Subgroups — #16810453

Order 3392.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13133153	C₂	1	2	yes	maximal
2	C₂×C₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₅₃	C₂²	1	1	yes	characteristic
4	#11719917	—	2	2	no	—
5	C₁₆×C₅₃	C₄	1	2	yes	—
6	C₂×C₄×C₅₃	D₄	1	1	yes	characteristic
7	C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
8	C₈×C₅₃	Q₈	1	1	yes	characteristic
9	#88322	—	4	2	no	—
10	C₂²×C₅₃	Q₁₆	1	1	yes	characteristic
11	C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₅₃	D₈	1	1	yes	characteristic
13	C₂×C₅₃	—	2	1	no	—
14	C₂×C₅₃	#107	1	1	yes	characteristic
15	#368	—	53	1	no	maximal, Sylow
16	C₅₃	#368	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₁₆	D₅₃	1	1	yes	characteristic
18	#108	—	53	2	no	—
19	M₁₆	—	106	2	no	—
20	C₂×C₈	C₂×D₅₃	1	1	yes	characteristic
21	C₁₆	Dic₅₃	1	2	yes	—
22	C₂×C₄	D₂₁₂	1	1	yes	characteristic
23	C₈	—	212	2	no	—
24	C₈	Dic₁₀₆	1	1	yes	characteristic
25	C₈	C₂×Dic₅₃	1	1	yes	characteristic
26	C₂²	Dic₂₁₂	1	1	yes	characteristic
27	C₄	D₄₂₄	1	1	yes	characteristic
28	C₄	C₄⋊Dic₅₃	1	1	yes	characteristic
29	C₂	—	2	1	no	—
30	C₂	#13133151	1	1	yes	characteristic

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

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

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