Subgroups — Dic₄₃⋊C₆₄ #24984492

Order 11008.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃⋊C₆₄	C₂	1	1	yes	maximal, characteristic
2	C₃₂×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×C₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₃⋊C₃₂	C₄	1	1	yes	characteristic
5	C₁₆×Dic₄₃	C₄	1	1	yes	characteristic
6	C₄₃⋊C₆₄	—	2	1	no	—
7	C₂×C₃₂×C₄₃	C₂²	1	1	yes	characteristic
8	C₄₃×C₆₄	—	2	1	no	—
9	C₂×C₄₃⋊C₁₆	C₈	1	1	yes	characteristic
10	C₈×Dic₄₃	C₈	1	1	yes	characteristic
11	C₄₃⋊C₃₂	—	2	1	no	—
12	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
13	C₃₂×C₄₃	D₄	1	1	yes	characteristic
14	C₃₂×C₄₃	Q₈	1	1	yes	characteristic
15	C₂×C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
16	C₄×Dic₄₃	C₁₆	1	1	yes	characteristic
17	C₂×C₄₃⋊C₈	C₁₆	1	1	yes	characteristic
18	C₁₆×C₄₃	C₄⋊C₄	1	1	yes	characteristic
19	C₁₆×C₄₃	M₁₆	1	1	yes	characteristic
20	C₄₃⋊C₁₆	—	2	1	no	—
21	C₂×C₄×C₄₃	C₂×C₁₆	1	1	yes	characteristic
22	C₂×Dic₄₃	C₃₂	1	1	yes	characteristic
23	C₂×Dic₄₃	C₃₂	1	1	yes	characteristic
24	C₈×C₄₃	C₄⋊C₈	1	1	yes	characteristic
25	C₈×C₄₃	M₃₂	1	1	yes	characteristic
26	C₄₃⋊C₈	—	2	1	no	—
27	C₄⋊C₆₄	—	43	1	no	maximal, Sylow
28	C₂²×C₄₃	C₂×C₃₂	1	1	yes	characteristic
29	C₄×C₄₃	C₄⋊C₁₆	1	1	yes	characteristic
30	C₄×C₄₃	M₆₄	1	1	yes	characteristic
31	Dic₄₃	—	2	1	no	—
32	Dic₄₃	C₆₄	1	2	yes	complemented
33	C₂×C₆₄	—	43	1	no	—
34	C₂×C₆₄	D₄₃	1	1	yes	characteristic
35	C₄×C₃₂	—	43	1	no	—
36	C₂×C₄₃	C₄⋊C₃₂	1	1	yes	characteristic
37	C₂×C₄₃	C₂×C₆₄	1	1	yes	characteristic
38	C₂×C₄₃	M₁₂₈	1	1	yes	characteristic
39	C₂×C₃₂	—	43	1	no	—
40	C₂×C₃₂	C₂×D₄₃	1	1	yes	characteristic
41	C₄×C₁₆	—	43	1	no	—
42	C₆₄	—	2	1	no	—
43	C₆₄	—	86	1	no	—
44	C₄₃	C₄⋊C₆₄	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₁₆	—	43	1	no	—
46	C₂×C₁₆	C₄×D₄₃	1	1	yes	characteristic
47	C₄×C₈	—	43	1	no	—
48	C₃₂	—	86	1	no	—
49	C₃₂	Dic₈₆	1	1	yes	characteristic
50	C₃₂	C₂²⋊D₄₃	1	1	yes	characteristic
51	C₂×C₈	—	43	1	no	—
52	C₂×C₈	C₈×D₄₃	1	1	yes	characteristic
53	C₄²	—	43	1	no	—
54	C₁₆	—	86	1	no	—
55	C₁₆	#10621872	1	1	yes	characteristic
56	C₁₆	Dic₄₃⋊C₄	1	1	yes	characteristic
57	C₂×C₄	—	43	1	no	—
58	C₂×C₄	—	43	1	no	—
59	C₂×C₄	C₁₆×D₄₃	1	1	yes	characteristic
60	C₈	—	86	1	no	—
61	C₈	Dic₄₃⋊C₈	1	1	yes	characteristic
62	C₈	#13063264	1	1	yes	characteristic
63	C₂²	C₃₂×D₄₃	1	1	yes	characteristic
64	C₄	—	43	2	no	—
65	C₄	—	86	1	no	—
66	C₄	Dic₄₃⋊C₁₆	1	1	yes	characteristic
67	C₄	#14582732	1	1	yes	characteristic
68	C₂	Dic₄₃⋊C₃₂	1	1	yes	characteristic
69	C₂	C₆₄×D₄₃	1	1	yes	characteristic
70	C₂	#19132805	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₃₂	C₂×D₄₃
commutator	C₂×C₄₃	C₂×C₆₄
Fitting	C₂×C₄₃×C₆₄	C₂
socle, prime radical	C₂²×C₄₃	C₂×C₃₂
cosocle	C₂×C₃₂×C₄₃	C₂²
hypercenter	C₂×C₆₄	D₄₃
hypocenter	C₄₃	C₄⋊C₆₄
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
32. Dic₄₃	C₆₄	semidirect
44. C₄₃	C₄⋊C₆₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃⋊C₆₄	2
C₃₂×Dic₄₃	2
C₂×C₄₃×C₆₄	2
C₄⋊C₆₄	43

Subgroups — Dic43⋊C64 #24984492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₄₃⋊C₆₄ #24984492