Subgroups — #13113052

Order 1664.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₀₈	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₁₀₄	—	2	1	no	—
5	D₂₀₈	—	2	1	no	—
6	C₁₃×C₃₂	C₂²	1	1	yes	characteristic
7	Dic₅₂	—	4	1	no	—
8	D₁₀₄	—	4	1	no	—
9	C₁₃×C₁₆	D₄	1	1	yes	characteristic
10	SD₁₂₈	—	13	1	no	maximal, Sylow
11	D₅₂	—	8	1	no	—
12	Dic₂₆	—	8	1	no	—
13	C₈×C₁₃	D₈	1	1	yes	characteristic
14	Q₆₄	—	13	1	no	—
15	D₃₂	—	13	1	no	—
16	C₆₄	D₁₃	1	1	yes	characteristic, complemented
17	C₂×D₁₃	—	16	1	no	—
18	C₄×C₁₃	D₁₆	1	1	yes	characteristic
19	Dic₁₃	—	16	1	no	—
20	Q₃₂	—	26	1	no	—
21	D₁₆	—	26	1	no	—
22	C₃₂	C₂×D₁₃	1	1	yes	characteristic
23	C₂×C₁₃	D₃₂	1	1	yes	characteristic
24	D₁₃	—	32	1	no	—
25	Q₁₆	—	52	1	no	—
26	D₈	—	52	1	no	—
27	C₁₆	D₅₂	1	1	yes	characteristic
28	C₁₃	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
29	Q₈	—	104	1	no	—
30	D₄	—	104	1	no	—
31	C₈	D₁₀₄	1	1	yes	characteristic
32	C₂²	—	208	1	no	—
33	C₄	—	208	1	no	—
34	C₄	D₂₀₈	1	1	yes	characteristic
35	C₂	—	416	1	no	—
36	C₂	D₄₁₆	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.