Subgroups — D₁₂₁₅₉ #37566513

Order 24318.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×C₁₉₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₀₅₃	—	3	1	no	maximal
3	C₃×C₇×C₁₉₃	D₃	1	1	yes	characteristic
4	D₁₇₃₇	—	7	1	no	maximal, Hall
5	D₁₃₅₁	—	9	1	no	Hall
6	C₉×C₁₉₃	D₇	1	1	yes	characteristic, complemented, Hall
7	C₇×C₁₉₃	D₉	1	1	yes	characteristic, complemented, Hall
8	D₅₇₉	—	21	1	no	—
9	C₃×C₁₉₃	D₂₁	1	1	yes	characteristic
10	D₁₉₃	—	63	1	no	Hall
11	C₁₉₃	D₆₃	1	1	yes	characteristic, complemented, Sylow
12	D₆₃	—	193	1	no	maximal, Hall
13	C₇×C₉	D₁₉₃	1	1	yes	characteristic, complemented, Hall
14	D₂₁	—	579	1	no	—
15	C₃×C₇	D₅₇₉	1	1	yes	characteristic
16	D₉	—	1351	1	no	Hall
17	D₇	—	1737	1	no	Hall
18	C₉	D₁₃₅₁	1	1	yes	characteristic, complemented, Sylow
19	C₇	D₁₇₃₇	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	4053	1	no	—
21	C₃	D₄₀₅₃	1	1	yes	characteristic
22	C₂	—	12159	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₇×C₉×C₁₉₃	C₂
Frattini	C₃	D₄₀₅₃
socle	C₃×C₇×C₁₉₃	D₃
LCS	G ▷ C₇×C₉×C₁₉₃
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.