Subgroups — Dic₃×C₄₁×C₄₇ #37528849

Order 23124.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄₁×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄₁×C₄₇	—	3	1	no	maximal, Hall
3	C₃×C₄₁×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₄₁×C₄₇	D₃	1	1	yes	characteristic
5	C₄₁×C₄₇	Dic₃	1	1	yes	characteristic, direct product factor, Hall
6	Dic₃×C₄₇	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	Dic₃×C₄₁	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₄₇	C₂×C₄₁	1	1	yes	characteristic
9	C₂×C₃×C₄₁	C₂×C₄₇	1	1	yes	characteristic
10	C₄×C₄₇	—	3	1	no	Hall
11	C₄×C₄₁	—	3	1	no	Hall
12	C₃×C₄₇	C₄×C₄₁	1	1	yes	characteristic, complemented, Hall
13	C₃×C₄₁	C₄×C₄₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₄₇	D₃×C₄₁	1	1	yes	characteristic
15	C₂×C₄₁	D₃×C₄₇	1	1	yes	characteristic
16	C₄₇	Dic₃×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
17	C₄₁	Dic₃×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
18	Dic₃	C₄₁×C₄₇	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃	C₂×C₄₁×C₄₇	1	1	yes	characteristic
20	C₄	—	3	1	no	Sylow
21	C₃	C₄×C₄₁×C₄₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₃×C₄₁×C₄₇	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.