Subgroups — D₁₁₇ #6616

Order 234.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₉	—	3	1	no	maximal
3	C₃×C₁₃	D₃	1	1	yes	characteristic
4	D₁₃	—	9	1	no	Hall
5	D₉	—	13	1	no	maximal, Hall
6	C₁₃	D₉	1	1	yes	characteristic, complemented, Sylow
7	C₉	D₁₃	1	1	yes	characteristic, complemented, Sylow
8	D₃	—	39	1	no	—
9	C₃	D₃₉	1	1	yes	characteristic
10	C₂	—	117	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₃	C₂
Frattini	C₃	D₃₉
socle	C₃×C₁₃	D₃
LCS	G ▷ C₉×C₁₃
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.