Subgroups — #44567965

Order 32288.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30633344	C₂	1	2	yes	maximal, complemented
2	C₂×#22549054	C₂	1	1	yes	maximal, characteristic
3	#22549054	C₄	1	1	yes	characteristic
4	#22549054	C₂²	1	1	yes	characteristic
5	C₂×Dic₁₀₀₉	C₄	1	1	yes	characteristic
6	C₂²×C₁₀₀₉	C₈	1	1	yes	characteristic
7	Dic₁₀₀₉	C₈	1	1	yes	characteristic
8	Dic₁₀₀₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₁₀₀₉	—	2	1	no	—
10	C₂×C₁₀₀₉	C₂×C₈	1	1	yes	characteristic
11	C₁₀₀₉	M₃₂	1	1	yes	characteristic, complemented, Sylow
12	M₃₂	—	1009	1	no	maximal, Sylow
13	C₂×C₈	—	1009	1	no	—
14	C₁₆	—	1009	2	no	—
15	C₂×C₄	—	1009	1	no	—
16	C₈	—	1009	1	no	—
17	C₈	—	1009	1	no	—
18	C₂²	#22549056	1	1	yes	characteristic
19	C₄	—	1009	1	no	—
20	C₄	—	1009	1	no	—
21	C₂	—	2	1	no	—
22	C₂	C₂×#22549056	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #30633344	C₂	semidirect
11. C₁₀₀₉	M₃₂	semidirect

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