Subgroups — D₁₃₄₃₁ #41001735

Order 26862.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₇×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₄₇₇	—	3	1	no	maximal, Hall
3	C₃₇×C₁₂₁	D₃	1	1	yes	characteristic, complemented, Hall
4	D₁₂₂₁	—	11	1	no	maximal
5	C₃×C₁₁×C₃₇	D₁₁	1	1	yes	characteristic
6	D₄₀₇	—	33	1	no	—
7	D₃₆₃	—	37	1	no	maximal, Hall
8	C₁₁×C₃₇	D₃₃	1	1	yes	characteristic
9	C₃×C₁₂₁	D₃₇	1	1	yes	characteristic, complemented, Hall
10	D₁₂₁	—	111	1	no	Hall
11	D₁₁₁	—	121	1	no	Hall
12	C₁₂₁	D₁₁₁	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₃₇	D₁₂₁	1	1	yes	characteristic, complemented, Hall
14	D₃₇	—	363	1	no	Hall
15	D₃₃	—	407	1	no	—
16	C₃₇	D₃₆₃	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₁₁	D₄₀₇	1	1	yes	characteristic
18	D₁₁	—	1221	1	no	—
19	C₁₁	D₁₂₂₁	1	1	yes	characteristic
20	D₃	—	4477	1	no	Hall
21	C₃	D₄₄₇₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	13431	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₃₇×C₁₂₁	C₂
Frattini	C₁₁	D₁₂₂₁
socle	C₃×C₁₁×C₃₇	D₁₁
LCS	G ▷ C₃×C₃₇×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.