Subgroups — C₂⁴×C₄×D₃₁ #16860500

Order 3968.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×D₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×Dic₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₄×D₃₁	C₂	1	60	yes	maximal, direct product factor
4	C₂⁴×C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁵×C₃₁	C₂²	1	1	yes	characteristic
6	C₂⁴×D₃₁	C₄	1	32	yes	direct product factor
7	C₂⁴×D₃₁	C₂²	1	30	yes	—
8	C₂³×C₄×C₃₁	C₂²	1	30	yes	complemented
9	C₂³×Dic₃₁	C₂²	1	30	yes	complemented
10	C₂²×C₄×D₃₁	C₂²	1	560	yes	direct product factor
11	C₂⁴×C₃₁	C₂×C₄	1	16	yes	complemented
12	C₂⁴×C₃₁	C₂³	1	15	yes	—
13	C₂³×D₃₁	C₂×C₄	1	480	yes	direct product factor
14	C₂³×D₃₁	C₂³	1	140	yes	—
15	C₂²×C₄×C₃₁	C₂³	1	140	yes	complemented
16	C₂²×Dic₃₁	C₂³	1	140	yes	complemented
17	C₂×C₄×D₃₁	C₂³	1	960	yes	direct product factor
18	C₂³×C₃₁	C₂²×C₄	1	120	yes	complemented
19	C₂³×C₃₁	C₂⁴	1	35	yes	—
20	C₂²×D₃₁	C₂²×C₄	1	1120	yes	direct product factor
21	C₂²×D₃₁	C₂⁴	1	120	yes	—
22	C₂×C₄×C₃₁	C₂⁴	1	120	yes	complemented
23	C₂×Dic₃₁	C₂⁴	1	120	yes	complemented
24	C₄×D₃₁	C₂⁴	1	256	yes	direct product factor
25	C₂⁵×C₄	—	31	1	no	maximal, Sylow
26	C₂²×C₃₁	C₂³×C₄	1	140	yes	complemented
27	C₂²×C₃₁	C₂⁵	1	15	yes	—
28	C₂×D₃₁	C₂³×C₄	1	480	yes	direct product factor
29	C₂×D₃₁	C₂⁵	1	16	yes	—
30	C₄×C₃₁	C₂⁵	1	16	yes	complemented
31	Dic₃₁	C₂⁵	1	16	yes	complemented
32	C₂⁶	—	31	1	no	—
33	C₂⁴×C₄	—	31	1	no	—
34	C₂⁴×C₄	—	31	60	no	—
35	C₂⁴×C₄	D₃₁	1	1	yes	characteristic, direct product factor
36	C₂×C₃₁	C₂⁴×C₄	1	30	yes	complemented
37	C₂×C₃₁	C₂⁶	1	1	yes	characteristic
38	D₃₁	C₂⁴×C₄	1	32	yes	direct product factor
39	C₂⁵	—	31	32	no	—
40	C₂⁵	—	31	30	no	—
41	C₂⁵	C₂×D₃₁	1	1	yes	characteristic
42	C₂³×C₄	—	31	30	no	—
43	C₂³×C₄	—	31	560	no	—
44	C₂³×C₄	C₂×D₃₁	1	30	yes	direct product factor
45	C₃₁	C₂⁵×C₄	1	1	yes	characteristic, complemented, Sylow
46	C₂⁴	—	31	480	no	—
47	C₂⁴	—	31	140	no	—
48	C₂⁴	C₄×D₃₁	1	16	yes	direct product factor
49	C₂⁴	C₂²×D₃₁	1	15	yes	—
50	C₂²×C₄	—	31	140	no	—
51	C₂²×C₄	—	31	960	no	—
52	C₂²×C₄	C₂²×D₃₁	1	140	yes	direct product factor
53	C₂³	—	31	1120	no	—
54	C₂³	—	31	120	no	—
55	C₂³	C₂×C₄×D₃₁	1	120	yes	direct product factor
56	C₂³	C₂³×D₃₁	1	35	yes	—
57	C₂×C₄	—	31	120	no	—
58	C₂×C₄	—	31	256	no	—
59	C₂×C₄	C₂³×D₃₁	1	120	yes	direct product factor
60	C₂²	—	31	480	no	—
61	C₂²	—	31	16	no	—
62	C₂²	C₂²×C₄×D₃₁	1	140	yes	direct product factor
63	C₂²	C₂⁴×D₃₁	1	15	yes	—
64	C₄	—	31	16	no	—
65	C₄	C₂⁴×D₃₁	1	16	yes	direct product factor
66	C₂	—	31	32	no	—
67	C₂	C₂³×C₄×D₃₁	1	30	yes	direct product factor
68	C₂	C₂⁵×D₃₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴×C₄	D₃₁
commutator, hypocenter	C₃₁	C₂⁵×C₄
Frattini	C₂	C₂⁵×D₃₁
Fitting	C₂⁴×C₄×C₃₁	C₂
socle	C₂⁵×C₃₁	C₂²
prime radical	C₂⁵×D₃₁	C₂
cosocle	C₂×C₃₁	C₂⁶
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂⁴×C₄

Complements

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

N	H ≅ G/N	type
2. C₂⁴×Dic₃₁	C₂	semidirect
3. C₂³×C₄×D₃₁	C₂	direct (N × H)
4. C₂⁴×C₄×C₃₁	C₂	semidirect
6. C₂⁴×D₃₁	C₄	direct (N × H)
8. C₂³×C₄×C₃₁	C₂²	semidirect
9. C₂³×Dic₃₁	C₂²	semidirect
10. C₂²×C₄×D₃₁	C₂²	direct (N × H)
11. C₂⁴×C₃₁	C₂×C₄	semidirect
13. C₂³×D₃₁	C₂×C₄	direct (N × H)
15. C₂²×C₄×C₃₁	C₂³	semidirect
16. C₂²×Dic₃₁	C₂³	semidirect
17. C₂×C₄×D₃₁	C₂³	direct (N × H)
18. C₂³×C₃₁	C₂²×C₄	semidirect
20. C₂²×D₃₁	C₂²×C₄	direct (N × H)
22. C₂×C₄×C₃₁	C₂⁴	semidirect
23. C₂×Dic₃₁	C₂⁴	semidirect
24. C₄×D₃₁	C₂⁴	direct (N × H)
26. C₂²×C₃₁	C₂³×C₄	semidirect
28. C₂×D₃₁	C₂³×C₄	direct (N × H)
30. C₄×C₃₁	C₂⁵	semidirect
31. Dic₃₁	C₂⁵	semidirect
35. C₂⁴×C₄	D₃₁	direct (N × H)
36. C₂×C₃₁	C₂⁴×C₄	semidirect
38. D₃₁	C₂⁴×C₄	direct (N × H)
44. C₂³×C₄	C₂×D₃₁	direct (N × H)
45. C₃₁	C₂⁵×C₄	semidirect
48. C₂⁴	C₄×D₃₁	direct (N × H)
52. C₂²×C₄	C₂²×D₃₁	direct (N × H)
55. C₂³	C₂×C₄×D₃₁	direct (N × H)
59. C₂×C₄	C₂³×D₃₁	direct (N × H)
62. C₂²	C₂²×C₄×D₃₁	direct (N × H)
65. C₄	C₂⁴×D₃₁	direct (N × H)
67. C₂	C₂³×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
C₂⁵×D₃₁	2
C₂⁴×Dic₃₁	2
C₂³×C₄×D₃₁	2
C₂⁴×C₄×C₃₁	2
C₂⁵×C₄	31

Subgroups — C24×C4×D31 #16860500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₄×D₃₁ #16860500