Subgroups — C₂²×PSU(3,𝔽₂) #64384

Order 288.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#157	C₂	1	3	yes	maximal
2	C₂×PSU(3,𝔽₂)	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₃⋊D₃	C₂²	1	1	yes	characteristic
4	C₂×#157	C₂²	1	18	yes	—
5	PSU(3,𝔽₂)	C₂²	1	16	yes	direct product factor
6	C₂²×C₃²	Q₈	1	1	yes	characteristic, complemented
7	C₂×C₃⋊D₃	Q₈	1	3	yes	complemented
8	C₂×C₃⋊D₃	C₂³	1	3	yes	—
9	#157	C₂³	1	12	yes	—
10	C₂²×Q₈	—	9	1	no	maximal, Sylow
11	C₂²×D₃	—	12	1	no	—
12	C₂×C₃²	C₂×Q₈	1	3	yes	complemented
13	C₃⋊D₃	C₂×Q₈	1	3	yes	complemented
14	C₃⋊D₃	C₂⁴	1	1	yes	characteristic
15	C₂×Q₈	—	9	12	no	—
16	C₂²×C₄	—	9	3	no	—
17	C₂²×C₃	—	4	1	no	—
18	C₂×D₃	—	12	3	no	—
19	C₂×D₃	—	12	3	no	—
20	C₃²	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
21	C₂³	—	9	1	no	—
22	Q₈	—	9	16	no	—
23	C₂×C₄	—	9	18	no	—
24	C₂×C₃	—	4	3	no	—
25	D₃	—	12	3	no	—
26	D₃	—	12	1	no	—
27	C₂²	—	9	3	no	—
28	C₂²	—	9	3	no	—
29	C₂²	PSU(3,𝔽₂)	1	1	yes	characteristic, direct product factor
30	C₄	—	9	12	no	—
31	C₃	—	4	1	no	—
32	C₂	—	9	1	no	—
33	C₂	—	9	3	no	—
34	C₂	C₂×PSU(3,𝔽₂)	1	3	yes	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.