Subgroups — D₂₁₆ #88361

Order 432.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₀₈	C₂	1	2	yes	maximal, complemented
2	C₈×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₇₂	—	3	1	no	maximal
4	C₂×D₂₇	—	2	2	no	—
5	C₄×C₂₇	C₂²	1	1	yes	characteristic
6	D₃₆	—	3	2	no	—
7	C₈×C₉	D₃	1	1	yes	characteristic
8	C₂×C₂₇	D₄	1	1	yes	characteristic
9	D₂₇	—	4	2	no	—
10	D₂₄	—	9	1	no	—
11	C₂×D₉	—	6	2	no	—
12	C₄×C₉	C₂×D₃	1	1	yes	characteristic
13	C₂₇	D₈	1	1	yes	characteristic, complemented, Sylow
14	D₁₂	—	9	2	no	—
15	C₃×C₈	D₉	1	1	yes	characteristic
16	C₂×C₉	D₁₂	1	1	yes	characteristic
17	D₉	—	12	2	no	—
18	D₈	—	27	1	no	Sylow
19	C₂×D₃	—	18	2	no	—
20	C₃×C₄	C₂×D₉	1	1	yes	characteristic
21	C₉	D₂₄	1	1	yes	characteristic
22	D₄	—	27	2	no	—
23	C₈	D₂₇	1	1	yes	characteristic, complemented
24	C₂×C₃	D₃₆	1	1	yes	characteristic
25	D₃	—	36	2	no	—
26	C₂²	—	54	2	no	—
27	C₄	C₂×D₂₇	1	1	yes	characteristic
28	C₃	D₇₂	1	1	yes	characteristic
29	C₂	—	108	2	no	—
30	C₂	D₁₀₈	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.