Subgroups — C₉×C₄⋊C₈ #63407

Order 288.

57 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₉	C₂	1	2	yes	maximal
2	C₄²×C₉	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄⋊C₈	C₃	1	1	yes	maximal, characteristic
4	C₂×C₄×C₉	C₄	1	1	yes	characteristic
5	C₂×C₄×C₉	C₄	1	1	yes	characteristic
6	C₂×C₄×C₉	C₂²	1	1	yes	characteristic
7	C₈×C₉	—	2	2	no	—
8	C₂×C₃×C₈	C₂×C₃	1	2	yes	—
9	C₃×C₄²	C₂×C₃	1	1	yes	characteristic
10	C₂²×C₉	C₂×C₄	1	1	yes	characteristic
11	C₄×C₉	—	2	1	no	—
12	C₄×C₉	C₈	1	2	yes	complemented
13	C₄×C₉	D₄	1	1	yes	characteristic
14	C₄×C₉	Q₈	1	1	yes	characteristic
15	C₄⋊C₈	C₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃×C₄	C₃×C₄	1	1	yes	characteristic
17	C₂×C₃×C₄	C₃×C₄	1	1	yes	characteristic
18	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
19	C₃×C₈	—	2	2	no	—
20	C₂×C₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₉	C₂×C₈	1	1	yes	characteristic
22	C₂×C₉	M₁₆	1	1	yes	characteristic
23	C₂×C₈	C₂×C₉	1	2	yes	—
24	C₄²	C₂×C₉	1	1	yes	characteristic
25	C₂²×C₃	C₂×C₃×C₄	1	1	yes	characteristic
26	C₃×C₄	—	2	1	no	—
27	C₃×C₄	C₃×C₈	1	2	yes	—
28	C₃×C₄	C₃×D₄	1	1	yes	characteristic
29	C₃×C₄	C₃×Q₈	1	1	yes	characteristic
30	C₉	C₄⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₄	C₄×C₉	1	1	yes	characteristic
32	C₂×C₄	C₄×C₉	1	1	yes	characteristic
33	C₂×C₄	C₂²×C₉	1	1	yes	characteristic
34	C₈	—	2	2	no	—
35	C₂×C₃	C₃×C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₃	C₂×C₃×C₈	1	1	yes	characteristic
37	C₂×C₃	C₃×M₁₆	1	1	yes	characteristic
38	C₂²	C₂×C₄×C₉	1	1	yes	characteristic
39	C₄	—	2	1	no	—
40	C₄	C₈×C₉	1	2	yes	complemented
41	C₄	D₄×C₉	1	1	yes	characteristic
42	C₄	Q₈×C₉	1	1	yes	characteristic
43	C₃	C₃×C₄⋊C₈	1	1	yes	characteristic
44	C₂	C₉×C₄⋊C₄	1	1	yes	characteristic
45	C₂	C₂×C₈×C₉	1	1	yes	characteristic
46	C₂	C₉×M₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂²
commutator	C₂	C₂×C₈×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂²×C₃
socle, prime radical	C₂²×C₃	C₂×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
12. C₄×C₉	C₈	semidirect
15. C₄⋊C₈	C₉	direct (N × H)
30. C₉	C₄⋊C₈	direct (N × H)
40. C₄	C₈×C₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×C₉	2
C₄²×C₉	2
C₃×C₄⋊C₈	3

Subgroups — C9×C4⋊C8 #63407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₄⋊C₈ #63407