Subgroups — #21422313

Order 7552.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₉₄₄	C₂	1	1	yes	maximal, characteristic
2	C₅₉⋊C₆₄	C₂	1	1	yes	maximal, characteristic
3	C₅₉×Q₆₄	C₂	1	1	yes	maximal, characteristic
4	Dic₄₇₂	—	2	1	no	—
5	Q₃₂×C₅₉	—	2	1	no	—
6	C₃₂×C₅₉	C₂²	1	1	yes	characteristic
7	Q₁₆×C₅₉	—	4	1	no	—
8	Dic₂₃₆	—	4	1	no	—
9	C₁₆×C₅₉	D₄	1	1	yes	characteristic
10	Q₈×C₅₉	—	8	1	no	—
11	Dic₁₁₈	—	8	1	no	—
12	C₈×C₅₉	D₈	1	1	yes	characteristic
13	C₄×C₅₉	—	16	1	no	—
14	C₄×C₅₉	D₁₆	1	1	yes	characteristic
15	Dic₅₉	—	16	1	no	—
16	Q₁₂₈	—	59	1	no	maximal, Sylow
17	C₂×C₅₉	D₃₂	1	1	yes	characteristic
18	Q₆₄	—	59	1	no	—
19	Q₆₄	D₅₉	1	1	yes	characteristic
20	C₆₄	—	59	1	no	—
21	C₅₉	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
22	Q₃₂	—	2	1	no	—
23	Q₃₂	—	118	1	no	—
24	C₃₂	C₂×D₅₉	1	1	yes	characteristic
25	Q₁₆	—	4	1	no	—
26	Q₁₆	—	236	1	no	—
27	C₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
28	Q₈	—	8	1	no	—
29	Q₈	—	472	1	no	—
30	C₈	#11745669	1	1	yes	characteristic
31	C₄	—	16	1	no	—
32	C₄	—	944	1	no	—
33	C₄	#14273668	1	1	yes	characteristic
34	C₂	#16837237	1	1	yes	characteristic

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

N	H ≅ G/N	type
21. C₅₉	Q₁₂₈	semidirect