Subgroups — C₂³×C₄⋊Dic₃₁ #16858872

Order 3968.

2488 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	—	2	16	no	—
8	C₂³×Dic₃₁	C₂²	1	28	yes	—
9	C₂×C₄⋊Dic₃₁	C₂²	1	112	yes	direct product factor
10	C₂⁴×C₃₁	C₂×C₄	1	8	yes	—
11	C₂⁴×C₃₁	D₄	1	8	yes	—
12	C₂⁴×C₃₁	Q₈	1	8	yes	—
13	C₂⁴×C₃₁	C₂³	1	7	yes	—
14	C₂²×C₄×C₃₁	C₂×C₄	1	112	yes	complemented
15	C₂²×C₄×C₃₁	C₂³	1	28	yes	—
16	C₂²×Dic₃₁	—	2	112	no	—
17	C₂²×Dic₃₁	C₂³	1	56	yes	—
18	C₄⋊Dic₃₁	C₂³	1	64	yes	direct product factor
19	C₂³×C₃₁	C₄⋊C₄	1	64	yes	complemented
20	C₂³×C₃₁	C₂²×C₄	1	28	yes	—
21	C₂³×C₃₁	C₂×D₄	1	28	yes	—
22	C₂³×C₃₁	C₂×Q₈	1	28	yes	—
23	C₂³×C₃₁	C₂⁴	1	7	yes	—
24	C₂×C₄×C₃₁	C₂²×C₄	1	112	yes	complemented
25	C₂×C₄×C₃₁	C₂⁴	1	8	yes	—
26	C₂×Dic₃₁	—	2	112	no	—
27	C₂×Dic₃₁	C₂⁴	1	16	yes	—
28	C₂³×C₄⋊C₄	—	31	1	no	maximal, Sylow
29	C₂²×C₃₁	C₂×C₄⋊C₄	1	112	yes	complemented
30	C₂²×C₃₁	C₂³×C₄	1	14	yes	—
31	C₂²×C₃₁	C₂²×D₄	1	14	yes	—
32	C₂²×C₃₁	C₂²×Q₈	1	14	yes	—
33	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
34	C₄×C₃₁	C₂³×C₄	1	16	yes	complemented
35	Dic₃₁	—	2	16	no	—
36	C₂⁴×C₄	—	31	2	no	—
37	C₂⁴×C₄	D₃₁	1	1	yes	characteristic
38	C₂²×C₄⋊C₄	—	31	28	no	—
39	C₂×C₃₁	C₂²×C₄⋊C₄	1	28	yes	complemented
40	C₂×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
41	C₂×C₃₁	C₂³×D₄	1	1	yes	characteristic
42	C₂×C₃₁	C₂³×Q₈	1	1	yes	characteristic
43	C₂⁵	C₂×D₃₁	1	1	yes	characteristic
44	C₂³×C₄	—	31	28	no	—
45	C₂³×C₄	—	62	16	no	—
46	C₂³×C₄	Dic₃₁	1	16	yes	complemented
47	C₂³×C₄	C₂×D₃₁	1	14	yes	—
48	C₂×C₄⋊C₄	—	31	112	no	—
49	C₃₁	C₂³×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
50	C₂⁴	Dic₆₂	1	8	yes	—
51	C₂⁴	D₁₂₄	1	8	yes	—
52	C₂⁴	C₂×Dic₃₁	1	8	yes	—
53	C₂⁴	C₂²×D₃₁	1	7	yes	—
54	C₂²×C₄	—	31	56	no	—
55	C₂²×C₄	—	62	112	no	—
56	C₂²×C₄	C₂×Dic₃₁	1	112	yes	complemented
57	C₂²×C₄	C₂²×D₃₁	1	28	yes	—
58	C₄⋊C₄	—	31	64	no	—
59	C₂³	C₄⋊Dic₃₁	1	64	yes	direct product factor
60	C₂³	C₂×Dic₆₂	1	28	yes	—
61	C₂³	C₂×D₁₂₄	1	28	yes	—
62	C₂³	C₂²×Dic₃₁	1	28	yes	—
63	C₂³	C₂³×D₃₁	1	7	yes	—
64	C₂×C₄	—	31	16	no	—
65	C₂×C₄	—	62	112	no	—
66	C₂×C₄	C₂²×Dic₃₁	1	112	yes	complemented
67	C₂×C₄	C₂³×D₃₁	1	8	yes	—
68	C₂²	C₂×C₄⋊Dic₃₁	1	112	yes	direct product factor
69	C₂²	C₂²×Dic₆₂	1	14	yes	—
70	C₂²	C₂²×D₁₂₄	1	14	yes	—
71	C₂²	C₂³×Dic₃₁	1	14	yes	—
72	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
73	C₄	—	62	16	no	—
74	C₄	C₂³×Dic₃₁	1	16	yes	complemented
75	C₂	C₂²×C₄⋊Dic₃₁	1	28	yes	direct product factor
76	C₂	C₂⁴×Dic₃₁	1	1	yes	characteristic
77	C₂	C₂³×D₁₂₄	1	1	yes	characteristic
78	C₂	C₂³×Dic₆₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁵	C₂×D₃₁
commutator	C₂×C₃₁	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₃₁
Fitting	C₂⁴×C₄×C₃₁	C₂
socle, prime radical	C₂⁵×C₃₁	C₂²
cosocle	C₂²×C₃₁	C₂⁵
hypercenter	C₂⁴×C₄	D₃₁
hypocenter	C₃₁	C₂³×C₄⋊C₄
LCS	G ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂⁵ ◁ 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
9. C₂×C₄⋊Dic₃₁	C₂²	direct (N × H)
14. C₂²×C₄×C₃₁	C₂×C₄	semidirect
18. C₄⋊Dic₃₁	C₂³	direct (N × H)
19. C₂³×C₃₁	C₄⋊C₄	semidirect
24. C₂×C₄×C₃₁	C₂²×C₄	semidirect
29. C₂²×C₃₁	C₂×C₄⋊C₄	semidirect
34. C₄×C₃₁	C₂³×C₄	semidirect
39. C₂×C₃₁	C₂²×C₄⋊C₄	semidirect
46. C₂³×C₄	Dic₃₁	semidirect
49. C₃₁	C₂³×C₄⋊C₄	semidirect
56. C₂²×C₄	C₂×Dic₃₁	semidirect
59. C₂³	C₄⋊Dic₃₁	direct (N × H)
66. C₂×C₄	C₂²×Dic₃₁	semidirect
68. C₂²	C₂×C₄⋊Dic₃₁	direct (N × H)
74. C₄	C₂³×Dic₃₁	semidirect
75. 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×C₄⋊C₄	31

Subgroups — C23×C4⋊Dic31 #16858872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄⋊Dic₃₁ #16858872