Subgroups — C₃₁×Dic₂₃⋊C₁₁ #44535874

Order 31372.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×C₂₃⋊C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₃₁×C₂₃⋊C₁₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃₁×Dic₂₃	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₂₃×C₃₁	C₂×C₁₁	1	1	yes	characteristic
5	C₄×C₁₁×C₃₁	—	23	1	no	maximal, Hall
6	Dic₂₃⋊C₁₁	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂₃×C₃₁	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₁×C₃₁	—	23	1	no	—
9	C₂×C₂₃⋊C₁₁	C₂×C₃₁	1	1	yes	characteristic
10	C₁₁×C₃₁	—	23	1	no	Hall
11	C₂₃⋊C₁₁	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
12	C₄×C₃₁	—	23	1	no	Hall
13	Dic₂₃	C₁₁×C₃₁	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃₁	AGL(1,𝔽₂₃)	1	1	yes	characteristic
15	C₂×C₂₃	C₂×C₁₁×C₃₁	1	1	yes	characteristic
16	C₄×C₁₁	—	23	1	no	Hall
17	C₃₁	Dic₂₃⋊C₁₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₂₃	C₄×C₁₁×C₃₁	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₁₁	—	23	1	no	—
20	C₁₁	—	23	1	no	Sylow
21	C₄	—	23	1	no	Sylow
22	C₂	C₃₁×AGL(1,𝔽₂₃)	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.