Subgroups — #30595318

Order 15616.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21460634	C₂	1	2	yes	maximal, complemented
2	C₆₄×D₆₁	C₂	1	1	yes	maximal, characteristic
3	C₃₂×D₆₁	C₄	1	1	yes	characteristic
4	#16839481	C₂²	1	1	yes	characteristic
5	C₆₁×C₆₄	C₄	1	1	yes	characteristic
6	C₁₆×D₆₁	C₈	1	1	yes	characteristic
7	#14519683	C₈	1	1	yes	characteristic
8	C₃₂×C₆₁	C₂×C₄	1	1	yes	characteristic
9	C₈×D₆₁	C₁₆	1	1	yes	characteristic
10	C₁₆×C₆₁	C₂×C₈	1	1	yes	characteristic
11	#11758185	C₁₆	1	1	yes	characteristic
12	C₄×D₆₁	C₃₂	1	1	yes	characteristic
13	C₈×C₆₁	C₂×C₁₆	1	1	yes	characteristic
14	#92418	C₃₂	1	1	yes	characteristic
15	M₂₅₆	—	61	1	no	maximal, Sylow
16	C₂×D₆₁	C₆₄	1	1	yes	characteristic
17	C₄×C₆₁	C₂×C₃₂	1	1	yes	characteristic
18	Dic₆₁	C₆₄	1	1	yes	characteristic
19	C₂×C₆₄	—	61	1	no	—
20	C₁₂₈	—	61	2	no	—
21	C₂×C₆₁	C₂×C₆₄	1	1	yes	characteristic
22	D₆₁	—	2	1	no	—
23	C₂×C₃₂	—	61	1	no	—
24	C₆₄	—	61	1	no	—
25	C₆₄	#6923	1	1	yes	characteristic
26	C₆₁	M₂₅₆	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₆	—	61	1	no	—
28	C₃₂	—	61	1	no	—
29	C₃₂	C₂×#6923	1	1	yes	characteristic
30	C₂×C₈	—	61	1	no	—
31	C₁₆	—	61	1	no	—
32	C₁₆	D₆₁⋊C₈	1	1	yes	characteristic
33	C₂×C₄	—	61	1	no	—
34	C₈	—	61	1	no	—
35	C₈	D₆₁⋊C₁₆	1	1	yes	characteristic
36	C₂²	—	61	1	no	—
37	C₄	—	61	1	no	—
38	C₄	D₆₁⋊C₃₂	1	1	yes	characteristic
39	C₂	—	122	1	no	—
40	C₂	D₆₁⋊C₆₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #21460634	C₂	semidirect
26. C₆₁	M₂₅₆	semidirect

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