Subgroups — #49147243

Order 36905.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×C₆₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
2	#16809824	—	11	12	no	maximal
3	C₁₁×C₆₁	C₁₁⋊C₅	1	12	yes	complemented
4	#10597243	—	61	1	no	maximal, Hall
5	C₆₁⋊C₅	—	121	1	no	Hall
6	C₁₁²	C₆₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
7	C₆₁	#10597243	1	1	yes	characteristic, complemented, Sylow
8	C₁₁⋊C₅	—	671	12	no	—
9	C₁₁	#16809824	1	12	yes	complemented
10	C₅	—	7381	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁²×C₆₁	C₅
LCS	G ▷ C₁₁²×C₆₁
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.