Subgroups — #44567857

Order 32288.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₀₁₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄₀₃₆	C₂	1	1	yes	maximal, characteristic
3	#30633309	C₂	1	4	yes	maximal, complemented
4	C₄²×C₁₀₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₁₀₀₉	C₂²	1	2	yes	—
6	Dic₂₀₁₈	—	2	2	no	—
7	D₄₀₃₆	—	2	2	no	—
8	C₂×Dic₁₀₀₉	C₂²	1	2	yes	—
9	C₂×C₄×C₁₀₀₉	C₂²	1	2	yes	—
10	C₂×C₄×C₁₀₀₉	C₂²	1	1	yes	characteristic
11	C₂²×C₁₀₀₉	C₂³	1	1	yes	characteristic
12	C₂×D₁₀₀₉	—	2	2	no	—
13	C₂×D₁₀₀₉	—	2	4	no	—
14	C₄×C₁₀₀₉	—	2	2	no	—
15	C₄×C₁₀₀₉	D₄	1	2	yes	—
16	Dic₁₀₀₉	—	2	2	no	—
17	C₂×C₁₀₀₉	C₂×D₄	1	1	yes	characteristic
18	C₂×C₁₀₀₉	#41	1	2	yes	—
19	D₁₀₀₉	—	4	2	no	—
20	C₁₀₀₉	#124	1	1	yes	characteristic, complemented, Sylow
21	#124	—	1009	1	no	maximal, Sylow
22	C₂×Q₈	—	1009	1	no	—
23	C₂×D₄	—	1009	1	no	—
24	C₂²⋊C₄	—	1009	4	no	—
25	C₄²	D₁₀₀₉	1	1	yes	characteristic, complemented
26	C₂³	—	1009	2	no	—
27	Q₈	—	2018	2	no	—
28	D₄	—	2018	2	no	—
29	C₂×C₄	—	1009	2	no	—
30	C₂×C₄	C₂×D₁₀₀₉	1	2	yes	—
31	C₂×C₄	C₂×D₁₀₀₉	1	1	yes	characteristic
32	C₂²	—	2018	2	no	—
33	C₂²	—	2018	4	no	—
34	C₂²	C₂²×D₁₀₀₉	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	2018	2	no	—
37	C₄	D₄₀₃₆	1	2	yes	—
38	C₂	—	4036	2	no	—
39	C₂	C₂×D₄₀₃₆	1	1	yes	characteristic
40	C₂	#30633332	1	2	yes	—

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.