Subgroups — C₃×C₁₇⋊(D₁₀₃⋊C₃) #44538563

Order 31518.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×C₁₀₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇⋊(D₁₀₃⋊C₃)	C₃	1	3	yes	maximal, direct product factor
3	C₃×D₁₇₅₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₇×C₁₀₃	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₇×C₁₀₃⋊C₃	C₂×C₃	1	3	yes	complemented
6	D₁₇₅₁	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×D₁₀₃⋊C₃	—	17	1	no	maximal, Hall
8	C₁₇×C₁₀₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₀₃⋊C₃	D₁₇	1	1	yes	characteristic, complemented, Hall
10	C₃×D₁₀₃	—	17	1	no	—
11	D₁₀₃⋊C₃	—	17	3	no	—
12	C₃×C₁₀₃	C₃×D₁₇	1	1	yes	characteristic, complemented
13	C₁₀₃⋊C₃	C₃×D₁₇	1	3	yes	complemented
14	C₃²×D₁₇	—	103	1	no	maximal, Hall
15	D₁₀₃	—	17	1	no	Hall
16	C₃²×C₁₇	—	103	1	no	Hall
17	C₁₀₃	C₃²×D₁₇	1	1	yes	characteristic, complemented, Sylow
18	C₃×D₁₇	—	103	3	no	—
19	C₃×D₁₇	—	103	1	no	—
20	C₃×C₁₇	—	103	3	no	—
21	C₃×C₁₇	D₁₀₃⋊C₃	1	1	yes	characteristic, complemented
22	D₁₇	—	103	1	no	Hall
23	C₂×C₃²	—	1751	1	no	Hall
24	C₁₇	C₃×D₁₀₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₃²	—	103	1	no	Sylow
26	C₂×C₃	—	1751	3	no	—
27	C₂×C₃	—	1751	1	no	—
28	C₃	—	103	3	no	—
29	C₃	C₁₇⋊(D₁₀₃⋊C₃)	1	1	yes	characteristic, direct product factor
30	C₂	—	1751	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₁₇⋊(D₁₀₃⋊C₃)
commutator, cosocle, hypocenter	C₁₇×C₁₀₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₁₇×C₁₀₃	C₂×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.