Subgroups — C₇⋊D₇×C₃₃₇ #45682806

Order 33026.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₃₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇×C₃₃₇	—	7	8	no	maximal
3	C₇×C₃₃₇	D₇	1	8	yes	complemented
4	C₂×C₃₃₇	—	49	1	no	Hall
5	C₃₃₇	C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
6	C₇⋊D₇	C₃₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇²	C₂×C₃₃₇	1	1	yes	characteristic, complemented, Sylow
8	D₇	—	7	8	no	—
9	C₇	D₇×C₃₃₇	1	8	yes	complemented
10	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₃₇	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂×C₃₃₇
Frattini	C₁	G
Fitting, socle	C₇²×C₃₃₇	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃₃₇

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.