Subgroups — D₁₅₈₇₃ #44540807

Order 31746.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₁₃×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₂₉₁	—	3	1	no	maximal, Hall
3	C₁₁×C₁₃×C₃₇	D₃	1	1	yes	characteristic, complemented, Hall
4	D₁₄₄₃	—	11	1	no	maximal, Hall
5	D₁₂₂₁	—	13	1	no	maximal, Hall
6	C₃×C₁₃×C₃₇	D₁₁	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₁×C₃₇	D₁₃	1	1	yes	characteristic, complemented, Hall
8	D₄₈₁	—	33	1	no	Hall
9	D₄₂₉	—	37	1	no	maximal, Hall
10	D₄₀₇	—	39	1	no	Hall
11	C₁₃×C₃₇	D₃₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₁×C₁₃	D₃₇	1	1	yes	characteristic, complemented, Hall
13	C₁₁×C₃₇	D₃₉	1	1	yes	characteristic, complemented, Hall
14	D₁₄₃	—	111	1	no	Hall
15	D₁₁₁	—	143	1	no	Hall
16	C₁₁×C₁₃	D₁₁₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₃₇	D₁₄₃	1	1	yes	characteristic, complemented, Hall
18	D₃₉	—	407	1	no	Hall
19	D₃₇	—	429	1	no	Hall
20	D₃₃	—	481	1	no	Hall
21	C₃×C₁₃	D₄₀₇	1	1	yes	characteristic, complemented, Hall
22	C₃₇	D₄₂₉	1	1	yes	characteristic, complemented, Sylow
23	C₃×C₁₁	D₄₈₁	1	1	yes	characteristic, complemented, Hall
24	D₁₃	—	1221	1	no	Hall
25	D₁₁	—	1443	1	no	Hall
26	C₁₃	D₁₂₂₁	1	1	yes	characteristic, complemented, Sylow
27	C₁₁	D₁₄₄₃	1	1	yes	characteristic, complemented, Sylow
28	D₃	—	5291	1	no	Hall
29	C₃	D₅₂₉₁	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	15873	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁×C₁₃×C₃₇	C₂
LCS	G ▷ C₃×C₁₁×C₁₃×C₃₇
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.