Subgroups — #24905680

Order 10624.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₃₂₈	C₂	1	1	yes	maximal, characteristic
2	C₈₃⋊C₆₄	C₂	1	1	yes	maximal, characteristic
3	Q₆₄×C₈₃	C₂	1	1	yes	maximal, characteristic
4	Dic₆₆₄	—	2	1	no	—
5	Q₃₂×C₈₃	—	2	1	no	—
6	C₃₂×C₈₃	C₂²	1	1	yes	characteristic
7	Dic₃₃₂	—	4	1	no	—
8	Q₁₆×C₈₃	—	4	1	no	—
9	C₁₆×C₈₃	D₄	1	1	yes	characteristic
10	Q₈×C₈₃	—	8	1	no	—
11	Dic₁₆₆	—	8	1	no	—
12	C₈×C₈₃	D₈	1	1	yes	characteristic
13	C₄×C₈₃	—	16	1	no	—
14	C₄×C₈₃	D₁₆	1	1	yes	characteristic
15	Dic₈₃	—	16	1	no	—
16	C₂×C₈₃	D₃₂	1	1	yes	characteristic
17	Q₁₂₈	—	83	1	no	maximal, Sylow
18	C₈₃	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	Q₆₄	—	83	1	no	—
20	Q₆₄	D₈₃	1	1	yes	characteristic
21	C₆₄	—	83	1	no	—
22	Q₃₂	—	2	1	no	—
23	Q₃₂	—	166	1	no	—
24	C₃₂	C₂×D₈₃	1	1	yes	characteristic
25	Q₁₆	—	4	1	no	—
26	Q₁₆	—	332	1	no	—
27	C₁₆	C₂²⋊D₈₃	1	1	yes	characteristic
28	Q₈	—	8	1	no	—
29	Q₈	—	664	1	no	—
30	C₈	#13050575	1	1	yes	characteristic
31	C₄	—	16	1	no	—
32	C₄	—	1328	1	no	—
33	C₄	#14581733	1	1	yes	characteristic
34	C₂	#19127536	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₈₃	Q₁₂₈	semidirect