Subgroups — #13182004

Order 1744.

10 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₀₉	C₄	1	1	yes	characteristic
3	C₂×C₁₀₉	C₈	1	1	yes	characteristic
4	C₁₀₉	C₁₆	1	1	yes	characteristic, complemented, Sylow
5	C₁₆	—	109	1	no	maximal, Sylow
6	C₈	D₁₀₉	1	1	yes	characteristic
7	C₄	Dic₁₀₉	1	1	yes	characteristic
8	C₂	#11724784	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₈	D₁₀₉
commutator, hypocenter	C₁₀₉	C₁₆
Fitting, cosocle	C₈×C₁₀₉	C₂
socle, prime radical	C₂×C₁₀₉	C₈
LCS	G ▷ C₁₀₉
UCS	C₁ ◁ C₈

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

N	H ≅ G/N	type
4. C₁₀₉	C₁₆	semidirect

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

subgroup	index
C₈×C₁₀₉	2
C₁₆	109