Subgroups — C₂₃×C₃₁×Dic₁₁ #44535869

Order 31372.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₂₃×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₂₃×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄×C₂₃×C₃₁	—	11	1	no	maximal, Hall
4	C₂×C₂₃×C₃₁	D₁₁	1	1	yes	characteristic
5	C₃₁×Dic₁₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂₃×Dic₁₁	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂₃×C₃₁	Dic₁₁	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₁₁×C₃₁	C₂×C₂₃	1	1	yes	characteristic
9	C₂×C₁₁×C₂₃	C₂×C₃₁	1	1	yes	characteristic
10	C₁₁×C₃₁	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
11	C₁₁×C₂₃	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
12	C₄×C₃₁	—	11	1	no	Hall
13	C₄×C₂₃	—	11	1	no	Hall
14	C₂×C₃₁	D₁₁×C₂₃	1	1	yes	characteristic
15	C₂×C₂₃	D₁₁×C₃₁	1	1	yes	characteristic
16	Dic₁₁	C₂₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
17	C₃₁	C₂₃×Dic₁₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₂₃	C₃₁×Dic₁₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₁₁	C₂×C₂₃×C₃₁	1	1	yes	characteristic
20	C₁₁	C₄×C₂₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	11	1	no	Sylow
22	C₂	D₁₁×C₂₃×C₃₁	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.