Subgroups — Ω⁺(4,𝔽₃) #64212

Order 288.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#997	C₃	1	2	yes	maximal, complemented
2	#994	C₃	1	2	yes	maximal, complemented
3	C₃×SL(2,𝔽₃)	—	4	2	no	maximal
4	#41⋊C₃	—	3	2	no	—
5	H(5,𝔽₂)	C₃²	1	1	yes	characteristic, complemented, Sylow
6	C₂×A₄	—	12	2	no	—
7	C₃×Q₈	—	4	2	no	—
8	SL(2,𝔽₃)	—	4	4	no	—
9	SL(2,𝔽₃)	A₄	1	2	yes	complemented
10	C₂×C₃²	—	16	1	no	—
11	#41	—	3	2	no	—
12	C₂×D₄	—	9	1	no	—
13	A₄	—	12	2	no	—
14	C₃×C₄	—	12	2	no	—
15	C₃²	—	16	1	no	Sylow
16	C₂³	—	3	2	no	—
17	Q₈	C₃×A₄	1	2	yes	—
18	D₄	—	9	2	no	—
19	C₂×C₄	—	9	1	no	—
20	C₂×C₃	—	4	2	no	—
21	C₂×C₃	—	16	2	no	—
22	C₂²	—	9	1	no	—
23	C₂²	—	12	2	no	—
24	C₄	—	3	2	no	—
25	C₃	—	4	2	no	—
26	C₃	—	16	2	no	—
27	C₂	—	18	1	no	—
28	C₂	A₄²	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, socle, hypercenter	C₂	A₄²
commutator, Fitting, cosocle, hypocenter	H(5,𝔽₂)	C₃²
LCS	G ▷ H(5,𝔽₂)
UCS	C₁ ◁ C₂

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.