Subgroups — C₂×SU(3,𝔽₂) #88884

Order 432.

67 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1088	C₂	1	3	yes	maximal
2	SU(3,𝔽₂)	C₂	1	4	yes	maximal, direct product factor
3	C₂×#272	C₂²	1	1	yes	characteristic
4	#1088	C₂²	1	6	yes	—
5	C₂×H(3,𝔽₃)	Q₈	1	1	yes	characteristic, complemented
6	#272	Q₈	1	1	yes	characteristic, complemented
7	#272	C₂³	1	1	yes	characteristic
8	C₂×C₃×Q₈	—	9	1	no	maximal
9	C₂×C₃×D₃	—	12	1	no	—
10	H(3,𝔽₃)	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
11	C₃×Q₈	—	9	4	no	—
12	C₂×C₃×C₄	—	9	3	no	—
13	C₂×C₃²	—	4	1	no	—
14	C₃×D₃	—	12	1	no	—
15	C₃×D₃	—	12	1	no	—
16	C₂×Q₈	—	9	1	no	Sylow
17	C₂²×C₃	—	9	1	no	—
18	C₂×D₃	—	12	1	no	—
19	C₃×C₄	—	9	6	no	—
20	C₃²	—	4	1	no	—
21	Q₈	—	9	4	no	—
22	C₂×C₄	—	9	3	no	—
23	C₂×C₃	—	9	1	no	—
24	C₂×C₃	—	9	1	no	—
25	C₂×C₃	—	12	1	no	—
26	C₂×C₃	PSU(3,𝔽₂)	1	1	yes	characteristic
27	D₃	—	12	1	no	—
28	D₃	—	12	1	no	—
29	C₂²	—	9	1	no	—
30	C₄	—	9	6	no	—
31	C₃	—	12	1	no	—
32	C₃	C₂×PSU(3,𝔽₂)	1	1	yes	characteristic
33	C₂	—	9	1	no	—
34	C₂	—	9	1	no	—
35	C₂	SU(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.