Subgroups — C₁₀₉×D₁₂₁ #40995813

Order 26378.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₉×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₁×C₁₀₉	—	11	1	no	maximal
3	C₁₁×C₁₀₉	D₁₁	1	1	yes	characteristic
4	D₁₂₁	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₀₉	—	121	1	no	Hall
6	C₁₂₁	C₂×C₁₀₉	1	1	yes	characteristic, complemented, Sylow
7	C₁₀₉	D₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
8	D₁₁	—	11	1	no	—
9	C₁₁	D₁₁×C₁₀₉	1	1	yes	characteristic
10	C₂	—	121	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₀₉	D₁₂₁
commutator, cosocle, hypocenter	C₁₂₁	C₂×C₁₀₉
Frattini	C₁₁	D₁₁×C₁₀₉
Fitting	C₁₀₉×C₁₂₁	C₂
socle	C₁₁×C₁₀₉	D₁₁
LCS	G ▷ C₁₂₁
UCS	C₁ ◁ C₁₀₉

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.