Subgroups — #27272004

Order 13568.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₃₉₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#20272534	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×D₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₆₉₆	—	2	1	no	—
5	C₅₃×D₃₂	—	2	1	no	—
6	C₅₃×C₆₄	C₂²	1	1	yes	characteristic
7	D₈₄₈	—	4	1	no	—
8	D₁₆×C₅₃	—	4	1	no	—
9	C₃₂×C₅₃	D₄	1	1	yes	characteristic
10	D₈×C₅₃	—	8	1	no	—
11	D₄₂₄	—	8	1	no	—
12	C₁₆×C₅₃	D₈	1	1	yes	characteristic
13	D₄×C₅₃	—	16	1	no	—
14	D₂₁₂	—	16	1	no	—
15	C₈×C₅₃	D₁₆	1	1	yes	characteristic
16	D₁₂₈	—	53	1	no	maximal, Sylow
17	C₂²×C₅₃	—	32	1	no	—
18	C₂×D₅₃	—	32	1	no	—
19	C₄×C₅₃	D₃₂	1	1	yes	characteristic
20	D₆₄	—	53	1	no	—
21	D₆₄	D₅₃	1	1	yes	characteristic, complemented
22	C₁₂₈	—	53	1	no	—
23	C₂×C₅₃	—	64	1	no	—
24	C₂×C₅₃	D₆₄	1	1	yes	characteristic
25	D₅₃	—	64	1	no	—
26	D₃₂	—	2	1	no	—
27	D₃₂	—	106	1	no	—
28	C₆₄	C₂×D₅₃	1	1	yes	characteristic
29	C₅₃	D₁₂₈	1	1	yes	characteristic, complemented, Sylow
30	D₁₆	—	4	1	no	—
31	D₁₆	—	212	1	no	—
32	C₃₂	C₂²⋊D₅₃	1	1	yes	characteristic
33	D₈	—	8	1	no	—
34	D₈	—	424	1	no	—
35	C₁₆	#11719922	1	1	yes	characteristic
36	D₄	—	16	1	no	—
37	D₄	—	848	1	no	—
38	C₈	#13133158	1	1	yes	characteristic
39	C₂²	—	32	1	no	—
40	C₂²	—	1696	1	no	—
41	C₄	#16810458	1	1	yes	characteristic
42	C₂	—	64	1	no	—
43	C₂	—	3392	1	no	—
44	C₂	#20272927	1	1	yes	characteristic

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

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