Subgroups — (C₄₃⋊C₃)⋊#6923 #44538355

Order 31476.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₁×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄₃⋊#6923	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₆₁×C₄₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄₃×D₆₁	C₂×C₃	1	1	yes	characteristic
5	C₄₃×C₆₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×#6923	—	43	1	no	maximal, Hall
7	(C₄₃⋊C₃)⋊C₄	—	61	1	no	maximal, Hall
8	C₃×D₆₁	—	43	1	no	—
9	C₂×C₄₃⋊C₃	—	61	1	no	—
10	#6923	—	43	1	no	Hall
11	C₃×C₆₁	—	43	1	no	Hall
12	Dic₄₃	—	61	1	no	Hall
13	C₄₃⋊C₃	#6923	1	1	yes	characteristic, complemented, Hall
14	D₆₁	D₄₃⋊C₃	1	1	yes	characteristic
15	C₂×C₄₃	—	61	1	no	—
16	C₆₁	(C₄₃⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
17	C₄₃	C₃×#6923	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	2623	1	no	Hall
19	C₂×C₃	—	2623	1	no	—
20	C₄	—	2623	1	no	Sylow
21	C₃	—	43	1	no	Sylow
22	C₂	—	61	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₄₃×C₆₁	C₃×C₄
prime radical	D₆₁×C₄₃⋊C₃	C₂
cosocle	C₄₃×D₆₁	C₂×C₃
LCS	G ▷ C₄₃×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.