Subgroups — GO⁺(4,𝔽₂) #643

Order 72.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃²	C₂	1	2	yes	maximal, complemented
2	#157	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₃	C₂²	1	1	yes	characteristic
4	C₃×D₃	—	2	2	no	—
5	C₂×D₃	—	6	2	no	—
6	C₃²	D₄	1	1	yes	characteristic, complemented, Sylow
7	D₄	—	9	1	no	maximal, Sylow
8	C₂×C₃	—	6	2	no	—
9	D₃	—	2	2	no	—
10	D₃	—	6	2	no	—
11	C₂²	—	9	2	no	—
12	C₄	—	9	1	no	—
13	C₃	—	2	2	no	—
14	C₂	—	6	2	no	—
15	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle	C₃⋊D₃	C₂²
Fitting, socle, hypocenter	C₃²	D₄
LCS	G ▷ C₃⋊D₃ ▷ C₃²
UCS	C₁

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.