Subgroups — C₂×C₉×Dic₃ #6219

Order 216.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
2. C₉×Dic₃	C₂	direct (N × H)
5. C₂×C₃×C₉	C₄	semidirect
12. C₃×C₉	C₂×C₄	semidirect
14. C₂×Dic₃	C₉	direct (N × H)
19. C₂×C₉	Dic₃	direct (N × H)
25. Dic₃	C₂×C₉	direct (N × H)
28. C₉	C₂×Dic₃	direct (N × H)
32. C₂×C₃	C₄×C₉	semidirect
39. C₃	C₂×C₄×C₉	semidirect
41. C₂	C₉×Dic₃	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×C₃×C₉	2
C₉×Dic₃	2
C₂×C₃×Dic₃	3
C₂×C₄×C₉	3

Subgroups — C2×C9×Dic3 #6219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×Dic₃ #6219