Subgroups — #45683046

Order 33056.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₁₃₂	C₂	1	1	yes	maximal, characteristic
2	#30658309	C₂	1	1	yes	maximal, characteristic, complemented
3	M₁₆×C₁₀₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₁₀₃₃	C₄	1	2	yes	—
5	D₄₁₃₂	—	2	1	no	—
6	D₄₁₃₂	—	2	1	no	—
7	#22551916	—	2	1	no	—
8	C₂×C₄×C₁₀₃₃	C₂²	1	1	yes	characteristic
9	C₈×C₁₀₃₃	—	2	1	no	—
10	C₂²×C₁₀₃₃	C₂×C₄	1	1	yes	characteristic
11	C₂×D₁₀₃₃	—	2	2	no	—
12	C₂×D₁₀₃₃	—	4	2	no	—
13	C₄×C₁₀₃₃	D₄	1	1	yes	characteristic
14	C₄×C₁₀₃₃	D₄	1	1	yes	characteristic
15	C₂×C₁₀₃₃	—	2	1	no	—
16	C₂×C₁₀₃₃	C₂²⋊C₄	1	1	yes	characteristic
17	D₁₀₃₃	—	4	2	no	—
18	C₁₀₃₃	#100	1	1	yes	characteristic, complemented, Sylow
19	#100	—	1033	1	no	maximal, Sylow
20	C₂×D₄	—	1033	1	no	—
21	M₁₆	—	1033	1	no	—
22	M₁₆	D₁₀₃₃	1	1	yes	characteristic, complemented
23	C₂³	—	1033	2	no	—
24	D₄	—	2066	1	no	—
25	D₄	—	2066	1	no	—
26	C₂×C₄	C₂×D₁₀₃₃	1	1	yes	characteristic
27	C₈	—	2	1	no	—
28	C₈	—	2066	1	no	—
29	C₂²	—	2066	2	no	—
30	C₂²	—	4132	2	no	—
31	C₂²	C₄×D₁₀₃₃	1	1	yes	characteristic
32	C₄	C₂²⋊D₁₀₃₃	1	1	yes	characteristic
33	C₄	D₄₁₃₂	1	1	yes	characteristic
34	C₂	—	2	1	no	—
35	C₂	—	4132	2	no	—
36	C₂	#30658302	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.