Subgroups — #20272932

Order 6784.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₈₄₈	C₂	1	1	yes	maximal, characteristic
2	#16810342	C₂	1	1	yes	maximal, characteristic
3	C₅₃×Q₆₄	C₂	1	1	yes	maximal, characteristic
4	Dic₄₂₄	—	2	1	no	—
5	Q₃₂×C₅₃	—	2	1	no	—
6	C₃₂×C₅₃	C₂²	1	1	yes	characteristic
7	Q₁₆×C₅₃	—	4	1	no	—
8	Dic₂₁₂	—	4	1	no	—
9	C₁₆×C₅₃	D₄	1	1	yes	characteristic
10	Q₈×C₅₃	—	8	1	no	—
11	Dic₁₀₆	—	8	1	no	—
12	C₈×C₅₃	D₈	1	1	yes	characteristic
13	C₄×C₅₃	—	16	1	no	—
14	C₄×C₅₃	D₁₆	1	1	yes	characteristic
15	Dic₅₃	—	16	1	no	—
16	Q₁₂₈	—	53	1	no	maximal, Sylow
17	C₂×C₅₃	D₃₂	1	1	yes	characteristic
18	Q₆₄	—	53	1	no	—
19	Q₆₄	D₅₃	1	1	yes	characteristic
20	C₆₄	—	53	1	no	—
21	C₅₃	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
22	Q₃₂	—	2	1	no	—
23	Q₃₂	—	106	1	no	—
24	C₃₂	C₂×D₅₃	1	1	yes	characteristic
25	Q₁₆	—	4	1	no	—
26	Q₁₆	—	212	1	no	—
27	C₁₆	C₂²⋊D₅₃	1	1	yes	characteristic
28	Q₈	—	8	1	no	—
29	Q₈	—	424	1	no	—
30	C₈	#11719922	1	1	yes	characteristic
31	C₄	—	16	1	no	—
32	C₄	—	848	1	no	—
33	C₄	#13133158	1	1	yes	characteristic
34	C₂	#16810458	1	1	yes	characteristic

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

N	H ≅ G/N	type
21. C₅₃	Q₁₂₈	semidirect