Subgroups — #30657872

Order 16448.

14 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22551693	C₂	1	1	yes	maximal, characteristic
2	#16861632	C₄	1	1	yes	characteristic
3	#14523348	C₈	1	1	yes	characteristic
4	#11759967	C₁₆	1	1	yes	characteristic
5	D₂₅₇	C₃₂	1	1	yes	characteristic
6	C₂₅₇	C₆₄	1	1	yes	characteristic, complemented, Sylow
7	C₆₄	—	257	1	no	maximal, Sylow
8	C₃₂	—	257	1	no	—
9	C₁₆	—	257	1	no	—
10	C₈	—	257	1	no	—
11	C₄	—	257	1	no	—
12	C₂	—	257	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₂₅₇	C₆₄
prime radical	D₂₅₇	C₃₂
cosocle	#22551693	C₂
LCS	G ▷ C₂₅₇
UCS	C₁

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

N	H ≅ G/N	type
6. C₂₅₇	C₆₄	semidirect

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

subgroup	index
#22551693	2
C₆₄	257