Subgroups — Q₁₂₈×D₈₉ #36475476

Order 22784.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₆₄×D₈₉	C₂	1	2	yes	maximal
2	Dic₂₈₄₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#26018469	C₂	1	2	yes	maximal, complemented
4	C₆₄×D₈₉	C₂	1	1	yes	maximal, characteristic
5	C₈₉×Q₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₃₂×D₈₉	—	2	2	no	—
7	Dic₁₄₂₄	C₂²	1	2	yes	—
8	#19151438	—	2	2	no	—
9	C₃₂×D₈₉	C₂²	1	1	yes	characteristic
10	#19151317	C₂²	1	1	yes	characteristic
11	Q₆₄×C₈₉	C₂²	1	2	yes	—
12	C₆₄×C₈₉	C₂²	1	1	yes	characteristic
13	Q₁₆×D₈₉	—	4	2	no	—
14	Dic₇₁₂	—	2	2	no	—
15	#15667958	—	4	2	no	—
16	C₁₆×D₈₉	D₄	1	1	yes	characteristic
17	#15667918	D₄	1	1	yes	characteristic
18	Q₃₂×C₈₉	—	2	2	no	—
19	C₃₂×C₈₉	C₂³	1	1	yes	characteristic
20	Q₈×D₈₉	—	8	2	no	—
21	Dic₃₅₆	—	4	2	no	—
22	#13083564	—	8	2	no	—
23	C₈×D₈₉	D₈	1	1	yes	characteristic
24	#13083549	D₈	1	1	yes	characteristic
25	Q₁₆×C₈₉	—	4	2	no	—
26	C₁₆×C₈₉	C₂×D₄	1	1	yes	characteristic
27	Q₈×C₈₉	—	8	2	no	—
28	C₄×D₈₉	—	16	2	no	—
29	C₄×D₈₉	D₁₆	1	1	yes	characteristic
30	Dic₁₇₈	—	8	2	no	—
31	Dic₁₇₈	—	16	2	no	—
32	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
33	#10623494	D₁₆	1	1	yes	characteristic
34	C₂×D₈₉	D₃₂	1	1	yes	characteristic
35	C₄×C₈₉	—	16	2	no	—
36	C₄×C₈₉	C₂×D₁₆	1	1	yes	characteristic
37	Dic₈₉	—	16	2	no	—
38	Dic₈₉	D₃₂	1	1	yes	characteristic
39	C₂×Q₁₂₈	—	89	1	no	maximal, Sylow
40	C₂×C₈₉	C₂×D₃₂	1	1	yes	characteristic
41	D₈₉	Q₁₂₈	1	2	yes	direct product factor
42	C₂×Q₆₄	—	89	2	no	—
43	Q₁₂₈	—	89	2	no	—
44	Q₁₂₈	—	89	1	no	—
45	Q₁₂₈	D₈₉	1	1	yes	characteristic, direct product factor
46	C₂×C₆₄	—	89	1	no	—
47	C₈₉	C₂×Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
48	C₂×Q₃₂	—	178	2	no	—
49	Q₆₄	—	89	2	no	—
50	Q₆₄	—	178	2	no	—
51	Q₆₄	C₂×D₈₉	1	2	yes	—
52	C₂×C₃₂	—	89	1	no	—
53	C₆₄	—	89	1	no	—
54	C₆₄	C₂×D₈₉	1	1	yes	characteristic
55	C₂×Q₁₆	—	356	2	no	—
56	Q₃₂	—	2	2	no	—
57	Q₃₂	—	356	2	no	—
58	Q₃₂	—	178	2	no	—
59	C₂×C₁₆	—	89	1	no	—
60	C₃₂	—	89	1	no	—
61	C₃₂	C₂²×D₈₉	1	1	yes	characteristic
62	C₂×Q₈	—	712	2	no	—
63	Q₁₆	—	4	2	no	—
64	Q₁₆	—	356	2	no	—
65	Q₁₆	—	712	2	no	—
66	C₂×C₈	—	89	1	no	—
67	C₁₆	—	89	1	no	—
68	C₁₆	D₄×D₈₉	1	1	yes	characteristic
69	Q₈	—	8	2	no	—
70	Q₈	—	1424	2	no	—
71	Q₈	—	712	2	no	—
72	C₂×C₄	—	89	1	no	—
73	C₂×C₄	—	1424	2	no	—
74	C₈	—	89	1	no	—
75	C₈	D₈×D₈₉	1	1	yes	characteristic
76	C₂²	—	89	1	no	—
77	C₄	—	16	2	no	—
78	C₄	—	89	1	no	—
79	C₄	—	1424	2	no	—
80	C₄	D₁₆×D₈₉	1	1	yes	characteristic
81	C₂	—	89	2	no	—
82	C₂	D₃₂×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃₂×D₈₉
commutator, cosocle	C₃₂×C₈₉	C₂³
Frattini	C₃₂	C₂²×D₈₉
Fitting	C₈₉×Q₁₂₈	C₂
socle	C₂×C₈₉	C₂×D₃₂
prime radical	C₂×D₈₉	D₃₂
hypercenter	Q₁₂₈	D₈₉
hypocenter	C₈₉	C₂×Q₁₂₈
LCS	G ▷ C₃₂×C₈₉ ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
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. Dic₂₈₄₈	C₂	semidirect
3. #26018469	C₂	semidirect
5. C₈₉×Q₁₂₈	C₂	semidirect
41. D₈₉	Q₁₂₈	direct (N × H)
45. Q₁₂₈	D₈₉	direct (N × H)
47. C₈₉	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×D₈₉	2
Dic₂₈₄₈	2
#26018469	2
C₆₄×D₈₉	2
C₈₉×Q₁₂₈	2
C₂×Q₁₂₈	89

Subgroups — Q128×D89 #36475476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₁₂₈×D₈₉ #36475476