Subgroups — C₄²×C₁₃₁⋊C₈ #30665643

Order 16768.

408 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃₁⋊C₈	C₂	1	6	yes	maximal
2	C₄³×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₃₁⋊C₈	C₂²	1	4	yes	—
4	C₄×C₁₃₁⋊C₈	C₄	1	24	yes	direct product factor
5	C₂×C₄²×C₁₃₁	C₄	1	4	yes	—
6	C₂×C₄²×C₁₃₁	C₂²	1	3	yes	—
7	C₂×C₁₃₁⋊C₈	C₂×C₄	1	24	yes	—
8	C₂²×C₄×C₁₃₁	C₂×C₄	1	6	yes	—
9	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
10	C₄²×C₁₃₁	C₈	1	16	yes	complemented
11	C₄²×C₁₃₁	C₂×C₄	1	12	yes	—
12	C₁₃₁⋊C₈	C₄²	1	16	yes	direct product factor
13	C₂³×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₃₁	C₄²	1	12	yes	—
15	C₂×C₄×C₁₃₁	C₂×C₈	1	24	yes	—
16	C₂×C₄×C₁₃₁	C₂²×C₄	1	6	yes	—
17	C₂²×C₁₃₁	C₂×C₄²	1	3	yes	—
18	C₂²×C₁₃₁	C₂²×C₈	1	4	yes	—
19	C₄×C₁₃₁	C₄×C₈	1	24	yes	complemented
20	C₄×C₁₃₁	C₂×C₄²	1	4	yes	—
21	C₂×C₁₃₁	C₄³	1	1	yes	characteristic
22	C₂×C₁₃₁	C₂×C₄×C₈	1	6	yes	—
23	C₁₃₁	C₄²×C₈	1	1	yes	characteristic, complemented, Sylow
24	C₄²×C₈	—	131	1	no	maximal, Sylow
25	C₂×C₄×C₈	—	131	6	no	—
26	C₄³	D₁₃₁	1	1	yes	characteristic
27	C₂²×C₈	—	131	4	no	—
28	C₂×C₄²	Dic₁₃₁	1	4	yes	—
29	C₂×C₄²	C₂×D₁₃₁	1	3	yes	—
30	C₄×C₈	—	131	24	no	—
31	C₂²×C₄	C₂×Dic₁₃₁	1	6	yes	—
32	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
33	C₂×C₈	—	131	24	no	—
34	C₄²	C₁₃₁⋊C₈	1	16	yes	direct product factor
35	C₄²	C₄×D₁₃₁	1	12	yes	—
36	C₂³	C₂²×Dic₁₃₁	1	1	yes	characteristic
37	C₂×C₄	C₄×Dic₁₃₁	1	12	yes	—
38	C₂×C₄	C₂×C₁₃₁⋊C₈	1	24	yes	—
39	C₂×C₄	C₂×C₄×D₁₃₁	1	6	yes	—
40	C₈	—	131	16	no	—
41	C₂²	C₂×C₄×Dic₁₃₁	1	3	yes	—
42	C₂²	C₂²×C₁₃₁⋊C₈	1	4	yes	—
43	C₄	C₄×C₁₃₁⋊C₈	1	24	yes	direct product factor
44	C₄	C₄²×D₁₃₁	1	4	yes	—
45	C₂	C₄²×Dic₁₃₁	1	1	yes	characteristic
46	C₂	C₂×C₄×C₁₃₁⋊C₈	1	6	yes	—

	subgroup	G/H
center, hypercenter	C₄³	D₁₃₁
commutator, hypocenter	C₁₃₁	C₄²×C₈
Frattini	C₂²×C₄	C₂²×D₁₃₁
Fitting	C₄³×C₁₃₁	C₂
socle, prime radical	C₂³×C₁₃₁	C₂²×C₄
cosocle	C₂²×C₄×C₁₃₁	C₂³
LCS	G ▷ C₁₃₁
UCS	C₁ ◁ C₄³

Complements

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

N	H ≅ G/N	type
4. C₄×C₁₃₁⋊C₈	C₄	direct (N × H)
10. C₄²×C₁₃₁	C₈	semidirect
12. C₁₃₁⋊C₈	C₄²	direct (N × H)
19. C₄×C₁₃₁	C₄×C₈	semidirect
23. C₁₃₁	C₄²×C₈	semidirect
34. C₄²	C₁₃₁⋊C₈	direct (N × H)
43. C₄	C₄×C₁₃₁⋊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×C₁₃₁⋊C₈	2
C₄³×C₁₃₁	2
C₄²×C₈	131

Subgroups — C42×C131⋊C8 #30665643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×C₁₃₁⋊C₈ #30665643