Subgroups — #30595073

Order 15616.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21460854	C₂	1	2	yes	maximal
2	C₃₂×Dic₆₁	C₂	1	1	yes	maximal, characteristic
3	#16840684	—	2	2	no	—
4	C₂×#14519683	C₄	1	1	yes	characteristic
5	C₁₆×Dic₆₁	C₂²	1	1	yes	characteristic
6	C₂×C₃₂×C₆₁	C₄	1	1	yes	characteristic
7	#14519851	—	4	2	no	—
8	C₂×#11758185	Q₈	1	1	yes	characteristic
9	C₈×Dic₆₁	D₄	1	1	yes	characteristic
10	#14519683	C₈	1	2	yes	—
11	C₂×C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₆₁	—	2	1	no	—
13	C₂×C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
14	C₄×Dic₆₁	Q₁₆	1	1	yes	characteristic
15	C₂×#92418	D₈	1	1	yes	characteristic
16	#11758187	—	8	2	no	—
17	C₁₆×C₆₁	C₂×C₈	1	1	yes	characteristic
18	C₁₆×C₆₁	M₁₆	1	1	yes	characteristic
19	#11758185	—	2	1	no	—
20	C₂×C₄×C₆₁	#107	1	1	yes	characteristic
21	C₂×Dic₆₁	—	2	1	no	—
22	C₈×C₆₁	C₄⋊C₈	1	1	yes	characteristic
23	C₈×C₆₁	#108	1	1	yes	characteristic
24	#92418	D₁₆	1	1	yes	characteristic
25	#92418	Q₃₂	1	1	yes	characteristic
26	#7462	—	61	1	no	maximal, Sylow
27	C₂²×C₆₁	#368	1	1	yes	characteristic
28	C₄×C₆₁	#335	1	1	yes	characteristic
29	C₄×C₆₁	#366	1	1	yes	characteristic
30	Dic₆₁	—	2	2	no	—
31	C₄×C₃₂	—	61	1	no	—
32	#1373	—	61	2	no	—
33	C₂×C₆₁	—	2	1	no	—
34	C₂×C₆₁	#1371	1	1	yes	characteristic
35	C₂×C₃₂	—	61	1	no	—
36	C₂×C₃₂	#6923	1	1	yes	characteristic
37	#364	—	122	2	no	—
38	C₄×C₁₆	—	61	1	no	—
39	C₆₁	#7462	1	1	yes	characteristic, complemented, Sylow
40	M₃₂	—	244	2	no	—
41	C₂×C₁₆	—	61	1	no	—
42	C₂×C₁₆	C₂×#6923	1	1	yes	characteristic
43	C₄×C₈	—	61	1	no	—
44	C₃₂	—	2	1	no	—
45	C₃₂	—	61	2	no	—
46	C₂×C₈	—	61	1	no	—
47	C₂×C₈	C₄⋊#6923	1	1	yes	characteristic
48	C₄²	—	61	1	no	—
49	C₁₆	—	122	1	no	—
50	C₁₆	—	488	2	no	—
51	C₁₆	D₆₁⋊C₈	1	1	yes	characteristic
52	C₁₆	#11758217	1	1	yes	characteristic
53	C₂×C₄	—	122	1	no	—
54	C₂×C₄	#14519846	1	1	yes	characteristic
55	C₈	—	61	1	no	—
56	C₈	—	61	1	no	—
57	C₈	#14519844	1	1	yes	characteristic
58	C₈	#14519847	1	1	yes	characteristic
59	C₂²	#16840691	1	1	yes	characteristic
60	C₄	—	122	2	no	—
61	C₄	#16840626	1	1	yes	characteristic
62	C₄	#16840688	1	1	yes	characteristic
63	C₂	—	2	1	no	—
64	C₂	#21460851	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#16840688
commutator	C₁₆×C₆₁	C₂×C₈
Frattini	C₂×C₁₆	C₂×#6923
Fitting	C₂×C₃₂×C₆₁	C₄
socle	C₂×C₆₁	#1371
prime radical	C₂²×C₆₁	#368
cosocle	C₁₆×Dic₆₁	C₂²
hypercenter	C₂×C₃₂	#6923
hypocenter	C₆₁	#7462
LCS	G ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
39. C₆₁	#7462	semidirect

Maximal subgroups

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

subgroup	index
#21460854	2
C₃₂×Dic₆₁	2
#7462	61