Subgroups — C₂×C₄⁴×C₄₃ #72199513

Order 22016.

27012 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄³×C₄₃	C₂	1	15	yes	maximal
2	C₄⁴×C₄₃	C₂	1	16	yes	maximal, direct product factor
3	C₂³×C₄²×C₄₃	C₂²	1	35	yes	—
4	C₂×C₄³×C₄₃	C₄	1	240	yes	direct product factor
5	C₂×C₄³×C₄₃	C₂²	1	120	yes	—
6	C₂⁴×C₄×C₄₃	C₂³	1	15	yes	—
7	C₂²×C₄²×C₄₃	C₂×C₄	1	840	yes	—
8	C₂²×C₄²×C₄₃	C₂³	1	140	yes	—
9	C₄³×C₄₃	C₂×C₄	1	960	yes	direct product factor
10	C₂⁵×C₄₃	C₂⁴	1	1	yes	characteristic
11	C₂³×C₄×C₄₃	C₂²×C₄	1	420	yes	—
12	C₂³×C₄×C₄₃	C₂⁴	1	30	yes	—
13	C₂×C₄²×C₄₃	C₄²	1	2240	yes	direct product factor
14	C₂×C₄²×C₄₃	C₂²×C₄	1	1680	yes	—
15	C₂⁴×C₄₃	C₂³×C₄	1	30	yes	—
16	C₂⁴×C₄₃	C₂⁵	1	1	yes	characteristic
17	C₂²×C₄×C₄₃	C₂×C₄²	1	1680	yes	—
18	C₂²×C₄×C₄₃	C₂³×C₄	1	420	yes	—
19	C₄²×C₄₃	C₂×C₄²	1	2240	yes	direct product factor
20	C₂×C₄⁴	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂³×C₄₃	C₂²×C₄²	1	140	yes	—
22	C₂³×C₄₃	C₂⁴×C₄	1	15	yes	—
23	C₂×C₄×C₄₃	C₄³	1	960	yes	direct product factor
24	C₂×C₄×C₄₃	C₂²×C₄²	1	840	yes	—
25	C₂²×C₄³	C₂×C₄₃	1	15	yes	—
26	C₄⁴	C₂×C₄₃	1	16	yes	direct product factor
27	C₂²×C₄₃	C₂×C₄³	1	120	yes	—
28	C₂²×C₄₃	C₂³×C₄²	1	35	yes	—
29	C₄×C₄₃	C₂×C₄³	1	240	yes	direct product factor
30	C₂³×C₄²	C₂²×C₄₃	1	35	yes	—
31	C₂×C₄³	C₄×C₄₃	1	240	yes	direct product factor
32	C₂×C₄³	C₂²×C₄₃	1	120	yes	—
33	C₂×C₄₃	C₄⁴	1	16	yes	direct product factor
34	C₂×C₄₃	C₂²×C₄³	1	15	yes	—
35	C₂⁴×C₄	C₂³×C₄₃	1	15	yes	—
36	C₂²×C₄²	C₂×C₄×C₄₃	1	840	yes	—
37	C₂²×C₄²	C₂³×C₄₃	1	140	yes	—
38	C₄³	C₂×C₄×C₄₃	1	960	yes	direct product factor
39	C₄₃	C₂×C₄⁴	1	1	yes	characteristic, direct product factor, Sylow
40	C₂⁵	C₂⁴×C₄₃	1	1	yes	characteristic
41	C₂³×C₄	C₂²×C₄×C₄₃	1	420	yes	—
42	C₂³×C₄	C₂⁴×C₄₃	1	30	yes	—
43	C₂×C₄²	C₄²×C₄₃	1	2240	yes	direct product factor
44	C₂×C₄²	C₂²×C₄×C₄₃	1	1680	yes	—
45	C₂⁴	C₂³×C₄×C₄₃	1	30	yes	—
46	C₂⁴	C₂⁵×C₄₃	1	1	yes	characteristic
47	C₂²×C₄	C₂×C₄²×C₄₃	1	1680	yes	—
48	C₂²×C₄	C₂³×C₄×C₄₃	1	420	yes	—
49	C₄²	C₂×C₄²×C₄₃	1	2240	yes	direct product factor
50	C₂³	C₂²×C₄²×C₄₃	1	140	yes	—
51	C₂³	C₂⁴×C₄×C₄₃	1	15	yes	—
52	C₂×C₄	C₄³×C₄₃	1	960	yes	direct product factor
53	C₂×C₄	C₂²×C₄²×C₄₃	1	840	yes	—
54	C₂²	C₂×C₄³×C₄₃	1	120	yes	—
55	C₂²	C₂³×C₄²×C₄₃	1	35	yes	—
56	C₄	C₂×C₄³×C₄₃	1	240	yes	direct product factor
57	C₂	C₄⁴×C₄₃	1	16	yes	direct product factor
58	C₂	C₂²×C₄³×C₄₃	1	15	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂⁴	C₂⁵×C₄₃
socle, prime radical	C₂⁵×C₄₃	C₂⁴
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄⁴×C₄₃	C₂	direct (N × H)
4. C₂×C₄³×C₄₃	C₄	direct (N × H)
9. C₄³×C₄₃	C₂×C₄	direct (N × H)
13. C₂×C₄²×C₄₃	C₄²	direct (N × H)
19. C₄²×C₄₃	C₂×C₄²	direct (N × H)
20. C₂×C₄⁴	C₄₃	direct (N × H)
23. C₂×C₄×C₄₃	C₄³	direct (N × H)
26. C₄⁴	C₂×C₄₃	direct (N × H)
29. C₄×C₄₃	C₂×C₄³	direct (N × H)
31. C₂×C₄³	C₄×C₄₃	direct (N × H)
33. C₂×C₄₃	C₄⁴	direct (N × H)
38. C₄³	C₂×C₄×C₄₃	direct (N × H)
39. C₄₃	C₂×C₄⁴	direct (N × H)
43. C₂×C₄²	C₄²×C₄₃	direct (N × H)
49. C₄²	C₂×C₄²×C₄₃	direct (N × H)
52. C₂×C₄	C₄³×C₄₃	direct (N × H)
56. C₄	C₂×C₄³×C₄₃	direct (N × H)
57. C₂	C₄⁴×C₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄³×C₄₃	2
C₄⁴×C₄₃	2
C₂×C₄⁴	43

Subgroups — C2×C44×C43 #72199513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄⁴×C₄₃ #72199513