Subgroups — C₉⋊(D₁₀₃⋊C₁₇) #44538546

Order 31518.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₀₃⋊C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(D₁₀₃⋊C₁₇)	—	3	1	no	maximal
3	C₃×C₁₀₃⋊C₁₇	D₃	1	1	yes	characteristic
4	D₁₀₃⋊C₁₇	—	9	1	no	Hall
5	D₉₂₇	C₁₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₁₀₃⋊C₁₇	D₉	1	1	yes	characteristic, complemented, Hall
7	C₉×C₁₀₃	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
8	D₃₀₉	—	3	1	no	—
9	C₃×C₁₀₃	D₃×C₁₇	1	1	yes	characteristic
10	C₁₇×D₉	—	103	1	no	maximal, Hall
11	D₁₀₃	—	9	1	no	Hall
12	C₉×C₁₇	—	103	1	no	Hall
13	C₁₀₃	C₁₇×D₉	1	1	yes	characteristic, complemented, Sylow
14	D₃×C₁₇	—	309	1	no	—
15	C₃×C₁₇	—	103	1	no	—
16	C₂×C₁₇	—	927	1	no	Hall
17	D₉	—	103	1	no	Hall
18	C₁₇	—	103	1	no	Sylow
19	C₉	D₁₀₃⋊C₁₇	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	309	1	no	—
21	C₃	C₃⋊(D₁₀₃⋊C₁₇)	1	1	yes	characteristic
22	C₂	—	927	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₀₃	C₂×C₁₇
Frattini	C₃	C₃⋊(D₁₀₃⋊C₁₇)
socle	C₃×C₁₀₃	D₃×C₁₇
LCS	G ▷ C₉×C₁₀₃
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.