Subgroups — #27165643

Order 12832.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₆×C₄₀₁	C₂	1	1	yes	maximal, characteristic
2	C₈×C₄₀₁	C₄	1	1	yes	characteristic
3	C₄×C₄₀₁	C₈	1	1	yes	characteristic
4	C₂×C₄₀₁	C₁₆	1	1	yes	characteristic
5	C₄₀₁	C₃₂	1	1	yes	characteristic, complemented, Sylow
6	C₃₂	—	401	1	no	maximal, Sylow
7	C₁₆	D₄₀₁	1	1	yes	characteristic
8	C₈	Dic₄₀₁	1	1	yes	characteristic
9	C₄	#15691999	1	1	yes	characteristic
10	C₂	#20264341	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₁₆	D₄₀₁
commutator, hypocenter	C₄₀₁	C₃₂
Fitting, cosocle	C₁₆×C₄₀₁	C₂
socle, prime radical	C₂×C₄₀₁	C₁₆
LCS	G ▷ C₄₀₁
UCS	C₁ ◁ C₁₆

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
5. C₄₀₁	C₃₂	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₆×C₄₀₁	2
C₃₂	401