Subgroups — C₄×C₁₁×C₂₃×C₃₁ #44535864

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, direct product factor, Hall
3	C₄×C₂₃×C₃₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₂₃×C₃₁	C₂×C₁₁	1	1	yes	characteristic
5	C₄×C₁₁×C₃₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₄×C₁₁×C₂₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂₃×C₃₁	C₄×C₁₁	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, direct product factor, Hall
11	C₁₁×C₂₃	C₄×C₃₁	1	1	yes	characteristic, direct product factor, Hall
12	C₄×C₃₁	C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Hall
13	C₄×C₂₃	C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃₁	C₂×C₁₁×C₂₃	1	1	yes	characteristic
15	C₂×C₂₃	C₂×C₁₁×C₃₁	1	1	yes	characteristic
16	C₄×C₁₁	C₂₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
17	C₃₁	C₄×C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₂₃	C₄×C₁₁×C₃₁	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, direct product factor, Sylow
21	C₄	C₁₁×C₂₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₁₁×C₂₃×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₁₁×C₂₃×C₃₁
socle, prime radical	C₂×C₁₁×C₂₃×C₃₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₁×C₂₃×C₃₁	C₄	direct (N × H)
3. C₄×C₂₃×C₃₁	C₁₁	direct (N × H)
5. C₄×C₁₁×C₃₁	C₂₃	direct (N × H)
6. C₄×C₁₁×C₂₃	C₃₁	direct (N × H)
7. C₂₃×C₃₁	C₄×C₁₁	direct (N × H)
10. C₁₁×C₃₁	C₄×C₂₃	direct (N × H)
11. C₁₁×C₂₃	C₄×C₃₁	direct (N × H)
12. C₄×C₃₁	C₁₁×C₂₃	direct (N × H)
13. C₄×C₂₃	C₁₁×C₃₁	direct (N × H)
16. C₄×C₁₁	C₂₃×C₃₁	direct (N × H)
17. C₃₁	C₄×C₁₁×C₂₃	direct (N × H)
18. C₂₃	C₄×C₁₁×C₃₁	direct (N × H)
20. C₁₁	C₄×C₂₃×C₃₁	direct (N × H)
21. C₄	C₁₁×C₂₃×C₃₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₁×C₂₃×C₃₁	2
C₄×C₂₃×C₃₁	11
C₄×C₁₁×C₃₁	23
C₄×C₁₁×C₂₃	31

Subgroups — C4×C11×C23×C31 #44535864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₁×C₂₃×C₃₁ #44535864