Subgroups — C₂²×C₄×Dic₃₁ #14521494

Order 1984.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×Dic₃₁	C₂	direct (N × H)
5. C₂²×C₄×C₃₁	C₄	semidirect
7. C₂²×Dic₃₁	C₄	direct (N × H)
9. C₄×Dic₃₁	C₂²	direct (N × H)
13. C₂×C₄×C₃₁	C₂×C₄	semidirect
15. C₂×Dic₃₁	C₂×C₄	direct (N × H)
17. C₂²×C₃₁	C₄²	semidirect
21. C₄×C₃₁	C₂²×C₄	semidirect
22. Dic₃₁	C₂²×C₄	direct (N × H)
24. C₂×C₃₁	C₂×C₄²	semidirect
30. C₃₁	C₂²×C₄²	semidirect
34. C₂²×C₄	Dic₃₁	direct (N × H)
42. C₂×C₄	C₂×Dic₃₁	direct (N × H)
44. C₂²	C₄×Dic₃₁	direct (N × H)
49. C₄	C₂²×Dic₃₁	direct (N × H)
50. C₂	C₂×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
C₂³×C₄×C₃₁	2
C₂³×Dic₃₁	2
C₂×C₄×Dic₃₁	2
C₂²×C₄²	31

Subgroups — C22×C4×Dic31 #14521494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×Dic₃₁ #14521494