Subgroups — D₁₅₆₀₉ #44530193

Order 31218.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₂₀₃	—	3	1	no	maximal, Hall
3	C₄₃×C₁₂₁	D₃	1	1	yes	characteristic, complemented, Hall
4	D₁₄₁₉	—	11	1	no	maximal
5	C₃×C₁₁×C₄₃	D₁₁	1	1	yes	characteristic
6	D₄₇₃	—	33	1	no	—
7	D₃₆₃	—	43	1	no	maximal, Hall
8	C₁₁×C₄₃	D₃₃	1	1	yes	characteristic
9	C₃×C₁₂₁	D₄₃	1	1	yes	characteristic, complemented, Hall
10	D₁₂₉	—	121	1	no	Hall
11	D₁₂₁	—	129	1	no	Hall
12	C₃×C₄₃	D₁₂₁	1	1	yes	characteristic, complemented, Hall
13	C₁₂₁	D₁₂₉	1	1	yes	characteristic, complemented, Sylow
14	D₄₃	—	363	1	no	Hall
15	D₃₃	—	473	1	no	—
16	C₄₃	D₃₆₃	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₁₁	D₄₇₃	1	1	yes	characteristic
18	D₁₁	—	1419	1	no	—
19	C₁₁	D₁₄₁₉	1	1	yes	characteristic
20	D₃	—	5203	1	no	Hall
21	C₃	D₅₂₀₃	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	15609	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₄₃×C₁₂₁	C₂
Frattini	C₁₁	D₁₄₁₉
socle	C₃×C₁₁×C₄₃	D₁₁
LCS	G ▷ C₃×C₄₃×C₁₂₁
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.