Subgroups — #20272929

Order 6784.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆₉₆	C₂	1	1	yes	maximal, characteristic
2	#16810342	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	D₈₄₈	—	2	1	no	—
5	Q₃₂×C₅₃	—	2	1	no	—
6	C₃₂×C₅₃	C₂²	1	1	yes	characteristic
7	Q₁₆×C₅₃	—	4	1	no	—
8	D₄₂₄	—	4	1	no	—
9	C₁₆×C₅₃	D₄	1	1	yes	characteristic
10	Q₈×C₅₃	—	8	1	no	—
11	D₂₁₂	—	8	1	no	—
12	C₈×C₅₃	D₈	1	1	yes	characteristic
13	C₂×D₅₃	—	16	1	no	—
14	C₄×C₅₃	—	16	1	no	—
15	C₄×C₅₃	D₁₆	1	1	yes	characteristic
16	SD₁₂₈	—	53	1	no	maximal, Sylow
17	C₂×C₅₃	D₃₂	1	1	yes	characteristic
18	D₅₃	—	32	1	no	—
19	Q₆₄	D₅₃	1	1	yes	characteristic, complemented
20	D₃₂	—	53	1	no	—
21	C₆₄	—	53	1	no	—
22	C₅₃	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
23	Q₃₂	—	2	1	no	—
24	D₁₆	—	106	1	no	—
25	C₃₂	C₂×D₅₃	1	1	yes	characteristic
26	Q₁₆	—	4	1	no	—
27	D₈	—	212	1	no	—
28	C₁₆	C₂²⋊D₅₃	1	1	yes	characteristic
29	Q₈	—	8	1	no	—
30	D₄	—	424	1	no	—
31	C₈	#11719922	1	1	yes	characteristic
32	C₂²	—	848	1	no	—
33	C₄	—	16	1	no	—
34	C₄	#13133158	1	1	yes	characteristic
35	C₂	—	1696	1	no	—
36	C₂	#16810458	1	1	yes	characteristic

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