Subgroups — C₂³×C₄×Dic₃₁ #16858866

Order 3968.

3000 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Dic₃₁	C₂	1	2	yes	maximal
2	C₂²×C₄×Dic₃₁	C₂	1	28	yes	maximal, direct product factor
3	C₂⁴×C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂⁵×C₃₁	C₂²	1	1	yes	characteristic
5	C₂³×C₄×C₃₁	C₄	1	16	yes	complemented
6	C₂³×C₄×C₃₁	C₂²	1	14	yes	—
7	C₂³×Dic₃₁	C₄	1	32	yes	direct product factor
8	C₂³×Dic₃₁	C₂²	1	28	yes	—
9	C₂×C₄×Dic₃₁	C₂²	1	112	yes	direct product factor
10	C₂⁴×C₃₁	C₂×C₄	1	16	yes	—
11	C₂⁴×C₃₁	C₂×C₄	1	8	yes	—
12	C₂⁴×C₃₁	C₂³	1	7	yes	—
13	C₂²×C₄×C₃₁	C₂×C₄	1	112	yes	complemented
14	C₂²×C₄×C₃₁	C₂³	1	28	yes	—
15	C₂²×Dic₃₁	C₂×C₄	1	224	yes	direct product factor
16	C₂²×Dic₃₁	C₂³	1	56	yes	—
17	C₄×Dic₃₁	C₂³	1	64	yes	direct product factor
18	C₂³×C₃₁	C₄²	1	64	yes	complemented
19	C₂³×C₃₁	C₂²×C₄	1	56	yes	—
20	C₂³×C₃₁	C₂²×C₄	1	28	yes	—
21	C₂³×C₃₁	C₂⁴	1	7	yes	—
22	C₂×C₄×C₃₁	C₂²×C₄	1	112	yes	complemented
23	C₂×C₄×C₃₁	C₂⁴	1	8	yes	—
24	C₂×Dic₃₁	C₂²×C₄	1	224	yes	direct product factor
25	C₂×Dic₃₁	C₂⁴	1	16	yes	—
26	C₂³×C₄²	—	31	1	no	maximal, Sylow
27	C₂²×C₃₁	C₂×C₄²	1	112	yes	complemented
28	C₂²×C₃₁	C₂³×C₄	1	28	yes	—
29	C₂²×C₃₁	C₂³×C₄	1	14	yes	—
30	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
31	C₄×C₃₁	C₂³×C₄	1	16	yes	complemented
32	Dic₃₁	C₂³×C₄	1	32	yes	direct product factor
33	C₂⁴×C₄	—	31	2	no	—
34	C₂⁴×C₄	D₃₁	1	1	yes	characteristic
35	C₂²×C₄²	—	31	28	no	—
36	C₂×C₃₁	C₂²×C₄²	1	28	yes	complemented
37	C₂×C₃₁	C₂⁴×C₄	1	2	yes	—
38	C₂×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
39	C₂⁵	C₂×D₃₁	1	1	yes	characteristic
40	C₂³×C₄	—	31	32	no	—
41	C₂³×C₄	—	31	28	no	—
42	C₂³×C₄	Dic₃₁	1	16	yes	direct product factor
43	C₂³×C₄	C₂×D₃₁	1	14	yes	—
44	C₂×C₄²	—	31	112	no	—
45	C₃₁	C₂³×C₄²	1	1	yes	characteristic, complemented, Sylow
46	C₂⁴	C₄×D₃₁	1	16	yes	—
47	C₂⁴	C₂×Dic₃₁	1	8	yes	—
48	C₂⁴	C₂²×D₃₁	1	7	yes	—
49	C₂²×C₄	—	31	224	no	—
50	C₂²×C₄	—	31	56	no	—
51	C₂²×C₄	C₂×Dic₃₁	1	112	yes	direct product factor
52	C₂²×C₄	C₂²×D₃₁	1	28	yes	—
53	C₄²	—	31	64	no	—
54	C₂³	C₄×Dic₃₁	1	64	yes	direct product factor
55	C₂³	C₂×C₄×D₃₁	1	56	yes	—
56	C₂³	C₂²×Dic₃₁	1	28	yes	—
57	C₂³	C₂³×D₃₁	1	7	yes	—
58	C₂×C₄	—	31	224	no	—
59	C₂×C₄	—	31	16	no	—
60	C₂×C₄	C₂²×Dic₃₁	1	112	yes	direct product factor
61	C₂×C₄	C₂³×D₃₁	1	8	yes	—
62	C₂²	C₂×C₄×Dic₃₁	1	112	yes	direct product factor
63	C₂²	C₂²×C₄×D₃₁	1	28	yes	—
64	C₂²	C₂³×Dic₃₁	1	14	yes	—
65	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
66	C₄	—	31	32	no	—
67	C₄	C₂³×Dic₃₁	1	16	yes	direct product factor
68	C₂	C₂²×C₄×Dic₃₁	1	28	yes	direct product factor
69	C₂	C₂³×C₄×D₃₁	1	2	yes	—
70	C₂	C₂⁴×Dic₃₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴×C₄	D₃₁
commutator, hypocenter	C₃₁	C₂³×C₄²
Frattini	C₂²	C₂⁴×D₃₁
Fitting	C₂⁴×C₄×C₃₁	C₂
socle, prime radical	C₂⁵×C₃₁	C₂²
cosocle	C₂²×C₃₁	C₂⁵
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂⁴×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×Dic₃₁	C₂	direct (N × H)
5. C₂³×C₄×C₃₁	C₄	semidirect
7. C₂³×Dic₃₁	C₄	direct (N × H)
9. C₂×C₄×Dic₃₁	C₂²	direct (N × H)
13. C₂²×C₄×C₃₁	C₂×C₄	semidirect
15. C₂²×Dic₃₁	C₂×C₄	direct (N × H)
17. C₄×Dic₃₁	C₂³	direct (N × H)
18. C₂³×C₃₁	C₄²	semidirect
22. C₂×C₄×C₃₁	C₂²×C₄	semidirect
24. C₂×Dic₃₁	C₂²×C₄	direct (N × H)
27. C₂²×C₃₁	C₂×C₄²	semidirect
31. C₄×C₃₁	C₂³×C₄	semidirect
32. Dic₃₁	C₂³×C₄	direct (N × H)
36. C₂×C₃₁	C₂²×C₄²	semidirect
42. C₂³×C₄	Dic₃₁	direct (N × H)
45. C₃₁	C₂³×C₄²	semidirect
51. C₂²×C₄	C₂×Dic₃₁	direct (N × H)
54. C₂³	C₄×Dic₃₁	direct (N × H)
60. C₂×C₄	C₂²×Dic₃₁	direct (N × H)
62. C₂²	C₂×C₄×Dic₃₁	direct (N × H)
67. C₄	C₂³×Dic₃₁	direct (N × H)
68. C₂	C₂²×C₄×Dic₃₁	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×Dic₃₁	2
C₂²×C₄×Dic₃₁	2
C₂⁴×C₄×C₃₁	2
C₂³×C₄²	31

Subgroups — C23×C4×Dic31 #16858866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄×Dic₃₁ #16858866