Subgroups — C₃×#95⋊C₃ #63582

Order 288.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#95	C₃	1	1	yes	maximal, characteristic, complemented
2	#95⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₂×C₃×A₄	—	4	1	no	maximal
4	C₂²×C₃×C₄	—	3	1	no	—
5	C₃×A₄	—	4	1	no	—
6	#95	C₃²	1	1	yes	characteristic, complemented, Sylow
7	C₂³×C₃	A₄	1	1	yes	characteristic
8	C₂×A₄	—	4	3	no	—
9	C₂×C₃×C₄	—	3	2	no	—
10	C₂×C₃×C₄	—	6	2	no	—
11	C₂×C₃²	—	16	1	no	—
12	C₂²×C₄	—	3	1	no	—
13	C₂²×C₃	—	3	1	no	—
14	C₂²×C₃	—	3	1	no	—
15	C₂²×C₃	SL(2,𝔽₃)	1	1	yes	characteristic
16	A₄	—	4	3	no	—
17	C₃×C₄	—	6	2	no	—
18	C₃²	—	16	1	no	Sylow
19	C₂³	C₃×A₄	1	1	yes	characteristic
20	C₂×C₄	—	3	2	no	—
21	C₂×C₄	—	6	2	no	—
22	C₂×C₃	—	3	1	no	—
23	C₂×C₃	—	3	1	no	—
24	C₂×C₃	—	16	3	no	—
25	C₂×C₃	C₄²⋊C₃	1	1	yes	characteristic
26	C₂²	—	3	1	no	—
27	C₂²	—	3	1	no	—
28	C₂²	C₃×SL(2,𝔽₃)	1	1	yes	characteristic
29	C₄	—	6	2	no	—
30	C₃	—	16	3	no	—
31	C₃	#95⋊C₃	1	1	yes	characteristic, direct product factor
32	C₂	—	3	1	no	—
33	C₂	—	3	1	no	—
34	C₂	C₃×C₄²⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	C₄²⋊C₃
commutator, cosocle, hypocenter	#95	C₃²
Frattini	C₂³	C₃×A₄
Fitting	C₃×#95	C₃
socle	C₂³×C₃	A₄
LCS	G ▷ #95
UCS	C₁ ◁ C₂×C₃

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.