Subgroups — #29567916

Order 15616.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16839481	C₂	1	1	yes	maximal, characteristic
2	#21444023	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#1425	C₂	1	1	yes	maximal, characteristic
4	#16839592	—	2	1	no	—
5	#16839481	C₄	1	2	yes	—
6	C₂×C₃₂×C₆₁	C₂²	1	1	yes	characteristic
7	C₆₁×#368	—	2	1	no	—
8	#14519713	—	4	1	no	—
9	C₂×C₁₆×C₆₁	D₄	1	1	yes	characteristic
10	#108×C₆₁	—	4	1	no	—
11	C₃₂×C₆₁	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₆₁	Q₈	1	1	yes	characteristic
13	M₁₆×C₆₁	—	8	1	no	—
14	C₂×C₈×C₆₁	D₈	1	1	yes	characteristic
15	#11758194	—	8	1	no	—
16	C₁₆×C₆₁	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₆₁	Q₁₆	1	1	yes	characteristic
18	C₂×C₄×C₆₁	D₁₆	1	1	yes	characteristic
19	C₈×C₆₁	—	16	1	no	—
20	C₈×C₆₁	#107	1	1	yes	characteristic
21	C₈×C₆₁	Q₃₂	1	1	yes	characteristic
22	#92418	—	16	1	no	—
23	#7547	—	61	1	no	maximal, Sylow
24	C₂²×C₆₁	Q₆₄	1	1	yes	characteristic
25	C₄×C₆₁	#366	1	1	yes	characteristic
26	C₄×C₆₁	D₃₂	1	1	yes	characteristic
27	C₂×C₆₄	—	61	1	no	—
28	#1425	—	61	1	no	—
29	#1425	D₆₁	1	1	yes	characteristic
30	C₂×C₆₁	—	2	1	no	—
31	C₂×C₆₁	#1423	1	1	yes	characteristic
32	C₂×C₃₂	C₂×D₆₁	1	1	yes	characteristic
33	#368	—	2	1	no	—
34	#368	—	122	1	no	—
35	C₆₄	—	61	2	no	—
36	C₆₁	#7547	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₁₆	C₂²⋊D₆₁	1	1	yes	characteristic
38	#108	—	4	1	no	—
39	#108	—	244	1	no	—
40	C₃₂	Dic₁₂₂	1	1	yes	characteristic
41	C₃₂	C₄×D₆₁	1	1	yes	characteristic
42	M₁₆	—	8	1	no	—
43	M₁₆	—	488	1	no	—
44	C₂×C₈	#11758199	1	1	yes	characteristic
45	C₁₆	#11758196	1	1	yes	characteristic
46	C₁₆	#11758202	1	1	yes	characteristic
47	C₂×C₄	#14519718	1	1	yes	characteristic
48	C₈	—	16	1	no	—
49	C₈	—	976	1	no	—
50	C₈	#14519710	1	1	yes	characteristic
51	C₈	#14519723	1	1	yes	characteristic
52	C₂²	#16839602	1	1	yes	characteristic
53	C₄	#16839587	1	1	yes	characteristic
54	C₄	#16839597	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#21444018	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#16839597
commutator	C₃₂×C₆₁	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₆₁
Fitting	C₆₁×#1425	C₂
socle	C₂×C₆₁	#1423
prime radical	C₂²×C₆₁	Q₆₄
cosocle	C₂×C₃₂×C₆₁	C₂²
hypercenter	#1425	D₆₁
hypocenter	C₆₁	#7547
LCS	G ▷ C₃₂×C₆₁ ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1425

Complements

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

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

Maximal subgroups

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

subgroup	index
C₂×#16839481	2
#21444023	2
C₆₁×#1425	2
#7547	61