Subgroups — #29567903

Order 15616.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21444030	C₂	1	1	yes	maximal, characteristic, complemented
2	#21444023	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×D₃₂	C₂	1	1	yes	maximal, characteristic
4	#16839592	—	2	1	no	—
5	#16839481	—	2	1	no	—
6	C₂×D₁₆×C₆₁	—	2	1	no	—
7	C₆₁×D₃₂	—	2	1	no	—
8	C₆₁×D₃₂	C₄	1	2	yes	—
9	C₂×C₃₂×C₆₁	C₂²	1	1	yes	characteristic
10	#14519713	—	4	1	no	—
11	C₂×D₈×C₆₁	—	4	1	no	—
12	D₁₆×C₆₁	—	2	2	no	—
13	D₁₆×C₆₁	—	4	1	no	—
14	C₂×C₁₆×C₆₁	D₄	1	1	yes	characteristic
15	C₃₂×C₆₁	C₂×C₄	1	1	yes	characteristic
16	C₃₂×C₆₁	D₄	1	1	yes	characteristic
17	C₂×D₄×C₆₁	—	8	1	no	—
18	D₈×C₆₁	—	4	2	no	—
19	D₈×C₆₁	—	8	1	no	—
20	C₂×C₈×C₆₁	D₈	1	1	yes	characteristic
21	#11758194	—	8	1	no	—
22	C₁₆×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆×C₆₁	SD₁₆	1	1	yes	characteristic
24	C₂³×C₆₁	—	16	1	no	—
25	D₄×C₆₁	—	8	2	no	—
26	D₄×C₆₁	—	16	1	no	—
27	C₂×C₄×C₆₁	D₁₆	1	1	yes	characteristic
28	C₈×C₆₁	#102	1	1	yes	characteristic
29	C₈×C₆₁	SD₃₂	1	1	yes	characteristic
30	#92418	—	16	1	no	—
31	#7541	—	61	1	no	maximal, Sylow
32	C₂²×C₆₁	—	16	2	no	—
33	C₂²×C₆₁	—	32	2	no	—
34	C₂²×C₆₁	SD₆₄	1	1	yes	characteristic
35	C₄×C₆₁	#357	1	1	yes	characteristic
36	C₄×C₆₁	D₃₂	1	1	yes	characteristic
37	C₂×D₃₂	D₆₁	1	1	yes	characteristic
38	M₁₂₈	—	61	1	no	—
39	#1425	—	61	1	no	—
40	C₂×C₆₁	—	2	1	no	—
41	C₂×C₆₁	—	32	2	no	—
42	C₂×C₆₁	#1415	1	1	yes	characteristic
43	C₂×D₁₆	—	2	1	no	—
44	D₃₂	—	2	1	no	—
45	D₃₂	Dic₆₁	1	2	yes	—
46	C₂×C₃₂	C₂×D₆₁	1	1	yes	characteristic
47	#368	—	122	1	no	—
48	C₆₄	—	122	1	no	—
49	C₆₁	#7541	1	1	yes	characteristic, complemented, Sylow
50	C₂×D₈	—	4	1	no	—
51	D₁₆	—	2	2	no	—
52	D₁₆	—	4	1	no	—
53	C₂×C₁₆	C₂²⋊D₆₁	1	1	yes	characteristic
54	#108	—	244	1	no	—
55	C₃₂	C₂×Dic₆₁	1	1	yes	characteristic
56	C₃₂	C₂²⋊D₆₁	1	1	yes	characteristic
57	C₂×D₄	—	8	1	no	—
58	D₈	—	4	2	no	—
59	D₈	—	8	1	no	—
60	M₁₆	—	488	1	no	—
61	C₂×C₈	#11758199	1	1	yes	characteristic
62	C₁₆	#11758200	1	1	yes	characteristic
63	C₁₆	C₂²⋊Dic₆₁	1	1	yes	characteristic
64	C₂³	—	16	1	no	—
65	D₄	—	8	2	no	—
66	D₄	—	16	1	no	—
67	C₂×C₄	#14519718	1	1	yes	characteristic
68	C₈	—	976	1	no	—
69	C₈	#14519698	1	1	yes	characteristic
70	C₈	#14519721	1	1	yes	characteristic
71	C₂²	—	16	2	no	—
72	C₂²	—	32	2	no	—
73	C₂²	#16839600	1	1	yes	characteristic
74	C₄	#16839563	1	1	yes	characteristic
75	C₄	#16839597	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	32	2	no	—
78	C₂	#21443997	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#21443997
commutator	C₃₂×C₆₁	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₆₁
Fitting, prime radical	C₂×C₆₁×D₃₂	C₂
socle	C₂×C₆₁	#1415
cosocle	C₂×C₃₂×C₆₁	C₂²
hypercenter	C₂×D₃₂	D₆₁
hypocenter	C₆₁	#7541
LCS	G ▷ C₃₂×C₆₁ ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×D₃₂

Complements

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

N	H ≅ G/N	type
1. #21444030	C₂	semidirect
2. #21444023	C₂	semidirect
49. C₆₁	#7541	semidirect

Maximal subgroups

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

subgroup	index
#21444030	2
#21444023	2
C₂×C₆₁×D₃₂	2
#7541	61