Subgroups — #27272008

Order 13568.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₆₉₆	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃₃₉₂	C₂	1	1	yes	maximal, characteristic
3	C₅₃×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₈₄₈	—	2	1	no	—
5	D₁₆₉₆	—	2	1	no	—
6	C₅₃×C₆₄	C₂²	1	1	yes	characteristic
7	Dic₄₂₄	—	4	1	no	—
8	D₈₄₈	—	4	1	no	—
9	C₃₂×C₅₃	D₄	1	1	yes	characteristic
10	Dic₂₁₂	—	8	1	no	—
11	D₄₂₄	—	8	1	no	—
12	C₁₆×C₅₃	D₈	1	1	yes	characteristic
13	D₂₁₂	—	16	1	no	—
14	Dic₁₀₆	—	16	1	no	—
15	C₈×C₅₃	D₁₆	1	1	yes	characteristic
16	SD₂₅₆	—	53	1	no	maximal, Sylow
17	C₂×D₅₃	—	32	1	no	—
18	C₄×C₅₃	D₃₂	1	1	yes	characteristic
19	Dic₅₃	—	32	1	no	—
20	Q₁₂₈	—	53	1	no	—
21	D₆₄	—	53	1	no	—
22	C₁₂₈	D₅₃	1	1	yes	characteristic, complemented
23	C₂×C₅₃	D₆₄	1	1	yes	characteristic
24	D₅₃	—	64	1	no	—
25	Q₆₄	—	106	1	no	—
26	D₃₂	—	106	1	no	—
27	C₆₄	C₂×D₅₃	1	1	yes	characteristic
28	C₅₃	SD₂₅₆	1	1	yes	characteristic, complemented, Sylow
29	Q₃₂	—	212	1	no	—
30	D₁₆	—	212	1	no	—
31	C₃₂	D₂₁₂	1	1	yes	characteristic
32	Q₁₆	—	424	1	no	—
33	D₈	—	424	1	no	—
34	C₁₆	D₄₂₄	1	1	yes	characteristic
35	Q₈	—	848	1	no	—
36	D₄	—	848	1	no	—
37	C₈	D₈₄₈	1	1	yes	characteristic
38	C₂²	—	1696	1	no	—
39	C₄	—	1696	1	no	—
40	C₄	D₁₆₉₆	1	1	yes	characteristic
41	C₂	—	3392	1	no	—
42	C₂	D₃₃₉₂	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.