Subgroups — C₄×D₃×C₉ #6210

Order 216.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₉	C₂	semidirect
3. C₉×Dic₃	C₂	semidirect
7. D₃×C₉	C₄	direct (N × H)
14. C₄×C₉	D₃	direct (N × H)
15. C₃×C₉	C₂×C₄	semidirect
17. C₄×D₃	C₉	direct (N × H)
27. C₃×C₄	C₂×C₉	semidirect
29. Dic₃	C₂×C₉	semidirect
32. C₉	C₄×D₃	direct (N × H)
38. D₃	C₄×C₉	direct (N × H)
41. C₄	D₃×C₉	direct (N × H)
43. C₃	C₂×C₄×C₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×C₉	2
C₃×C₄×C₉	2
C₉×Dic₃	2
C₃×C₄×D₃	3
C₂×C₄×C₉	3

Subgroups — C4×D3×C9 #6210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₃×C₉ #6210