Subgroups — #44548567

Order 32128.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30631513	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₂₅₁	C₂	1	1	yes	maximal, characteristic
3	#22548649	—	2	2	no	—
4	C₂×C₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
5	C₃₂×C₂₅₁	C₄	1	2	yes	complemented
6	C₄⋊Dic₂₅₁	—	4	2	no	—
7	C₂×C₈×C₂₅₁	D₄	1	1	yes	characteristic
8	C₁₆×C₂₅₁	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₂₅₁	Q₈	1	1	yes	characteristic
10	C₂×Dic₂₅₁	—	8	2	no	—
11	C₂×C₄×C₂₅₁	D₈	1	1	yes	characteristic
12	C₈×C₂₅₁	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₂₅₁	Q₁₆	1	1	yes	characteristic
14	C₂²×C₂₅₁	D₁₆	1	1	yes	characteristic
15	C₄×C₂₅₁	#107	1	1	yes	characteristic
16	C₄×C₂₅₁	Q₃₂	1	1	yes	characteristic
17	Dic₂₅₁	—	16	2	no	—
18	C₂×C₂₅₁	#366	1	1	yes	characteristic
19	C₂×C₂₅₁	SD₆₄	1	2	yes	—
20	C₂₅₁	#1424	1	1	yes	characteristic, complemented, Sylow
21	#1424	—	251	1	no	maximal, Sylow
22	C₂×C₃₂	D₂₅₁	1	1	yes	characteristic
23	#366	—	251	2	no	—
24	C₂×C₁₆	C₂×D₂₅₁	1	1	yes	characteristic
25	#107	—	502	2	no	—
26	C₃₂	Dic₂₅₁	1	2	yes	complemented
27	C₂×C₈	D₁₀₀₄	1	1	yes	characteristic
28	C₄⋊C₄	—	1004	2	no	—
29	C₁₆	C₂×Dic₂₅₁	1	1	yes	characteristic
30	C₁₆	Dic₅₀₂	1	1	yes	characteristic
31	C₂×C₄	—	2008	2	no	—
32	C₂×C₄	D₂₀₀₈	1	1	yes	characteristic
33	C₈	C₄⋊Dic₂₅₁	1	1	yes	characteristic
34	C₈	Dic₁₀₀₄	1	1	yes	characteristic
35	C₂²	D₄₀₁₆	1	1	yes	characteristic
36	C₄	—	4016	2	no	—
37	C₄	#22548649	1	1	yes	characteristic
38	C₄	Dic₂₀₀₈	1	1	yes	characteristic
39	C₂	#30631513	1	1	yes	characteristic
40	C₂	#30631526	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄₀₁₆
commutator	C₁₆×C₂₅₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₅₁
Fitting	C₂×C₃₂×C₂₅₁	C₂
socle, prime radical	C₂²×C₂₅₁	D₁₆
cosocle	C₂×C₁₆×C₂₅₁	C₂²
hypercenter	C₂×C₃₂	D₂₅₁
hypocenter	C₂₅₁	#1424
LCS	G ▷ C₁₆×C₂₅₁ ▷ C₈×C₂₅₁ ▷ C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
5. C₃₂×C₂₅₁	C₄	semidirect
20. C₂₅₁	#1424	semidirect
26. C₃₂	Dic₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30631513	2
C₂×C₃₂×C₂₅₁	2
#1424	251