Subgroups — #16811549

Order 3392.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13133286	C₂	1	2	yes	maximal
2	C₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#6157	—	2	2	no	—
4	C₈×D₅₃	C₂²	1	1	yes	characteristic
5	C₁₆×C₅₃	C₄	1	1	yes	characteristic, complemented
6	#11719908	C₄	1	1	yes	characteristic, complemented
7	C₂×#6157	—	4	2	no	—
8	C₄×D₅₃	D₄	1	1	yes	characteristic
9	C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
10	#88322	Q₈	1	1	yes	characteristic
11	C₂×D₅₃	D₈	1	1	yes	characteristic
12	#6157	—	8	2	no	—
13	C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
14	Dic₅₃	Q₁₆	1	1	yes	characteristic
15	C₂×C₅₃	#107	1	1	yes	characteristic
16	D₅₃	D₁₆	1	1	yes	characteristic
17	D₅₃	Q₃₂	1	1	yes	characteristic
18	#366	—	53	1	no	maximal, Sylow
19	C₅₃	#366	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₁₆	—	53	1	no	—
21	#107	—	53	2	no	—
22	C₂×C₈	—	53	1	no	—
23	C₄⋊C₄	—	106	2	no	—
24	C₁₆	—	53	1	no	—
25	C₁₆	#6157	1	1	yes	characteristic, complemented
26	C₂×C₄	—	53	1	no	—
27	C₂×C₄	—	212	2	no	—
28	C₈	—	53	1	no	—
29	C₈	C₂×#6157	1	1	yes	characteristic
30	C₂²	—	53	1	no	—
31	C₄	—	53	1	no	—
32	C₄	—	424	2	no	—
33	C₄	C₄⋊#6157	1	1	yes	characteristic
34	C₂	—	53	1	no	—
35	C₂	—	53	1	no	—
36	C₂	#13133286	1	1	yes	characteristic

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.