Subgroups — C₈×C₁₆₃⋊C₁₆ #35212451

Order 20864.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₆₃⋊C₁₆	C₂	1	2	yes	maximal
2	C₈²×C₁₆₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆₃⋊C₁₆	C₄	1	4	yes	—
4	C₄×C₈×C₁₆₃	C₄	1	2	yes	—
5	C₄×C₈×C₁₆₃	C₂²	1	1	yes	characteristic
6	C₁₆₃⋊C₁₆	C₈	1	8	yes	direct product factor
7	C₂×C₈×C₁₆₃	C₈	1	4	yes	—
8	C₂×C₈×C₁₆₃	C₂×C₄	1	2	yes	—
9	C₄²×C₁₆₃	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₁₆₃	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₁₆₃	C₂×C₈	1	2	yes	—
12	C₈×C₁₆₃	C₁₆	1	8	yes	complemented
13	C₈×C₁₆₃	C₂×C₈	1	4	yes	—
14	C₂²×C₁₆₃	C₄×C₈	1	1	yes	characteristic
15	C₄×C₁₆₃	C₄×C₈	1	2	yes	—
16	C₄×C₁₆₃	C₂×C₁₆	1	4	yes	—
17	C₂×C₁₆₃	C₈²	1	1	yes	characteristic
18	C₂×C₁₆₃	C₄×C₁₆	1	2	yes	—
19	C₁₆₃	C₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
20	C₈×C₁₆	—	163	1	no	maximal, Sylow
21	C₄×C₁₆	—	163	2	no	—
22	C₈²	D₁₆₃	1	1	yes	characteristic
23	C₂×C₁₆	—	163	4	no	—
24	C₄×C₈	Dic₁₆₃	1	2	yes	—
25	C₄×C₈	C₂×D₁₆₃	1	1	yes	characteristic
26	C₂×C₈	C₁₆₃⋊C₈	1	4	yes	—
27	C₂×C₈	C₄×D₁₆₃	1	2	yes	—
28	C₄²	C₂×Dic₁₆₃	1	1	yes	characteristic
29	C₁₆	—	163	8	no	—
30	C₂×C₄	C₄×Dic₁₆₃	1	1	yes	characteristic
31	C₂×C₄	C₂×C₁₆₃⋊C₈	1	2	yes	—
32	C₈	C₁₆₃⋊C₁₆	1	8	yes	direct product factor
33	C₈	C₈×D₁₆₃	1	4	yes	—
34	C₂²	C₄×C₁₆₃⋊C₈	1	1	yes	characteristic
35	C₄	C₈×Dic₁₆₃	1	2	yes	—
36	C₄	C₂×C₁₆₃⋊C₁₆	1	4	yes	—
37	C₂	C₈×C₁₆₃⋊C₈	1	1	yes	characteristic
38	C₂	C₄×C₁₆₃⋊C₁₆	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₈²	D₁₆₃
commutator, hypocenter	C₁₆₃	C₈×C₁₆
Frattini	C₄×C₈	C₂×D₁₆₃
Fitting	C₈²×C₁₆₃	C₂
socle, prime radical	C₂²×C₁₆₃	C₄×C₈
cosocle	C₄×C₈×C₁₆₃	C₂²
LCS	G ▷ C₁₆₃
UCS	C₁ ◁ C₈²

Complements

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

N	H ≅ G/N	type
6. C₁₆₃⋊C₁₆	C₈	direct (N × H)
12. C₈×C₁₆₃	C₁₆	semidirect
19. C₁₆₃	C₈×C₁₆	semidirect
32. C₈	C₁₆₃⋊C₁₆	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₁₆₃⋊C₁₆	2
C₈²×C₁₆₃	2
C₈×C₁₆	163

Subgroups — C8×C163⋊C16 #35212451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₁₆₃⋊C₁₆ #35212451