Subgroups — D₈₁₂₈ #30636943

Order 16256.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₀₆₄	C₂	1	2	yes	maximal, complemented
2	C₆₄×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₂₀₃₂	—	2	2	no	—
4	C₃₂×C₁₂₇	C₂²	1	1	yes	characteristic
5	D₁₀₁₆	—	4	2	no	—
6	C₁₆×C₁₂₇	D₄	1	1	yes	characteristic
7	D₅₀₈	—	8	2	no	—
8	C₈×C₁₂₇	D₈	1	1	yes	characteristic
9	C₂×D₁₂₇	—	16	2	no	—
10	C₄×C₁₂₇	D₁₆	1	1	yes	characteristic
11	C₂×C₁₂₇	D₃₂	1	1	yes	characteristic
12	D₁₂₇	—	32	2	no	—
13	D₆₄	—	127	1	no	maximal, Sylow
14	C₁₂₇	D₆₄	1	1	yes	characteristic, complemented, Sylow
15	D₃₂	—	127	2	no	—
16	C₆₄	D₁₂₇	1	1	yes	characteristic, complemented
17	D₁₆	—	254	2	no	—
18	C₃₂	C₂×D₁₂₇	1	1	yes	characteristic
19	D₈	—	508	2	no	—
20	C₁₆	D₅₀₈	1	1	yes	characteristic
21	D₄	—	1016	2	no	—
22	C₈	D₁₀₁₆	1	1	yes	characteristic
23	C₂²	—	2032	2	no	—
24	C₄	D₂₀₃₂	1	1	yes	characteristic
25	C₂	—	4064	2	no	—
26	C₂	D₄₀₆₄	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.