Subgroups — #43269643

Order 28548.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28384442	C₂	1	1	yes	maximal, characteristic
2	C₃×#15691758	C₃	1	1	yes	maximal, characteristic
3	#20297358	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×D₇₉₃	C₂×C₃	1	1	yes	characteristic
5	#15691758	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃×C₆₁	C₃×C₄	1	1	yes	characteristic
7	#6923⋊C₉	—	13	1	no	maximal, Hall
8	D₇₉₃	C₂×C₉	1	1	yes	characteristic
9	D₆₁⋊C₉	—	13	1	no	—
10	C₁₃×C₆₁	C₄×C₉	1	1	yes	characteristic, complemented, Hall
11	C₃×#6923	—	39	1	no	—
12	C₆₁⋊C₉	—	13	1	no	Hall
13	#261⋊C₉	—	61	1	no	maximal, Hall
14	C₃×D₆₁	—	39	1	no	—
15	#6923	—	39	1	no	Hall
16	D₁₃⋊C₉	—	61	1	no	—
17	C₃×C₆₁	AGL(1,𝔽₁₃)	1	1	yes	characteristic
18	C₃×#261	—	183	1	no	—
19	D₆₁	—	39	1	no	—
20	C₁₃⋊C₉	—	61	1	no	Hall
21	C₃×D₁₃	—	183	1	no	—
22	C₆₁	#261⋊C₉	1	1	yes	characteristic, complemented, Sylow
23	#261	—	183	1	no	Hall
24	C₃×C₁₃	#6923⋊C₃	1	1	yes	characteristic
25	C₄×C₉	—	793	1	no	Hall
26	D₁₃	—	183	1	no	—
27	C₂×C₉	—	793	1	no	—
28	C₁₃	#6923⋊C₉	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	2379	1	no	—
30	C₉	—	793	1	no	Sylow
31	C₂×C₃	—	2379	1	no	—
32	C₄	—	2379	1	no	Sylow
33	C₃	#23748920	1	1	yes	characteristic
34	C₂	—	2379	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	#23748920
commutator, hypocenter	C₁₃×C₆₁	C₄×C₉
Fitting, socle	C₃×C₁₃×C₆₁	C₃×C₄
prime radical, cosocle	C₃×D₇₉₃	C₂×C₃
LCS	G ▷ C₁₃×C₆₁
UCS	C₁ ◁ C₃

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.