Subgroups — C₇₁⋊C₃₄₃ #37567004

Order 24353.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₉×C₇₁	C₇	1	1	yes	maximal, characteristic
2	C₇×C₇₁	C₄₉	1	1	yes	characteristic
3	C₃₄₃	—	71	1	no	maximal, Sylow
4	C₇₁	C₃₄₃	1	1	yes	characteristic, complemented, Sylow
5	C₄₉	C₇₁⋊C₇	1	1	yes	characteristic
6	C₇	C₇₁⋊C₄₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄₉	C₇₁⋊C₇
commutator, hypocenter	C₇₁	C₃₄₃
Fitting, cosocle	C₄₉×C₇₁	C₇
socle, prime radical	C₇×C₇₁	C₄₉
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₄₉

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₇₁	C₃₄₃	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄₉×C₇₁	7
C₃₄₃	71