Subgroups — Dic₁₆₂₂₇ #72301034

Order 64908.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₇×C₆₀₁	C₂	1	1	yes	maximal, characteristic
2	Dic₅₄₀₉	—	3	1	no	maximal
3	C₂₇×C₆₀₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₉×C₆₀₁	D₃	1	1	yes	characteristic
5	Dic₁₈₀₃	—	9	1	no	—
6	C₉×C₆₀₁	Dic₃	1	1	yes	characteristic
7	C₂×C₃×C₆₀₁	D₉	1	1	yes	characteristic
8	Dic₆₀₁	—	27	1	no	Hall
9	C₃×C₆₀₁	Dic₉	1	1	yes	characteristic
10	C₂×C₆₀₁	D₂₇	1	1	yes	characteristic
11	C₆₀₁	Dic₂₇	1	1	yes	characteristic, complemented, Sylow
12	Dic₂₇	—	601	1	no	maximal, Hall
13	C₂×C₂₇	D₆₀₁	1	1	yes	characteristic
14	Dic₉	—	1803	1	no	—
15	C₂₇	Dic₆₀₁	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₉	D₁₈₀₃	1	1	yes	characteristic
17	Dic₃	—	5409	1	no	—
18	C₉	Dic₁₈₀₃	1	1	yes	characteristic
19	C₂×C₃	D₅₄₀₉	1	1	yes	characteristic
20	C₄	—	16227	1	no	Sylow
21	C₃	Dic₅₄₀₉	1	1	yes	characteristic
22	C₂	D₁₆₂₂₇	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.