Subgroups — #44548569

Order 32128.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30631517	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₂₅₁	C₂	1	1	yes	maximal, characteristic
3	#22548651	—	2	2	no	—
4	C₂×C₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
5	C₃₂×C₂₅₁	C₄	1	2	yes	—
6	#16860794	—	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	C₂₅₁⋊C₈	—	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	Q₃₂	1	1	yes	characteristic
15	C₄×C₂₅₁	#107	1	1	yes	characteristic
16	C₄×C₂₅₁	D₁₆	1	1	yes	characteristic
17	C₂×C₂₅₁	—	2	1	no	—
18	C₂×C₂₅₁	#366	1	1	yes	characteristic
19	C₂₅₁	#1425	1	1	yes	characteristic, complemented, Sylow
20	#1425	—	251	1	no	maximal, Sylow
21	C₂×C₃₂	D₂₅₁	1	1	yes	characteristic
22	#368	—	251	2	no	—
23	C₂×C₁₆	C₂×D₂₅₁	1	1	yes	characteristic
24	#108	—	502	2	no	—
25	C₃₂	Dic₂₅₁	1	2	yes	—
26	M₁₆	—	1004	2	no	—
27	C₂×C₈	D₁₀₀₄	1	1	yes	characteristic
28	C₁₆	C₂×Dic₂₅₁	1	1	yes	characteristic
29	C₁₆	Dic₅₀₂	1	1	yes	characteristic
30	C₂×C₄	D₂₀₀₈	1	1	yes	characteristic
31	C₈	—	2008	2	no	—
32	C₈	C₄⋊Dic₂₅₁	1	1	yes	characteristic
33	C₈	Dic₁₀₀₄	1	1	yes	characteristic
34	C₂²	Dic₂₀₀₈	1	1	yes	characteristic
35	C₄	#22548649	1	1	yes	characteristic
36	C₄	D₄₀₁₆	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#30631513	1	1	yes	characteristic

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

N	H ≅ G/N	type
19. C₂₅₁	#1425	semidirect

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