Subgroups — C₂×PSU(3,𝔽₂)⋊C₃ #89088

Order 432.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	PSU(3,𝔽₂)⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂×PSU(3,𝔽₂)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×(C₃⋊D₃)⋊C₃	—	4	1	no	maximal
4	C₂×#157	—	3	1	no	—
5	PSU(3,𝔽₂)	—	3	1	no	—
6	PSU(3,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×H(3,𝔽₃)	—	4	1	no	—
8	(C₃⋊D₃)⋊C₃	—	4	1	no	—
9	(C₃⋊D₃)⋊C₃	—	4	1	no	—
10	C₂×SL(2,𝔽₃)	—	9	1	no	maximal
11	C₂×C₃⋊D₃	A₄	1	1	yes	characteristic
12	C₂×C₃×D₃	—	12	1	no	—
13	#157	—	3	1	no	—
14	#157	—	3	1	no	—
15	H(3,𝔽₃)	—	4	1	no	Sylow
16	SL(2,𝔽₃)	—	9	1	no	—
17	C₂×C₃²	—	4	1	no	—
18	C₂×C₃²	—	8	1	no	—
19	C₂×C₃²	SL(2,𝔽₃)	1	1	yes	characteristic, complemented
20	C₃⋊D₃	SL(2,𝔽₃)	1	1	yes	characteristic, complemented
21	C₃⋊D₃	C₂×A₄	1	1	yes	characteristic
22	C₃×D₃	—	12	1	no	—
23	C₃×D₃	—	12	1	no	—
24	C₂×Q₈	—	9	1	no	Sylow
25	C₂²×C₃	—	36	1	no	—
26	C₂×D₃	—	12	1	no	—
27	C₃²	—	4	1	no	—
28	C₃²	—	8	1	no	—
29	C₃²	C₂×SL(2,𝔽₃)	1	1	yes	characteristic, complemented
30	Q₈	—	9	1	no	—
31	Q₈	—	27	1	no	—
32	C₂×C₄	—	27	1	no	—
33	C₂×C₃	—	4	1	no	—
34	C₂×C₃	—	12	1	no	—
35	C₂×C₃	—	24	1	no	—
36	C₂×C₃	—	36	1	no	—
37	C₂×C₃	—	36	1	no	—
38	D₃	—	12	1	no	—
39	D₃	—	12	1	no	—
40	C₂²	—	9	1	no	—
41	C₄	—	27	1	no	—
42	C₄	—	27	1	no	—
43	C₃	—	4	1	no	—
44	C₃	—	12	1	no	—
45	C₃	—	24	1	no	—
46	C₂	—	9	1	no	—
47	C₂	—	9	1	no	—
48	C₂	PSU(3,𝔽₂)⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	PSU(3,𝔽₂)⋊C₃
commutator, cosocle, hypocenter	PSU(3,𝔽₂)	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²	SL(2,𝔽₃)
LCS	G ▷ PSU(3,𝔽₂)
UCS	C₁ ◁ C₂

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.