Subgroups — C₃⋊(C₁₇⋊(D₁₀₃⋊C₃)) #44538567

Order 31518.

36 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)	—	3	1	no	maximal
3	D₅₂₅₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₇×C₁₀₃	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₇×C₁₀₃⋊C₃	—	2	1	no	—
6	C₁₇×C₁₀₃⋊C₃	D₃	1	1	yes	characteristic, complemented
7	D₁₇₅₁	—	3	1	no	Hall
8	C₃⋊(D₁₀₃⋊C₃)	—	17	1	no	maximal, Hall
9	C₁₇×C₁₀₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃×C₁₀₃⋊C₃	D₁₇	1	1	yes	characteristic, complemented, Hall
11	D₃₀₉	—	17	1	no	—
12	D₁₀₃⋊C₃	—	51	1	no	—
13	C₃×C₁₀₃	C₃×D₁₇	1	1	yes	characteristic, complemented
14	C₁₀₃⋊C₃	—	2	1	no	—
15	C₁₀₃⋊C₃	D₅₁	1	1	yes	characteristic, complemented
16	C₃×D₅₁	—	103	1	no	maximal, Hall
17	D₁₀₃	—	51	1	no	Hall
18	C₃²×C₁₇	—	103	1	no	Hall
19	C₁₀₃	C₃×D₅₁	1	1	yes	characteristic, complemented, Sylow
20	D₅₁	—	103	1	no	—
21	C₃×D₁₇	—	309	1	no	—
22	C₃×C₁₇	—	103	1	no	—
23	C₃×C₁₇	—	206	1	no	—
24	C₃×C₁₇	D₁₀₃⋊C₃	1	1	yes	characteristic, complemented
25	D₁₇	—	309	1	no	Hall
26	C₃×D₃	—	1751	1	no	Hall
27	C₁₇	C₃⋊(D₁₀₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
28	C₃²	—	103	1	no	Sylow
29	C₂×C₃	—	5253	1	no	—
30	D₃	—	1751	1	no	—
31	C₃	—	103	1	no	—
32	C₃	—	206	1	no	—
33	C₃	C₁₇⋊(D₁₀₃⋊C₃)	1	1	yes	characteristic, complemented
34	C₂	—	5253	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₇×C₁₀₃	C₂×C₃
LCS	G ▷ C₃×C₁₇×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.