Subgroups — C₁₇⋊(D₁₀₃⋊C₉) #44538549

Order 31518.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₁₀₃⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₇₅₁	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₇×C₁₀₃	C₂×C₃	1	1	yes	characteristic
4	D₁₇₅₁	C₉	1	1	yes	characteristic, complemented, Hall
5	D₁₀₃⋊C₉	—	17	1	no	maximal, Hall
6	C₁₇×C₁₀₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
7	C₁₀₃⋊C₉	D₁₇	1	1	yes	characteristic, complemented, Hall
8	C₃×D₁₀₃	—	17	1	no	—
9	C₃×C₁₀₃	C₃×D₁₇	1	1	yes	characteristic
10	C₉×D₁₇	—	103	1	no	maximal, Hall
11	D₁₀₃	—	17	1	no	Hall
12	C₉×C₁₇	—	103	1	no	Hall
13	C₁₀₃	C₉×D₁₇	1	1	yes	characteristic, complemented, Sylow
14	C₃×D₁₇	—	103	1	no	—
15	C₃×C₁₇	D₁₀₃⋊C₃	1	1	yes	characteristic
16	D₁₇	—	103	1	no	Hall
17	C₂×C₉	—	1751	1	no	Hall
18	C₁₇	D₁₀₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
19	C₉	—	103	1	no	Sylow
20	C₂×C₃	—	1751	1	no	—
21	C₃	C₁₇⋊(D₁₀₃⋊C₃)	1	1	yes	characteristic
22	C₂	—	1751	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₁₇⋊(D₁₀₃⋊C₃)
commutator, hypocenter	C₁₇×C₁₀₃	C₂×C₉
Fitting, socle, cosocle	C₃×C₁₇×C₁₀₃	C₂×C₃
prime radical	C₃×D₁₇₅₁	C₃
LCS	G ▷ C₁₇×C₁₀₃
UCS	C₁ ◁ C₃

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.