Subgroups — #29567689

Order 15616.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14519683	C₂	1	1	yes	maximal, characteristic
2	#21443891	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#1371	C₂	1	1	yes	maximal, characteristic
4	C₂×#14519683	C₄	1	1	yes	characteristic
5	C₂×#14519683	C₄	1	1	yes	characteristic
6	#16839515	—	2	1	no	—
7	C₄×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
8	C₆₁×#335	—	2	1	no	—
9	C₄⋊#92418	—	4	1	no	—
10	#14519683	—	2	1	no	—
11	#14519683	C₈	1	2	yes	complemented
12	C₂×C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₆×C₆₁	Q₈	1	1	yes	characteristic
14	C₄⋊C₈×C₆₁	—	4	1	no	—
15	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
16	C₂×C₈×C₆₁	—	8	1	no	—
17	C₂×C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₈×C₆₁	Q₁₆	1	1	yes	characteristic
19	C₄²×C₆₁	D₈	1	1	yes	characteristic
20	C₂×#92418	—	8	1	no	—
21	C₁₆×C₆₁	—	2	1	no	—
22	C₁₆×C₆₁	C₂×C₈	1	1	yes	characteristic
23	C₁₆×C₆₁	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₆₁	#107	1	1	yes	characteristic
25	C₂×C₄×C₆₁	D₁₆	1	1	yes	characteristic
26	C₂×C₄×C₆₁	Q₃₂	1	1	yes	characteristic
27	C₈×C₆₁	—	2	1	no	—
28	C₈×C₆₁	—	16	1	no	—
29	C₈×C₆₁	C₄⋊C₈	1	1	yes	characteristic
30	C₈×C₆₁	#108	1	1	yes	characteristic
31	#92418	—	16	1	no	—
32	#7460	—	61	1	no	maximal, Sylow
33	C₂²×C₆₁	#366	1	1	yes	characteristic
34	C₄×C₆₁	—	2	1	no	—
35	C₄×C₆₁	#335	1	1	yes	characteristic
36	C₄×C₆₁	#368	1	1	yes	characteristic
37	C₄×C₆₁	D₃₂	1	1	yes	characteristic
38	C₄×C₆₁	Q₆₄	1	1	yes	characteristic
39	C₄×C₃₂	—	61	1	no	—
40	#1371	—	61	1	no	—
41	#1371	D₆₁	1	1	yes	characteristic
42	C₂×C₆₁	#1371	1	1	yes	characteristic
43	C₂×C₆₁	#1423	1	1	yes	characteristic
44	C₂×C₆₁	#1425	1	1	yes	characteristic
45	C₂×C₃₂	—	61	1	no	—
46	C₂×C₃₂	—	61	1	no	—
47	C₄×C₁₆	C₂×D₆₁	1	1	yes	characteristic
48	#335	—	2	1	no	—
49	#335	—	122	1	no	—
50	C₆₁	#7460	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₁₆	Dic₁₂₂	1	1	yes	characteristic
52	C₂×C₁₆	C₄×D₆₁	1	1	yes	characteristic
53	C₄⋊C₈	—	4	1	no	—
54	C₄⋊C₈	—	244	1	no	—
55	C₄×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
56	C₃₂	—	61	2	no	—
57	C₃₂	—	122	1	no	—
58	C₂×C₈	—	8	1	no	—
59	C₂×C₈	—	488	1	no	—
60	C₂×C₈	#11758196	1	1	yes	characteristic
61	C₂×C₈	#11758202	1	1	yes	characteristic
62	C₄²	#11758199	1	1	yes	characteristic
63	C₁₆	—	2	1	no	—
64	C₁₆	C₈×D₆₁	1	1	yes	characteristic
65	C₁₆	#11758189	1	1	yes	characteristic
66	C₂×C₄	#14519710	1	1	yes	characteristic
67	C₂×C₄	#14519718	1	1	yes	characteristic
68	C₂×C₄	#14519723	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	16	1	no	—
71	C₈	—	976	1	no	—
72	C₈	#14519706	1	1	yes	characteristic
73	C₈	#14519712	1	1	yes	characteristic
74	C₂²	#16839587	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	#16839514	1	1	yes	characteristic
77	C₄	#16839591	1	1	yes	characteristic
78	C₄	#16839597	1	1	yes	characteristic
79	C₄	#16839602	1	1	yes	characteristic
80	C₂	#21443890	1	1	yes	characteristic
81	C₂	#21444018	1	1	yes	characteristic
82	C₂	#21444022	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14519718
commutator	C₁₆×C₆₁	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₆₁
Fitting	C₆₁×#1371	C₂
socle, prime radical	C₂²×C₆₁	#366
cosocle	C₄×C₁₆×C₆₁	C₂²
hypercenter	#1371	D₆₁
hypocenter	C₆₁	#7460
LCS	G ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1371

Complements

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

N	H ≅ G/N	type
11. #14519683	C₈	semidirect
50. C₆₁	#7460	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14519683	2
#21443891	2
C₆₁×#1371	2
#7460	61