Subgroups — C₂³×C₄×D₃₁ #14521867

Order 1984.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×Dic₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₃₁	C₂	1	28	yes	maximal, direct product factor
5	C₂⁴×C₃₁	C₂²	1	1	yes	characteristic
6	C₂³×D₃₁	C₄	1	16	yes	direct product factor
7	C₂³×D₃₁	C₂²	1	14	yes	—
8	C₂²×C₄×C₃₁	C₂²	1	14	yes	complemented
9	C₂²×Dic₃₁	C₂²	1	14	yes	complemented
10	C₂×C₄×D₃₁	C₂²	1	112	yes	direct product factor
11	C₂³×C₃₁	C₂×C₄	1	8	yes	complemented
12	C₂³×C₃₁	C₂³	1	7	yes	—
13	C₂²×D₃₁	C₂×C₄	1	112	yes	direct product factor
14	C₂²×D₃₁	C₂³	1	28	yes	—
15	C₂×C₄×C₃₁	C₂³	1	28	yes	complemented
16	C₂×Dic₃₁	C₂³	1	28	yes	complemented
17	C₄×D₃₁	C₂³	1	64	yes	direct product factor
18	C₂²×C₃₁	C₂²×C₄	1	28	yes	complemented
19	C₂²×C₃₁	C₂⁴	1	7	yes	—
20	C₂×D₃₁	C₂²×C₄	1	112	yes	direct product factor
21	C₂×D₃₁	C₂⁴	1	8	yes	—
22	C₄×C₃₁	C₂⁴	1	8	yes	complemented
23	Dic₃₁	C₂⁴	1	8	yes	complemented
24	C₂⁴×C₄	—	31	1	no	maximal, Sylow
25	C₂×C₃₁	C₂³×C₄	1	14	yes	complemented
26	C₂×C₃₁	C₂⁵	1	1	yes	characteristic
27	D₃₁	C₂³×C₄	1	16	yes	direct product factor
28	C₂⁵	—	31	1	no	—
29	C₂³×C₄	—	31	1	no	—
30	C₂³×C₄	—	31	28	no	—
31	C₂³×C₄	D₃₁	1	1	yes	characteristic, direct product factor
32	C₃₁	C₂⁴×C₄	1	1	yes	characteristic, complemented, Sylow
33	C₂⁴	—	31	16	no	—
34	C₂⁴	—	31	14	no	—
35	C₂⁴	C₂×D₃₁	1	1	yes	characteristic
36	C₂²×C₄	—	31	14	no	—
37	C₂²×C₄	—	31	112	no	—
38	C₂²×C₄	C₂×D₃₁	1	14	yes	direct product factor
39	C₂³	—	31	112	no	—
40	C₂³	—	31	28	no	—
41	C₂³	C₄×D₃₁	1	8	yes	direct product factor
42	C₂³	C₂²×D₃₁	1	7	yes	—
43	C₂×C₄	—	31	28	no	—
44	C₂×C₄	—	31	64	no	—
45	C₂×C₄	C₂²×D₃₁	1	28	yes	direct product factor
46	C₂²	—	31	112	no	—
47	C₂²	—	31	8	no	—
48	C₂²	C₂×C₄×D₃₁	1	28	yes	direct product factor
49	C₂²	C₂³×D₃₁	1	7	yes	—
50	C₄	—	31	8	no	—
51	C₄	C₂³×D₃₁	1	8	yes	direct product factor
52	C₂	—	31	16	no	—
53	C₂	C₂²×C₄×D₃₁	1	14	yes	direct product factor
54	C₂	C₂⁴×D₃₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₄	D₃₁
commutator, hypocenter	C₃₁	C₂⁴×C₄
Frattini	C₂	C₂⁴×D₃₁
Fitting	C₂³×C₄×C₃₁	C₂
socle	C₂⁴×C₃₁	C₂²
prime radical	C₂⁴×D₃₁	C₂
cosocle	C₂×C₃₁	C₂⁵
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄×C₃₁	C₂	semidirect
3. C₂³×Dic₃₁	C₂	semidirect
4. C₂²×C₄×D₃₁	C₂	direct (N × H)
6. C₂³×D₃₁	C₄	direct (N × H)
8. C₂²×C₄×C₃₁	C₂²	semidirect
9. C₂²×Dic₃₁	C₂²	semidirect
10. C₂×C₄×D₃₁	C₂²	direct (N × H)
11. C₂³×C₃₁	C₂×C₄	semidirect
13. C₂²×D₃₁	C₂×C₄	direct (N × H)
15. C₂×C₄×C₃₁	C₂³	semidirect
16. C₂×Dic₃₁	C₂³	semidirect
17. C₄×D₃₁	C₂³	direct (N × H)
18. C₂²×C₃₁	C₂²×C₄	semidirect
20. C₂×D₃₁	C₂²×C₄	direct (N × H)
22. C₄×C₃₁	C₂⁴	semidirect
23. Dic₃₁	C₂⁴	semidirect
25. C₂×C₃₁	C₂³×C₄	semidirect
27. D₃₁	C₂³×C₄	direct (N × H)
31. C₂³×C₄	D₃₁	direct (N × H)
32. C₃₁	C₂⁴×C₄	semidirect
38. C₂²×C₄	C₂×D₃₁	direct (N × H)
41. C₂³	C₄×D₃₁	direct (N × H)
45. C₂×C₄	C₂²×D₃₁	direct (N × H)
48. C₂²	C₂×C₄×D₃₁	direct (N × H)
51. C₄	C₂³×D₃₁	direct (N × H)
53. C₂	C₂²×C₄×D₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₃₁	2
C₂³×C₄×C₃₁	2
C₂³×Dic₃₁	2
C₂²×C₄×D₃₁	2
C₂⁴×C₄	31

Subgroups — C23×C4×D31 #14521867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄×D₃₁ #14521867