Subgroups — D₁₅₈₅₆ #44540392

Order 31712.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₉₂₈	C₂	1	2	yes	maximal, complemented
2	C₁₆×C₉₉₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₉₆₄	—	2	2	no	—
4	C₈×C₉₉₁	C₂²	1	1	yes	characteristic
5	C₂×D₉₉₁	—	4	2	no	—
6	C₄×C₉₉₁	D₄	1	1	yes	characteristic
7	C₂×C₉₉₁	D₈	1	1	yes	characteristic
8	D₉₉₁	—	8	2	no	—
9	C₉₉₁	D₁₆	1	1	yes	characteristic, complemented, Sylow
10	D₁₆	—	991	1	no	maximal, Sylow
11	D₈	—	991	2	no	—
12	C₁₆	D₉₉₁	1	1	yes	characteristic, complemented
13	D₄	—	1982	2	no	—
14	C₈	C₂×D₉₉₁	1	1	yes	characteristic
15	C₂²	—	3964	2	no	—
16	C₄	D₃₉₆₄	1	1	yes	characteristic
17	C₂	—	7928	2	no	—
18	C₂	D₇₉₂₈	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.