Subgroups — C₈×C₂₅₁⋊C₁₆ #44548280

Order 32128.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂₅₁⋊C₁₆	C₂	1	2	yes	maximal
2	C₈²×C₂₅₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₅₁⋊C₁₆	C₄	1	4	yes	—
4	C₄×C₈×C₂₅₁	C₄	1	2	yes	—
5	C₄×C₈×C₂₅₁	C₂²	1	1	yes	characteristic
6	C₂₅₁⋊C₁₆	C₈	1	8	yes	direct product factor
7	C₂×C₈×C₂₅₁	C₈	1	4	yes	—
8	C₂×C₈×C₂₅₁	C₂×C₄	1	2	yes	—
9	C₄²×C₂₅₁	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₂₅₁	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₂₅₁	C₂×C₈	1	2	yes	—
12	C₈×C₂₅₁	C₁₆	1	8	yes	complemented
13	C₈×C₂₅₁	C₂×C₈	1	4	yes	—
14	C₂²×C₂₅₁	C₄×C₈	1	1	yes	characteristic
15	C₄×C₂₅₁	C₄×C₈	1	2	yes	—
16	C₄×C₂₅₁	C₂×C₁₆	1	4	yes	—
17	C₂×C₂₅₁	C₈²	1	1	yes	characteristic
18	C₂×C₂₅₁	C₄×C₁₆	1	2	yes	—
19	C₂₅₁	C₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
20	C₈×C₁₆	—	251	1	no	maximal, Sylow
21	C₄×C₁₆	—	251	2	no	—
22	C₈²	D₂₅₁	1	1	yes	characteristic
23	C₂×C₁₆	—	251	4	no	—
24	C₄×C₈	Dic₂₅₁	1	2	yes	—
25	C₄×C₈	C₂×D₂₅₁	1	1	yes	characteristic
26	C₂×C₈	C₂₅₁⋊C₈	1	4	yes	—
27	C₂×C₈	C₄×D₂₅₁	1	2	yes	—
28	C₄²	C₂×Dic₂₅₁	1	1	yes	characteristic
29	C₁₆	—	251	8	no	—
30	C₂×C₄	C₄×Dic₂₅₁	1	1	yes	characteristic
31	C₂×C₄	C₂×C₂₅₁⋊C₈	1	2	yes	—
32	C₈	C₂₅₁⋊C₁₆	1	8	yes	direct product factor
33	C₈	C₈×D₂₅₁	1	4	yes	—
34	C₂²	C₄×C₂₅₁⋊C₈	1	1	yes	characteristic
35	C₄	C₈×Dic₂₅₁	1	2	yes	—
36	C₄	C₂×C₂₅₁⋊C₁₆	1	4	yes	—
37	C₂	C₈×C₂₅₁⋊C₈	1	1	yes	characteristic
38	C₂	C₄×C₂₅₁⋊C₁₆	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₈²	D₂₅₁
commutator, hypocenter	C₂₅₁	C₈×C₁₆
Frattini	C₄×C₈	C₂×D₂₅₁
Fitting	C₈²×C₂₅₁	C₂
socle, prime radical	C₂²×C₂₅₁	C₄×C₈
cosocle	C₄×C₈×C₂₅₁	C₂²
LCS	G ▷ C₂₅₁
UCS	C₁ ◁ C₈²

Complements

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

N	H ≅ G/N	type
6. C₂₅₁⋊C₁₆	C₈	direct (N × H)
12. C₈×C₂₅₁	C₁₆	semidirect
19. C₂₅₁	C₈×C₁₆	semidirect
32. C₈	C₂₅₁⋊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×C₂₅₁⋊C₁₆	2
C₈²×C₂₅₁	2
C₈×C₁₆	251

Subgroups — C8×C251⋊C16 #44548280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₂₅₁⋊C₁₆ #44548280