Subgroups — C₃×#4176 #92273

Order 486.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#731	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×#272	C₃	1	1	yes	maximal, characteristic
3	C₃×D₃×C₉	—	3	1	no	maximal
4	#4176	C₃	1	3	yes	maximal, direct product factor
5	C₃×3₋¹⁺²	—	2	1	no	—
6	C₃×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
7	C₃²×C₉	D₃	1	1	yes	characteristic, complemented
8	#731	—	2	3	no	—
9	#731	C₂×C₃	1	3	yes	complemented
10	C₃²×D₃	—	3	1	no	—
11	C₃²×D₃	—	9	1	no	—
12	C₂×C₃×C₉	—	9	1	no	—
13	#272	C₃²	1	1	yes	characteristic
14	D₃×C₉	—	3	3	no	—
15	C₃³	—	3	1	no	—
16	C₃³	C₃×D₃	1	1	yes	characteristic
17	3₋¹⁺²	—	2	3	no	—
18	3₋¹⁺²	—	6	2	no	—
19	H(3,𝔽₃)	—	2	1	no	—
20	H(3,𝔽₃)	—	6	1	no	—
21	H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
22	C₃×C₉	—	3	1	no	—
23	C₃×C₉	—	6	1	no	—
24	C₃×C₉	—	6	1	no	—
25	C₃×C₉	C₃×D₃	1	3	yes	complemented
26	C₂×C₃²	—	9	1	no	—
27	C₃×D₃	—	3	3	no	—
28	C₃×D₃	—	3	1	no	—
29	C₃×D₃	—	9	1	no	—
30	C₃×D₃	—	9	3	no	—
31	C₂×C₉	—	9	3	no	—
32	C₃²	—	2	1	no	—
33	C₃²	—	3	3	no	—
34	C₃²	—	3	1	no	—
35	C₃²	—	6	1	no	—
36	C₃²	—	9	3	no	—
37	C₃²	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
38	C₃²	C₃²×D₃	1	1	yes	characteristic
39	C₉	—	3	3	no	—
40	C₉	—	6	3	no	—
41	C₂×C₃	—	9	3	no	—
42	C₂×C₃	—	9	1	no	—
43	D₃	—	3	1	no	—
44	D₃	—	9	1	no	—
45	C₃	—	3	1	no	—
46	C₃	—	6	1	no	—
47	C₃	—	9	1	no	—
48	C₃	—	18	1	no	—
49	C₃	#4176	1	3	yes	direct product factor
50	C₃	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
51	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, socle, hypercenter	C₃²	(C₃⋊D₃)⋊C₃
commutator, cosocle, hypocenter	H(3,𝔽₃)	C₂×C₃²
Frattini	C₃²	C₃²×D₃
Fitting	C₃×#731	C₂
prime radical	C₃×#272	C₃
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₃²

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

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