Subgroups — #30595312

Order 15616.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21460982	C₂	1	2	yes	maximal
2	C₆₄×D₆₁	C₂	1	1	yes	maximal, characteristic
3	#16840690	—	2	2	no	—
4	C₃₂×D₆₁	C₂²	1	1	yes	characteristic
5	#16839481	C₄	1	1	yes	characteristic
6	C₆₁×C₆₄	C₄	1	1	yes	characteristic
7	#14519848	—	4	2	no	—
8	C₁₆×D₆₁	D₄	1	1	yes	characteristic
9	#14519683	Q₈	1	1	yes	characteristic
10	C₃₂×C₆₁	C₂×C₄	1	1	yes	characteristic
11	#11758213	—	8	2	no	—
12	C₈×D₆₁	D₈	1	1	yes	characteristic
13	C₁₆×C₆₁	C₄⋊C₄	1	1	yes	characteristic
14	#11758185	Q₁₆	1	1	yes	characteristic
15	C₄×D₆₁	D₁₆	1	1	yes	characteristic
16	#92420	—	16	2	no	—
17	C₈×C₆₁	#107	1	1	yes	characteristic
18	#92418	Q₃₂	1	1	yes	characteristic
19	#7547	—	61	1	no	maximal, Sylow
20	C₂×D₆₁	Q₆₄	1	1	yes	characteristic
21	C₄×C₆₁	#366	1	1	yes	characteristic
22	Dic₆₁	D₃₂	1	1	yes	characteristic
23	C₂×C₆₄	—	61	1	no	—
24	#1425	—	61	2	no	—
25	C₂×C₆₁	#1423	1	1	yes	characteristic
26	D₆₁	—	2	1	no	—
27	C₂×C₃₂	—	61	1	no	—
28	#368	—	122	2	no	—
29	C₆₄	—	61	1	no	—
30	C₆₄	#6923	1	1	yes	characteristic
31	C₆₁	#7547	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₁₆	—	61	1	no	—
33	#108	—	244	2	no	—
34	C₃₂	—	61	1	no	—
35	C₃₂	C₂×#6923	1	1	yes	characteristic
36	M₁₆	—	488	2	no	—
37	C₂×C₈	—	61	1	no	—
38	C₁₆	—	61	1	no	—
39	C₁₆	C₄⋊#6923	1	1	yes	characteristic
40	C₂×C₄	—	61	1	no	—
41	C₈	—	61	1	no	—
42	C₈	—	976	2	no	—
43	C₈	#14519846	1	1	yes	characteristic
44	C₂²	—	61	1	no	—
45	C₄	—	61	1	no	—
46	C₄	#16840688	1	1	yes	characteristic
47	C₂	—	122	1	no	—
48	C₂	#21460980	1	1	yes	characteristic

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

N	H ≅ G/N	type
31. C₆₁	#7547	semidirect

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