Subgroups — C₁₁×C₂₃×Dic₃₁ #44535866

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	C₂₃×Dic₃₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₂₃×C₃₁	C₂×C₁₁	1	1	yes	characteristic
5	C₁₁×Dic₃₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₄×C₁₁×C₂₃	—	31	1	no	maximal, Hall
7	C₂₃×C₃₁	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₁×C₃₁	C₂×C₂₃	1	1	yes	characteristic
9	C₂×C₁₁×C₂₃	D₃₁	1	1	yes	characteristic
10	C₁₁×C₃₁	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
11	C₁₁×C₂₃	Dic₃₁	1	1	yes	characteristic, direct product factor, Hall
12	Dic₃₁	C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Hall
13	C₄×C₂₃	—	31	1	no	Hall
14	C₂×C₃₁	C₂×C₁₁×C₂₃	1	1	yes	characteristic
15	C₂×C₂₃	C₁₁×D₃₁	1	1	yes	characteristic
16	C₄×C₁₁	—	31	1	no	Hall
17	C₃₁	C₄×C₁₁×C₂₃	1	1	yes	characteristic, complemented, Sylow
18	C₂₃	C₁₁×Dic₃₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₁₁	C₂₃×D₃₁	1	1	yes	characteristic
20	C₁₁	C₂₃×Dic₃₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	31	1	no	Sylow
22	C₂	C₁₁×C₂₃×D₃₁	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.