Subgroups — C₂×C₉×Q₁₆ #63536

Order 288.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₉	C₂	1	2	yes	maximal
2	C₉×Q₁₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×C₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×Q₁₆	C₃	1	1	yes	maximal, characteristic
5	Q₈×C₉	—	2	2	no	—
6	Q₈×C₉	C₂²	1	4	yes	—
7	C₂×C₄×C₉	—	2	2	no	—
8	C₂×C₄×C₉	C₂²	1	1	yes	characteristic
9	C₈×C₉	C₂²	1	2	yes	—
10	C₂×C₃×Q₈	C₂×C₃	1	2	yes	—
11	C₃×Q₁₆	C₂×C₃	1	4	yes	—
12	C₂×C₃×C₈	C₂×C₃	1	1	yes	characteristic
13	C₂²×C₉	D₄	1	1	yes	characteristic
14	C₄×C₉	—	2	4	no	—
15	C₄×C₉	D₄	1	1	yes	characteristic
16	C₄×C₉	C₂³	1	1	yes	characteristic
17	C₂×Q₁₆	C₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×Q₈	—	2	2	no	—
19	C₃×Q₈	C₂²×C₃	1	4	yes	—
20	C₂×C₃×C₄	—	2	2	no	—
21	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
22	C₃×C₈	C₂²×C₃	1	2	yes	—
23	C₂×C₉	Q₁₆	1	2	yes	direct product factor
24	C₂×C₉	C₂×D₄	1	1	yes	characteristic
25	C₂×Q₈	C₂×C₉	1	2	yes	—
26	Q₁₆	C₂×C₉	1	4	yes	direct product factor
27	C₂×C₈	C₂×C₉	1	1	yes	characteristic
28	C₂²×C₃	C₃×D₄	1	1	yes	characteristic
29	C₃×C₄	—	2	4	no	—
30	C₃×C₄	C₃×D₄	1	1	yes	characteristic
31	C₃×C₄	C₂³×C₃	1	1	yes	characteristic
32	C₉	C₂×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
33	Q₈	—	2	2	no	—
34	Q₈	C₂²×C₉	1	4	yes	—
35	C₂×C₄	—	2	2	no	—
36	C₂×C₄	C₂²×C₉	1	1	yes	characteristic
37	C₈	C₂²×C₉	1	2	yes	—
38	C₂×C₃	C₃×Q₁₆	1	2	yes	—
39	C₂×C₃	C₂×C₃×D₄	1	1	yes	characteristic
40	C₂²	D₄×C₉	1	1	yes	characteristic
41	C₄	—	2	4	no	—
42	C₄	D₄×C₉	1	1	yes	characteristic
43	C₄	C₂³×C₉	1	1	yes	characteristic
44	C₃	C₂×C₃×Q₁₆	1	1	yes	characteristic
45	C₂	C₉×Q₁₆	1	2	yes	direct product factor
46	C₂	C₂×D₄×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	D₄
commutator	C₄	C₂³×C₉
Frattini, cosocle	C₃×C₄	C₂³×C₃
socle, prime radical	C₂²×C₃	C₃×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×Q₁₆	C₂	direct (N × H)
17. C₂×Q₁₆	C₉	direct (N × H)
23. C₂×C₉	Q₁₆	direct (N × H)
26. Q₁₆	C₂×C₉	direct (N × H)
32. C₉	C₂×Q₁₆	direct (N × H)
45. C₂	C₉×Q₁₆	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×Q₈×C₉	2
C₉×Q₁₆	2
C₂×C₈×C₉	2
C₂×C₃×Q₁₆	3

Subgroups — C2×C9×Q16 #63536

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×Q₁₆ #63536