Subgroups — #24905679

Order 10624.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₃₂₈	C₂	1	1	yes	maximal, characteristic, complemented
2	D₂₆₅₆	C₂	1	1	yes	maximal, characteristic
3	C₆₄×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₆₆₄	—	2	1	no	—
5	D₁₃₂₈	—	2	1	no	—
6	C₃₂×C₈₃	C₂²	1	1	yes	characteristic
7	Dic₃₃₂	—	4	1	no	—
8	D₆₆₄	—	4	1	no	—
9	C₁₆×C₈₃	D₄	1	1	yes	characteristic
10	D₃₃₂	—	8	1	no	—
11	Dic₁₆₆	—	8	1	no	—
12	C₈×C₈₃	D₈	1	1	yes	characteristic
13	C₂×D₈₃	—	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	D₈₃	—	32	1	no	—
18	SD₁₂₈	—	83	1	no	maximal, Sylow
19	C₈₃	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
20	Q₆₄	—	83	1	no	—
21	D₃₂	—	83	1	no	—
22	C₆₄	D₈₃	1	1	yes	characteristic, complemented
23	Q₃₂	—	166	1	no	—
24	D₁₆	—	166	1	no	—
25	C₃₂	C₂×D₈₃	1	1	yes	characteristic
26	Q₁₆	—	332	1	no	—
27	D₈	—	332	1	no	—
28	C₁₆	D₃₃₂	1	1	yes	characteristic
29	Q₈	—	664	1	no	—
30	D₄	—	664	1	no	—
31	C₈	D₆₆₄	1	1	yes	characteristic
32	C₂²	—	1328	1	no	—
33	C₄	—	1328	1	no	—
34	C₄	D₁₃₂₈	1	1	yes	characteristic
35	C₂	—	2656	1	no	—
36	C₂	D₂₆₅₆	1	1	yes	characteristic

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