Subgroups — #44538345

Order 31476.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×C₆₁⋊C₃	C₂	1	1	yes	maximal, characteristic
2	Dic₂₆₂₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₃×C₆₁⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₄₃×C₆₁	C₂×C₃	1	1	yes	characteristic
5	C₄₃×C₆₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	Dic₆₁⋊C₃	—	43	1	no	maximal, Hall
7	C₃×Dic₄₃	—	61	1	no	maximal, Hall
8	C₂×C₆₁⋊C₃	D₄₃	1	1	yes	characteristic
9	C₂×C₃×C₄₃	—	61	1	no	—
10	Dic₆₁	—	43	1	no	Hall
11	C₆₁⋊C₃	Dic₄₃	1	1	yes	characteristic, complemented, Hall
12	Dic₄₃	—	61	1	no	Hall
13	C₃×C₄₃	—	61	1	no	Hall
14	C₂×C₆₁	C₃×D₄₃	1	1	yes	characteristic
15	C₂×C₄₃	D₆₁⋊C₃	1	1	yes	characteristic
16	C₆₁	C₃×Dic₄₃	1	1	yes	characteristic, complemented, Sylow
17	C₄₃	Dic₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	2623	1	no	Hall
19	C₂×C₃	—	61	1	no	—
20	C₄	—	2623	1	no	Sylow
21	C₃	—	61	1	no	Sylow
22	C₂	(C₆₁⋊C₃)⋊D₄₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	(C₆₁⋊C₃)⋊D₄₃
commutator, hypocenter	C₄₃×C₆₁	C₃×C₄
Fitting, socle, cosocle	C₂×C₄₃×C₆₁	C₂×C₃
prime radical	C₂×C₄₃×C₆₁⋊C₃	C₂
LCS	G ▷ C₄₃×C₆₁
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.