Subgroups — Q₈⋊(C₁₃⋊C₃) #64610

Order 312.

14 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₃⋊C₃	—	4	1	no	maximal
3	C₄×C₁₃	—	3	1	no	—
4	C₁₃⋊C₃	—	4	1	no	Hall
5	C₂×C₁₃	A₄	1	1	yes	characteristic
6	SL(2,𝔽₃)	—	13	1	no	maximal, Hall
7	C₁₃	SL(2,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
8	Q₈	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
9	C₂×C₃	—	52	1	no	—
10	C₄	—	3	1	no	—
11	C₃	—	52	1	no	Sylow
12	C₂	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₂²⋊(C₁₃⋊C₃)
commutator, Fitting, cosocle, hypocenter	Q₈×C₁₃	C₃
socle	C₂×C₁₃	A₄
LCS	G ▷ Q₈×C₁₃
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.