Subgroups — C₄³×D₃₁ #16848032

Order 3968.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₃₁	C₂	1	7	yes	maximal
2	C₄²×Dic₃₁	C₂	1	7	yes	maximal, complemented
3	C₄³×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₃₁	C₂²	1	7	yes	—
5	C₂×C₄²×C₃₁	C₂²	1	7	yes	—
6	C₂×C₄×Dic₃₁	C₂²	1	21	yes	—
7	C₄²×D₃₁	C₄	1	56	yes	direct product factor
8	C₂³×D₃₁	C₂³	1	1	yes	characteristic
9	C₂²×C₄×C₃₁	C₂³	1	7	yes	—
10	C₂²×Dic₃₁	C₂³	1	7	yes	—
11	C₂×C₄×D₃₁	C₂×C₄	1	84	yes	—
12	C₄²×C₃₁	C₂×C₄	1	28	yes	complemented
13	C₄×Dic₃₁	C₂×C₄	1	84	yes	complemented
14	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
15	C₂²×D₃₁	C₂²×C₄	1	14	yes	—
16	C₂×C₄×C₃₁	C₂²×C₄	1	42	yes	—
17	C₂×Dic₃₁	C₂²×C₄	1	42	yes	—
18	C₄×D₃₁	C₄²	1	112	yes	direct product factor
19	C₂×C₄³	—	31	1	no	maximal, Sylow
20	C₂²×C₃₁	C₂³×C₄	1	7	yes	—
21	C₂×D₃₁	C₂×C₄²	1	28	yes	—
22	C₄×C₃₁	C₂×C₄²	1	28	yes	complemented
23	Dic₃₁	C₂×C₄²	1	28	yes	complemented
24	C₂²×C₄²	—	31	7	no	—
25	C₄³	—	31	7	no	—
26	C₄³	D₃₁	1	1	yes	characteristic, direct product factor
27	C₂×C₃₁	C₂²×C₄²	1	7	yes	—
28	D₃₁	C₄³	1	8	yes	direct product factor
29	C₂³×C₄	—	31	7	no	—
30	C₂×C₄²	—	31	21	no	—
31	C₂×C₄²	—	31	56	no	—
32	C₂×C₄²	C₂×D₃₁	1	7	yes	—
33	C₃₁	C₂×C₄³	1	1	yes	characteristic, complemented, Sylow
34	C₂⁴	—	31	1	no	—
35	C₂²×C₄	—	31	7	no	—
36	C₂²×C₄	—	31	84	no	—
37	C₂²×C₄	C₂²×D₃₁	1	7	yes	—
38	C₄²	—	31	84	no	—
39	C₄²	C₄×D₃₁	1	28	yes	direct product factor
40	C₂³	—	31	14	no	—
41	C₂³	C₂³×D₃₁	1	1	yes	characteristic
42	C₂×C₄	—	31	42	no	—
43	C₂×C₄	—	31	112	no	—
44	C₂×C₄	C₂×C₄×D₃₁	1	42	yes	—
45	C₂²	—	31	28	no	—
46	C₂²	C₂²×C₄×D₃₁	1	7	yes	—
47	C₄	—	31	28	no	—
48	C₄	C₄²×D₃₁	1	28	yes	direct product factor
49	C₂	—	31	8	no	—
50	C₂	C₂×C₄²×D₃₁	1	7	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₄²×Dic₃₁	C₂	semidirect
3. C₄³×C₃₁	C₂	semidirect
7. C₄²×D₃₁	C₄	direct (N × H)
12. C₄²×C₃₁	C₂×C₄	semidirect
13. C₄×Dic₃₁	C₂×C₄	semidirect
18. C₄×D₃₁	C₄²	direct (N × H)
22. C₄×C₃₁	C₂×C₄²	semidirect
23. Dic₃₁	C₂×C₄²	semidirect
26. C₄³	D₃₁	direct (N × H)
28. D₃₁	C₄³	direct (N × H)
33. C₃₁	C₂×C₄³	semidirect
39. C₄²	C₄×D₃₁	direct (N × H)
48. C₄	C₄²×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
C₂×C₄²×D₃₁	2
C₄²×Dic₃₁	2
C₄³×C₃₁	2
C₂×C₄³	31

Subgroups — C43×D31 #16848032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄³×D₃₁ #16848032