Finite Group Databasebeta

Subgroups — #29507436

Order 15424.

14 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₂×C₂₄₁	C₂	1	1	yes	maximal, characteristic
2	C₁₆×C₂₄₁	C₄	1	1	yes	characteristic
3	C₈×C₂₄₁	C₈	1	1	yes	characteristic
4	C₄×C₂₄₁	C₁₆	1	1	yes	characteristic
5	C₂×C₂₄₁	C₃₂	1	1	yes	characteristic
6	C₂₄₁	C₆₄	1	1	yes	characteristic, complemented, Sylow
7	C₆₄	—	241	1	no	maximal, Sylow
8	C₃₂	D₂₄₁	1	1	yes	characteristic
9	C₁₆	Dic₂₄₁	1	1	yes	characteristic
10	C₈	#14515349	1	1	yes	characteristic
11	C₄	#16838745	1	1	yes	characteristic
12	C₂	#21440548	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₃₂	D₂₄₁
commutator, hypocenter	C₂₄₁	C₆₄
Fitting, cosocle	C₃₂×C₂₄₁	C₂
socle, prime radical	C₂×C₂₄₁	C₃₂
LCS	G ▷ C₂₄₁
UCS	C₁ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
6. C₂₄₁	C₆₄	semidirect

Maximal subgroups

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

subgroup	index
C₃₂×C₂₄₁	2
C₆₄	241