Subgroups — #14519683

Order 1952.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₈×C₆₁	C₄	1	1	yes	characteristic
3	C₄×C₆₁	C₈	1	1	yes	characteristic
4	C₂×C₆₁	C₁₆	1	1	yes	characteristic
5	C₆₁	C₃₂	1	1	yes	characteristic, complemented, Sylow
6	C₃₂	—	61	1	no	maximal, Sylow
7	C₁₆	D₆₁	1	1	yes	characteristic
8	C₈	Dic₆₁	1	1	yes	characteristic
9	C₄	#92418	1	1	yes	characteristic
10	C₂	#11758185	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₁₆	D₆₁
commutator, hypocenter	C₆₁	C₃₂
Fitting, cosocle	C₁₆×C₆₁	C₂
socle, prime radical	C₂×C₆₁	C₁₆
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₁₆

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

N	H ≅ G/N	type
5. C₆₁	C₃₂	semidirect

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

subgroup	index
C₁₆×C₆₁	2
C₃₂	61