Subgroups — D₄₉×C₃₃₁ #44570041

Order 32438.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₉×C₃₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇×C₃₃₁	—	7	1	no	maximal
3	C₇×C₃₃₁	D₇	1	1	yes	characteristic
4	C₂×C₃₃₁	—	49	1	no	Hall
5	C₃₃₁	D₄₉	1	1	yes	characteristic, direct product factor, Sylow
6	D₄₉	C₃₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₄₉	C₂×C₃₃₁	1	1	yes	characteristic, complemented, Sylow
8	D₇	—	7	1	no	—
9	C₇	D₇×C₃₃₁	1	1	yes	characteristic
10	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₃₁	D₄₉
commutator, cosocle, hypocenter	C₄₉	C₂×C₃₃₁
Frattini	C₇	D₇×C₃₃₁
Fitting	C₄₉×C₃₃₁	C₂
socle	C₇×C₃₃₁	D₇
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₃₃₁

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.