Subgroups — C₆₄₃⋊#157 #37529092

Order 23148.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₆₄₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₆₄₃	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₆₄₃	—	6	2	no	—
4	Dic₆₄₃	—	9	1	no	maximal, Hall
5	C₃×C₆₄₃	—	2	2	no	—
6	C₂×C₆₄₃	—	9	1	no	—
7	C₆₄₃	#157	1	1	yes	characteristic, complemented, Sylow
8	#157	—	643	1	no	maximal, Hall
9	C₃⋊D₃	D₆₄₃	1	1	yes	characteristic
10	C₃²	Dic₆₄₃	1	1	yes	characteristic, complemented, Sylow
11	D₃	—	6	2	no	—
12	C₄	—	5787	1	no	Sylow
13	C₃	—	2	2	no	—
14	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₆₄₃	C₄
prime radical, cosocle	C₃⋊D₃×C₆₄₃	C₂
LCS	G ▷ C₃²×C₆₄₃
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.