Subgroups — Dic₁₃₉₆₉ #72290331

Order 55876.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×C₂₂₉	C₂	1	1	yes	maximal, characteristic
2	C₆₁×C₂₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₂₂₉	—	61	1	no	maximal, Hall
4	C₂×C₂₂₉	D₆₁	1	1	yes	characteristic
5	Dic₆₁	—	229	1	no	maximal, Hall
6	C₂₂₉	Dic₆₁	1	1	yes	characteristic, complemented, Sylow
7	C₂×C₆₁	D₂₂₉	1	1	yes	characteristic
8	C₆₁	Dic₂₂₉	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	13969	1	no	Sylow
10	C₂	D₁₃₉₆₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₃₉₆₉
commutator, hypocenter	C₆₁×C₂₂₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₆₁×C₂₂₉	C₂
LCS	G ▷ C₆₁×C₂₂₉
UCS	C₁ ◁ C₂

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

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