Subgroups — #37555545

Order 23556.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20238114	C₂	1	1	yes	maximal, characteristic
2	Dic₁₃×C₁₅₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#20238114	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃×C₁₅₁	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₁₅₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₄×C₁₅₁⋊C₃	—	13	1	no	maximal, Hall
7	C₂×C₁₅₁⋊C₃	—	26	1	no	—
8	C₄×C₁₅₁	—	13	1	no	Hall
9	C₁₅₁⋊C₃	—	26	1	no	Hall
10	C₂×C₁₅₁	D₁₃⋊C₃	1	1	yes	characteristic
11	Dic₁₃⋊C₃	—	151	1	no	maximal, Hall
12	C₁₅₁	Dic₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₁₃⋊C₃	—	151	1	no	—
14	Dic₁₃	C₁₅₁⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₁₃⋊C₃	—	151	1	no	Hall
16	C₂×C₁₃	C₂×C₁₅₁⋊C₃	1	1	yes	characteristic
17	C₁₃	C₄×C₁₅₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	1963	1	no	Hall
19	C₂×C₃	—	3926	1	no	—
20	C₄	—	13	1	no	Sylow
21	C₃	—	3926	1	no	Sylow
22	C₂	#26044501	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#26044501
commutator, hypocenter	C₁₃×C₁₅₁	C₃×C₄
Fitting, socle, cosocle	C₂×C₁₃×C₁₅₁	C₂×C₃
prime radical	C₂×#20238114	C₂
LCS	G ▷ C₁₃×C₁₅₁
UCS	C₁ ◁ C₂

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.