Subgroups — C₂×C₉×M₁₆ #63532

Order 288.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₉×M₁₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×C₉	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×M₁₆	C₃	1	1	yes	maximal, characteristic
5	C₂³×C₉	C₄	1	1	yes	characteristic
6	C₂×C₄×C₉	C₄	1	1	yes	characteristic
7	C₂×C₄×C₉	C₄	1	2	yes	—
8	C₂×C₄×C₉	C₂²	1	2	yes	—
9	C₂×C₄×C₉	C₂²	1	1	yes	characteristic
10	C₈×C₉	C₂²	1	4	yes	complemented
11	C₂²×C₃×C₄	C₂×C₃	1	1	yes	characteristic
12	C₃×M₁₆	C₂×C₃	1	4	yes	—
13	C₂×C₃×C₈	C₂×C₃	1	2	yes	—
14	C₂²×C₉	—	2	2	no	—
15	C₂²×C₉	C₂×C₄	1	2	yes	—
16	C₂²×C₉	C₂×C₄	1	1	yes	characteristic
17	C₄×C₉	C₂×C₄	1	2	yes	—
18	C₄×C₉	C₂×C₄	1	1	yes	characteristic
19	C₄×C₉	C₂³	1	1	yes	characteristic
20	C₂×M₁₆	C₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₂³×C₃	C₃×C₄	1	1	yes	characteristic
22	C₂×C₃×C₄	C₃×C₄	1	2	yes	—
23	C₂×C₃×C₄	C₃×C₄	1	1	yes	characteristic
24	C₂×C₃×C₄	C₂²×C₃	1	2	yes	—
25	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
26	C₃×C₈	C₂²×C₃	1	4	yes	—
27	C₂×C₉	—	2	2	no	—
28	C₂×C₉	M₁₆	1	2	yes	direct product factor
29	C₂×C₉	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₄	C₂×C₉	1	1	yes	characteristic
31	M₁₆	C₂×C₉	1	4	yes	direct product factor
32	C₂×C₈	C₂×C₉	1	2	yes	complemented
33	C₂²×C₃	—	2	2	no	—
34	C₂²×C₃	C₂×C₃×C₄	1	2	yes	—
35	C₂²×C₃	C₂×C₃×C₄	1	1	yes	characteristic
36	C₃×C₄	C₂×C₃×C₄	1	2	yes	—
37	C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
38	C₃×C₄	C₂³×C₃	1	1	yes	characteristic
39	C₉	C₂×M₁₆	1	1	yes	characteristic, direct product factor, Sylow
40	C₂³	C₄×C₉	1	1	yes	characteristic
41	C₂×C₄	C₄×C₉	1	2	yes	—
42	C₂×C₄	C₄×C₉	1	1	yes	characteristic
43	C₂×C₄	C₂²×C₉	1	1	yes	characteristic
44	C₂×C₄	C₂²×C₉	1	2	yes	—
45	C₈	C₂²×C₉	1	4	yes	complemented
46	C₂×C₃	—	2	2	no	—
47	C₂×C₃	C₃×M₁₆	1	2	yes	—
48	C₂×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
49	C₂²	—	2	2	no	—
50	C₂²	C₂×C₄×C₉	1	2	yes	—
51	C₂²	C₂×C₄×C₉	1	1	yes	characteristic
52	C₄	C₂×C₄×C₉	1	1	yes	characteristic
53	C₄	C₂×C₄×C₉	1	2	yes	—
54	C₄	C₂³×C₉	1	1	yes	characteristic
55	C₃	C₂×C₃×M₁₆	1	1	yes	characteristic
56	C₂	—	2	2	no	—
57	C₂	C₉×M₁₆	1	2	yes	direct product factor
58	C₂	C₂²×C₄×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂²
commutator	C₂	C₂²×C₄×C₉
Frattini, cosocle	C₃×C₄	C₂³×C₃
socle	C₂²×C₃	C₂×C₃×C₄
prime radical	C₂³×C₃	C₃×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×M₁₆	C₂	direct (N × H)
3. C₂×C₈×C₉	C₂	semidirect
10. C₈×C₉	C₂²	semidirect
20. C₂×M₁₆	C₉	direct (N × H)
28. C₂×C₉	M₁₆	direct (N × H)
31. M₁₆	C₂×C₉	direct (N × H)
32. C₂×C₈	C₂×C₉	semidirect
39. C₉	C₂×M₁₆	direct (N × H)
45. C₈	C₂²×C₉	semidirect
57. C₂	C₉×M₁₆	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×C₄×C₉	2
C₉×M₁₆	2
C₂×C₈×C₉	2
C₂×C₃×M₁₆	3

Subgroups — C2×C9×M16 #63532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×M₁₆ #63532