Subgroups — Dic₅₀₅₂ #72216632

Order 20208.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₅₂₆	C₂	1	2	yes	maximal
2	C₃×C₈×C₄₂₁	C₂	1	1	yes	maximal, characteristic
3	Dic₁₆₈₄	—	3	1	no	maximal, Hall
4	Dic₁₂₆₃	—	2	2	no	—
5	C₃×C₄×C₄₂₁	C₂²	1	1	yes	characteristic
6	Dic₈₄₂	—	3	2	no	—
7	C₈×C₄₂₁	D₃	1	1	yes	characteristic
8	C₂×C₃×C₄₂₁	D₄	1	1	yes	characteristic
9	C₄×C₄₂₁	C₂×D₃	1	1	yes	characteristic
10	Dic₄₂₁	—	6	2	no	—
11	C₃×C₄₂₁	Q₁₆	1	1	yes	characteristic, complemented, Hall
12	C₂×C₄₂₁	D₁₂	1	1	yes	characteristic
13	C₄₂₁	Dic₁₂	1	1	yes	characteristic, complemented, Sylow
14	Dic₁₂	—	421	1	no	maximal, Hall
15	Dic₆	—	421	2	no	—
16	C₃×C₈	D₄₂₁	1	1	yes	characteristic
17	Q₁₆	—	1263	1	no	Sylow
18	C₃×C₄	C₂×D₄₂₁	1	1	yes	characteristic
19	Dic₃	—	842	2	no	—
20	Q₈	—	1263	2	no	—
21	C₈	D₁₂₆₃	1	1	yes	characteristic
22	C₂×C₃	D₁₆₈₄	1	1	yes	characteristic
23	C₄	—	2526	2	no	—
24	C₄	C₂×D₁₂₆₃	1	1	yes	characteristic
25	C₃	Dic₁₆₈₄	1	1	yes	characteristic, complemented, Sylow
26	C₂	D₅₀₅₂	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.