Subgroups — #22575868

Order 8658.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864525	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₃×C₃₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₃×C₃₇	C₂×C₃	1	1	yes	characteristic
4	D₁₃×C₃₇	C₉	1	1	yes	characteristic, complemented, Hall
5	C₂×#66524	—	13	1	no	maximal, Hall
6	C₁₃×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
7	#66524	—	13	1	no	Hall
8	D₁₃⋊C₉	—	37	1	no	maximal, Hall
9	C₂×C₃×C₃₇	—	13	1	no	—
10	C₁₃⋊C₉	—	37	1	no	Hall
11	C₃×C₃₇	D₁₃⋊C₃	1	1	yes	characteristic
12	C₃×D₁₃	C₃₇⋊C₃	1	1	yes	characteristic
13	C₂×C₃₇	—	13	1	no	Hall
14	C₃×C₁₃	C₂×C₃₇⋊C₃	1	1	yes	characteristic
15	C₃₇	D₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
16	D₁₃	#66524	1	1	yes	characteristic, complemented, Hall
17	C₂×C₉	—	481	1	no	Hall
18	C₁₃	C₂×#66524	1	1	yes	characteristic, complemented, Sylow
19	C₉	—	481	1	no	Sylow
20	C₂×C₃	—	13	1	no	—
21	C₃	#15668364	1	1	yes	characteristic
22	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	#15668364
commutator, hypocenter	C₁₃×C₃₇	C₂×C₉
Fitting, socle	C₃×C₁₃×C₃₇	C₂×C₃
LCS	G ▷ C₁₃×C₃₇
UCS	C₁ ◁ C₃

Splittings G = N ⋊ H with N normal; H ≅ G/N.