Subgroups — D₆₁×Q₁₂₈ #29601061

Order 15616.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₆₄×D₆₁	C₂	1	2	yes	maximal
2	Dic₁₉₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#21444036	C₂	1	2	yes	maximal, complemented
4	C₆₄×D₆₁	C₂	1	1	yes	maximal, characteristic
5	C₆₁×Q₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₃₂×D₆₁	—	2	2	no	—
7	Dic₉₇₆	C₂²	1	2	yes	—
8	#16839602	—	2	2	no	—
9	C₃₂×D₆₁	C₂²	1	1	yes	characteristic
10	#16839481	C₂²	1	1	yes	characteristic
11	C₆₁×Q₆₄	C₂²	1	2	yes	—
12	C₆₁×C₆₄	C₂²	1	1	yes	characteristic
13	Q₁₆×D₆₁	—	4	2	no	—
14	Dic₄₈₈	—	2	2	no	—
15	#14519723	—	4	2	no	—
16	C₁₆×D₆₁	D₄	1	1	yes	characteristic
17	#14519683	D₄	1	1	yes	characteristic
18	Q₃₂×C₆₁	—	2	2	no	—
19	C₃₂×C₆₁	C₂³	1	1	yes	characteristic
20	Q₈×D₆₁	—	8	2	no	—
21	Q₁₆×C₆₁	—	4	2	no	—
22	#11758202	—	8	2	no	—
23	Dic₂₄₄	—	4	2	no	—
24	C₈×D₆₁	D₈	1	1	yes	characteristic
25	C₁₆×C₆₁	C₂×D₄	1	1	yes	characteristic
26	#11758185	D₈	1	1	yes	characteristic
27	Q₈×C₆₁	—	8	2	no	—
28	C₄×D₆₁	—	16	2	no	—
29	C₄×D₆₁	D₁₆	1	1	yes	characteristic
30	Dic₁₂₂	—	8	2	no	—
31	Dic₁₂₂	—	16	2	no	—
32	C₈×C₆₁	C₂×D₈	1	1	yes	characteristic
33	#92418	D₁₆	1	1	yes	characteristic
34	C₂×Q₁₂₈	—	61	1	no	maximal, Sylow
35	C₂×D₆₁	D₃₂	1	1	yes	characteristic
36	C₄×C₆₁	—	16	2	no	—
37	C₄×C₆₁	C₂×D₁₆	1	1	yes	characteristic
38	Dic₆₁	—	16	2	no	—
39	Dic₆₁	D₃₂	1	1	yes	characteristic
40	C₂×Q₆₄	—	61	2	no	—
41	Q₁₂₈	—	61	2	no	—
42	Q₁₂₈	—	61	1	no	—
43	Q₁₂₈	D₆₁	1	1	yes	characteristic, direct product factor
44	C₂×C₆₄	—	61	1	no	—
45	C₂×C₆₁	C₂×D₃₂	1	1	yes	characteristic
46	D₆₁	Q₁₂₈	1	2	yes	direct product factor
47	C₂×Q₃₂	—	122	2	no	—
48	Q₆₄	—	61	2	no	—
49	Q₆₄	—	122	2	no	—
50	Q₆₄	C₂×D₆₁	1	2	yes	—
51	C₂×C₃₂	—	61	1	no	—
52	C₆₄	—	61	1	no	—
53	C₆₄	C₂×D₆₁	1	1	yes	characteristic
54	C₆₁	C₂×Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₁₆	—	244	2	no	—
56	Q₃₂	—	2	2	no	—
57	Q₃₂	—	122	2	no	—
58	Q₃₂	—	244	2	no	—
59	C₂×C₁₆	—	61	1	no	—
60	C₃₂	—	61	1	no	—
61	C₃₂	C₂²×D₆₁	1	1	yes	characteristic
62	C₂×Q₈	—	488	2	no	—
63	Q₁₆	—	4	2	no	—
64	Q₁₆	—	488	2	no	—
65	Q₁₆	—	244	2	no	—
66	C₂×C₈	—	61	1	no	—
67	C₁₆	—	61	1	no	—
68	C₁₆	D₄×D₆₁	1	1	yes	characteristic
69	Q₈	—	8	2	no	—
70	Q₈	—	976	2	no	—
71	Q₈	—	488	2	no	—
72	C₂×C₄	—	61	1	no	—
73	C₂×C₄	—	976	2	no	—
74	C₈	—	61	1	no	—
75	C₈	D₈×D₆₁	1	1	yes	characteristic
76	C₂²	—	61	1	no	—
77	C₄	—	16	2	no	—
78	C₄	—	61	1	no	—
79	C₄	—	976	2	no	—
80	C₄	D₁₆×D₆₁	1	1	yes	characteristic
81	C₂	—	61	2	no	—
82	C₂	D₃₂×D₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃₂×D₆₁
commutator, cosocle	C₃₂×C₆₁	C₂³
Frattini	C₃₂	C₂²×D₆₁
Fitting	C₆₁×Q₁₂₈	C₂
socle	C₂×C₆₁	C₂×D₃₂
prime radical	C₂×D₆₁	D₃₂
hypercenter	Q₁₂₈	D₆₁
hypocenter	C₆₁	C₂×Q₁₂₈
LCS	G ▷ C₃₂×C₆₁ ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ Q₁₂₈

Complements

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

N	H ≅ G/N	type
2. Dic₁₉₅₂	C₂	semidirect
3. #21444036	C₂	semidirect
5. C₆₁×Q₁₂₈	C₂	semidirect
43. Q₁₂₈	D₆₁	direct (N × H)
46. D₆₁	Q₁₂₈	direct (N × H)
54. C₆₁	C₂×Q₁₂₈	semidirect

Maximal subgroups

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

subgroup	index
Q₆₄×D₆₁	2
Dic₁₉₅₂	2
#21444036	2
C₆₄×D₆₁	2
C₆₁×Q₁₂₈	2
C₂×Q₁₂₈	61

Subgroups — D61×Q128 #29601061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₆₁×Q₁₂₈ #29601061