Subgroups — C₂²×C₂²⋊C₄×C₃₁ #14520693

Order 1984.

674 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄×C₃₁	C₂	1	2	yes	maximal, complemented
3	C₂×C₂²⋊C₄×C₃₁	C₂	1	12	yes	maximal, direct product factor
4	C₂⁴×C₃₁	—	2	8	no	—
5	C₂⁴×C₃₁	C₄	1	8	yes	complemented
6	C₂⁴×C₃₁	C₂²	1	6	yes	—
7	C₂⁴×C₃₁	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₃₁	—	2	8	no	—
9	C₂²×C₄×C₃₁	C₂²	1	12	yes	complemented
10	C₂²⋊C₄×C₃₁	C₂²	1	16	yes	direct product factor
11	C₂³×C₃₁	—	2	32	no	—
12	C₂³×C₃₁	—	2	24	no	—
13	C₂³×C₃₁	C₂×C₄	1	4	yes	—
14	C₂³×C₃₁	C₂×C₄	1	24	yes	complemented
15	C₂³×C₃₁	D₄	1	8	yes	—
16	C₂³×C₃₁	C₂³	1	4	yes	—
17	C₂³×C₃₁	C₂³	1	3	yes	—
18	C₂×C₄×C₃₁	—	2	24	no	—
19	C₂×C₄×C₃₁	C₂³	1	8	yes	complemented
20	C₂²×C₃₁	—	2	48	no	—
21	C₂²×C₃₁	—	2	8	no	—
22	C₂²×C₃₁	C₂²⋊C₄	1	16	yes	direct product factor
23	C₂²×C₃₁	C₂²×C₄	1	6	yes	—
24	C₂²×C₃₁	C₂²×C₄	1	8	yes	complemented
25	C₂²×C₃₁	C₂×D₄	1	12	yes	—
26	C₂²×C₃₁	C₂⁴	1	1	yes	characteristic
27	C₄×C₃₁	—	2	8	no	—
28	C₂²×C₂²⋊C₄	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₂×C₃₁	—	2	8	no	—
30	C₂×C₃₁	C₂×C₂²⋊C₄	1	12	yes	direct product factor
31	C₂×C₃₁	C₂³×C₄	1	1	yes	characteristic
32	C₂×C₃₁	C₂²×D₄	1	2	yes	—
33	C₂⁵	C₂×C₃₁	1	1	yes	characteristic
34	C₂³×C₄	C₂×C₃₁	1	2	yes	complemented
35	C₂×C₂²⋊C₄	C₂×C₃₁	1	12	yes	direct product factor
36	C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
37	C₂⁴	—	2	8	no	—
38	C₂⁴	C₄×C₃₁	1	8	yes	complemented
39	C₂⁴	C₂²×C₃₁	1	6	yes	—
40	C₂⁴	C₂²×C₃₁	1	1	yes	characteristic
41	C₂²×C₄	—	2	8	no	—
42	C₂²×C₄	C₂²×C₃₁	1	12	yes	complemented
43	C₂²⋊C₄	C₂²×C₃₁	1	16	yes	direct product factor
44	C₂³	—	2	32	no	—
45	C₂³	—	2	24	no	—
46	C₂³	C₂×C₄×C₃₁	1	4	yes	—
47	C₂³	C₂×C₄×C₃₁	1	24	yes	complemented
48	C₂³	D₄×C₃₁	1	8	yes	—
49	C₂³	C₂³×C₃₁	1	4	yes	—
50	C₂³	C₂³×C₃₁	1	3	yes	—
51	C₂×C₄	—	2	24	no	—
52	C₂×C₄	C₂³×C₃₁	1	8	yes	complemented
53	C₂²	—	2	48	no	—
54	C₂²	—	2	8	no	—
55	C₂²	C₂²⋊C₄×C₃₁	1	16	yes	direct product factor
56	C₂²	C₂²×C₄×C₃₁	1	6	yes	—
57	C₂²	C₂²×C₄×C₃₁	1	8	yes	complemented
58	C₂²	C₂×D₄×C₃₁	1	12	yes	—
59	C₂²	C₂⁴×C₃₁	1	1	yes	characteristic
60	C₄	—	2	8	no	—
61	C₂	—	2	8	no	—
62	C₂	C₂×C₂²⋊C₄×C₃₁	1	12	yes	direct product factor
63	C₂	C₂³×C₄×C₃₁	1	1	yes	characteristic
64	C₂	C₂²×D₄×C₃₁	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄×C₃₁	C₂	semidirect
3. C₂×C₂²⋊C₄×C₃₁	C₂	direct (N × H)
5. C₂⁴×C₃₁	C₄	semidirect
9. C₂²×C₄×C₃₁	C₂²	semidirect
10. C₂²⋊C₄×C₃₁	C₂²	direct (N × H)
14. C₂³×C₃₁	C₂×C₄	semidirect
19. C₂×C₄×C₃₁	C₂³	semidirect
22. C₂²×C₃₁	C₂²⋊C₄	direct (N × H)
24. C₂²×C₃₁	C₂²×C₄	semidirect
28. C₂²×C₂²⋊C₄	C₃₁	direct (N × H)
30. C₂×C₃₁	C₂×C₂²⋊C₄	direct (N × H)
34. C₂³×C₄	C₂×C₃₁	semidirect
35. C₂×C₂²⋊C₄	C₂×C₃₁	direct (N × H)
36. C₃₁	C₂²×C₂²⋊C₄	direct (N × H)
38. C₂⁴	C₄×C₃₁	semidirect
42. C₂²×C₄	C₂²×C₃₁	semidirect
43. C₂²⋊C₄	C₂²×C₃₁	direct (N × H)
47. C₂³	C₂×C₄×C₃₁	semidirect
52. C₂×C₄	C₂³×C₃₁	semidirect
55. C₂²	C₂²⋊C₄×C₃₁	direct (N × H)
57. C₂²	C₂²×C₄×C₃₁	semidirect
62. C₂	C₂×C₂²⋊C₄×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
C₂⁵×C₃₁	2
C₂³×C₄×C₃₁	2
C₂×C₂²⋊C₄×C₃₁	2
C₂²×C₂²⋊C₄	31

Subgroups — C22×C22⋊C4×C31 #14520693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂²⋊C₄×C₃₁ #14520693