Subgroups — D₄₂₁⋊C₁₆ #27212439

Order 13472.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20269774	C₂	1	2	yes	maximal, complemented
2	C₈×D₄₂₁	C₂	1	1	yes	maximal, characteristic
3	C₄×D₄₂₁	C₄	1	1	yes	characteristic
4	#16809890	C₂²	1	1	yes	characteristic
5	C₈×C₄₂₁	C₄	1	1	yes	characteristic
6	C₂×D₄₂₁	C₈	1	1	yes	characteristic
7	C₄×C₄₂₁	C₂×C₄	1	1	yes	characteristic
8	Dic₄₂₁	C₈	1	1	yes	characteristic
9	C₂×C₄₂₁	C₂×C₈	1	1	yes	characteristic
10	D₄₂₁	C₁₆	1	2	yes	complemented
11	C₄₂₁	C₂×C₁₆	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₁₆	—	421	1	no	maximal, Sylow
13	C₂×C₈	—	421	1	no	—
14	C₁₆	—	421	2	no	—
15	C₂×C₄	—	421	1	no	—
16	C₈	—	421	1	no	—
17	C₈	#13132997	1	1	yes	characteristic
18	C₂²	—	421	1	no	—
19	C₄	—	421	1	no	—
20	C₄	C₂×#13132997	1	1	yes	characteristic
21	C₂	—	421	2	no	—
22	C₂	D₄₂₁⋊C₈	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.