Subgroups — #30595074

Order 15616.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21460852	C₂	1	2	yes	maximal
2	#21443952	C₂	1	1	yes	maximal, characteristic
3	#16840625	—	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	C₄⋊#92420	—	4	2	no	—
8	C₂×#11758185	Q₈	1	1	yes	characteristic
9	C₈×Dic₆₁	D₄	1	1	yes	characteristic
10	#14519683	—	2	1	no	—
11	C₂×C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₆₁	C₈	1	2	yes	complemented
13	C₂×#92420	—	8	2	no	—
14	C₂×C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
15	C₄×Dic₆₁	D₈	1	1	yes	characteristic
16	C₂×#92418	Q₁₆	1	1	yes	characteristic
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	SD₃₂	1	2	yes	—
22	#92420	—	16	2	no	—
23	C₈×C₆₁	C₄⋊C₈	1	1	yes	characteristic
24	C₈×C₆₁	#108	1	1	yes	characteristic
25	#92418	—	2	1	no	—
26	#7463	—	61	1	no	maximal, Sylow
27	C₂²×C₆₁	#367	1	1	yes	characteristic
28	C₄×C₆₁	#335	1	1	yes	characteristic
29	C₄×C₆₁	#368	1	1	yes	characteristic
30	Dic₆₁	—	2	2	no	—
31	#1397	—	61	1	no	—
32	#1372	—	61	2	no	—
33	C₂×C₆₁	#1372	1	1	yes	characteristic
34	C₂×C₆₁	#1426	1	2	yes	—
35	C₂×C₃₂	—	61	1	no	—
36	C₂×C₃₂	#6923	1	1	yes	characteristic
37	C₄×C₁₆	—	61	1	no	—
38	#335	—	122	2	no	—
39	C₆₁	#7463	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₁₆	—	61	1	no	—
41	C₂×C₁₆	C₂×#6923	1	1	yes	characteristic
42	C₄⋊C₈	—	244	2	no	—
43	C₄×C₈	—	61	1	no	—
44	C₃₂	—	122	1	no	—
45	C₃₂	#92420	1	2	yes	complemented
46	C₂×C₈	—	61	1	no	—
47	C₂×C₈	—	488	2	no	—
48	C₂×C₈	C₄⋊#6923	1	1	yes	characteristic
49	C₄²	—	61	1	no	—
50	C₁₆	—	122	1	no	—
51	C₁₆	#11758213	1	1	yes	characteristic
52	C₁₆	C₂×#92420	1	1	yes	characteristic
53	C₂×C₄	—	61	2	no	—
54	C₂×C₄	#14519846	1	1	yes	characteristic
55	C₈	—	122	1	no	—
56	C₈	—	976	2	no	—
57	C₈	C₄⋊#92420	1	1	yes	characteristic
58	C₈	#14519848	1	1	yes	characteristic
59	C₂²	#16840689	1	1	yes	characteristic
60	C₄	—	122	2	no	—
61	C₄	#16840625	1	1	yes	characteristic
62	C₄	#16840691	1	1	yes	characteristic
63	C₂	#21460852	1	1	yes	characteristic
64	C₂	#21460984	1	2	yes	—

	subgroup	G/H
center	C₂²	#16840689
commutator	C₁₆×C₆₁	C₂×C₈
Frattini	C₂×C₁₆	C₂×#6923
Fitting	C₂×C₃₂×C₆₁	C₄
socle, prime radical	C₂²×C₆₁	#367
cosocle	C₁₆×Dic₆₁	C₂²
hypercenter	C₂×C₃₂	#6923
hypocenter	C₆₁	#7463
LCS	G ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
12. C₃₂×C₆₁	C₈	semidirect
39. C₆₁	#7463	semidirect
45. C₃₂	#92420	semidirect

Maximal subgroups

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

subgroup	index
#21460852	2
#21443952	2
#7463	61