Subgroups — PSU(3,𝔽₂)⋊C₉ #10620015

Order 648.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×PSU(3,𝔽₂)	C₃	1	1	yes	maximal, characteristic
2	(C₃⋊D₃)⋊C₉	—	4	1	no	maximal
3	C₃×#157	—	3	1	no	—
4	C₃²⋊C₉	—	4	1	no	Sylow
5	PSU(3,𝔽₂)	C₉	1	1	yes	characteristic, complemented
6	Q₈⋊C₉	—	9	1	no	maximal
7	C₃×C₃⋊D₃	A₄	1	1	yes	characteristic
8	D₃×C₉	—	12	1	no	—
9	#157	—	3	1	no	—
10	C₃³	SL(2,𝔽₃)	1	1	yes	characteristic
11	C₃×C₉	—	4	1	no	—
12	C₃×C₉	—	8	1	no	—
13	C₃×Q₈	—	9	1	no	—
14	C₃⋊D₃	C₂²⋊C₉	1	1	yes	characteristic
15	C₃×D₃	—	12	1	no	—
16	C₂×C₉	—	36	1	no	—
17	C₃×C₄	—	27	1	no	—
18	C₃²	—	4	1	no	—
19	C₃²	—	8	1	no	—
20	C₃²	Q₈⋊C₉	1	1	yes	characteristic, complemented
21	C₉	—	12	1	no	—
22	C₉	—	24	1	no	—
23	Q₈	—	9	1	no	Sylow
24	C₂×C₃	—	9	1	no	—
25	D₃	—	12	1	no	—
26	C₄	—	27	1	no	—
27	C₃	—	4	1	no	—
28	C₃	—	8	1	no	—
29	C₃	PSU(3,𝔽₂)⋊C₃	1	1	yes	characteristic
30	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	PSU(3,𝔽₂)⋊C₃
commutator, hypocenter	PSU(3,𝔽₂)	C₉
Fitting, socle	C₃³	SL(2,𝔽₃)
prime radical	C₃×C₃⋊D₃	A₄
cosocle	C₃×PSU(3,𝔽₂)	C₃
LCS	G ▷ PSU(3,𝔽₂)
UCS	C₁ ◁ C₃

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
5. PSU(3,𝔽₂)	C₉	semidirect
20. C₃²	Q₈⋊C₉	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.