Subgroups — Dic₁₀₅₁⋊C₈ #46777608

Order 33632.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₀₅₁⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₁₀₅₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₁₀₅₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₀₅₁	C₄	1	1	yes	characteristic
5	C₂×Dic₁₀₅₁	C₄	1	1	yes	characteristic
6	C₁₀₅₁⋊C₈	—	2	1	no	—
7	C₂×C₄×C₁₀₅₁	C₂²	1	1	yes	characteristic
8	C₈×C₁₀₅₁	—	2	1	no	—
9	C₂²×C₁₀₅₁	C₂×C₄	1	1	yes	characteristic
10	C₄×C₁₀₅₁	D₄	1	1	yes	characteristic
11	C₄×C₁₀₅₁	Q₈	1	1	yes	characteristic
12	Dic₁₀₅₁	—	2	1	no	—
13	Dic₁₀₅₁	C₈	1	2	yes	complemented
14	C₂×C₁₀₅₁	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₁₀₅₁	C₂×C₈	1	1	yes	characteristic
16	C₂×C₁₀₅₁	M₁₆	1	1	yes	characteristic
17	C₁₀₅₁	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
18	C₄⋊C₈	—	1051	1	no	maximal, Sylow
19	C₂×C₈	—	1051	1	no	—
20	C₂×C₈	D₁₀₅₁	1	1	yes	characteristic
21	C₄²	—	1051	1	no	—
22	C₂×C₄	—	1051	1	no	—
23	C₂×C₄	—	1051	1	no	—
24	C₂×C₄	C₂×D₁₀₅₁	1	1	yes	characteristic
25	C₈	—	2	1	no	—
26	C₈	—	2102	1	no	—
27	C₂²	C₄×D₁₀₅₁	1	1	yes	characteristic
28	C₄	—	1051	2	no	—
29	C₄	—	2102	1	no	—
30	C₄	C₂²⋊D₁₀₅₁	1	1	yes	characteristic
31	C₄	Dic₂₁₀₂	1	1	yes	characteristic
32	C₂	Dic₁₀₅₁⋊C₄	1	1	yes	characteristic
33	C₂	C₈×D₁₀₅₁	1	1	yes	characteristic
34	C₂	#30681216	1	1	yes	characteristic

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

N	H ≅ G/N	type
13. Dic₁₀₅₁	C₈	semidirect
17. C₁₀₅₁	C₄⋊C₈	semidirect

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