Subgroups — C₃×#857 #63749

Order 288.

51 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#857	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×#104	—	3	1	no	maximal
4	C₃×S₄	—	4	1	no	maximal
5	C₃×#41	—	3	1	no	—
6	C₃×M₁₆	—	3	1	no	—
7	C₃×C₄²	D₃	1	1	yes	characteristic, complemented
8	C₄²⋊C₃	—	2	1	no	—
9	C₄²⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×A₄	—	4	1	no	—
11	#104	—	3	1	no	Sylow
12	S₄	—	4	1	no	—
13	C₃×Q₈	—	3	1	no	—
14	C₃×D₄	—	3	1	no	—
15	C₃×D₄	—	6	1	no	—
16	C₂×C₃×C₄	—	3	1	no	—
17	C₂×C₃×C₄	—	6	1	no	—
18	C₃×C₈	—	6	1	no	—
19	C₃×D₃	—	16	1	no	—
20	#41	—	3	1	no	—
21	M₁₆	—	3	1	no	—
22	C₄²	C₃×D₃	1	1	yes	characteristic, complemented
23	C₂²×C₃	—	6	1	no	—
24	C₂²×C₃	S₄	1	1	yes	characteristic
25	A₄	—	4	1	no	—
26	A₄	—	8	1	no	—
27	C₃×C₄	—	3	1	no	—
28	C₃×C₄	—	3	1	no	—
29	C₃×C₄	—	6	1	no	—
30	C₃²	—	16	1	no	Sylow
31	Q₈	—	3	1	no	—
32	D₄	—	3	1	no	—
33	D₄	—	6	1	no	—
34	C₂×C₄	—	3	1	no	—
35	C₂×C₄	—	6	1	no	—
36	C₈	—	6	1	no	—
37	C₂×C₃	—	3	1	no	—
38	C₂×C₃	—	12	1	no	—
39	D₃	—	16	1	no	—
40	C₂²	—	6	1	no	—
41	C₂²	C₃×S₄	1	1	yes	characteristic
42	C₄	—	3	1	no	—
43	C₄	—	3	1	no	—
44	C₄	—	6	1	no	—
45	C₃	—	16	1	no	—
46	C₃	—	32	1	no	—
47	C₃	#857	1	1	yes	characteristic, direct product factor
48	C₂	—	3	1	no	—
49	C₂	—	12	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#857
commutator, cosocle, hypocenter	C₄²⋊C₃	C₂×C₃
Frattini	C₂²	C₃×S₄
Fitting	C₃×C₄²	D₃
socle	C₂²×C₃	S₄
LCS	G ▷ C₄²⋊C₃
UCS	C₁ ◁ 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.