Subgroups — C₂×C₃×D₄×C₃₁ #13093608

Order 1488.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₃₁	C₂	1	2	yes	maximal, complemented
2	C₃×D₄×C₃₁	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃×C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×C₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×C₃₁	—	2	4	no	—
6	C₂²×C₃×C₃₁	C₂²	1	1	yes	characteristic
7	C₂²×C₃×C₃₁	C₂²	1	4	yes	complemented
8	C₃×C₄×C₃₁	C₂²	1	2	yes	complemented
9	C₂³×C₃₁	C₂×C₃	1	2	yes	complemented
10	D₄×C₃₁	C₂×C₃	1	4	yes	direct product factor
11	C₂×C₄×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×C₃×C₃₁	—	2	4	no	—
13	C₂×C₃×C₃₁	D₄	1	2	yes	direct product factor
14	C₂×C₃×C₃₁	C₂³	1	1	yes	characteristic
15	C₂²×C₃₁	—	2	4	no	—
16	C₂²×C₃₁	C₂²×C₃	1	1	yes	characteristic
17	C₂²×C₃₁	C₂²×C₃	1	4	yes	complemented
18	C₄×C₃₁	C₂²×C₃	1	2	yes	complemented
19	C₃×C₃₁	C₂×D₄	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃₁	—	2	4	no	—
21	C₂×C₃₁	C₃×D₄	1	2	yes	direct product factor
22	C₂×C₃₁	C₂³×C₃	1	1	yes	characteristic
23	C₂×C₃×D₄	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₃₁	C₂×C₃×D₄	1	1	yes	characteristic, direct product factor, Sylow
25	C₂³×C₃	C₂×C₃₁	1	2	yes	complemented
26	C₃×D₄	C₂×C₃₁	1	4	yes	direct product factor
27	C₂×C₃×C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
28	C₂×D₄	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²×C₃	—	2	4	no	—
30	C₂²×C₃	C₂²×C₃₁	1	1	yes	characteristic
31	C₂²×C₃	C₂²×C₃₁	1	4	yes	complemented
32	C₃×C₄	C₂²×C₃₁	1	2	yes	complemented
33	C₂³	C₂×C₃×C₃₁	1	2	yes	complemented
34	D₄	C₂×C₃×C₃₁	1	4	yes	direct product factor
35	C₂×C₄	C₂×C₃×C₃₁	1	1	yes	characteristic, complemented
36	C₂×C₃	—	2	4	no	—
37	C₂×C₃	D₄×C₃₁	1	2	yes	direct product factor
38	C₂×C₃	C₂³×C₃₁	1	1	yes	characteristic
39	C₂²	—	2	4	no	—
40	C₂²	C₂²×C₃×C₃₁	1	1	yes	characteristic
41	C₂²	C₂²×C₃×C₃₁	1	4	yes	complemented
42	C₄	C₂²×C₃×C₃₁	1	2	yes	complemented
43	C₃	C₂×D₄×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
44	C₂	—	2	4	no	—
45	C₂	C₃×D₄×C₃₁	1	2	yes	direct product factor
46	C₂	C₂³×C₃×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₃₁	C₂²
commutator, Frattini, cosocle	C₂	C₂³×C₃×C₃₁
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₃₁	C₂	semidirect
2. C₃×D₄×C₃₁	C₂	direct (N × H)
3. C₂×C₃×C₄×C₃₁	C₂	semidirect
4. C₂×D₄×C₃₁	C₃	direct (N × H)
7. C₂²×C₃×C₃₁	C₂²	semidirect
8. C₃×C₄×C₃₁	C₂²	semidirect
9. C₂³×C₃₁	C₂×C₃	semidirect
10. D₄×C₃₁	C₂×C₃	direct (N × H)
11. C₂×C₄×C₃₁	C₂×C₃	semidirect
13. C₂×C₃×C₃₁	D₄	direct (N × H)
17. C₂²×C₃₁	C₂²×C₃	semidirect
18. C₄×C₃₁	C₂²×C₃	semidirect
19. C₃×C₃₁	C₂×D₄	direct (N × H)
21. C₂×C₃₁	C₃×D₄	direct (N × H)
23. C₂×C₃×D₄	C₃₁	direct (N × H)
24. C₃₁	C₂×C₃×D₄	direct (N × H)
25. C₂³×C₃	C₂×C₃₁	semidirect
26. C₃×D₄	C₂×C₃₁	direct (N × H)
27. C₂×C₃×C₄	C₂×C₃₁	semidirect
28. C₂×D₄	C₃×C₃₁	direct (N × H)
31. C₂²×C₃	C₂²×C₃₁	semidirect
32. C₃×C₄	C₂²×C₃₁	semidirect
33. C₂³	C₂×C₃×C₃₁	semidirect
34. D₄	C₂×C₃×C₃₁	direct (N × H)
35. C₂×C₄	C₂×C₃×C₃₁	semidirect
37. C₂×C₃	D₄×C₃₁	direct (N × H)
41. C₂²	C₂²×C₃×C₃₁	semidirect
42. C₄	C₂²×C₃×C₃₁	semidirect
43. C₃	C₂×D₄×C₃₁	direct (N × H)
45. C₂	C₃×D₄×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
C₂³×C₃×C₃₁	2
C₃×D₄×C₃₁	2
C₂×C₃×C₄×C₃₁	2
C₂×D₄×C₃₁	3
C₂×C₃×D₄	31

Subgroups — C2×C3×D4×C31 #13093608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₄×C₃₁ #13093608