Subgroups — #23781491

Order 10432.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19104669	C₂	1	2	yes	maximal
2	C₂×C₁₆×C₁₆₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₁₆₃	—	2	2	no	—
4	C₂×C₈×C₁₆₃	C₂²	1	1	yes	characteristic
5	C₁₆×C₁₆₃	C₄	1	2	yes	complemented
6	C₂×Dic₁₆₃	—	4	2	no	—
7	C₂×C₄×C₁₆₃	D₄	1	1	yes	characteristic
8	C₈×C₁₆₃	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₆₃	Q₈	1	1	yes	characteristic
10	C₂²×C₁₆₃	D₈	1	1	yes	characteristic
11	C₄×C₁₆₃	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₁₆₃	Q₁₆	1	1	yes	characteristic
13	Dic₁₆₃	—	8	2	no	—
14	C₂×C₁₆₃	#107	1	1	yes	characteristic
15	C₂×C₁₆₃	D₁₆	1	1	yes	characteristic
16	C₂×C₁₆₃	Q₃₂	1	1	yes	characteristic
17	C₁₆₃	#366	1	1	yes	characteristic, complemented, Sylow
18	#366	—	163	1	no	maximal, Sylow
19	C₂×C₁₆	D₁₆₃	1	1	yes	characteristic
20	#107	—	163	2	no	—
21	C₂×C₈	C₂×D₁₆₃	1	1	yes	characteristic
22	C₄⋊C₄	—	326	2	no	—
23	C₁₆	Dic₁₆₃	1	2	yes	complemented
24	C₂×C₄	—	652	2	no	—
25	C₂×C₄	D₆₅₂	1	1	yes	characteristic
26	C₈	C₂×Dic₁₆₃	1	1	yes	characteristic
27	C₈	Dic₃₂₆	1	1	yes	characteristic
28	C₂²	D₁₃₀₄	1	1	yes	characteristic
29	C₄	—	1304	2	no	—
30	C₄	C₄⋊Dic₁₆₃	1	1	yes	characteristic
31	C₄	Dic₆₅₂	1	1	yes	characteristic
32	C₂	#19104669	1	1	yes	characteristic
33	C₂	D₂₆₀₈	1	1	yes	characteristic
34	C₂	Dic₁₃₀₄	1	1	yes	characteristic

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