Subgroups — #15692329

Order 3232.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13108077	C₂	1	2	yes	maximal, complemented
2	C₂×#11717579	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₀₁	C₄	1	1	yes	characteristic
4	#11717579	C₄	1	1	yes	characteristic
5	#11717579	C₂²	1	1	yes	characteristic
6	C₂²×C₁₀₁	C₈	1	1	yes	characteristic
7	C₄×C₁₀₁	C₈	1	1	yes	characteristic
8	C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
9	C₂×C₁₀₁	—	2	1	no	—
10	C₂×C₁₀₁	C₂×C₈	1	1	yes	characteristic
11	C₁₀₁	M₃₂	1	1	yes	characteristic, complemented, Sylow
12	M₃₂	—	101	1	no	maximal, Sylow
13	C₂×C₈	—	101	1	no	—
14	C₁₆	—	101	2	no	—
15	C₂×C₄	#87938	1	1	yes	characteristic
16	C₈	—	101	1	no	—
17	C₈	—	101	1	no	—
18	C₂²	#11717581	1	1	yes	characteristic
19	C₄	#11717581	1	1	yes	characteristic
20	C₄	C₂×#87938	1	1	yes	characteristic
21	C₂	—	2	1	no	—
22	C₂	C₂×#11717581	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #13108077	C₂	semidirect
11. C₁₀₁	M₃₂	semidirect

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