Subgroups — C₄×PSU(3,𝔽₂) #64244

Order 288.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×PSU(3,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₄×#157	C₂	1	3	yes	maximal
3	#3777	C₂	1	3	yes	maximal
4	C₂×#157	C₂²	1	3	yes	—
5	C₂×#157	C₂²	1	3	yes	—
6	PSU(3,𝔽₂)	C₄	1	4	yes	direct product factor
7	C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
8	C₂×C₃⋊D₃	C₂³	1	1	yes	characteristic
9	#157	—	2	3	no	—
10	#157	C₂×C₄	1	6	yes	—
11	C₃²×C₄	Q₈	1	1	yes	characteristic, complemented
12	C₃⋊Dic₃	Q₈	1	1	yes	characteristic, complemented
13	C₄×Q₈	—	9	1	no	maximal, Sylow
14	C₄×D₃	—	12	1	no	—
15	C₂×C₃²	C₂×Q₈	1	1	yes	characteristic
16	C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
17	C₃⋊D₃	#41	1	1	yes	characteristic
18	C₂×Q₈	—	9	1	no	—
19	C₄⋊C₄	—	9	3	no	—
20	C₄²	—	9	3	no	—
21	C₂×D₃	—	12	1	no	—
22	C₃×C₄	—	4	1	no	—
23	Dic₃	—	12	1	no	—
24	C₃²	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
25	Q₈	—	9	4	no	—
26	C₂×C₄	—	9	3	no	—
27	C₂×C₄	—	9	1	no	—
28	C₂×C₄	—	9	3	no	—
29	C₂×C₃	—	4	1	no	—
30	D₃	—	12	1	no	—
31	D₃	—	12	1	no	—
32	C₂²	—	9	1	no	—
33	C₄	—	9	6	no	—
34	C₄	—	9	1	no	—
35	C₄	—	18	3	no	—
36	C₄	PSU(3,𝔽₂)	1	1	yes	characteristic, direct product factor
37	C₃	—	4	1	no	—
38	C₂	—	9	1	no	—
39	C₂	—	9	1	no	—
40	C₂	C₂×PSU(3,𝔽₂)	1	1	yes	characteristic

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.