Subgroups — #27272009

Order 13568.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₆₉₆	C₂	1	1	yes	maximal, characteristic
2	#20272534	C₂	1	1	yes	maximal, characteristic
3	C₅₃×Q₁₂₈	C₂	1	1	yes	maximal, characteristic
4	Dic₈₄₈	—	2	1	no	—
5	C₅₃×Q₆₄	—	2	1	no	—
6	C₅₃×C₆₄	C₂²	1	1	yes	characteristic
7	Dic₄₂₄	—	4	1	no	—
8	Q₃₂×C₅₃	—	4	1	no	—
9	C₃₂×C₅₃	D₄	1	1	yes	characteristic
10	Q₁₆×C₅₃	—	8	1	no	—
11	Dic₂₁₂	—	8	1	no	—
12	C₁₆×C₅₃	D₈	1	1	yes	characteristic
13	Q₈×C₅₃	—	16	1	no	—
14	Dic₁₀₆	—	16	1	no	—
15	C₈×C₅₃	D₁₆	1	1	yes	characteristic
16	Q₂₅₆	—	53	1	no	maximal, Sylow
17	C₄×C₅₃	—	32	1	no	—
18	C₄×C₅₃	D₃₂	1	1	yes	characteristic
19	Dic₅₃	—	32	1	no	—
20	Q₁₂₈	—	53	1	no	—
21	Q₁₂₈	D₅₃	1	1	yes	characteristic
22	C₁₂₈	—	53	1	no	—
23	C₂×C₅₃	D₆₄	1	1	yes	characteristic
24	Q₆₄	—	2	1	no	—
25	Q₆₄	—	106	1	no	—
26	C₆₄	C₂×D₅₃	1	1	yes	characteristic
27	C₅₃	Q₂₅₆	1	1	yes	characteristic, complemented, Sylow
28	Q₃₂	—	4	1	no	—
29	Q₃₂	—	212	1	no	—
30	C₃₂	C₂²⋊D₅₃	1	1	yes	characteristic
31	Q₁₆	—	8	1	no	—
32	Q₁₆	—	424	1	no	—
33	C₁₆	#11719922	1	1	yes	characteristic
34	Q₈	—	16	1	no	—
35	Q₈	—	848	1	no	—
36	C₈	#13133158	1	1	yes	characteristic
37	C₄	—	32	1	no	—
38	C₄	—	1696	1	no	—
39	C₄	#16810458	1	1	yes	characteristic
40	C₂	#20272927	1	1	yes	characteristic

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

N	H ≅ G/N	type
27. C₅₃	Q₂₅₆	semidirect

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