Subgroups — #21460980

Order 7808.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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