Subgroups — D₄₃×Q₁₂₈ #25017645

Order 11008.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₆₄×D₄₃	C₂	1	2	yes	maximal
2	Dic₁₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#19132812	C₂	1	2	yes	maximal, complemented
4	C₆₄×D₄₃	C₂	1	1	yes	maximal, characteristic
5	C₄₃×Q₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₃₂×D₄₃	—	2	2	no	—
7	Dic₆₈₈	C₂²	1	2	yes	—
8	#14582739	—	2	2	no	—
9	C₃₂×D₄₃	C₂²	1	1	yes	characteristic
10	C₄₃⋊C₆₄	C₂²	1	1	yes	characteristic
11	C₄₃×Q₆₄	C₂²	1	2	yes	—
12	C₄₃×C₆₄	C₂²	1	1	yes	characteristic
13	Q₁₆×D₄₃	—	4	2	no	—
14	Dic₃₄₄	—	2	2	no	—
15	#13063271	—	4	2	no	—
16	C₁₆×D₄₃	D₄	1	1	yes	characteristic
17	C₄₃⋊C₃₂	D₄	1	1	yes	characteristic
18	Q₃₂×C₄₃	—	2	2	no	—
19	C₃₂×C₄₃	C₂³	1	1	yes	characteristic
20	Q₈×D₄₃	—	8	2	no	—
21	Q₁₆×C₄₃	—	4	2	no	—
22	#10621885	—	8	2	no	—
23	Dic₁₇₂	—	4	2	no	—
24	C₈×D₄₃	D₈	1	1	yes	characteristic
25	C₁₆×C₄₃	C₂×D₄	1	1	yes	characteristic
26	C₄₃⋊C₁₆	D₈	1	1	yes	characteristic
27	Q₈×C₄₃	—	8	2	no	—
28	C₄×D₄₃	—	16	2	no	—
29	C₄×D₄₃	D₁₆	1	1	yes	characteristic
30	Dic₈₆	—	8	2	no	—
31	Dic₈₆	—	16	2	no	—
32	C₈×C₄₃	C₂×D₈	1	1	yes	characteristic
33	C₄₃⋊C₈	D₁₆	1	1	yes	characteristic
34	C₂×Q₁₂₈	—	43	1	no	maximal, Sylow
35	C₂×D₄₃	D₃₂	1	1	yes	characteristic
36	C₄×C₄₃	—	16	2	no	—
37	C₄×C₄₃	C₂×D₁₆	1	1	yes	characteristic
38	Dic₄₃	—	16	2	no	—
39	Dic₄₃	D₃₂	1	1	yes	characteristic
40	C₂×Q₆₄	—	43	2	no	—
41	Q₁₂₈	—	43	2	no	—
42	Q₁₂₈	—	43	1	no	—
43	Q₁₂₈	D₄₃	1	1	yes	characteristic, direct product factor
44	C₂×C₆₄	—	43	1	no	—
45	C₂×C₄₃	C₂×D₃₂	1	1	yes	characteristic
46	D₄₃	Q₁₂₈	1	2	yes	direct product factor
47	C₂×Q₃₂	—	86	2	no	—
48	Q₆₄	—	43	2	no	—
49	Q₆₄	—	86	2	no	—
50	Q₆₄	C₂×D₄₃	1	2	yes	—
51	C₂×C₃₂	—	43	1	no	—
52	C₆₄	—	43	1	no	—
53	C₆₄	C₂×D₄₃	1	1	yes	characteristic
54	C₄₃	C₂×Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₁₆	—	172	2	no	—
56	Q₃₂	—	2	2	no	—
57	Q₃₂	—	86	2	no	—
58	Q₃₂	—	172	2	no	—
59	C₂×C₁₆	—	43	1	no	—
60	C₃₂	—	43	1	no	—
61	C₃₂	C₂²×D₄₃	1	1	yes	characteristic
62	C₂×Q₈	—	344	2	no	—
63	Q₁₆	—	4	2	no	—
64	Q₁₆	—	344	2	no	—
65	Q₁₆	—	172	2	no	—
66	C₂×C₈	—	43	1	no	—
67	C₁₆	—	43	1	no	—
68	C₁₆	D₄×D₄₃	1	1	yes	characteristic
69	Q₈	—	8	2	no	—
70	Q₈	—	344	2	no	—
71	Q₈	—	688	2	no	—
72	C₂×C₄	—	43	1	no	—
73	C₂×C₄	—	688	2	no	—
74	C₈	—	43	1	no	—
75	C₈	D₈×D₄₃	1	1	yes	characteristic
76	C₂²	—	43	1	no	—
77	C₄	—	16	2	no	—
78	C₄	—	43	1	no	—
79	C₄	—	688	2	no	—
80	C₄	D₁₆×D₄₃	1	1	yes	characteristic
81	C₂	—	43	2	no	—
82	C₂	D₃₂×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃₂×D₄₃
commutator, cosocle	C₃₂×C₄₃	C₂³
Frattini	C₃₂	C₂²×D₄₃
Fitting	C₄₃×Q₁₂₈	C₂
socle	C₂×C₄₃	C₂×D₃₂
prime radical	C₂×D₄₃	D₃₂
hypercenter	Q₁₂₈	D₄₃
hypocenter	C₄₃	C₂×Q₁₂₈
LCS	G ▷ C₃₂×C₄₃ ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
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. Dic₁₃₇₆	C₂	semidirect
3. #19132812	C₂	semidirect
5. C₄₃×Q₁₂₈	C₂	semidirect
43. Q₁₂₈	D₄₃	direct (N × H)
46. D₄₃	Q₁₂₈	direct (N × H)
54. C₄₃	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×D₄₃	2
Dic₁₃₇₆	2
#19132812	2
C₆₄×D₄₃	2
C₄₃×Q₁₂₈	2
C₂×Q₁₂₈	43

Subgroups — D43×Q128 #25017645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×Q₁₂₈ #25017645