Subgroups — C₃×SU(3,𝔽₂) #10620031

Order 648.

63 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#1088	C₂	1	3	yes	maximal
2	SU(3,𝔽₂)	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×#272	C₂²	1	1	yes	characteristic
4	#1088	C₂×C₃	1	3	yes	—
5	C₃×H(3,𝔽₃)	Q₈	1	1	yes	characteristic, complemented, Sylow
6	C₃²×Q₈	—	9	1	no	maximal
7	C₃²×D₃	—	12	1	no	—
8	#272	C₂²×C₃	1	1	yes	characteristic
9	C₃²×C₄	—	9	3	no	—
10	C₃³	—	4	1	no	—
11	H(3,𝔽₃)	—	8	1	no	—
12	H(3,𝔽₃)	C₃×Q₈	1	1	yes	characteristic, complemented
13	C₃×Q₈	—	9	1	no	—
14	C₃×Q₈	—	9	3	no	—
15	C₂×C₃²	—	9	1	no	—
16	C₃×D₃	—	12	1	no	—
17	C₃×D₃	—	12	3	no	—
18	C₃×C₄	—	9	3	no	—
19	C₃×C₄	—	9	9	no	—
20	C₃²	—	4	1	no	—
21	C₃²	—	8	1	no	—
22	C₃²	—	12	3	no	—
23	C₃²	PSU(3,𝔽₂)	1	1	yes	characteristic
24	Q₈	—	9	1	no	Sylow
25	C₂×C₃	—	9	3	no	—
26	C₂×C₃	—	9	1	no	—
27	D₃	—	12	1	no	—
28	C₄	—	9	3	no	—
29	C₃	—	12	1	no	—
30	C₃	—	24	1	no	—
31	C₃	SU(3,𝔽₂)	1	3	yes	direct product factor
32	C₃	C₃×PSU(3,𝔽₂)	1	1	yes	characteristic
33	C₂	—	9	1	no	—

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.