Subgroups — C₃⋊(#127⋊C₃) #63757

Order 288.

59 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	#874	C₃	1	1	yes	maximal, characteristic, complemented
3	#127⋊C₃	—	3	1	no	maximal
4	D₃×A₄	—	4	1	no	maximal
5	C₂×D₁₂	—	3	1	no	—
6	C₂×D₁₂	—	3	1	no	—
7	C₃×C₄²	C₂×C₃	1	1	yes	characteristic, complemented
8	C₄²⋊C₃	—	2	1	no	—
9	C₄²⋊C₃	D₃	1	1	yes	characteristic, complemented
10	C₃×A₄	—	4	1	no	—
11	#127	—	3	1	no	Sylow
12	C₂²×D₃	—	3	1	no	—
13	C₂²×D₃	A₄	1	1	yes	characteristic
14	C₂×A₄	—	12	1	no	—
15	C₂×C₃×C₄	—	3	1	no	—
16	D₁₂	—	6	2	no	—
17	D₁₂	—	6	2	no	—
18	C₃×D₃	—	16	1	no	—
19	C₂×D₄	—	9	1	no	—
20	C₂×D₄	—	9	1	no	—
21	C₄²	C₃×D₃	1	1	yes	characteristic, complemented
22	C₂²×C₃	C₂×A₄	1	1	yes	characteristic
23	C₂×D₃	—	6	1	no	—
24	C₂×D₃	—	6	1	no	—
25	C₂×D₃	—	6	2	no	—
26	A₄	—	4	1	no	—
27	A₄	—	8	1	no	—
28	C₃×C₄	—	3	2	no	—
29	C₃²	—	16	1	no	Sylow
30	C₂³	—	3	1	no	—
31	C₂³	—	9	1	no	—
32	D₄	—	18	2	no	—
33	D₄	—	18	2	no	—
34	C₂×C₄	—	3	1	no	—
35	C₂×C₃	—	3	1	no	—
36	C₂×C₃	—	48	1	no	—
37	D₃	—	4	1	no	—
38	D₃	—	12	1	no	—
39	C₂²	—	18	1	no	—
40	C₂²	—	18	1	no	—
41	C₂²	—	18	2	no	—
42	C₂²	D₃×A₄	1	1	yes	characteristic
43	C₄	—	3	2	no	—
44	C₃	—	16	1	no	—
45	C₃	—	32	1	no	—
46	C₃	#127⋊C₃	1	1	yes	characteristic, complemented
47	C₂	—	3	1	no	—
48	C₂	—	12	1	no	—
49	C₂	—	36	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₄²	C₂×C₃
Frattini	C₂²	D₃×A₄
socle	C₂²×C₃	C₂×A₄
LCS	G ▷ C₃×C₄²
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.