Subgroups — C₃⋊(#126⋊C₃) #63758

Order 288.

43 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	#876	C₃	1	1	yes	maximal, characteristic, complemented
3	#126⋊C₃	—	3	1	no	maximal
4	D₃×A₄	—	4	1	no	maximal
5	C₃×C₄²	C₂×C₃	1	1	yes	characteristic, complemented
6	(C₂×D₃)⋊C₄	—	3	1	no	—
7	Dic₃⋊C₄	—	3	1	no	—
8	C₄²⋊C₃	—	2	1	no	—
9	C₄²⋊C₃	D₃	1	1	yes	characteristic, complemented
10	C₃×A₄	—	4	1	no	—
11	#126	—	3	1	no	Sylow
12	C₂²×D₃	A₄	1	1	yes	characteristic
13	C₂×A₄	—	12	1	no	—
14	C₂×C₃×C₄	—	3	1	no	—
15	C₂×Dic₃	—	3	1	no	—
16	C₃×D₃	—	16	1	no	—
17	C₄⋊C₄	—	9	1	no	—
18	C₂²⋊C₄	—	9	1	no	—
19	C₄²	C₃×D₃	1	1	yes	characteristic, complemented
20	C₂²×C₃	C₂×A₄	1	1	yes	characteristic
21	C₂×D₃	—	6	1	no	—
22	A₄	—	4	1	no	—
23	A₄	—	8	1	no	—
24	C₃×C₄	—	6	1	no	—
25	Dic₃	—	6	1	no	—
26	C₃²	—	16	1	no	Sylow
27	C₂³	—	3	1	no	—
28	C₂×C₄	—	3	1	no	—
29	C₂×C₄	—	9	1	no	—
30	C₂×C₃	—	3	1	no	—
31	C₂×C₃	—	48	1	no	—
32	D₃	—	4	1	no	—
33	C₂²	—	18	1	no	—
34	C₂²	D₃×A₄	1	1	yes	characteristic
35	C₄	—	6	1	no	—
36	C₄	—	18	1	no	—
37	C₃	—	16	1	no	—
38	C₃	—	32	1	no	—
39	C₃	#126⋊C₃	1	1	yes	characteristic, complemented
40	C₂	—	3	1	no	—
41	C₂	—	12	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.