Subgroups — D₇₂₁₆ #72212607

Order 14432.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₆₀₈	C₂	1	2	yes	maximal, complemented
2	D₁₈₀₄	—	2	2	no	—
3	C₁₁×C₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×C₁₁×C₄₁	C₂²	1	1	yes	characteristic
5	C₂×D₄₅₁	—	4	2	no	—
6	C₄×C₁₁×C₄₁	D₄	1	1	yes	characteristic
7	D₆₅₆	—	11	1	no	maximal, Hall
8	C₂×C₁₁×C₄₁	D₈	1	1	yes	characteristic
9	D₄₅₁	—	8	2	no	—
10	D₃₂₈	—	11	2	no	—
11	C₁₆×C₄₁	D₁₁	1	1	yes	characteristic, complemented
12	C₁₁×C₄₁	D₁₆	1	1	yes	characteristic, complemented, Hall
13	D₁₇₆	—	41	1	no	maximal, Hall
14	D₁₆₄	—	22	2	no	—
15	C₈×C₄₁	C₂×D₁₁	1	1	yes	characteristic
16	D₈₈	—	41	2	no	—
17	C₁₁×C₁₆	D₄₁	1	1	yes	characteristic, complemented
18	C₂×D₄₁	—	44	2	no	—
19	C₄×C₄₁	D₄₄	1	1	yes	characteristic
20	D₄₄	—	82	2	no	—
21	C₈×C₁₁	C₂×D₄₁	1	1	yes	characteristic
22	C₂×C₄₁	D₈₈	1	1	yes	characteristic
23	D₄₁	—	88	2	no	—
24	C₂×D₁₁	—	164	2	no	—
25	C₄×C₁₁	D₁₆₄	1	1	yes	characteristic
26	C₄₁	D₁₇₆	1	1	yes	characteristic, complemented, Sylow
27	D₁₆	—	451	1	no	Sylow
28	C₂×C₁₁	D₃₂₈	1	1	yes	characteristic
29	D₁₁	—	328	2	no	—
30	D₈	—	451	2	no	—
31	C₁₆	D₄₅₁	1	1	yes	characteristic, complemented
32	C₁₁	D₆₅₆	1	1	yes	characteristic, complemented, Sylow
33	D₄	—	902	2	no	—
34	C₈	C₂×D₄₅₁	1	1	yes	characteristic
35	C₂²	—	1804	2	no	—
36	C₄	D₁₈₀₄	1	1	yes	characteristic
37	C₂	—	3608	2	no	—
38	C₂	D₃₆₀₈	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.