Subgroups — C₂×C₄²×Dic₃₁ #16848033

Order 3968.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Dic₃₁	C₂	1	6	yes	maximal
2	C₄²×Dic₃₁	C₂	1	8	yes	maximal, direct product factor
3	C₂²×C₄²×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₄×C₃₁	C₂²	1	3	yes	—
5	C₂³×Dic₃₁	C₂²	1	4	yes	—
6	C₂×C₄²×C₃₁	C₄	1	8	yes	complemented
7	C₂×C₄²×C₃₁	C₂²	1	4	yes	—
8	C₂×C₄×Dic₃₁	C₄	1	48	yes	direct product factor
9	C₂×C₄×Dic₃₁	C₂²	1	24	yes	—
10	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
11	C₂²×C₄×C₃₁	C₂×C₄	1	24	yes	—
12	C₂²×C₄×C₃₁	C₂×C₄	1	12	yes	—
13	C₂²×C₄×C₃₁	C₂³	1	6	yes	—
14	C₂²×Dic₃₁	C₂×C₄	1	48	yes	—
15	C₂²×Dic₃₁	C₂³	1	8	yes	—
16	C₄²×C₃₁	C₂×C₄	1	16	yes	complemented
17	C₄×Dic₃₁	C₂×C₄	1	96	yes	direct product factor
18	C₂³×C₃₁	C₂²×C₄	1	12	yes	—
19	C₂³×C₃₁	C₂²×C₄	1	2	yes	—
20	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
21	C₂×C₄×C₃₁	C₄²	1	48	yes	complemented
22	C₂×C₄×C₃₁	C₂²×C₄	1	24	yes	—
23	C₂×C₄×C₃₁	C₂²×C₄	1	12	yes	—
24	C₂×Dic₃₁	C₄²	1	64	yes	direct product factor
25	C₂×Dic₃₁	C₂²×C₄	1	48	yes	—
26	C₂×C₄³	—	31	1	no	maximal, Sylow
27	C₂²×C₃₁	C₂×C₄²	1	16	yes	—
28	C₂²×C₃₁	C₂×C₄²	1	12	yes	—
29	C₂²×C₃₁	C₂³×C₄	1	6	yes	—
30	C₂²×C₃₁	C₂³×C₄	1	1	yes	characteristic
31	C₄×C₃₁	C₂×C₄²	1	24	yes	complemented
32	Dic₃₁	C₂×C₄²	1	32	yes	direct product factor
33	C₂²×C₄²	—	31	6	no	—
34	C₂²×C₄²	D₃₁	1	1	yes	characteristic
35	C₄³	—	31	8	no	—
36	C₂×C₃₁	C₄³	1	8	yes	complemented
37	C₂×C₃₁	C₂²×C₄²	1	4	yes	—
38	C₂×C₃₁	C₂²×C₄²	1	3	yes	—
39	C₂³×C₄	—	31	4	no	—
40	C₂³×C₄	C₂×D₃₁	1	3	yes	—
41	C₂×C₄²	—	31	48	no	—
42	C₂×C₄²	—	31	24	no	—
43	C₂×C₄²	Dic₃₁	1	8	yes	direct product factor
44	C₂×C₄²	C₂×D₃₁	1	4	yes	—
45	C₃₁	C₂×C₄³	1	1	yes	characteristic, complemented, Sylow
46	C₂⁴	C₂²×D₃₁	1	1	yes	characteristic
47	C₂²×C₄	—	31	48	no	—
48	C₂²×C₄	—	31	8	no	—
49	C₂²×C₄	C₄×D₃₁	1	24	yes	—
50	C₂²×C₄	C₂×Dic₃₁	1	12	yes	—
51	C₂²×C₄	C₂²×D₃₁	1	6	yes	—
52	C₄²	—	31	96	no	—
53	C₄²	C₂×Dic₃₁	1	16	yes	direct product factor
54	C₂³	C₂×C₄×D₃₁	1	12	yes	—
55	C₂³	C₂²×Dic₃₁	1	2	yes	—
56	C₂³	C₂³×D₃₁	1	1	yes	characteristic
57	C₂×C₄	—	31	64	no	—
58	C₂×C₄	—	31	48	no	—
59	C₂×C₄	C₄×Dic₃₁	1	48	yes	direct product factor
60	C₂×C₄	C₂×C₄×D₃₁	1	24	yes	—
61	C₂×C₄	C₂²×Dic₃₁	1	12	yes	—
62	C₂²	C₄²×D₃₁	1	16	yes	—
63	C₂²	C₂×C₄×Dic₃₁	1	12	yes	—
64	C₂²	C₂²×C₄×D₃₁	1	6	yes	—
65	C₂²	C₂³×Dic₃₁	1	1	yes	characteristic
66	C₄	—	31	32	no	—
67	C₄	C₂×C₄×Dic₃₁	1	24	yes	direct product factor
68	C₂	C₄²×Dic₃₁	1	8	yes	direct product factor
69	C₂	C₂×C₄²×D₃₁	1	4	yes	—
70	C₂	C₂²×C₄×Dic₃₁	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₂²×C₄²	D₃₁
commutator, hypocenter	C₃₁	C₂×C₄³
Frattini	C₂³	C₂³×D₃₁
Fitting	C₂²×C₄²×C₃₁	C₂
socle, prime radical	C₂⁴×C₃₁	C₂³
cosocle	C₂³×C₃₁	C₂⁴
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
2. C₄²×Dic₃₁	C₂	direct (N × H)
6. C₂×C₄²×C₃₁	C₄	semidirect
8. C₂×C₄×Dic₃₁	C₄	direct (N × H)
16. C₄²×C₃₁	C₂×C₄	semidirect
17. C₄×Dic₃₁	C₂×C₄	direct (N × H)
21. C₂×C₄×C₃₁	C₄²	semidirect
24. C₂×Dic₃₁	C₄²	direct (N × H)
31. C₄×C₃₁	C₂×C₄²	semidirect
32. Dic₃₁	C₂×C₄²	direct (N × H)
36. C₂×C₃₁	C₄³	semidirect
43. C₂×C₄²	Dic₃₁	direct (N × H)
45. C₃₁	C₂×C₄³	semidirect
53. C₄²	C₂×Dic₃₁	direct (N × H)
59. C₂×C₄	C₄×Dic₃₁	direct (N × H)
67. C₄	C₂×C₄×Dic₃₁	direct (N × H)
68. C₂	C₄²×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
C₂²×C₄×Dic₃₁	2
C₄²×Dic₃₁	2
C₂²×C₄²×C₃₁	2
C₂×C₄³	31

Subgroups — C2×C42×Dic31 #16848033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄²×Dic₃₁ #16848033