Subgroups — #44538340

Order 31476.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#21463501	C₂	1	1	yes	maximal, characteristic
2	C₄₃×Dic₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#21463501	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	C₄×C₄₃⋊C₃	—	61	1	no	maximal, Hall
8	C₂×C₆₁⋊C₃	—	43	1	no	—
9	C₂×C₄₃⋊C₃	—	61	1	no	—
10	Dic₆₁	C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
11	C₆₁⋊C₃	—	43	1	no	Hall
12	C₄×C₄₃	—	61	1	no	Hall
13	C₄₃⋊C₃	—	61	1	no	Hall
14	C₂×C₆₁	C₂×C₄₃⋊C₃	1	1	yes	characteristic
15	C₂×C₄₃	D₆₁⋊C₃	1	1	yes	characteristic
16	C₆₁	C₄×C₄₃⋊C₃	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	—	2623	1	no	—
20	C₄	—	61	1	no	Sylow
21	C₃	—	2623	1	no	Sylow
22	C₂	#30628680	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#30628680
commutator, hypocenter	C₄₃×C₆₁	C₃×C₄
Fitting, socle, cosocle	C₂×C₄₃×C₆₁	C₂×C₃
prime radical	C₂×#21463501	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.