Subgroups — C₂⁶×C₃⋊D₃ #11919299

Order 1152.

175272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×C₃²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁵×C₃⋊D₃	C₂	1	126	yes	maximal, direct product factor
3	C₂⁶×D₃	—	3	4	no	maximal
4	C₂⁵×C₃²	C₂²	1	63	yes	complemented
5	C₂⁴×C₃⋊D₃	C₂²	1	2604	yes	direct product factor
6	C₂⁶×C₃	D₃	1	4	yes	complemented
7	C₂⁵×D₃	—	3	504	no	—
8	C₂⁴×C₃²	C₂³	1	651	yes	complemented
9	C₂³×C₃⋊D₃	C₂³	1	11160	yes	direct product factor
10	C₂⁷	—	9	1	no	Sylow
11	C₂⁵×C₃	C₂×D₃	1	252	yes	complemented
12	C₂⁴×D₃	—	3	10416	no	—
13	C₂³×C₃²	C₂⁴	1	1395	yes	complemented
14	C₂²×C₃⋊D₃	C₂⁴	1	10416	yes	direct product factor
15	C₂⁶	—	9	126	no	—
16	C₂⁶	C₃⋊D₃	1	1	yes	characteristic, direct product factor
17	C₂⁴×C₃	C₂²×D₃	1	2604	yes	complemented
18	C₂³×D₃	—	3	44640	no	—
19	C₂²×C₃²	C₂⁵	1	651	yes	complemented
20	C₂×C₃⋊D₃	C₂⁵	1	2016	yes	direct product factor
21	C₂⁵	—	9	2604	no	—
22	C₂⁵	C₂×C₃⋊D₃	1	63	yes	direct product factor
23	C₂³×C₃	C₂³×D₃	1	5580	yes	complemented
24	C₂²×D₃	—	3	41664	no	—
25	C₂×C₃²	C₂⁶	1	63	yes	complemented
26	C₃⋊D₃	C₂⁶	1	64	yes	direct product factor
27	C₂⁴	—	9	11160	no	—
28	C₂⁴	C₂²×C₃⋊D₃	1	651	yes	direct product factor
29	C₂²×C₃	C₂⁴×D₃	1	2604	yes	complemented
30	C₂×D₃	—	3	8064	no	—
31	C₃²	C₂⁷	1	1	yes	characteristic, complemented, Sylow
32	C₂³	—	9	10416	no	—
33	C₂³	C₂³×C₃⋊D₃	1	1395	yes	direct product factor
34	C₂×C₃	C₂⁵×D₃	1	252	yes	complemented
35	D₃	—	3	256	no	—
36	C₂²	—	9	2016	no	—
37	C₂²	C₂⁴×C₃⋊D₃	1	651	yes	direct product factor
38	C₃	C₂⁶×D₃	1	4	yes	complemented
39	C₂	—	9	64	no	—
40	C₂	C₂⁵×C₃⋊D₃	1	63	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁶	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂⁷
Frattini	C₁	G
Fitting, socle	C₂⁶×C₃²	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂⁶

Complements

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

N	H ≅ G/N	type
1. C₂⁶×C₃²	C₂	semidirect
2. C₂⁵×C₃⋊D₃	C₂	direct (N × H)
4. C₂⁵×C₃²	C₂²	semidirect
5. C₂⁴×C₃⋊D₃	C₂²	direct (N × H)
6. C₂⁶×C₃	D₃	semidirect
8. C₂⁴×C₃²	C₂³	semidirect
9. C₂³×C₃⋊D₃	C₂³	direct (N × H)
11. C₂⁵×C₃	C₂×D₃	semidirect
13. C₂³×C₃²	C₂⁴	semidirect
14. C₂²×C₃⋊D₃	C₂⁴	direct (N × H)
16. C₂⁶	C₃⋊D₃	direct (N × H)
17. C₂⁴×C₃	C₂²×D₃	semidirect
19. C₂²×C₃²	C₂⁵	semidirect
20. C₂×C₃⋊D₃	C₂⁵	direct (N × H)
22. C₂⁵	C₂×C₃⋊D₃	direct (N × H)
23. C₂³×C₃	C₂³×D₃	semidirect
25. C₂×C₃²	C₂⁶	semidirect
26. C₃⋊D₃	C₂⁶	direct (N × H)
28. C₂⁴	C₂²×C₃⋊D₃	direct (N × H)
29. C₂²×C₃	C₂⁴×D₃	semidirect
31. C₃²	C₂⁷	semidirect
33. C₂³	C₂³×C₃⋊D₃	direct (N × H)
34. C₂×C₃	C₂⁵×D₃	semidirect
37. C₂²	C₂⁴×C₃⋊D₃	direct (N × H)
38. C₃	C₂⁶×D₃	semidirect
40. C₂	C₂⁵×C₃⋊D₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁶×C₃²	2
C₂⁵×C₃⋊D₃	2
C₂⁶×D₃	3

Subgroups — C26×C3⋊D3 #11919299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×C₃⋊D₃ #11919299