Subgroups — C₃²×C₈₁₁⋊C₃ #36346366

Order 21897.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₈₁₁	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×C₈₁₁⋊C₃	C₃	1	12	yes	maximal, direct product factor
3	C₃×C₈₁₁	C₃²	1	4	yes	complemented
4	C₈₁₁⋊C₃	C₃²	1	9	yes	direct product factor
5	C₈₁₁	C₃³	1	1	yes	characteristic, complemented, Sylow
6	C₃³	—	811	1	no	maximal, Sylow
7	C₃²	—	811	12	no	—
8	C₃²	C₈₁₁⋊C₃	1	1	yes	characteristic, direct product factor
9	C₃	—	811	9	no	—
10	C₃	C₃×C₈₁₁⋊C₃	1	4	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₃²	C₈₁₁⋊C₃
commutator, cosocle, hypocenter	C₈₁₁	C₃³
Frattini	C₁	G
Fitting, socle	C₃²×C₈₁₁	C₃
LCS	G ▷ C₈₁₁
UCS	C₁ ◁ C₃²

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.