Subgroups — C₂×C₄₁²⋊C₇ #37555253

Order 23534.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

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.