Subgroups — C₄⋊Dic₂₂₅₁ #49112839

Order 36016.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₂₅₁	C₂	1	2	yes	maximal
2	C₂×C₄×C₂₂₅₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂₂₅₁	C₂²	1	1	yes	characteristic
4	C₄×C₂₂₅₁	C₄	1	2	yes	complemented
5	Dic₂₂₅₁	—	2	2	no	—
6	C₂×C₂₂₅₁	C₂×C₄	1	1	yes	characteristic
7	C₂×C₂₂₅₁	D₄	1	1	yes	characteristic
8	C₂×C₂₂₅₁	Q₈	1	1	yes	characteristic
9	C₂₂₅₁	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
10	C₄⋊C₄	—	2251	1	no	maximal, Sylow
11	C₂×C₄	—	2251	2	no	—
12	C₂×C₄	D₂₂₅₁	1	1	yes	characteristic
13	C₂²	C₂×D₂₂₅₁	1	1	yes	characteristic
14	C₄	—	4502	2	no	—
15	C₄	Dic₂₂₅₁	1	2	yes	complemented
16	C₂	C₂×Dic₂₂₅₁	1	1	yes	characteristic
17	C₂	D₉₀₀₄	1	1	yes	characteristic
18	C₂	Dic₄₅₀₂	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.