Subgroups — C₃×#625 #6284

Order 216.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×D₃	C₂	1	2	yes	maximal, complemented
2	C₃×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#67	—	3	2	no	maximal
4	#625	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₃³	C₂²	1	1	yes	characteristic
6	C₃²×D₃	—	2	2	no	—
7	C₂²×C₃²	—	3	2	no	—
8	C₂×C₃×D₃	—	2	2	no	—
9	C₂×C₃×D₃	D₃	1	2	yes	complemented
10	C₂×C₃×D₃	C₂×C₃	1	2	yes	complemented
11	C₃⋊Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×Dic₃	—	3	2	no	—
13	C₃×Dic₃	—	6	1	no	—
14	C₃³	D₄	1	1	yes	characteristic, complemented, Sylow
15	C₃×D₄	—	9	1	no	—
16	#67	—	3	2	no	—
17	C₂×C₃²	—	2	1	no	—
18	C₂×C₃²	—	2	2	no	—
19	C₂×C₃²	—	4	1	no	—
20	C₂×C₃²	—	6	2	no	—
21	C₂×C₃²	C₂×D₃	1	2	yes	—
22	C₂×C₃²	C₂²×C₃	1	1	yes	characteristic
23	C₃×D₃	—	2	4	no	—
24	C₃×D₃	—	2	2	no	—
25	C₃×D₃	—	2	2	no	—
26	C₂²×C₃	—	3	2	no	—
27	C₂²×C₃	—	3	2	no	—
28	C₂²×C₃	—	6	2	no	—
29	C₂×D₃	C₃×D₃	1	2	yes	complemented
30	C₃×C₄	—	9	1	no	—
31	Dic₃	—	3	2	no	—
32	Dic₃	—	6	1	no	—
33	C₃²	—	2	1	no	—
34	C₃²	—	2	2	no	—
35	C₃²	—	4	1	no	—
36	C₃²	#67	1	2	yes	complemented
37	C₃²	C₃×D₄	1	1	yes	characteristic, complemented
38	D₄	—	9	1	no	Sylow
39	C₂×C₃	—	2	1	no	—
40	C₂×C₃	—	2	2	no	—
41	C₂×C₃	—	4	1	no	—
42	C₂×C₃	—	6	4	no	—
43	C₂×C₃	—	6	2	no	—
44	C₂×C₃	—	6	2	no	—
45	C₂×C₃	D₃²	1	1	yes	characteristic
46	C₂×C₃	C₂×C₃×D₃	1	2	yes	—
47	D₃	—	2	2	no	—
48	C₂²	—	3	2	no	—
49	C₄	—	9	1	no	—
50	C₃	—	2	2	no	—
51	C₃	—	2	1	no	—
52	C₃	—	4	1	no	—
53	C₃	#625	1	1	yes	characteristic, direct product factor
54	C₃	C₃×#67	1	2	yes	complemented
55	C₂	—	6	2	no	—
56	C₂	C₃×D₃²	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	D₃²
commutator, cosocle	C₂×C₃²	C₂²×C₃
Frattini	C₂	C₃×D₃²
Fitting, socle	C₂×C₃³	C₂²
hypocenter	C₃²	C₃×D₄
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×D₃	C₂	semidirect
2. C₃×C₃⋊Dic₃	C₂	semidirect
4. #625	C₃	direct (N × H)
9. C₂×C₃×D₃	D₃	semidirect
10. C₂×C₃×D₃	C₂×C₃	semidirect
11. C₃⋊Dic₃	C₂×C₃	semidirect
14. C₃³	D₄	semidirect
29. C₂×D₃	C₃×D₃	semidirect
36. C₃²	#67	semidirect
37. C₃²	C₃×D₄	semidirect
53. C₃	#625	direct (N × H)
54. C₃	C₃×#67	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×D₃	2
C₃×C₃⋊Dic₃	2
C₃×#67	3
#625	3

Subgroups — C3×#625 #6284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#625 #6284