Subgroups — C₂×(C₁₀₃⋊C₉)⋊C₁₇ #44538536

Order 31518.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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.