Subgroups — C₂×C₃×Dic₉ #6218

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

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

Complements

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

N	H ≅ G/N	type
2. C₃×Dic₉	C₂	direct (N × H)
4. C₂×Dic₉	C₃	direct (N × H)
5. C₂×C₃×C₉	C₄	semidirect
11. Dic₉	C₂×C₃	direct (N × H)
12. C₃×C₉	C₂×C₄	semidirect
19. C₂×C₉	C₃×C₄	semidirect
28. C₉	C₂×C₃×C₄	semidirect
32. C₂×C₃	Dic₉	direct (N × H)
39. C₃	C₂×Dic₉	direct (N × H)
41. C₂	C₃×Dic₉	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
C₃×Dic₉	2
C₂×C₃×Dic₃	3
C₂×Dic₉	3

Subgroups — C2×C3×Dic9 #6218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×Dic₉ #6218