Subgroups — C₃×C₄₃×Dic₆₁ #44538330

Order 31476.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄₃×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₄₃×Dic₆₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₄₃×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₄₃×C₆₁	C₂×C₃	1	1	yes	characteristic
5	C₄₃×C₆₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×Dic₆₁	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₄×C₄₃	—	61	1	no	maximal, Hall
8	C₂×C₃×C₆₁	C₂×C₄₃	1	1	yes	characteristic
9	C₂×C₃×C₄₃	D₆₁	1	1	yes	characteristic
10	Dic₆₁	C₃×C₄₃	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₆₁	C₄×C₄₃	1	1	yes	characteristic, complemented, Hall
12	C₄×C₄₃	—	61	1	no	Hall
13	C₃×C₄₃	Dic₆₁	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₆₁	C₂×C₃×C₄₃	1	1	yes	characteristic
15	C₂×C₄₃	C₃×D₆₁	1	1	yes	characteristic
16	C₆₁	C₃×C₄×C₄₃	1	1	yes	characteristic, complemented, Sylow
17	C₄₃	C₃×Dic₆₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₄	—	61	1	no	Hall
19	C₂×C₃	C₄₃×D₆₁	1	1	yes	characteristic
20	C₄	—	61	1	no	Sylow
21	C₃	C₄₃×Dic₆₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×C₄₃×D₆₁	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.