Subgroups — #20272927

Order 6784.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆₉₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#16810342	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×D₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	D₈₄₈	—	2	1	no	—
5	D₁₆×C₅₃	—	2	1	no	—
6	C₃₂×C₅₃	C₂²	1	1	yes	characteristic
7	D₈×C₅₃	—	4	1	no	—
8	D₄₂₄	—	4	1	no	—
9	C₁₆×C₅₃	D₄	1	1	yes	characteristic
10	D₄×C₅₃	—	8	1	no	—
11	D₂₁₂	—	8	1	no	—
12	C₈×C₅₃	D₈	1	1	yes	characteristic
13	C₂²×C₅₃	—	16	1	no	—
14	C₂×D₅₃	—	16	1	no	—
15	C₄×C₅₃	D₁₆	1	1	yes	characteristic
16	D₆₄	—	53	1	no	maximal, Sylow
17	C₂×C₅₃	—	32	1	no	—
18	C₂×C₅₃	D₃₂	1	1	yes	characteristic
19	D₅₃	—	32	1	no	—
20	D₃₂	—	53	1	no	—
21	D₃₂	D₅₃	1	1	yes	characteristic, complemented
22	C₆₄	—	53	1	no	—
23	C₅₃	D₆₄	1	1	yes	characteristic, complemented, Sylow
24	D₁₆	—	2	1	no	—
25	D₁₆	—	106	1	no	—
26	C₃₂	C₂×D₅₃	1	1	yes	characteristic
27	D₈	—	4	1	no	—
28	D₈	—	212	1	no	—
29	C₁₆	C₂²⋊D₅₃	1	1	yes	characteristic
30	D₄	—	8	1	no	—
31	D₄	—	424	1	no	—
32	C₈	#11719922	1	1	yes	characteristic
33	C₂²	—	16	1	no	—
34	C₂²	—	848	1	no	—
35	C₄	#13133158	1	1	yes	characteristic
36	C₂	—	32	1	no	—
37	C₂	—	1696	1	no	—
38	C₂	#16810458	1	1	yes	characteristic

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