Subgroups — #30595069

Order 15616.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21460850	C₂	1	2	yes	maximal
2	C₃₂×Dic₆₁	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	C₈	1	2	yes	complemented
11	C₂×C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₆₁	—	2	1	no	—
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	D₁₆	1	1	yes	characteristic
22	C₂×Dic₆₁	Q₃₂	1	1	yes	characteristic
23	#92420	—	16	2	no	—
24	C₈×C₆₁	C₄⋊C₈	1	1	yes	characteristic
25	C₈×C₆₁	#108	1	1	yes	characteristic
26	#92418	—	2	1	no	—
27	#7460	—	61	1	no	maximal, Sylow
28	C₂²×C₆₁	#366	1	1	yes	characteristic
29	C₄×C₆₁	#335	1	1	yes	characteristic
30	C₄×C₆₁	#368	1	1	yes	characteristic
31	Dic₆₁	—	2	1	no	—
32	Dic₆₁	D₃₂	1	1	yes	characteristic
33	Dic₆₁	Q₆₄	1	1	yes	characteristic
34	C₄×C₃₂	—	61	1	no	—
35	#1371	—	61	2	no	—
36	C₂×C₆₁	#1371	1	1	yes	characteristic
37	C₂×C₆₁	#1423	1	1	yes	characteristic
38	C₂×C₆₁	#1425	1	1	yes	characteristic
39	C₂×C₃₂	—	61	1	no	—
40	C₂×C₃₂	#6923	1	1	yes	characteristic
41	C₄×C₁₆	—	61	1	no	—
42	#335	—	122	2	no	—
43	C₆₁	#7460	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₁₆	—	61	1	no	—
45	C₂×C₁₆	C₂×#6923	1	1	yes	characteristic
46	C₄⋊C₈	—	244	2	no	—
47	C₄×C₈	—	61	1	no	—
48	C₃₂	—	2	1	no	—
49	C₃₂	—	61	2	no	—
50	C₂×C₈	—	61	1	no	—
51	C₂×C₈	—	488	2	no	—
52	C₂×C₈	C₄⋊#6923	1	1	yes	characteristic
53	C₄²	—	61	1	no	—
54	C₁₆	—	122	1	no	—
55	C₁₆	D₆₁⋊C₈	1	1	yes	characteristic
56	C₁₆	#11758217	1	1	yes	characteristic
57	C₂×C₄	—	61	1	no	—
58	C₂×C₄	—	61	1	no	—
59	C₂×C₄	#14519846	1	1	yes	characteristic
60	C₈	—	122	1	no	—
61	C₈	—	976	2	no	—
62	C₈	#14519844	1	1	yes	characteristic
63	C₈	#14519847	1	1	yes	characteristic
64	C₂²	#16840688	1	1	yes	characteristic
65	C₄	—	61	1	no	—
66	C₄	—	61	1	no	—
67	C₄	—	122	1	no	—
68	C₄	#16840626	1	1	yes	characteristic
69	C₄	#16840691	1	1	yes	characteristic
70	C₂	#21460851	1	1	yes	characteristic
71	C₂	#21460980	1	1	yes	characteristic
72	C₂	#21460983	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16840688
commutator	C₁₆×C₆₁	C₂×C₈
Frattini	C₂×C₁₆	C₂×#6923
Fitting	C₂×C₃₂×C₆₁	C₄
socle, prime radical	C₂²×C₆₁	#366
cosocle	C₁₆×Dic₆₁	C₂²
hypercenter	C₂×C₃₂	#6923
hypocenter	C₆₁	#7460
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
10. #14519683	C₈	semidirect
43. C₆₁	#7460	semidirect

Maximal subgroups

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

subgroup	index
#21460850	2
C₃₂×Dic₆₁	2
#7460	61