Subgroups — C₄⋊#20268824 #40997256

Order 26512.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20268824	C₂	1	2	yes	maximal
2	C₄×D₁₆₅₇	C₂	1	1	yes	maximal, characteristic
3	C₂×D₁₆₅₇	C₂²	1	1	yes	characteristic
4	#20268824	—	2	2	no	—
5	C₄×C₁₆₅₇	C₄	1	1	yes	characteristic, complemented
6	Dic₁₆₅₇	C₄	1	1	yes	characteristic, complemented
7	C₂×C₁₆₅₇	C₂×C₄	1	1	yes	characteristic
8	D₁₆₅₇	D₄	1	1	yes	characteristic
9	D₁₆₅₇	Q₈	1	1	yes	characteristic
10	C₁₆₅₇	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
11	C₄⋊C₄	—	1657	1	no	maximal, Sylow
12	C₂×C₄	—	1657	1	no	—
13	C₂×C₄	—	1657	2	no	—
14	C₂²	—	1657	1	no	—
15	C₄	—	1657	1	no	—
16	C₄	—	3314	2	no	—
17	C₄	#20268824	1	1	yes	characteristic, complemented
18	C₂	—	1657	1	no	—
19	C₂	—	1657	1	no	—
20	C₂	C₂×#20268824	1	1	yes	characteristic

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

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