Subgroups — #23781500

Order 10432.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₆₀₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₆₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃₀₄	—	2	1	no	—
5	D₈×C₁₆₃	—	2	1	no	—
6	C₁₆×C₁₆₃	C₂²	1	1	yes	characteristic
7	D₆₅₂	—	4	1	no	—
8	D₄×C₁₆₃	—	4	1	no	—
9	C₈×C₁₆₃	D₄	1	1	yes	characteristic
10	C₂²×C₁₆₃	—	8	1	no	—
11	C₂×D₁₆₃	—	8	1	no	—
12	C₄×C₁₆₃	D₈	1	1	yes	characteristic
13	C₂×C₁₆₃	—	16	1	no	—
14	C₂×C₁₆₃	D₁₆	1	1	yes	characteristic
15	D₁₆₃	—	16	1	no	—
16	C₁₆₃	D₃₂	1	1	yes	characteristic, complemented, Sylow
17	D₃₂	—	163	1	no	maximal, Sylow
18	D₁₆	—	163	1	no	—
19	D₁₆	D₁₆₃	1	1	yes	characteristic, complemented
20	C₃₂	—	163	1	no	—
21	D₈	—	2	1	no	—
22	D₈	—	326	1	no	—
23	C₁₆	C₂×D₁₆₃	1	1	yes	characteristic
24	D₄	—	4	1	no	—
25	D₄	—	652	1	no	—
26	C₈	C₂²⋊D₁₆₃	1	1	yes	characteristic
27	C₂²	—	8	1	no	—
28	C₂²	—	1304	1	no	—
29	C₄	#14579684	1	1	yes	characteristic
30	C₂	—	16	1	no	—
31	C₂	—	2608	1	no	—
32	C₂	#19104676	1	1	yes	characteristic

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