Subgroups — D₄₃×C₃₆₇ #44538830

Order 31562.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×C₃₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₃₆₇	—	43	1	no	maximal, Hall
3	C₃₆₇	D₄₃	1	1	yes	characteristic, direct product factor, Sylow
4	D₄₃	C₃₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₄₃	C₂×C₃₆₇	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	43	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₆₇	D₄₃
commutator, cosocle, hypocenter	C₄₃	C₂×C₃₆₇
Frattini	C₁	G
Fitting, socle	C₄₃×C₃₆₇	C₂
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₃₆₇

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.