Subgroups — Dic₃₀₉₇ #27136559

Order 12388.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×C₁₆₃	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₁₆₃	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₆₃	—	19	1	no	maximal, Hall
4	C₂×C₁₆₃	D₁₉	1	1	yes	characteristic
5	C₁₆₃	Dic₁₉	1	1	yes	characteristic, complemented, Sylow
6	Dic₁₉	—	163	1	no	maximal, Hall
7	C₂×C₁₉	D₁₆₃	1	1	yes	characteristic
8	C₁₉	Dic₁₆₃	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	3097	1	no	Sylow
10	C₂	D₃₀₉₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃₀₉₇
commutator, hypocenter	C₁₉×C₁₆₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₉×C₁₆₃	C₂
LCS	G ▷ C₁₉×C₁₆₃
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.