Subgroups — #23781494

Order 10432.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#19104671	C₂	1	1	yes	maximal, characteristic
3	#108×C₁₆₃	C₂	1	1	yes	maximal, characteristic
4	#14579683	—	2	1	no	—
5	C₁₆₃⋊C₁₆	C₄	1	2	yes	—
6	M₁₆×C₁₆₃	—	2	1	no	—
7	C₂×C₈×C₁₆₃	C₂²	1	1	yes	characteristic
8	C₁₆₃⋊C₈	—	4	1	no	—
9	C₂×C₄×C₁₆₃	D₄	1	1	yes	characteristic
10	C₈×C₁₆₃	—	4	1	no	—
11	C₈×C₁₆₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₆₃	Q₈	1	1	yes	characteristic
13	C₂²×C₁₆₃	Q₁₆	1	1	yes	characteristic
14	C₄×C₁₆₃	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₆₃	D₈	1	1	yes	characteristic
16	C₂×C₁₆₃	—	2	1	no	—
17	C₂×C₁₆₃	#107	1	1	yes	characteristic
18	C₁₆₃	#368	1	1	yes	characteristic, complemented, Sylow
19	#368	—	163	1	no	maximal, Sylow
20	C₂×C₁₆	—	163	1	no	—
21	#108	—	163	1	no	—
22	#108	D₁₆₃	1	1	yes	characteristic
23	M₁₆	—	2	1	no	—
24	M₁₆	—	326	1	no	—
25	C₂×C₈	C₂×D₁₆₃	1	1	yes	characteristic
26	C₁₆	—	163	2	no	—
27	C₂×C₄	C₂²⋊D₁₆₃	1	1	yes	characteristic
28	C₈	—	4	1	no	—
29	C₈	—	652	1	no	—
30	C₈	C₄×D₁₆₃	1	1	yes	characteristic
31	C₈	Dic₃₂₆	1	1	yes	characteristic
32	C₂²	#14579689	1	1	yes	characteristic
33	C₄	Dic₁₆₃⋊C₄	1	1	yes	characteristic
34	C₄	#14579684	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#19104668	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₁₆₃	#368	semidirect