Subgroups — Dic₇₈₃₁ #44531202

Order 31324.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×C₁₉₁	C₂	1	1	yes	maximal, characteristic
2	C₄₁×C₁₉₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₉₁	—	41	1	no	maximal, Hall
4	C₂×C₁₉₁	D₄₁	1	1	yes	characteristic
5	C₁₉₁	Dic₄₁	1	1	yes	characteristic, complemented, Sylow
6	Dic₄₁	—	191	1	no	maximal, Hall
7	C₂×C₄₁	D₁₉₁	1	1	yes	characteristic
8	C₄₁	Dic₁₉₁	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	7831	1	no	Sylow
10	C₂	D₇₈₃₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇₈₃₁
commutator, hypocenter	C₄₁×C₁₉₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₄₁×C₁₉₁	C₂
LCS	G ▷ C₄₁×C₁₉₁
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.