Subgroups — #16810452

Order 3392.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719908	C₂	1	1	yes	maximal, characteristic
2	#13133153	C₂	1	1	yes	maximal, characteristic
3	#108×C₅₃	C₂	1	1	yes	maximal, characteristic
4	M₁₆×C₅₃	—	2	1	no	—
5	C₂×C₈×C₅₃	C₂²	1	1	yes	characteristic
6	#11719917	—	2	1	no	—
7	#11719908	C₄	1	2	yes	—
8	C₂×C₄×C₅₃	D₄	1	1	yes	characteristic
9	C₈×C₅₃	—	4	1	no	—
10	C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
11	C₈×C₅₃	Q₈	1	1	yes	characteristic
12	#88322	—	4	1	no	—
13	C₂²×C₅₃	Q₁₆	1	1	yes	characteristic
14	C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₅₃	D₈	1	1	yes	characteristic
16	C₂×C₅₃	—	2	1	no	—
17	C₂×C₅₃	#107	1	1	yes	characteristic
18	#368	—	53	1	no	maximal, Sylow
19	C₅₃	#368	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₁₆	—	53	1	no	—
21	#108	—	53	1	no	—
22	#108	D₅₃	1	1	yes	characteristic
23	M₁₆	—	2	1	no	—
24	M₁₆	—	106	1	no	—
25	C₂×C₈	C₂×D₅₃	1	1	yes	characteristic
26	C₁₆	—	53	2	no	—
27	C₂×C₄	C₂²⋊D₅₃	1	1	yes	characteristic
28	C₈	—	4	1	no	—
29	C₈	—	212	1	no	—
30	C₈	Dic₁₀₆	1	1	yes	characteristic
31	C₈	C₄×D₅₃	1	1	yes	characteristic
32	C₂²	#11719925	1	1	yes	characteristic
33	C₄	#11719919	1	1	yes	characteristic
34	C₄	#11719922	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#13133150	1	1	yes	characteristic

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

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

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