Subgroups — D₂₀₄ #87990

Order 408.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₁	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₆₈	—	3	1	no	maximal, Hall
4	C₂×C₃×C₁₇	C₂²	1	1	yes	characteristic
5	D₅₁	—	2	2	no	—
6	C₂×D₁₇	—	3	2	no	—
7	C₄×C₁₇	D₃	1	1	yes	characteristic, complemented
8	C₃×C₁₇	D₄	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₇	C₂×D₃	1	1	yes	characteristic
10	D₁₇	—	6	2	no	—
11	D₁₂	—	17	1	no	maximal, Hall
12	C₁₇	D₁₂	1	1	yes	characteristic, complemented, Sylow
13	C₂×D₃	—	17	2	no	—
14	C₃×C₄	D₁₇	1	1	yes	characteristic, complemented
15	D₄	—	51	1	no	Sylow
16	C₂×C₃	C₂×D₁₇	1	1	yes	characteristic
17	D₃	—	34	2	no	—
18	C₂²	—	51	2	no	—
19	C₄	D₅₁	1	1	yes	characteristic, complemented
20	C₃	D₆₈	1	1	yes	characteristic, complemented, Sylow
21	C₂	—	102	2	no	—
22	C₂	C₂×D₅₁	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.