Subgroups — C₂×PSU(3,𝔽₂) #3844

Order 144.

43 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#157	C₂	1	3	yes	maximal
2	PSU(3,𝔽₂)	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃⋊D₃	C₂²	1	1	yes	characteristic
4	#157	C₂²	1	6	yes	—
5	C₂×C₃²	Q₈	1	1	yes	characteristic, complemented
6	C₃⋊D₃	Q₈	1	1	yes	characteristic, complemented
7	C₃⋊D₃	C₂³	1	1	yes	characteristic
8	C₂×Q₈	—	9	1	no	maximal, Sylow
9	C₂×D₃	—	12	1	no	—
10	C₃²	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
11	Q₈	—	9	4	no	—
12	C₂×C₄	—	9	3	no	—
13	C₂×C₃	—	4	1	no	—
14	D₃	—	12	1	no	—
15	D₃	—	12	1	no	—
16	C₂²	—	9	1	no	—
17	C₄	—	9	6	no	—
18	C₃	—	4	1	no	—
19	C₂	—	9	1	no	—
20	C₂	—	9	1	no	—
21	C₂	PSU(3,𝔽₂)	1	1	yes	characteristic, direct product factor

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.