Subgroups — #16811552

Order 3392.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13133288	C₂	1	2	yes	maximal
2	C₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#11719936	—	2	2	no	—
4	C₈×D₅₃	C₂²	1	1	yes	characteristic
5	C₁₆×C₅₃	C₄	1	1	yes	characteristic
6	#11719908	C₄	1	1	yes	characteristic
7	C₄×D₅₃	D₄	1	1	yes	characteristic
8	#88324	—	4	2	no	—
9	C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
10	#88322	Q₈	1	1	yes	characteristic
11	C₂×D₅₃	Q₁₆	1	1	yes	characteristic
12	C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
13	Dic₅₃	D₈	1	1	yes	characteristic
14	C₂×C₅₃	#107	1	1	yes	characteristic
15	D₅₃	—	2	1	no	—
16	#368	—	53	1	no	maximal, Sylow
17	C₅₃	#368	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₁₆	—	53	1	no	—
19	#108	—	53	2	no	—
20	M₁₆	—	106	2	no	—
21	C₂×C₈	—	53	1	no	—
22	C₁₆	—	53	1	no	—
23	C₁₆	#6157	1	1	yes	characteristic
24	C₂×C₄	—	53	1	no	—
25	C₈	—	53	1	no	—
26	C₈	—	212	2	no	—
27	C₈	C₂×#6157	1	1	yes	characteristic
28	C₂²	—	53	1	no	—
29	C₄	—	53	1	no	—
30	C₄	C₄⋊#6157	1	1	yes	characteristic
31	C₂	—	106	1	no	—
32	C₂	#13133286	1	1	yes	characteristic

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

N	H ≅ G/N	type
17. C₅₃	#368	semidirect

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