Subgroups — #45683064

Order 33056.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Dic₁₀₃₃	C₂	1	2	yes	maximal
2	C₂×C₈×C₁₀₃₃	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₁₀₃₃	—	2	2	no	—
4	C₂×C₄×C₁₀₃₃	C₂²	1	1	yes	characteristic
5	C₈×C₁₀₃₃	C₄	1	2	yes	complemented
6	C₂²×C₁₀₃₃	D₄	1	1	yes	characteristic
7	C₄×C₁₀₃₃	C₂×C₄	1	1	yes	characteristic
8	C₄×C₁₀₃₃	Q₈	1	1	yes	characteristic
9	Dic₁₀₃₃	—	4	2	no	—
10	C₂×C₁₀₃₃	C₄⋊C₄	1	1	yes	characteristic
11	C₂×C₁₀₃₃	D₈	1	1	yes	characteristic
12	C₂×C₁₀₃₃	Q₁₆	1	1	yes	characteristic
13	C₁₀₃₃	#107	1	1	yes	characteristic, complemented, Sylow
14	#107	—	1033	1	no	maximal, Sylow
15	C₂×C₈	D₁₀₃₃	1	1	yes	characteristic
16	C₄⋊C₄	—	1033	2	no	—
17	C₂×C₄	—	2066	2	no	—
18	C₂×C₄	C₂×D₁₀₃₃	1	1	yes	characteristic
19	C₈	Dic₁₀₃₃	1	2	yes	complemented
20	C₂²	D₄₁₃₂	1	1	yes	characteristic
21	C₄	—	4132	2	no	—
22	C₄	C₂×Dic₁₀₃₃	1	1	yes	characteristic
23	C₄	Dic₂₀₆₆	1	1	yes	characteristic
24	C₂	C₄⋊Dic₁₀₃₃	1	1	yes	characteristic
25	C₂	D₈₂₆₄	1	1	yes	characteristic
26	C₂	Dic₄₁₃₂	1	1	yes	characteristic

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

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