Subgroups — D₇₃₀₁ #28410285

Order 14602.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₉×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₀₄₃	—	7	1	no	maximal
3	C₇×C₁₄₉	D₇	1	1	yes	characteristic
4	D₁₄₉	—	49	1	no	Hall
5	C₁₄₉	D₄₉	1	1	yes	characteristic, complemented, Sylow
6	D₄₉	—	149	1	no	maximal, Hall
7	C₄₉	D₁₄₉	1	1	yes	characteristic, complemented, Sylow
8	D₇	—	1043	1	no	—
9	C₇	D₁₀₄₃	1	1	yes	characteristic
10	C₂	—	7301	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₄₉×C₁₄₉	C₂
Frattini	C₇	D₁₀₄₃
socle	C₇×C₁₄₉	D₇
LCS	G ▷ C₄₉×C₁₄₉
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.