Subgroups — C₈×C₉×C₃₃₁ #72201136

Order 23832.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₈×C₃₃₁	C₃	1	1	yes	maximal, characteristic
2	C₄×C₉×C₃₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₉×C₃₃₁	C₄	1	1	yes	characteristic
4	C₃×C₄×C₃₃₁	C₂×C₃	1	1	yes	characteristic
5	C₉×C₃₃₁	C₈	1	1	yes	characteristic, direct product factor, Hall
6	C₈×C₃₃₁	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₃₃₁	C₃×C₄	1	1	yes	characteristic
8	C₄×C₃₃₁	C₂×C₉	1	1	yes	characteristic
9	C₃×C₃₃₁	C₃×C₈	1	1	yes	characteristic
10	C₂×C₃₃₁	C₄×C₉	1	1	yes	characteristic
11	C₃₃₁	C₈×C₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₈×C₉	C₃₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₄×C₉	C₂×C₃₃₁	1	1	yes	characteristic
14	C₃×C₈	C₃×C₃₃₁	1	1	yes	characteristic
15	C₂×C₉	C₄×C₃₃₁	1	1	yes	characteristic
16	C₃×C₄	C₂×C₃×C₃₃₁	1	1	yes	characteristic
17	C₉	C₈×C₃₃₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₈	C₉×C₃₃₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	C₃×C₄×C₃₃₁	1	1	yes	characteristic
20	C₄	C₂×C₉×C₃₃₁	1	1	yes	characteristic
21	C₃	C₃×C₈×C₃₃₁	1	1	yes	characteristic
22	C₂	C₄×C₉×C₃₃₁	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.