Subgroups — C₄²×C₃₁⋊C₈ #16845393

Order 3968.

408 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₃₁⋊C₈	C₂	1	6	yes	maximal
2	C₄³×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×C₃₁	C₄	1	4	yes	—
4	C₂×C₄²×C₃₁	C₂²	1	3	yes	—
5	C₂²×C₃₁⋊C₈	C₂²	1	4	yes	—
6	C₄×C₃₁⋊C₈	C₄	1	24	yes	direct product factor
7	C₂²×C₄×C₃₁	C₂×C₄	1	6	yes	—
8	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
9	C₄²×C₃₁	C₈	1	16	yes	complemented
10	C₄²×C₃₁	C₂×C₄	1	12	yes	—
11	C₂×C₃₁⋊C₈	C₂×C₄	1	24	yes	—
12	C₂³×C₃₁	C₂²×C₄	1	1	yes	characteristic
13	C₂×C₄×C₃₁	C₄²	1	12	yes	—
14	C₂×C₄×C₃₁	C₂×C₈	1	24	yes	—
15	C₂×C₄×C₃₁	C₂²×C₄	1	6	yes	—
16	C₃₁⋊C₈	C₄²	1	16	yes	direct product factor
17	C₄²×C₈	—	31	1	no	maximal, Sylow
18	C₂²×C₃₁	C₂×C₄²	1	3	yes	—
19	C₂²×C₃₁	C₂²×C₈	1	4	yes	—
20	C₄×C₃₁	C₄×C₈	1	24	yes	complemented
21	C₄×C₃₁	C₂×C₄²	1	4	yes	—
22	C₂×C₄×C₈	—	31	6	no	—
23	C₄³	D₃₁	1	1	yes	characteristic
24	C₂×C₃₁	C₄³	1	1	yes	characteristic
25	C₂×C₃₁	C₂×C₄×C₈	1	6	yes	—
26	C₂²×C₈	—	31	4	no	—
27	C₂×C₄²	Dic₃₁	1	4	yes	—
28	C₂×C₄²	C₂×D₃₁	1	3	yes	—
29	C₄×C₈	—	31	24	no	—
30	C₃₁	C₄²×C₈	1	1	yes	characteristic, complemented, Sylow
31	C₂²×C₄	C₂×Dic₃₁	1	6	yes	—
32	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
33	C₂×C₈	—	31	24	no	—
34	C₄²	C₃₁⋊C₈	1	16	yes	direct product factor
35	C₄²	C₄×D₃₁	1	12	yes	—
36	C₂³	C₂²×Dic₃₁	1	1	yes	characteristic
37	C₂×C₄	C₂×C₃₁⋊C₈	1	24	yes	—
38	C₂×C₄	C₄×Dic₃₁	1	12	yes	—
39	C₂×C₄	C₂×C₄×D₃₁	1	6	yes	—
40	C₈	—	31	16	no	—
41	C₂²	C₂²×C₃₁⋊C₈	1	4	yes	—
42	C₂²	C₂×C₄×Dic₃₁	1	3	yes	—
43	C₄	C₄×C₃₁⋊C₈	1	24	yes	direct product factor
44	C₄	C₄²×D₃₁	1	4	yes	—
45	C₂	C₄²×Dic₃₁	1	1	yes	characteristic
46	C₂	C₂×C₄×C₃₁⋊C₈	1	6	yes	—

	subgroup	G/H
center, hypercenter	C₄³	D₃₁
commutator, hypocenter	C₃₁	C₄²×C₈
Frattini	C₂²×C₄	C₂²×D₃₁
Fitting	C₄³×C₃₁	C₂
socle, prime radical	C₂³×C₃₁	C₂²×C₄
cosocle	C₂²×C₄×C₃₁	C₂³
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₄³

Complements

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

N	H ≅ G/N	type
6. C₄×C₃₁⋊C₈	C₄	direct (N × H)
9. C₄²×C₃₁	C₈	semidirect
16. C₃₁⋊C₈	C₄²	direct (N × H)
20. C₄×C₃₁	C₄×C₈	semidirect
30. C₃₁	C₄²×C₈	semidirect
34. C₄²	C₃₁⋊C₈	direct (N × H)
43. C₄	C₄×C₃₁⋊C₈	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×C₄×C₃₁⋊C₈	2
C₄³×C₃₁	2
C₄²×C₈	31

Subgroups — C42×C31⋊C8 #16845393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×C₃₁⋊C₈ #16845393