Subgroups — C₃×C₄×D₉ #6208

Order 216.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×D₃	—	3	1	no	maximal
5	C₄×D₉	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃×C₉	C₂²	1	1	yes	characteristic
7	C₃×D₉	C₄	1	2	yes	direct product factor
8	C₂×C₃×D₃	—	3	1	no	—
9	C₃²×C₄	D₃	1	1	yes	characteristic
10	C₃×Dic₃	—	3	1	no	—
11	C₂×D₉	C₂×C₃	1	1	yes	characteristic
12	C₄×C₉	—	2	1	no	—
13	C₄×C₉	C₂×C₃	1	1	yes	characteristic, complemented
14	Dic₉	C₂×C₃	1	1	yes	characteristic, complemented
15	C₃×C₉	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×C₄	—	9	1	no	—
17	C₄×D₃	—	3	1	no	—
18	C₂×C₃²	C₂×D₃	1	1	yes	characteristic
19	C₃×D₃	—	3	2	no	—
20	C₂×C₉	—	2	1	no	—
21	C₂×C₉	C₂²×C₃	1	1	yes	characteristic
22	D₉	C₃×C₄	1	2	yes	direct product factor
23	C₂²×C₃	—	9	1	no	—
24	C₂×D₃	—	3	1	no	—
25	C₃×C₄	—	2	1	no	—
26	C₃×C₄	—	9	1	no	—
27	C₃×C₄	D₉	1	1	yes	characteristic, direct product factor
28	C₃×C₄	C₃×D₃	1	1	yes	characteristic
29	Dic₃	—	3	1	no	—
30	C₃²	C₄×D₃	1	1	yes	characteristic
31	C₉	—	2	1	no	—
32	C₉	C₂×C₃×C₄	1	1	yes	characteristic, complemented
33	C₂×C₄	—	9	1	no	Sylow
34	C₂×C₃	—	2	1	no	—
35	C₂×C₃	—	9	2	no	—
36	C₂×C₃	C₂×D₉	1	1	yes	characteristic
37	C₂×C₃	C₂×C₃×D₃	1	1	yes	characteristic
38	D₃	—	3	2	no	—
39	C₂²	—	9	1	no	—
40	C₄	—	9	1	no	—
41	C₄	C₃×D₉	1	1	yes	characteristic, direct product factor
42	C₃	—	2	1	no	—
43	C₃	C₄×D₉	1	1	yes	characteristic, direct product factor
44	C₃	C₃×C₄×D₃	1	1	yes	characteristic
45	C₂	—	9	2	no	—
46	C₂	C₂×C₃×D₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄	D₉
commutator, hypocenter	C₉	C₂×C₃×C₄
Frattini	C₂×C₃	C₂×C₃×D₃
Fitting	C₃×C₄×C₉	C₂
socle	C₂×C₃²	C₂×D₃
prime radical	C₂×C₃×D₉	C₂
cosocle	C₂×C₉	C₂²×C₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₉	C₂	semidirect
3. C₃×Dic₉	C₂	semidirect
5. C₄×D₉	C₃	direct (N × H)
7. C₃×D₉	C₄	direct (N × H)
13. C₄×C₉	C₂×C₃	semidirect
14. Dic₉	C₂×C₃	semidirect
15. C₃×C₉	C₂×C₄	semidirect
22. D₉	C₃×C₄	direct (N × H)
27. C₃×C₄	D₉	direct (N × H)
32. C₉	C₂×C₃×C₄	semidirect
41. C₄	C₃×D₉	direct (N × H)
43. C₃	C₄×D₉	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×C₃×D₉	2
C₃×C₄×C₉	2
C₃×Dic₉	2
C₃×C₄×D₃	3
C₄×D₉	3

Subgroups — C3×C4×D9 #6208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×D₉ #6208