Subgroups — C₇²×D₃₄₇ #46801008

Order 34006.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₃₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₃₄₇	C₇	1	8	yes	maximal, direct product factor
3	C₇×C₃₄₇	C₂×C₇	1	8	yes	complemented
4	D₃₄₇	C₇²	1	1	yes	characteristic, direct product factor, Hall
5	C₃₄₇	C₂×C₇²	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₇²	—	347	1	no	maximal, Hall
7	C₇²	D₃₄₇	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×C₇	—	347	8	no	—
9	C₇	C₇×D₃₄₇	1	8	yes	direct product factor
10	C₂	—	347	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇²	D₃₄₇
commutator, cosocle, hypocenter	C₃₄₇	C₂×C₇²
Frattini	C₁	G
Fitting, socle	C₇²×C₃₄₇	C₂
LCS	G ▷ C₃₄₇
UCS	C₁ ◁ C₇²

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.