Subgroups — #46777611

Order 33632.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Dic₁₀₅₁	C₂	1	2	yes	maximal
2	C₂×C₈×C₁₀₅₁	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₁₀₅₁	—	2	2	no	—
4	C₂×C₄×C₁₀₅₁	C₂²	1	1	yes	characteristic
5	C₈×C₁₀₅₁	C₄	1	2	yes	complemented
6	C₂²×C₁₀₅₁	D₄	1	1	yes	characteristic
7	C₄×C₁₀₅₁	C₂×C₄	1	1	yes	characteristic
8	C₄×C₁₀₅₁	Q₈	1	1	yes	characteristic
9	Dic₁₀₅₁	—	4	2	no	—
10	C₂×C₁₀₅₁	C₄⋊C₄	1	1	yes	characteristic
11	C₂×C₁₀₅₁	SD₁₆	1	2	yes	—
12	C₁₀₅₁	#106	1	1	yes	characteristic, complemented, Sylow
13	#106	—	1051	1	no	maximal, Sylow
14	C₂×C₈	D₁₀₅₁	1	1	yes	characteristic
15	C₄⋊C₄	—	1051	2	no	—
16	C₂×C₄	—	2102	2	no	—
17	C₂×C₄	C₂×D₁₀₅₁	1	1	yes	characteristic
18	C₈	Dic₁₀₅₁	1	2	yes	complemented
19	C₂²	D₄₂₀₄	1	1	yes	characteristic
20	C₄	—	4204	2	no	—
21	C₄	C₂×Dic₁₀₅₁	1	1	yes	characteristic
22	C₄	Dic₂₁₀₂	1	1	yes	characteristic
23	C₂	C₄⋊Dic₁₀₅₁	1	1	yes	characteristic
24	C₂	#30681222	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.