Subgroups — #20267630

Order 6592.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₈₂₄	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₆₄₈	C₂	1	1	yes	maximal, characteristic
3	C₃₂×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₄₁₂	—	2	1	no	—
5	D₈₂₄	—	2	1	no	—
6	C₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
7	D₄₁₂	—	4	1	no	—
8	Dic₂₀₆	—	4	1	no	—
9	C₈×C₁₀₃	D₄	1	1	yes	characteristic
10	C₂×D₁₀₃	—	8	1	no	—
11	C₄×C₁₀₃	D₈	1	1	yes	characteristic
12	Dic₁₀₃	—	8	1	no	—
13	C₂×C₁₀₃	D₁₆	1	1	yes	characteristic
14	D₁₀₃	—	16	1	no	—
15	C₁₀₃	SD₆₄	1	1	yes	characteristic, complemented, Sylow
16	SD₆₄	—	103	1	no	maximal, Sylow
17	Q₃₂	—	103	1	no	—
18	D₁₆	—	103	1	no	—
19	C₃₂	D₁₀₃	1	1	yes	characteristic, complemented
20	Q₁₆	—	206	1	no	—
21	D₈	—	206	1	no	—
22	C₁₆	C₂×D₁₀₃	1	1	yes	characteristic
23	Q₈	—	412	1	no	—
24	D₄	—	412	1	no	—
25	C₈	D₄₁₂	1	1	yes	characteristic
26	C₂²	—	824	1	no	—
27	C₄	—	824	1	no	—
28	C₄	D₈₂₄	1	1	yes	characteristic
29	C₂	—	1648	1	no	—
30	C₂	D₁₆₄₈	1	1	yes	characteristic

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