Subgroups — #49178113

Order 37596.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₂₄₁⋊C₃)⋊D₁₃	C₂	1	1	yes	maximal, characteristic
2	#27159927	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×C₂₄₁⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	D₃₁₃₃	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₂₄₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	#11757210⋊C₃	—	13	1	no	maximal, Hall
7	D₂₄₁⋊C₃	—	13	1	no	—
8	#11757210	—	13	1	no	Hall
9	C₂₄₁⋊C₃	#261	1	1	yes	characteristic, complemented, Hall
10	D₂₄₁	—	13	1	no	—
11	C₂₄₁	C₃×#261	1	1	yes	characteristic, complemented, Sylow
12	C₃×#261	—	241	1	no	maximal, Hall
13	C₃×D₁₃	—	241	1	no	—
14	#261	—	241	1	no	Hall
15	C₃×C₁₃	—	241	1	no	Hall
16	D₁₃	—	241	1	no	—
17	C₁₃	#11757210⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	3133	1	no	Hall
19	C₂×C₃	—	3133	1	no	—
20	C₄	—	3133	1	no	Sylow
21	C₃	—	241	1	no	Sylow
22	C₂	—	3133	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃×C₂₄₁	C₃×C₄
prime radical	(C₂₄₁⋊C₃)⋊D₁₃	C₂
cosocle	D₃₁₃₃	C₂×C₃
LCS	G ▷ C₁₃×C₂₄₁
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.