Subgroups — C₁₁⋊#15691760 #46853085

Order 34892.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₁₃×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₃×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
3	#15691760	—	11	1	no	maximal, Hall
4	Dic₆₇₁	—	13	1	no	maximal, Hall
5	D₁₃×C₆₁	D₁₁	1	1	yes	characteristic
6	C₂×C₁₁×C₆₁	—	13	1	no	—
7	C₁₃×C₆₁	Dic₁₁	1	1	yes	characteristic, complemented, Hall
8	C₁₁×C₆₁	#261	1	1	yes	characteristic, complemented, Hall
9	C₁₁⋊#261	—	61	1	no	maximal, Hall
10	C₁₁×D₁₃	D₆₁	1	1	yes	characteristic
11	Dic₆₁	—	143	1	no	Hall
12	C₁₁×C₁₃	Dic₆₁	1	1	yes	characteristic, complemented, Hall
13	C₂×C₆₁	—	13	1	no	—
14	C₆₁	C₁₁⋊#261	1	1	yes	characteristic, complemented, Sylow
15	#261	—	671	1	no	Hall
16	Dic₁₁	—	793	1	no	Hall
17	D₁₃	D₆₇₁	1	1	yes	characteristic
18	C₂×C₁₁	—	13	1	no	—
19	C₁₃	Dic₆₇₁	1	1	yes	characteristic, complemented, Sylow
20	C₁₁	#15691760	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	8723	1	no	Sylow
22	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₁×C₁₃×C₆₁	C₄
prime radical, cosocle	C₁₁×D₁₃×C₆₁	C₂
LCS	G ▷ C₁₁×C₁₃×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.