Subgroups — C₂²×C₉×C₁₆ #10589056

Order 576.

147 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×C₁₆	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃×C₁₆	C₃	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₉	C₄	1	1	yes	characteristic
5	C₂×C₈×C₉	C₄	1	3	yes	—
6	C₂×C₈×C₉	C₂²	1	3	yes	—
7	C₉×C₁₆	C₂²	1	4	yes	direct product factor
8	C₂²×C₃×C₈	C₂×C₃	1	1	yes	characteristic
9	C₂×C₃×C₁₆	C₂×C₃	1	6	yes	—
10	C₂³×C₉	C₈	1	1	yes	characteristic
11	C₂×C₄×C₉	C₈	1	3	yes	—
12	C₂×C₄×C₉	C₂×C₄	1	3	yes	—
13	C₈×C₉	C₂×C₄	1	3	yes	—
14	C₈×C₉	C₂³	1	1	yes	characteristic
15	C₂²×C₁₆	C₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₂²×C₃×C₄	C₃×C₄	1	1	yes	characteristic
17	C₂×C₃×C₈	C₃×C₄	1	3	yes	—
18	C₂×C₃×C₈	C₂²×C₃	1	3	yes	—
19	C₃×C₁₆	C₂²×C₃	1	4	yes	—
20	C₂²×C₉	C₁₆	1	4	yes	direct product factor
21	C₂²×C₉	C₂×C₈	1	3	yes	—
22	C₄×C₉	C₂×C₈	1	3	yes	—
23	C₄×C₉	C₂²×C₄	1	1	yes	characteristic
24	C₂²×C₈	C₂×C₉	1	1	yes	characteristic
25	C₂×C₁₆	C₂×C₉	1	6	yes	direct product factor
26	C₂³×C₃	C₃×C₈	1	1	yes	characteristic
27	C₂×C₃×C₄	C₃×C₈	1	3	yes	—
28	C₂×C₃×C₄	C₂×C₃×C₄	1	3	yes	—
29	C₃×C₈	C₂×C₃×C₄	1	3	yes	—
30	C₃×C₈	C₂³×C₃	1	1	yes	characteristic
31	C₂×C₉	C₂×C₁₆	1	6	yes	direct product factor
32	C₂×C₉	C₂²×C₈	1	1	yes	characteristic
33	C₂²×C₄	C₄×C₉	1	1	yes	characteristic
34	C₂×C₈	C₄×C₉	1	3	yes	—
35	C₂×C₈	C₂²×C₉	1	3	yes	—
36	C₁₆	C₂²×C₉	1	4	yes	direct product factor
37	C₂²×C₃	C₃×C₁₆	1	4	yes	—
38	C₂²×C₃	C₂×C₃×C₈	1	3	yes	—
39	C₃×C₄	C₂×C₃×C₈	1	3	yes	—
40	C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
41	C₉	C₂²×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
42	C₂³	C₈×C₉	1	1	yes	characteristic
43	C₂×C₄	C₈×C₉	1	3	yes	—
44	C₂×C₄	C₂×C₄×C₉	1	3	yes	—
45	C₈	C₂×C₄×C₉	1	3	yes	—
46	C₈	C₂³×C₉	1	1	yes	characteristic
47	C₂×C₃	C₂×C₃×C₁₆	1	6	yes	—
48	C₂×C₃	C₂²×C₃×C₈	1	1	yes	characteristic
49	C₂²	C₉×C₁₆	1	4	yes	direct product factor
50	C₂²	C₂×C₈×C₉	1	3	yes	—
51	C₄	C₂×C₈×C₉	1	3	yes	—
52	C₄	C₂²×C₄×C₉	1	1	yes	characteristic
53	C₃	C₂²×C₃×C₁₆	1	1	yes	characteristic
54	C₂	C₂×C₉×C₁₆	1	6	yes	direct product factor
55	C₂	C₂²×C₈×C₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₈	C₂³×C₃
socle, prime radical	C₂³×C₃	C₃×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₉×C₁₆	C₂	direct (N × H)
7. C₉×C₁₆	C₂²	direct (N × H)
15. C₂²×C₁₆	C₉	direct (N × H)
20. C₂²×C₉	C₁₆	direct (N × H)
25. C₂×C₁₆	C₂×C₉	direct (N × H)
31. C₂×C₉	C₂×C₁₆	direct (N × H)
36. C₁₆	C₂²×C₉	direct (N × H)
41. C₉	C₂²×C₁₆	direct (N × H)
49. C₂²	C₉×C₁₆	direct (N × H)
54. C₂	C₂×C₉×C₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₈×C₉	2
C₂×C₉×C₁₆	2
C₂²×C₃×C₁₆	3

Subgroups — C22×C9×C16 #10589056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₉×C₁₆ #10589056