Subgroups — #45683065

Order 33056.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30658309	C₂	1	1	yes	maximal, characteristic
2	C₂×#22551916	C₂	1	1	yes	maximal, characteristic
3	M₁₆×C₁₀₃₃	C₂	1	1	yes	maximal, characteristic
4	#22551916	—	2	1	no	—
5	#22551916	C₄	1	2	yes	—
6	C₂×C₄×C₁₀₃₃	C₂²	1	1	yes	characteristic
7	C₈×C₁₀₃₃	—	2	1	no	—
8	C₂²×C₁₀₃₃	Q₈	1	1	yes	characteristic
9	C₄×C₁₀₃₃	C₂×C₄	1	1	yes	characteristic
10	C₄×C₁₀₃₃	D₄	1	1	yes	characteristic
11	C₂×C₁₀₃₃	—	2	1	no	—
12	C₂×C₁₀₃₃	C₄⋊C₄	1	1	yes	characteristic
13	C₁₀₃₃	#108	1	1	yes	characteristic, complemented, Sylow
14	#108	—	1033	1	no	maximal, Sylow
15	M₁₆	—	1033	1	no	—
16	M₁₆	D₁₀₃₃	1	1	yes	characteristic
17	C₂×C₈	—	1033	1	no	—
18	C₂×C₄	C₂×D₁₀₃₃	1	1	yes	characteristic
19	C₈	—	2	1	no	—
20	C₈	—	1033	2	no	—
21	C₈	—	2066	1	no	—
22	C₂²	Dic₂₀₆₆	1	1	yes	characteristic
23	C₄	C₄×D₁₀₃₃	1	1	yes	characteristic
24	C₄	C₂²⋊D₁₀₃₃	1	1	yes	characteristic
25	C₂	—	2	1	no	—
26	C₂	#30658304	1	1	yes	characteristic

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

N	H ≅ G/N	type
13. C₁₀₃₃	#108	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.