Subgroups — C₄×C₄₃⋊C₆₄ #24984400

Order 11008.

86 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	C₄	1	4	yes	direct product factor
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	C₈	1	2	yes	—
11	C₃₂×C₄₃	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₄₃	C₁₆	1	1	yes	characteristic
13	C₂×C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
14	C₄²×C₄₃	C₁₆	1	1	yes	characteristic
15	C₁₆×C₄₃	C₁₆	1	2	yes	—
16	C₁₆×C₄₃	C₄²	1	1	yes	characteristic
17	C₁₆×C₄₃	C₂×C₈	1	1	yes	characteristic
18	C₂×C₄×C₄₃	C₃₂	1	2	yes	—
19	C₂×C₄×C₄₃	C₂×C₁₆	1	1	yes	characteristic
20	C₈×C₄₃	C₃₂	1	2	yes	—
21	C₈×C₄₃	C₄×C₈	1	1	yes	characteristic
22	C₈×C₄₃	C₂×C₁₆	1	1	yes	characteristic
23	C₄×C₆₄	—	43	1	no	maximal, Sylow
24	C₂²×C₄₃	C₂×C₃₂	1	1	yes	characteristic
25	C₄×C₄₃	C₆₄	1	4	yes	complemented
26	C₄×C₄₃	C₄×C₁₆	1	1	yes	characteristic
27	C₄×C₄₃	C₂×C₃₂	1	1	yes	characteristic
28	C₂×C₆₄	—	43	2	no	—
29	C₄×C₃₂	D₄₃	1	1	yes	characteristic
30	C₂×C₄₃	C₄×C₃₂	1	1	yes	characteristic
31	C₂×C₄₃	C₂×C₆₄	1	2	yes	—
32	C₂×C₃₂	Dic₄₃	1	1	yes	characteristic
33	C₂×C₃₂	C₂×D₄₃	1	1	yes	characteristic
34	C₄×C₁₆	Dic₄₃	1	1	yes	characteristic
35	C₆₄	—	43	4	no	—
36	C₄₃	C₄×C₆₄	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₁₆	C₄₃⋊C₈	1	1	yes	characteristic
38	C₂×C₁₆	C₂×Dic₄₃	1	1	yes	characteristic
39	C₄×C₈	C₄₃⋊C₈	1	1	yes	characteristic
40	C₃₂	C₄₃⋊C₈	1	2	yes	—
41	C₃₂	C₄×D₄₃	1	2	yes	—
42	C₂×C₈	C₄₃⋊C₁₆	1	1	yes	characteristic
43	C₂×C₈	C₂×C₄₃⋊C₈	1	1	yes	characteristic
44	C₄²	C₄₃⋊C₁₆	1	1	yes	characteristic
45	C₁₆	C₄₃⋊C₁₆	1	2	yes	—
46	C₁₆	C₂×C₄₃⋊C₈	1	1	yes	characteristic
47	C₁₆	C₄×Dic₄₃	1	1	yes	characteristic
48	C₂×C₄	C₄₃⋊C₃₂	1	2	yes	—
49	C₂×C₄	C₂×C₄₃⋊C₁₆	1	1	yes	characteristic
50	C₈	C₄₃⋊C₃₂	1	2	yes	—
51	C₈	C₄×C₄₃⋊C₈	1	1	yes	characteristic
52	C₈	C₂×C₄₃⋊C₁₆	1	1	yes	characteristic
53	C₂²	C₂×C₄₃⋊C₃₂	1	1	yes	characteristic
54	C₄	C₄₃⋊C₆₄	1	4	yes	direct product factor
55	C₄	C₄×C₄₃⋊C₁₆	1	1	yes	characteristic
56	C₄	C₂×C₄₃⋊C₃₂	1	1	yes	characteristic
57	C₂	C₄×C₄₃⋊C₃₂	1	1	yes	characteristic
58	C₂	C₂×C₄₃⋊C₆₄	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₄₃⋊C₆₄	C₄	direct (N × H)
25. C₄×C₄₃	C₆₄	semidirect
36. C₄₃	C₄×C₆₄	semidirect
54. C₄	C₄₃⋊C₆₄	direct (N × H)

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 #24984400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄₃⋊C₆₄ #24984400