Subgroups — #30595303

Order 15616.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21460989	C₂	1	1	yes	maximal, characteristic, complemented
2	#21460983	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₂×D₆₁	C₂	1	1	yes	maximal, characteristic
4	#16840690	—	2	1	no	—
5	#16840601	—	2	1	no	—
6	D₁₆×D₆₁	—	2	1	no	—
7	D₁₉₅₂	C₄	1	1	yes	characteristic
8	#16839597	—	2	1	no	—
9	C₃₂×D₆₁	C₂²	1	1	yes	characteristic
10	C₆₁×D₃₂	C₄	1	1	yes	characteristic
11	#14519848	—	4	1	no	—
12	D₈×D₆₁	—	4	1	no	—
13	D₉₇₆	—	2	1	no	—
14	#14519718	—	4	1	no	—
15	C₁₆×D₆₁	D₄	1	1	yes	characteristic
16	#14519683	D₄	1	1	yes	characteristic
17	D₁₆×C₆₁	—	2	1	no	—
18	C₃₂×C₆₁	C₂×C₄	1	1	yes	characteristic
19	D₄×D₆₁	—	8	1	no	—
20	#11758213	—	8	1	no	—
21	D₈×C₆₁	—	4	1	no	—
22	#11758199	—	8	1	no	—
23	D₄₈₈	—	4	1	no	—
24	C₈×D₆₁	D₈	1	1	yes	characteristic
25	C₁₆×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
26	#11758185	SD₁₆	1	1	yes	characteristic
27	C₂²×D₆₁	—	16	1	no	—
28	D₄×C₆₁	—	8	1	no	—
29	C₂²⋊D₆₁	—	16	1	no	—
30	D₂₄₄	—	8	1	no	—
31	C₄×D₆₁	D₁₆	1	1	yes	characteristic
32	#92420	—	16	1	no	—
33	C₈×C₆₁	#102	1	1	yes	characteristic
34	#92418	SD₃₂	1	1	yes	characteristic
35	#7541	—	61	1	no	maximal, Sylow
36	C₂²×C₆₁	—	16	1	no	—
37	C₂×D₆₁	—	16	1	no	—
38	C₂×D₆₁	—	32	2	no	—
39	C₂×D₆₁	SD₆₄	1	1	yes	characteristic
40	C₄×C₆₁	#357	1	1	yes	characteristic
41	Dic₆₁	D₃₂	1	1	yes	characteristic
42	C₂×D₃₂	—	61	1	no	—
43	M₁₂₈	—	61	1	no	—
44	#1425	—	61	1	no	—
45	C₂×C₆₁	—	32	1	no	—
46	C₂×C₆₁	#1415	1	1	yes	characteristic
47	D₆₁	—	2	1	no	—
48	D₆₁	—	32	1	no	—
49	C₂×D₁₆	—	122	1	no	—
50	D₃₂	—	61	1	no	—
51	D₃₂	—	122	1	no	—
52	D₃₂	#6923	1	1	yes	characteristic
53	C₂×C₃₂	—	61	1	no	—
54	#368	—	122	1	no	—
55	C₆₄	—	122	1	no	—
56	C₆₁	#7541	1	1	yes	characteristic, complemented, Sylow
57	C₂×D₈	—	244	1	no	—
58	D₁₆	—	2	1	no	—
59	D₁₆	—	122	1	no	—
60	D₁₆	—	244	1	no	—
61	C₂×C₁₆	—	61	1	no	—
62	#108	—	244	1	no	—
63	C₃₂	—	61	1	no	—
64	C₃₂	C₂×#6923	1	1	yes	characteristic
65	C₂×D₄	—	488	1	no	—
66	D₈	—	4	1	no	—
67	D₈	—	488	1	no	—
68	D₈	—	244	1	no	—
69	M₁₆	—	488	1	no	—
70	C₂×C₈	—	61	1	no	—
71	C₁₆	—	61	1	no	—
72	C₁₆	C₂²⋊#6923	1	1	yes	characteristic
73	C₂³	—	976	1	no	—
74	D₄	—	8	1	no	—
75	D₄	—	976	1	no	—
76	D₄	—	488	1	no	—
77	C₂×C₄	—	61	1	no	—
78	C₈	—	61	1	no	—
79	C₈	—	976	1	no	—
80	C₈	#14519839	1	1	yes	characteristic
81	C₂²	—	16	1	no	—
82	C₂²	—	61	1	no	—
83	C₂²	—	1952	2	no	—
84	C₂²	—	976	1	no	—
85	C₄	—	61	1	no	—
86	C₄	#16840674	1	1	yes	characteristic
87	C₂	—	32	1	no	—
88	C₂	—	122	1	no	—
89	C₂	—	1952	1	no	—
90	C₂	#21460968	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#21460968
commutator	C₃₂×C₆₁	C₂×C₄
Frattini	C₃₂	C₂×#6923
Fitting	C₆₁×D₃₂	C₄
socle	C₂×C₆₁	#1415
prime radical	D₃₂×D₆₁	C₂
cosocle	C₃₂×D₆₁	C₂²
hypercenter	D₃₂	#6923
hypocenter	C₆₁	#7541
LCS	G ▷ C₃₂×C₆₁ ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ D₃₂

Complements

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

N	H ≅ G/N	type
1. #21460989	C₂	semidirect
2. #21460983	C₂	semidirect
56. C₆₁	#7541	semidirect

Maximal subgroups

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

subgroup	index
#21460989	2
#21460983	2
D₃₂×D₆₁	2
#7541	61