Subgroups — #46776897

Order 33568.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₄₁₉₆	C₂	1	1	yes	maximal, characteristic
2	#30680891	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×C₁₀₄₉	C₂	1	1	yes	maximal, characteristic
4	Dic₂₀₉₈	—	2	1	no	—
5	Q₈×C₁₀₄₉	—	2	1	no	—
6	C₈×C₁₀₄₉	C₂²	1	1	yes	characteristic
7	C₄×C₁₀₄₉	—	4	1	no	—
8	C₄×C₁₀₄₉	D₄	1	1	yes	characteristic
9	Dic₁₀₄₉	—	4	1	no	—
10	C₂×C₁₀₄₉	D₈	1	1	yes	characteristic
11	C₁₀₄₉	Q₃₂	1	1	yes	characteristic, complemented, Sylow
12	Q₃₂	—	1049	1	no	maximal, Sylow
13	Q₁₆	—	1049	1	no	—
14	Q₁₆	D₁₀₄₉	1	1	yes	characteristic
15	C₁₆	—	1049	1	no	—
16	Q₈	—	2	1	no	—
17	Q₈	—	2098	1	no	—
18	C₈	C₂×D₁₀₄₉	1	1	yes	characteristic
19	C₄	—	4	1	no	—
20	C₄	—	4196	1	no	—
21	C₄	C₂²⋊D₁₀₄₉	1	1	yes	characteristic
22	C₂	#30680901	1	1	yes	characteristic

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

N	H ≅ G/N	type
11. C₁₀₄₉	Q₃₂	semidirect

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