Subgroups — C₇⋊D₁₆₇₃ #37552824

Order 23422.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₂₃₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₆₇₃	—	7	8	no	maximal
3	C₇×C₂₃₉	D₇	1	8	yes	complemented
4	D₂₃₉	—	49	1	no	Hall
5	C₂₃₉	C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
6	C₇⋊D₇	—	239	1	no	maximal, Hall
7	C₇²	D₂₃₉	1	1	yes	characteristic, complemented, Sylow
8	D₇	—	1673	8	no	—
9	C₇	D₁₆₇₃	1	8	yes	complemented
10	C₂	—	11711	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₂₃₉	C₂
LCS	G ▷ C₇²×C₂₃₉
UCS	C₁

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.