Subgroups — C₃×D₄₃×C₁₂₁ #44530187

Order 31218.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₃×C₁₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₄₃×C₁₂₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₁×D₄₃	C₁₁	1	1	yes	maximal, characteristic
5	C₃×C₁₁×C₄₃	C₂×C₁₁	1	1	yes	characteristic
6	C₁₁×D₄₃	C₃×C₁₁	1	1	yes	characteristic
7	C₂×C₃×C₁₂₁	—	43	1	no	maximal, Hall
8	C₁₁×C₄₃	C₂×C₃×C₁₁	1	1	yes	characteristic
9	C₃×C₁₂₁	D₄₃	1	1	yes	characteristic, direct product factor, Hall
10	C₃×D₄₃	C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₁₂₁	—	43	1	no	Hall
12	C₃×C₄₃	C₂×C₁₂₁	1	1	yes	characteristic, complemented, Hall
13	C₁₂₁	C₃×D₄₃	1	1	yes	characteristic, direct product factor, Sylow
14	D₄₃	C₃×C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃×C₁₁	—	43	1	no	—
16	C₄₃	C₂×C₃×C₁₂₁	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₁₁	C₁₁×D₄₃	1	1	yes	characteristic
18	C₂×C₁₁	—	43	1	no	—
19	C₁₁	C₃×C₁₁×D₄₃	1	1	yes	characteristic
20	C₂×C₃	—	43	1	no	Hall
21	C₃	D₄₃×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	43	1	no	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.