Subgroups — #24905674

Order 10624.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃⋊C₆₄	C₂	1	2	yes	maximal, complemented
2	C₂×C₃₂×C₈₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₈₃	C₄	1	1	yes	characteristic
4	C₃₂×C₈₃	C₄	1	1	yes	characteristic
5	C₃₂×C₈₃	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₈₃	C₈	1	1	yes	characteristic
7	C₁₆×C₈₃	C₈	1	1	yes	characteristic
8	C₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₈₃	C₁₆	1	1	yes	characteristic
10	C₈×C₈₃	C₁₆	1	1	yes	characteristic
11	C₈×C₈₃	C₂×C₈	1	1	yes	characteristic
12	C₂²×C₈₃	C₃₂	1	1	yes	characteristic
13	C₄×C₈₃	C₃₂	1	1	yes	characteristic
14	C₄×C₈₃	C₂×C₁₆	1	1	yes	characteristic
15	C₂×C₈₃	—	2	1	no	—
16	C₂×C₈₃	C₂×C₃₂	1	1	yes	characteristic
17	M₁₂₈	—	83	1	no	maximal, Sylow
18	C₈₃	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃₂	D₈₃	1	1	yes	characteristic
20	C₆₄	—	83	2	no	—
21	C₂×C₁₆	Dic₈₃	1	1	yes	characteristic
22	C₃₂	Dic₈₃	1	1	yes	characteristic
23	C₃₂	C₂×D₈₃	1	1	yes	characteristic
24	C₂×C₈	C₈₃⋊C₈	1	1	yes	characteristic
25	C₁₆	C₈₃⋊C₈	1	1	yes	characteristic
26	C₁₆	C₂×Dic₈₃	1	1	yes	characteristic
27	C₂×C₄	C₈₃⋊C₁₆	1	1	yes	characteristic
28	C₈	C₈₃⋊C₁₆	1	1	yes	characteristic
29	C₈	C₂×C₈₃⋊C₈	1	1	yes	characteristic
30	C₂²	C₈₃⋊C₃₂	1	1	yes	characteristic
31	C₄	C₈₃⋊C₃₂	1	1	yes	characteristic
32	C₄	C₂×C₈₃⋊C₁₆	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	C₂×C₈₃⋊C₃₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. C₈₃⋊C₆₄	C₂	semidirect
18. C₈₃	M₁₂₈	semidirect