Subgroups — C₂×C₃×C₁₃×C₁₁⋊D₁₁ #34038482

Order 18876.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₁₁⋊D₁₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₁²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×C₁₁⋊D₁₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₁²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃×C₁₁⋊D₁₁	C₂×C₃	1	2	yes	direct product factor
6	C₂×C₁₁²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₃×C₁₃×D₁₁	—	11	12	no	maximal
8	C₁₁²×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₁₁⋊D₁₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₁₁×C₁₃	D₁₁	1	12	yes	complemented
11	C₃×C₁₃×D₁₁	—	11	24	no	—
12	C₂×C₃×C₁₁²	C₂×C₁₃	1	1	yes	characteristic, complemented
13	C₃×C₁₁⋊D₁₁	C₂×C₁₃	1	2	yes	direct product factor
14	C₂×C₁₃×D₁₁	—	11	12	no	—
15	C₂×C₁₁⋊D₁₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₁×C₁₃	C₂×D₁₁	1	12	yes	complemented
17	C₃×C₁₁²	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₁×C₁₃	C₃×D₁₁	1	12	yes	complemented
19	C₁₃×D₁₁	—	11	24	no	—
20	C₂×C₁₁²	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
21	C₁₁⋊D₁₁	C₂×C₃×C₁₃	1	2	yes	direct product factor
22	C₂²×C₃×C₁₃	—	121	1	no	Hall
23	C₁₁×C₁₃	C₂×C₃×D₁₁	1	12	yes	complemented
24	C₂×C₃×D₁₁	—	11	12	no	—
25	C₁₁²	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃×C₁₃	—	121	2	no	—
27	C₂×C₃×C₁₃	C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor
28	C₂×C₃×C₁₁	C₁₃×D₁₁	1	12	yes	complemented
29	C₃×D₁₁	—	11	24	no	—
30	C₂²×C₁₃	—	121	1	no	Hall
31	C₂×D₁₁	—	11	12	no	—
32	C₃×C₁₃	C₂×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor, Hall
33	C₃×C₁₁	C₂×C₁₃×D₁₁	1	12	yes	complemented
34	C₂×C₁₃	—	121	2	no	—
35	C₂×C₁₃	C₃×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor
36	C₂×C₁₁	C₃×C₁₃×D₁₁	1	12	yes	complemented
37	D₁₁	—	11	24	no	—
38	C₁₃	C₂×C₃×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²×C₃	—	121	1	no	Hall
40	C₁₁	C₂×C₃×C₁₃×D₁₁	1	12	yes	complemented
41	C₂×C₃	—	121	2	no	—
42	C₂×C₃	C₁₃×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor
43	C₂²	—	121	1	no	Sylow
44	C₃	C₂×C₁₃×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	121	2	no	—
46	C₂	C₃×C₁₃×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	C₁₁⋊D₁₁
commutator, cosocle, hypocenter	C₁₁²	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₁²×C₁₃	C₂
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₂×C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×C₁₁⋊D₁₁	C₂	direct (N × H)
2. C₂×C₃×C₁₁²×C₁₃	C₂	semidirect
3. C₂×C₁₃×C₁₁⋊D₁₁	C₃	direct (N × H)
4. C₃×C₁₁²×C₁₃	C₂²	semidirect
5. C₁₃×C₁₁⋊D₁₁	C₂×C₃	direct (N × H)
6. C₂×C₁₁²×C₁₃	C₂×C₃	semidirect
8. C₁₁²×C₁₃	C₂²×C₃	semidirect
9. C₂×C₃×C₁₁⋊D₁₁	C₁₃	direct (N × H)
10. C₂×C₃×C₁₁×C₁₃	D₁₁	semidirect
12. C₂×C₃×C₁₁²	C₂×C₁₃	semidirect
13. C₃×C₁₁⋊D₁₁	C₂×C₁₃	direct (N × H)
15. C₂×C₁₁⋊D₁₁	C₃×C₁₃	direct (N × H)
16. C₃×C₁₁×C₁₃	C₂×D₁₁	semidirect
17. C₃×C₁₁²	C₂²×C₁₃	semidirect
18. C₂×C₁₁×C₁₃	C₃×D₁₁	semidirect
20. C₂×C₁₁²	C₂×C₃×C₁₃	semidirect
21. C₁₁⋊D₁₁	C₂×C₃×C₁₃	direct (N × H)
23. C₁₁×C₁₃	C₂×C₃×D₁₁	semidirect
25. C₁₁²	C₂²×C₃×C₁₃	semidirect
27. C₂×C₃×C₁₃	C₁₁⋊D₁₁	direct (N × H)
28. C₂×C₃×C₁₁	C₁₃×D₁₁	semidirect
32. C₃×C₁₃	C₂×C₁₁⋊D₁₁	direct (N × H)
33. C₃×C₁₁	C₂×C₁₃×D₁₁	semidirect
35. C₂×C₁₃	C₃×C₁₁⋊D₁₁	direct (N × H)
36. C₂×C₁₁	C₃×C₁₃×D₁₁	semidirect
38. C₁₃	C₂×C₃×C₁₁⋊D₁₁	direct (N × H)
40. C₁₁	C₂×C₃×C₁₃×D₁₁	semidirect
42. C₂×C₃	C₁₃×C₁₁⋊D₁₁	direct (N × H)
44. C₃	C₂×C₁₃×C₁₁⋊D₁₁	direct (N × H)
46. C₂	C₃×C₁₃×C₁₁⋊D₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₃×C₁₁⋊D₁₁	2
C₂×C₃×C₁₁²×C₁₃	2
C₂×C₁₃×C₁₁⋊D₁₁	3
C₂×C₃×C₁₃×D₁₁	11
C₂×C₃×C₁₁⋊D₁₁	13

Subgroups — C2×C3×C13×C11⋊D11 #34038482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₃×C₁₁⋊D₁₁ #34038482