Subgroups — D₁₀₄₃₁ #35209953

Order 20862.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₉×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₄₇₇	—	3	1	no	maximal
3	C₃×C₁₉×C₆₁	D₃	1	1	yes	characteristic
4	D₁₁₅₉	—	9	1	no	Hall
5	C₁₉×C₆₁	D₉	1	1	yes	characteristic, complemented, Hall
6	D₅₄₉	—	19	1	no	maximal, Hall
7	C₉×C₆₁	D₁₉	1	1	yes	characteristic, complemented, Hall
8	D₁₈₃	—	57	1	no	—
9	D₁₇₁	—	61	1	no	maximal, Hall
10	C₃×C₆₁	D₅₇	1	1	yes	characteristic
11	C₉×C₁₉	D₆₁	1	1	yes	characteristic, complemented, Hall
12	D₆₁	—	171	1	no	Hall
13	D₅₇	—	183	1	no	—
14	C₆₁	D₁₇₁	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₁₉	D₁₈₃	1	1	yes	characteristic
16	D₁₉	—	549	1	no	Hall
17	C₁₉	D₅₄₉	1	1	yes	characteristic, complemented, Sylow
18	D₉	—	1159	1	no	Hall
19	C₉	D₁₁₅₉	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	3477	1	no	—
21	C₃	D₃₄₇₇	1	1	yes	characteristic
22	C₂	—	10431	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₉×C₆₁	C₂
Frattini	C₃	D₃₄₇₇
socle	C₃×C₁₉×C₆₁	D₃
LCS	G ▷ C₉×C₁₉×C₆₁
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.