1	15	yes	—
28	C₄×C₈₉	C₂³×C₈	1	15	yes	—
29	C₄×C₈₉	C₂⁴×C₄	1	1	yes	characteristic
30	C₂⁴×C₁₆	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂×C₈₉	C₂³×C₁₆	1	30	yes	direct product factor
32	C₂×C₈₉	C₂⁴×C₈	1	1	yes	characteristic
33	C₂⁴×C₈	C₂×C₈₉	1	1	yes	characteristic
34	C₂³×C₁₆	C₂×C₈₉	1	30	yes	direct product factor
35	C₈₉	C₂⁴×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
36	C₂⁴×C₄	C₄×C₈₉	1	1	yes	characteristic
37	C₂³×C₈	C₄×C₈₉	1	15	yes	—
38	C₂³×C₈	C₂²×C₈₉	1	15	yes	—
39	C₂²×C₁₆	C₂²×C₈₉	1	140	yes	direct product factor
40	C₂⁵	C₈×C₈₉	1	1	yes	characteristic
41	C₂³×C₄	C₈×C₈₉	1	15	yes	—
42	C₂³×C₄	C₂×C₄×C₈₉	1	15	yes	—
43	C₂²×C₈	C₂×C₄×C₈₉	1	105	yes	—
44	C₂²×C₈	C₂³×C₈₉	1	35	yes	—
45	C₂×C₁₆	C₂³×C₈₉	1	120	yes	direct product factor
46	C₂⁴	C₁₆×C₈₉	1	16	yes	direct product factor
47	C₂⁴	C₂×C₈×C₈₉	1	15	yes	—
48	C₂²×C₄	C₂×C₈×C₈₉	1	105	yes	—
49	C₂²×C₄	C₂²×C₄×C₈₉	1	35	yes	—
50	C₂×C₈	C₂²×C₄×C₈₉	1	105	yes	—
51	C₂×C₈	C₂⁴×C₈₉	1	15	yes	—
52	C₁₆	C₂⁴×C₈₉	1	16	yes	direct product factor
53	C₂³	C₂×C₁₆×C₈₉	1	120	yes	direct product factor
54	C₂³	C₂²×C₈×C₈₉	1	35	yes	—
55	C₂×C₄	C₂²×C₈×C₈₉	1	105	yes	—
56	C₂×C₄	C₂³×C₄×C₈₉	1	15	yes	—
57	C₈	C₂³×C₄×C₈₉	1	15	yes	—
58	C₈	C₂⁵×C₈₉	1	1	yes	characteristic
59	C₂²	C₂²×C₁₆×C₈₉	1	140	yes	direct product factor
60	C₂²	C₂³×C₈×C₈₉	1	15	yes	—
61	C₄	C₂³×C₈×C₈₉	1	15	yes	—
62	C₄	C₂⁴×C₄×C₈₉	1	1	yes	characteristic
63	C₂	C₂³×C₁₆×C₈₉	1	30	yes	direct product factor
64	C₂	C₂⁴×C₈×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂⁵×C₈₉
socle, prime radical	C₂⁵×C₈₉	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₁₆×C₈₉	C₂	direct (N × H)
6. C₂²×C₁₆×C₈₉	C₂²	direct (N × H)
12. C₂×C₁₆×C₈₉	C₂³	direct (N × H)
13. C₂⁴×C₈₉	C₁₆	direct (N × H)
19. C₁₆×C₈₉	C₂⁴	direct (N × H)
20. C₂³×C₈₉	C₂×C₁₆	direct (N × H)
26. C₂²×C₈₉	C₂²×C₁₆	direct (N × H)
30. C₂⁴×C₁₆	C₈₉	direct (N × H)
31. C₂×C₈₉	C₂³×C₁₆	direct (N × H)
34. C₂³×C₁₆	C₂×C₈₉	direct (N × H)
35. C₈₉	C₂⁴×C₁₆	direct (N × H)
39. C₂²×C₁₆	C₂²×C₈₉	direct (N × H)
45. C₂×C₁₆	C₂³×C₈₉	direct (N × H)
46. C₂⁴	C₁₆×C₈₉	direct (N × H)
52. C₁₆	C₂⁴×C₈₉	direct (N × H)
53. C₂³	C₂×C₁₆×C₈₉	direct (N × H)
59. C₂²	C₂²×C₁₆×C₈₉	direct (N × H)
63. C₂	C₂³×C₁₆×C₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₈×C₈₉	2
C₂³×C₁₆×C₈₉	2
C₂⁴×C₁₆	89

Subgroups — C24×C16×C89 #36440468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₁₆×C₈₉ #36440468