Subgroups — #22553151

Order 8384.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₀₄₈	C₂	1	1	yes	maximal, characteristic, complemented
2	D₂₀₉₆	C₂	1	1	yes	maximal, characteristic
3	C₃₂×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₅₂₄	—	2	1	no	—
5	D₁₀₄₈	—	2	1	no	—
6	C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
7	Dic₂₆₂	—	4	1	no	—
8	D₅₂₄	—	4	1	no	—
9	C₈×C₁₃₁	D₄	1	1	yes	characteristic
10	C₂×D₁₃₁	—	8	1	no	—
11	C₄×C₁₃₁	D₈	1	1	yes	characteristic
12	Dic₁₃₁	—	8	1	no	—
13	C₂×C₁₃₁	D₁₆	1	1	yes	characteristic
14	D₁₃₁	—	16	1	no	—
15	C₁₃₁	SD₆₄	1	1	yes	characteristic, complemented, Sylow
16	SD₆₄	—	131	1	no	maximal, Sylow
17	Q₃₂	—	131	1	no	—
18	D₁₆	—	131	1	no	—
19	C₃₂	D₁₃₁	1	1	yes	characteristic, complemented
20	Q₁₆	—	262	1	no	—
21	D₈	—	262	1	no	—
22	C₁₆	C₂×D₁₃₁	1	1	yes	characteristic
23	Q₈	—	524	1	no	—
24	D₄	—	524	1	no	—
25	C₈	D₅₂₄	1	1	yes	characteristic
26	C₂²	—	1048	1	no	—
27	C₄	—	1048	1	no	—
28	C₄	D₁₀₄₈	1	1	yes	characteristic
29	C₂	—	2096	1	no	—
30	C₂	D₂₀₉₆	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.