Subgroups — #30594104

Order 15616.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21460848	C₂	1	2	yes	maximal
2	C₁₆×#92418	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11758187	—	2	2	no	—
4	C₄×#11758185	C₄	1	1	yes	characteristic
5	C₈×#92418	C₂²	1	1	yes	characteristic
6	C₄×C₁₆×C₆₁	C₄	1	1	yes	characteristic
7	C₂×#11758187	—	4	2	no	—
8	C₂×#11758185	—	2	1	no	—
9	C₄×#92418	D₄	1	1	yes	characteristic
10	C₄×#92418	Q₈	1	1	yes	characteristic
11	C₂×C₁₆×C₆₁	C₈	1	1	yes	characteristic
12	C₂×C₁₆×C₆₁	C₈	1	1	yes	characteristic
13	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
15	C₂×C₈×C₆₁	M₁₆	1	1	yes	characteristic
16	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
17	C₂×#92418	—	2	1	no	—
18	C₂×#92418	D₈	1	1	yes	characteristic
19	C₂×#92418	Q₁₆	1	1	yes	characteristic
20	#11758187	—	8	2	no	—
21	C₁₆×C₆₁	—	2	1	no	—
22	C₁₆×C₆₁	C₁₆	1	2	yes	complemented
23	#11758185	—	2	2	no	—
24	C₂×C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
25	C₂×C₄×C₆₁	#107	1	1	yes	characteristic
26	C₂×C₄×C₆₁	#108	1	1	yes	characteristic
27	C₈×C₆₁	—	2	1	no	—
28	C₈×C₆₁	C₂×C₁₆	1	1	yes	characteristic
29	C₈×C₆₁	M₃₂	1	1	yes	characteristic
30	#92418	—	2	2	no	—
31	#92418	—	2	1	no	—
32	#92418	SD₃₂	1	2	yes	—
33	#7101	—	61	1	no	maximal, Sylow
34	C₂²×C₆₁	#335	1	1	yes	characteristic
35	C₄×C₆₁	—	2	1	no	—
36	C₄×C₆₁	C₄⋊C₁₆	1	1	yes	characteristic
37	C₄×C₆₁	#364	1	1	yes	characteristic
38	C₄×C₆₁	#367	1	1	yes	characteristic
39	C₄×C₆₁	#368	1	1	yes	characteristic
40	#1370	—	61	2	no	—
41	C₈×C₁₆	—	61	1	no	—
42	C₂×C₆₁	#1370	1	1	yes	characteristic
43	C₂×C₆₁	#1372	1	1	yes	characteristic
44	C₂×C₆₁	#1373	1	1	yes	characteristic
45	C₄⋊C₁₆	—	122	2	no	—
46	C₄×C₁₆	—	61	1	no	—
47	C₄×C₁₆	#6923	1	1	yes	characteristic
48	C₈²	—	61	1	no	—
49	C₆₁	#7101	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₁₆	—	122	1	no	—
51	C₂×C₁₆	—	244	2	no	—
52	C₂×C₁₆	#92420	1	1	yes	characteristic
53	C₂×C₁₆	#92420	1	1	yes	characteristic
54	C₄×C₈	—	61	1	no	—
55	C₄×C₈	—	61	1	no	—
56	C₄×C₈	C₂×#6923	1	1	yes	characteristic
57	C₂×C₈	—	61	1	no	—
58	C₂×C₈	—	61	1	no	—
59	C₂×C₈	—	122	1	no	—
60	C₂×C₈	#11758213	1	1	yes	characteristic
61	C₂×C₈	C₂×#92420	1	1	yes	characteristic
62	C₄²	C₄⋊#6923	1	1	yes	characteristic
63	C₁₆	—	2	1	no	—
64	C₁₆	—	122	2	no	—
65	C₁₆	—	488	2	no	—
66	C₁₆	#11758187	1	2	yes	complemented
67	C₂×C₄	C₄⋊#92420	1	1	yes	characteristic
68	C₂×C₄	#14519846	1	1	yes	characteristic
69	C₂×C₄	#14519848	1	1	yes	characteristic
70	C₈	—	2	1	no	—
71	C₈	—	61	2	no	—
72	C₈	—	122	2	no	—
73	C₈	—	122	1	no	—
74	C₈	C₂×#11758187	1	1	yes	characteristic
75	C₈	#14519851	1	1	yes	characteristic
76	C₂²	#16840625	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	C₄⋊#11758187	1	1	yes	characteristic
79	C₄	#16840684	1	1	yes	characteristic
80	C₄	#16840689	1	1	yes	characteristic
81	C₄	#16840691	1	1	yes	characteristic
82	C₂	#21460848	1	1	yes	characteristic
83	C₂	#21460852	1	1	yes	characteristic
84	C₂	#21460854	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14519846
commutator	C₈×C₆₁	C₂×C₁₆
Frattini	C₄×C₈	C₂×#6923
Fitting	C₄×C₁₆×C₆₁	C₄
socle, prime radical	C₂²×C₆₁	#335
cosocle	C₈×#92418	C₂²
hypercenter	C₄×C₁₆	#6923
hypocenter	C₆₁	#7101
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
22. C₁₆×C₆₁	C₁₆	semidirect
49. C₆₁	#7101	semidirect
66. C₁₆	#11758187	semidirect

Maximal subgroups

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

subgroup	index
#21460848	2
C₁₆×#92418	2
#7101	61