Subgroups — Dic₁₆₀₃₆ #72298613

Order 64144.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₈₀₁₈	C₂	1	2	yes	maximal
2	C₈×C₁₉×C₂₁₁	C₂	1	1	yes	maximal, characteristic
3	Dic₄₀₀₉	—	2	2	no	—
4	C₄×C₁₉×C₂₁₁	C₂²	1	1	yes	characteristic
5	C₂×C₁₉×C₂₁₁	D₄	1	1	yes	characteristic
6	C₁₉×C₂₁₁	Q₁₆	1	1	yes	characteristic, complemented, Hall
7	Dic₈₄₄	—	19	1	no	maximal, Hall
8	Dic₄₂₂	—	19	2	no	—
9	C₈×C₂₁₁	D₁₉	1	1	yes	characteristic
10	C₄×C₂₁₁	C₂×D₁₉	1	1	yes	characteristic
11	Dic₂₁₁	—	38	2	no	—
12	C₂×C₂₁₁	D₇₆	1	1	yes	characteristic
13	Dic₇₆	—	211	1	no	maximal, Hall
14	C₂₁₁	Dic₇₆	1	1	yes	characteristic, complemented, Sylow
15	Dic₃₈	—	211	2	no	—
16	C₈×C₁₉	D₂₁₁	1	1	yes	characteristic
17	C₄×C₁₉	C₂×D₂₁₁	1	1	yes	characteristic
18	Dic₁₉	—	422	2	no	—
19	C₂×C₁₉	D₈₄₄	1	1	yes	characteristic
20	C₁₉	Dic₈₄₄	1	1	yes	characteristic, complemented, Sylow
21	Q₁₆	—	4009	1	no	Sylow
22	Q₈	—	4009	2	no	—
23	C₈	D₄₀₀₉	1	1	yes	characteristic
24	C₄	—	8018	2	no	—
25	C₄	C₂×D₄₀₀₉	1	1	yes	characteristic
26	C₂	D₁₆₀₃₆	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.