Subgroups — C₁₁⋊#11927415 #27211897

Order 13420.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×D₆₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁⋊#6923	—	5	1	no	maximal, Hall
4	C₁₁×D₆₁	D₅	1	1	yes	characteristic
5	#11927415	—	11	1	no	maximal, Hall
6	C₁₁×C₆₁	Dic₅	1	1	yes	characteristic, complemented, Hall
7	C₅×D₆₁	D₁₁	1	1	yes	characteristic
8	C₅×C₆₁	Dic₁₁	1	1	yes	characteristic, complemented, Hall
9	#6923	—	55	1	no	Hall
10	Dic₅₅	—	61	1	no	maximal, Hall
11	D₆₁	D₅₅	1	1	yes	characteristic
12	C₂×C₅×C₁₁	—	61	1	no	—
13	C₆₁	Dic₅₅	1	1	yes	characteristic, complemented, Sylow
14	C₅×C₁₁	#6923	1	1	yes	characteristic, complemented, Hall
15	Dic₁₁	—	305	1	no	Hall
16	C₂×C₁₁	—	61	1	no	—
17	Dic₅	—	671	1	no	Hall
18	C₁₁	#11927415	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	—	61	1	no	—
20	C₅	C₁₁⋊#6923	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	3355	1	no	Sylow
22	C₂	—	61	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₁×C₆₁	C₄
prime radical, cosocle	C₅×C₁₁×D₆₁	C₂
LCS	G ▷ C₅×C₁₁×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.