Subgroups — C₇×C₄₁⋊D₄₁ #37555255

Order 23534.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₄₁²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₁⋊D₄₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₄₁²	C₂×C₇	1	1	yes	characteristic, complemented, Sylow
4	C₇×D₄₁	—	41	42	no	maximal
5	C₇×C₄₁	D₄₁	1	42	yes	complemented
6	D₄₁	—	41	42	no	—
7	C₄₁	C₇×D₄₁	1	42	yes	complemented
8	C₂×C₇	—	1681	1	no	Hall
9	C₇	C₄₁⋊D₄₁	1	1	yes	characteristic, direct product factor, Sylow
10	C₂	—	1681	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	C₄₁⋊D₄₁
commutator, cosocle, hypocenter	C₄₁²	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₄₁²	C₂
LCS	G ▷ C₄₁²
UCS	C₁ ◁ C₇

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.