Subgroups — C₃²×D₁₀₃⋊C₁₇ #44538556

Order 31518.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₃²	D₁₀₃⋊C₁₇
commutator, cosocle, hypocenter	C₁₀₃	C₂×C₃²×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₀₃	C₂×C₁₇
LCS	G ▷ C₁₀₃
UCS	C₁ ◁ C₃²

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.