Subgroups — C₃⋊#857 #63753

Order 288.

60 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	—	3	3	no	maximal
3	#805	—	3	1	no	maximal
4	C₃⋊S₄	—	4	1	no	maximal
5	#235	—	3	1	no	—
6	C₃×C₄²	D₃	1	1	yes	characteristic, complemented
7	#208	—	3	1	no	—
8	C₄²⋊C₃	D₃	1	3	yes	complemented
9	C₃×A₄	—	4	1	no	—
10	#104	—	9	1	no	Sylow
11	S₄	—	12	3	no	—
12	C₂×C₃×C₄	—	3	1	no	—
13	#67	—	6	1	no	—
14	D₁₂	—	3	1	no	—
15	C₄×D₃	—	6	1	no	—
16	Dic₆	—	3	1	no	—
17	C₃⋊C₈	—	6	1	no	—
18	C₃⋊D₃	—	16	1	no	—
19	#41	—	9	1	no	—
20	M₁₆	—	9	1	no	—
21	C₄²	C₃⋊D₃	1	1	yes	characteristic, complemented
22	C₂²×C₃	S₄	1	1	yes	characteristic
23	C₂×D₃	—	6	1	no	—
24	A₄	—	4	3	no	—
25	C₃×C₄	—	3	1	no	—
26	C₃×C₄	—	3	1	no	—
27	Dic₃	—	6	1	no	—
28	C₃²	—	16	1	no	Sylow
29	Q₈	—	9	1	no	—
30	D₄	—	9	1	no	—
31	D₄	—	18	1	no	—
32	C₂×C₄	—	3	1	no	—
33	C₂×C₄	—	18	1	no	—
34	C₈	—	18	1	no	—
35	C₂×C₃	—	3	1	no	—
36	D₃	—	12	1	no	—
37	D₃	—	48	3	no	—
38	C₂²	—	18	1	no	—
39	C₂²	C₃⋊S₄	1	1	yes	characteristic
40	C₄	—	3	1	no	—
41	C₄	—	3	1	no	—
42	C₄	—	18	1	no	—
43	C₃	—	16	3	no	—
44	C₃	#857	1	1	yes	characteristic, complemented
45	C₂	—	3	1	no	—
46	C₂	—	36	1	no	—

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

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.