Subgroups — #22551667

Order 8224.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16861621	C₂	1	2	yes	maximal, complemented
2	C₈×D₂₅₇	C₂	1	1	yes	maximal, characteristic
3	C₄×D₂₅₇	C₄	1	1	yes	characteristic
4	#14523339	C₂²	1	1	yes	characteristic
5	C₈×C₂₅₇	C₄	1	1	yes	characteristic
6	C₂×D₂₅₇	C₈	1	1	yes	characteristic
7	C₄×C₂₅₇	C₂×C₄	1	1	yes	characteristic
8	Dic₂₅₇	C₈	1	1	yes	characteristic
9	C₂×C₂₅₇	C₂×C₈	1	1	yes	characteristic
10	D₂₅₇	—	2	1	no	—
11	C₂₅₇	M₃₂	1	1	yes	characteristic, complemented, Sylow
12	M₃₂	—	257	1	no	maximal, Sylow
13	C₂×C₈	—	257	1	no	—
14	C₁₆	—	257	2	no	—
15	C₂×C₄	—	257	1	no	—
16	C₈	—	257	1	no	—
17	C₈	#11759967	1	1	yes	characteristic
18	C₂²	—	257	1	no	—
19	C₄	—	257	1	no	—
20	C₄	C₂×#11759967	1	1	yes	characteristic
21	C₂	—	514	1	no	—
22	C₂	#16861626	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #16861621	C₂	semidirect
11. C₂₅₇	M₃₂	semidirect