Subgroups — C₄⋊(C₄₃⋊C₆₄) #24984493

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	2	yes	maximal
2	C₄×C₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄₃⋊C₆₄	—	2	2	no	—
4	C₂×C₃₂×C₄₃	C₄	1	1	yes	characteristic
5	C₂×C₃₂×C₄₃	C₂²	1	1	yes	characteristic
6	C₄×C₁₆×C₄₃	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₄₃	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈×C₄₃	C₈	1	1	yes	characteristic
10	C₃₂×C₄₃	—	2	1	no	—
11	C₃₂×C₄₃	D₄	1	1	yes	characteristic
12	C₃₂×C₄₃	Q₈	1	1	yes	characteristic
13	C₂×C₈×C₄₃	C₁₆	1	1	yes	characteristic
14	C₂×C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₄₃	C₁₆	1	1	yes	characteristic
16	C₁₆×C₄₃	—	2	1	no	—
17	C₁₆×C₄₃	C₄⋊C₄	1	1	yes	characteristic
18	C₁₆×C₄₃	M₁₆	1	1	yes	characteristic
19	C₂×C₄×C₄₃	C₃₂	1	1	yes	characteristic
20	C₂×C₄×C₄₃	C₃₂	1	1	yes	characteristic
21	C₂×C₄×C₄₃	C₂×C₁₆	1	1	yes	characteristic
22	C₈×C₄₃	—	2	1	no	—
23	C₈×C₄₃	C₄⋊C₈	1	1	yes	characteristic
24	C₈×C₄₃	M₃₂	1	1	yes	characteristic
25	C₄⋊C₆₄	—	43	1	no	maximal, Sylow
26	C₂²×C₄₃	C₂×C₃₂	1	1	yes	characteristic
27	C₄×C₄₃	—	2	1	no	—
28	C₄×C₄₃	C₆₄	1	2	yes	complemented
29	C₄×C₄₃	C₄⋊C₁₆	1	1	yes	characteristic
30	C₄×C₄₃	M₆₄	1	1	yes	characteristic
31	C₂×C₆₄	—	43	2	no	—
32	C₄×C₃₂	D₄₃	1	1	yes	characteristic
33	C₂×C₄₃	C₄⋊C₃₂	1	1	yes	characteristic
34	C₂×C₄₃	C₂×C₆₄	1	1	yes	characteristic
35	C₂×C₄₃	M₁₂₈	1	1	yes	characteristic
36	C₂×C₃₂	Dic₄₃	1	1	yes	characteristic
37	C₂×C₃₂	C₂×D₄₃	1	1	yes	characteristic
38	C₄×C₁₆	Dic₄₃	1	1	yes	characteristic
39	C₆₄	—	86	2	no	—
40	C₄₃	C₄⋊C₆₄	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₁₆	C₄₃⋊C₈	1	1	yes	characteristic
42	C₂×C₁₆	C₂×Dic₄₃	1	1	yes	characteristic
43	C₄×C₈	C₄₃⋊C₈	1	1	yes	characteristic
44	C₃₂	—	2	1	no	—
45	C₃₂	Dic₈₆	1	1	yes	characteristic
46	C₃₂	D₁₇₂	1	1	yes	characteristic
47	C₂×C₈	C₄₃⋊C₁₆	1	1	yes	characteristic
48	C₂×C₈	C₂×C₄₃⋊C₈	1	1	yes	characteristic
49	C₄²	C₄₃⋊C₁₆	1	1	yes	characteristic
50	C₁₆	—	2	1	no	—
51	C₁₆	#10621877	1	1	yes	characteristic
52	C₁₆	C₄⋊Dic₄₃	1	1	yes	characteristic
53	C₂×C₄	C₄₃⋊C₃₂	1	1	yes	characteristic
54	C₂×C₄	C₄₃⋊C₃₂	1	1	yes	characteristic
55	C₂×C₄	C₂×C₄₃⋊C₁₆	1	1	yes	characteristic
56	C₈	—	2	1	no	—
57	C₈	C₄⋊(C₄₃⋊C₈)	1	1	yes	characteristic
58	C₈	#13063265	1	1	yes	characteristic
59	C₂²	C₂×C₄₃⋊C₃₂	1	1	yes	characteristic
60	C₄	—	2	1	no	—
61	C₄	C₄₃⋊C₆₄	1	2	yes	complemented
62	C₄	C₄⋊(C₄₃⋊C₁₆)	1	1	yes	characteristic
63	C₄	#14582733	1	1	yes	characteristic
64	C₂	C₄⋊(C₄₃⋊C₃₂)	1	1	yes	characteristic
65	C₂	C₂×C₄₃⋊C₆₄	1	1	yes	characteristic
66	C₂	#19132806	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
28. C₄×C₄₃	C₆₄	semidirect
40. C₄₃	C₄⋊C₆₄	semidirect
61. C₄	C₄₃⋊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
C₄×C₃₂×C₄₃	2
C₄⋊C₆₄	43

Subgroups — C4⋊(C43⋊C64) #24984493

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊(C₄₃⋊C₆₄) #24984493