Subgroups — C₃×Dic₂₀₂₁ #37564635

Order 24252.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄₃×C₄₇	C₂	1	1	yes	maximal, characteristic
2	Dic₂₀₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₄₃×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₄₃×C₄₇	C₂×C₃	1	1	yes	characteristic
5	C₄₃×C₄₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×Dic₄₇	—	43	1	no	maximal, Hall
7	C₃×Dic₄₃	—	47	1	no	maximal, Hall
8	C₂×C₃×C₄₇	D₄₃	1	1	yes	characteristic
9	C₂×C₃×C₄₃	D₄₇	1	1	yes	characteristic
10	Dic₄₇	—	43	1	no	Hall
11	Dic₄₃	—	47	1	no	Hall
12	C₃×C₄₇	Dic₄₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₄₃	Dic₄₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₄₇	C₃×D₄₃	1	1	yes	characteristic
15	C₂×C₄₃	C₃×D₄₇	1	1	yes	characteristic
16	C₄₇	C₃×Dic₄₃	1	1	yes	characteristic, complemented, Sylow
17	C₄₃	C₃×Dic₄₇	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	2021	1	no	Hall
19	C₂×C₃	D₂₀₂₁	1	1	yes	characteristic
20	C₄	—	2021	1	no	Sylow
21	C₃	Dic₂₀₂₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×D₂₀₂₁	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.