Subgroups — C₃×C₃₁×Dic₄₇ #31775713

Order 17484.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃₁×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₃₁×Dic₄₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₃₁×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₁×C₄₇	C₂×C₃	1	1	yes	characteristic
5	C₃₁×C₄₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×Dic₄₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₄×C₃₁	—	47	1	no	maximal, Hall
8	C₂×C₃×C₄₇	C₂×C₃₁	1	1	yes	characteristic
9	Dic₄₇	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₃₁	D₄₇	1	1	yes	characteristic
11	C₃×C₄₇	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
12	C₄×C₃₁	—	47	1	no	Hall
13	C₂×C₄₇	C₂×C₃×C₃₁	1	1	yes	characteristic
14	C₃×C₃₁	Dic₄₇	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃₁	C₃×D₄₇	1	1	yes	characteristic
16	C₄₇	C₃×C₄×C₃₁	1	1	yes	characteristic, complemented, Sylow
17	C₃₁	C₃×Dic₄₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₄	—	47	1	no	Hall
19	C₂×C₃	C₃₁×D₄₇	1	1	yes	characteristic
20	C₄	—	47	1	no	Sylow
21	C₃	C₃₁×Dic₄₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×C₃₁×D₄₇	1	1	yes	characteristic

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.