Subgroups — #39907340

Order 26024.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₂₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₂₅₃	C₄	1	1	yes	characteristic
3	C₃₂₅₃	C₈	1	1	yes	characteristic, complemented, Sylow
4	C₈	—	3253	1	no	maximal, Sylow
5	C₄	—	3253	1	no	—
6	C₂	#27189008	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#27189008
commutator, hypocenter	C₃₂₅₃	C₈
Fitting, socle, prime radical	C₂×C₃₂₅₃	C₄
cosocle	Dic₃₂₅₃	C₂
LCS	G ▷ C₃₂₅₃
UCS	C₁ ◁ C₂

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

N	H ≅ G/N	type
3. C₃₂₅₃	C₈	semidirect

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

subgroup	index
Dic₃₂₅₃	2
C₈	3253