Subgroups — #19132805

Order 5504.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₂×D₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄₃⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₄₃	C₄	1	1	yes	characteristic
5	C₄₃⋊C₃₂	C₄	1	1	yes	characteristic
6	C₃₂×C₄₃	C₂²	1	1	yes	characteristic
7	C₈×D₄₃	C₈	1	1	yes	characteristic
8	C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
9	C₄₃⋊C₁₆	C₈	1	1	yes	characteristic
10	C₄×D₄₃	C₁₆	1	1	yes	characteristic
11	C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
12	C₄₃⋊C₈	C₁₆	1	1	yes	characteristic
13	C₂×D₄₃	C₃₂	1	1	yes	characteristic
14	C₄×C₄₃	C₂×C₁₆	1	1	yes	characteristic
15	Dic₄₃	C₃₂	1	1	yes	characteristic
16	M₁₂₈	—	43	1	no	maximal, Sylow
17	C₂×C₄₃	C₂×C₃₂	1	1	yes	characteristic
18	D₄₃	—	2	1	no	—
19	C₂×C₃₂	—	43	1	no	—
20	C₆₄	—	43	1	no	—
21	C₆₄	D₄₃	1	1	yes	characteristic, complemented
22	C₄₃	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₆	—	43	1	no	—
24	C₃₂	—	43	1	no	—
25	C₃₂	C₂×D₄₃	1	1	yes	characteristic
26	C₂×C₈	—	43	1	no	—
27	C₁₆	—	43	1	no	—
28	C₁₆	C₄×D₄₃	1	1	yes	characteristic
29	C₂×C₄	—	43	1	no	—
30	C₈	—	43	1	no	—
31	C₈	C₈×D₄₃	1	1	yes	characteristic
32	C₂²	—	43	1	no	—
33	C₄	—	43	1	no	—
34	C₄	C₁₆×D₄₃	1	1	yes	characteristic
35	C₂	—	86	1	no	—
36	C₂	C₃₂×D₄₃	1	1	yes	characteristic

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