Subgroups — #16810450

Order 3392.

46 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	#13133151	C₂	1	1	yes	maximal, characteristic
3	#107×C₅₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×C₅₃	C₂²	1	1	yes	characteristic
5	C₄⋊C₄×C₅₃	—	2	1	no	—
6	C₄⋊Dic₅₃	—	2	1	no	—
7	#11719908	C₄	1	2	yes	complemented
8	C₂×C₄×C₅₃	—	4	1	no	—
9	C₂×C₄×C₅₃	D₄	1	1	yes	characteristic
10	C₂×Dic₅₃	—	4	1	no	—
11	C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₅₃	Q₈	1	1	yes	characteristic
13	C₂²×C₅₃	D₈	1	1	yes	characteristic
14	C₄×C₅₃	—	8	1	no	—
15	C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₅₃	Q₁₆	1	1	yes	characteristic
17	Dic₅₃	—	8	1	no	—
18	C₂×C₅₃	#107	1	1	yes	characteristic
19	C₂×C₅₃	SD₃₂	1	1	yes	characteristic
20	C₂×C₅₃	SD₃₂	1	1	yes	characteristic
21	#367	—	53	1	no	maximal, Sylow
22	C₅₃	#367	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₆	—	53	1	no	—
24	#107	—	53	1	no	—
25	#107	D₅₃	1	1	yes	characteristic
26	C₂×C₈	C₂×D₅₃	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	106	1	no	—
29	C₁₆	—	53	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	212	1	no	—
32	C₂×C₄	C₂²⋊D₅₃	1	1	yes	characteristic
33	C₈	Dic₁₀₆	1	1	yes	characteristic
34	C₈	C₄×D₅₃	1	1	yes	characteristic
35	C₂²	#11719922	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	424	1	no	—
38	C₄	#11719919	1	1	yes	characteristic
39	C₄	#11719925	1	1	yes	characteristic
40	C₂	#13133150	1	1	yes	characteristic
41	C₂	#13133160	1	1	yes	characteristic
42	C₂	#13133161	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. #11719908	C₄	semidirect
22. C₅₃	#367	semidirect

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