Subgroups — D₁₂₃₃₇ #37590513

Order 24674.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×C₁₆₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₉₄₉	—	13	1	no	maximal
3	C₁₃×C₇₃	D₁₃	1	1	yes	characteristic
4	D₁₆₉	—	73	1	no	maximal, Hall
5	C₁₆₉	D₇₃	1	1	yes	characteristic, complemented, Sylow
6	D₇₃	—	169	1	no	Hall
7	C₇₃	D₁₆₉	1	1	yes	characteristic, complemented, Sylow
8	D₁₃	—	949	1	no	—
9	C₁₃	D₉₄₉	1	1	yes	characteristic
10	C₂	—	12337	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₇₃×C₁₆₉	C₂
Frattini	C₁₃	D₉₄₉
socle	C₁₃×C₇₃	D₁₃
LCS	G ▷ C₇₃×C₁₆₉
UCS	C₁

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.