Subgroups — C₂⁶×Dic₄₃ #26010472

Order 11008.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×Dic₄₃	C₂	1	126	yes	maximal, direct product factor
2	C₂⁷×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂⁴×Dic₄₃	C₂²	1	2604	yes	direct product factor
4	C₂⁶×C₄₃	C₄	1	64	yes	complemented
5	C₂⁶×C₄₃	C₂²	1	63	yes	—
6	C₂³×Dic₄₃	C₂³	1	11160	yes	direct product factor
7	C₂⁵×C₄₃	C₂×C₄	1	2016	yes	complemented
8	C₂⁵×C₄₃	C₂³	1	651	yes	—
9	C₂⁴×C₄₃	C₂²×C₄	1	10416	yes	complemented
10	C₂⁴×C₄₃	C₂⁴	1	1395	yes	—
11	C₂²×Dic₄₃	C₂⁴	1	10416	yes	direct product factor
12	C₂³×C₄₃	C₂³×C₄	1	11160	yes	complemented
13	C₂³×C₄₃	C₂⁵	1	651	yes	—
14	C₂×Dic₄₃	C₂⁵	1	2016	yes	direct product factor
15	C₂⁶×C₄	—	43	1	no	maximal, Sylow
16	C₂²×C₄₃	C₂⁴×C₄	1	2604	yes	complemented
17	C₂²×C₄₃	C₂⁶	1	63	yes	—
18	Dic₄₃	C₂⁶	1	64	yes	direct product factor
19	C₂⁷	D₄₃	1	1	yes	characteristic
20	C₂⁵×C₄	—	43	126	no	—
21	C₂×C₄₃	C₂⁵×C₄	1	126	yes	complemented
22	C₂×C₄₃	C₂⁷	1	1	yes	characteristic
23	C₂⁶	Dic₄₃	1	64	yes	direct product factor
24	C₂⁶	C₂×D₄₃	1	63	yes	—
25	C₂⁴×C₄	—	43	2604	no	—
26	C₄₃	C₂⁶×C₄	1	1	yes	characteristic, complemented, Sylow
27	C₂⁵	C₂×Dic₄₃	1	2016	yes	direct product factor
28	C₂⁵	C₂²×D₄₃	1	651	yes	—
29	C₂³×C₄	—	43	11160	no	—
30	C₂⁴	C₂²×Dic₄₃	1	10416	yes	direct product factor
31	C₂⁴	C₂³×D₄₃	1	1395	yes	—
32	C₂²×C₄	—	43	10416	no	—
33	C₂³	C₂³×Dic₄₃	1	11160	yes	direct product factor
34	C₂³	C₂⁴×D₄₃	1	651	yes	—
35	C₂×C₄	—	43	2016	no	—
36	C₂²	C₂⁴×Dic₄₃	1	2604	yes	direct product factor
37	C₂²	C₂⁵×D₄₃	1	63	yes	—
38	C₄	—	43	64	no	—
39	C₂	C₂⁵×Dic₄₃	1	126	yes	direct product factor
40	C₂	C₂⁶×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁷	D₄₃
commutator, hypocenter	C₄₃	C₂⁶×C₄
Frattini	C₂	C₂⁶×D₄₃
Fitting, socle, prime radical	C₂⁷×C₄₃	C₂
cosocle	C₂×C₄₃	C₂⁷
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂⁷

Complements

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

N	H ≅ G/N	type
1. C₂⁵×Dic₄₃	C₂	direct (N × H)
3. C₂⁴×Dic₄₃	C₂²	direct (N × H)
4. C₂⁶×C₄₃	C₄	semidirect
6. C₂³×Dic₄₃	C₂³	direct (N × H)
7. C₂⁵×C₄₃	C₂×C₄	semidirect
9. C₂⁴×C₄₃	C₂²×C₄	semidirect
11. C₂²×Dic₄₃	C₂⁴	direct (N × H)
12. C₂³×C₄₃	C₂³×C₄	semidirect
14. C₂×Dic₄₃	C₂⁵	direct (N × H)
16. C₂²×C₄₃	C₂⁴×C₄	semidirect
18. Dic₄₃	C₂⁶	direct (N × H)
21. C₂×C₄₃	C₂⁵×C₄	semidirect
23. C₂⁶	Dic₄₃	direct (N × H)
26. C₄₃	C₂⁶×C₄	semidirect
27. C₂⁵	C₂×Dic₄₃	direct (N × H)
30. C₂⁴	C₂²×Dic₄₃	direct (N × H)
33. C₂³	C₂³×Dic₄₃	direct (N × H)
36. C₂²	C₂⁴×Dic₄₃	direct (N × H)
39. C₂	C₂⁵×Dic₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×Dic₄₃	2
C₂⁷×C₄₃	2
C₂⁶×C₄	43

Subgroups — C26×Dic43 #26010472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×Dic₄₃ #26010472