Subgroups — D₁₂₂₅₆ #37588187

Order 24512.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₁₂₈	C₂	1	2	yes	maximal, complemented
2	C₃₂×C₃₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₀₆₄	—	2	2	no	—
4	C₁₆×C₃₈₃	C₂²	1	1	yes	characteristic
5	D₁₅₃₂	—	4	2	no	—
6	C₈×C₃₈₃	D₄	1	1	yes	characteristic
7	C₂×D₃₈₃	—	8	2	no	—
8	C₄×C₃₈₃	D₈	1	1	yes	characteristic
9	C₂×C₃₈₃	D₁₆	1	1	yes	characteristic
10	D₃₈₃	—	16	2	no	—
11	C₃₈₃	D₃₂	1	1	yes	characteristic, complemented, Sylow
12	D₃₂	—	383	1	no	maximal, Sylow
13	D₁₆	—	383	2	no	—
14	C₃₂	D₃₈₃	1	1	yes	characteristic, complemented
15	D₈	—	766	2	no	—
16	C₁₆	C₂×D₃₈₃	1	1	yes	characteristic
17	D₄	—	1532	2	no	—
18	C₈	D₁₅₃₂	1	1	yes	characteristic
19	C₂²	—	3064	2	no	—
20	C₄	D₃₀₆₄	1	1	yes	characteristic
21	C₂	—	6128	2	no	—
22	C₂	D₆₁₂₈	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.