Subgroups — C₁₁⋊#11924078 #27166296

Order 12892.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₂₉₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₂₉₃	C₄	1	1	yes	characteristic, complemented, Hall
3	#11924078	—	11	1	no	maximal, Hall
4	D₂₉₃	D₁₁	1	1	yes	characteristic
5	C₂₉₃	Dic₁₁	1	1	yes	characteristic, complemented, Sylow
6	Dic₁₁	—	293	1	no	maximal, Hall
7	C₂×C₁₁	—	293	1	no	—
8	C₁₁	#11924078	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	3223	1	no	Sylow
10	C₂	—	293	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₁×C₂₉₃	C₄
prime radical, cosocle	C₁₁×D₂₉₃	C₂
LCS	G ▷ C₁₁×C₂₉₃
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.