Subgroups — C₇×C₁₁×C₁₃×C₃⋊D₃ #31825084

Order 18018.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₇×C₁₁×C₁₃	—	3	4	no	maximal
3	C₃×C₇×C₁₁×C₁₃	D₃	1	4	yes	complemented
4	C₁₁×C₁₃×C₃⋊D₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₁₁×C₁₃	—	9	1	no	Hall
6	C₇×C₁₃×C₃⋊D₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇×C₁₁×C₃⋊D₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃²×C₁₁×C₁₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	C₇×C₁₁×C₁₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
10	D₃×C₁₁×C₁₃	—	3	4	no	—
11	C₃²×C₇×C₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₇×C₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
13	D₃×C₇×C₁₃	—	3	4	no	—
14	D₃×C₇×C₁₁	—	3	4	no	—
15	C₃×C₁₁×C₁₃	D₃×C₇	1	4	yes	complemented
16	C₂×C₁₁×C₁₃	—	9	1	no	Hall
17	C₃×C₇×C₁₃	D₃×C₁₁	1	4	yes	complemented
18	C₁₃×C₃⋊D₃	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₇×C₁₁	D₃×C₁₃	1	4	yes	complemented
20	C₁₁×C₃⋊D₃	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₇×C₁₃	—	9	1	no	Hall
22	C₂×C₇×C₁₁	—	9	1	no	Hall
23	C₁₁×C₁₃	C₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
24	C₇×C₃⋊D₃	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
25	C₃²×C₁₃	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented, Hall
26	C₃²×C₁₁	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
27	C₇×C₁₃	C₁₁×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
28	D₃×C₁₃	—	3	4	no	—
29	C₇×C₁₁	C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
30	D₃×C₁₁	—	3	4	no	—
31	C₃²×C₇	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Hall
32	D₃×C₇	—	3	4	no	—
33	C₃×C₁₃	D₃×C₇×C₁₁	1	4	yes	complemented
34	C₃×C₁₁	D₃×C₇×C₁₃	1	4	yes	complemented
35	C₂×C₁₃	—	9	1	no	Hall
36	C₂×C₁₁	—	9	1	no	Hall
37	C₃×C₇	D₃×C₁₁×C₁₃	1	4	yes	complemented
38	C₃⋊D₃	C₇×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₇	—	9	1	no	Hall
40	C₁₃	C₇×C₁₁×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
41	C₁₁	C₇×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₃²	C₂×C₇×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
43	C₇	C₁₁×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
44	D₃	—	3	4	no	—
45	C₃	D₃×C₇×C₁₁×C₁₃	1	4	yes	complemented
46	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₁×C₁₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₇×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁×C₁₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₇×C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₁×C₁₃	C₂	semidirect
3. C₃×C₇×C₁₁×C₁₃	D₃	semidirect
4. C₁₁×C₁₃×C₃⋊D₃	C₇	direct (N × H)
6. C₇×C₁₃×C₃⋊D₃	C₁₁	direct (N × H)
7. C₇×C₁₁×C₃⋊D₃	C₁₃	direct (N × H)
8. C₃²×C₁₁×C₁₃	C₂×C₇	semidirect
9. C₇×C₁₁×C₁₃	C₃⋊D₃	direct (N × H)
11. C₃²×C₇×C₁₃	C₂×C₁₁	semidirect
12. C₃²×C₇×C₁₁	C₂×C₁₃	semidirect
15. C₃×C₁₁×C₁₃	D₃×C₇	semidirect
17. C₃×C₇×C₁₃	D₃×C₁₁	semidirect
18. C₁₃×C₃⋊D₃	C₇×C₁₁	direct (N × H)
19. C₃×C₇×C₁₁	D₃×C₁₃	semidirect
20. C₁₁×C₃⋊D₃	C₇×C₁₃	direct (N × H)
23. C₁₁×C₁₃	C₇×C₃⋊D₃	direct (N × H)
24. C₇×C₃⋊D₃	C₁₁×C₁₃	direct (N × H)
25. C₃²×C₁₃	C₂×C₇×C₁₁	semidirect
26. C₃²×C₁₁	C₂×C₇×C₁₃	semidirect
27. C₇×C₁₃	C₁₁×C₃⋊D₃	direct (N × H)
29. C₇×C₁₁	C₁₃×C₃⋊D₃	direct (N × H)
31. C₃²×C₇	C₂×C₁₁×C₁₃	semidirect
33. C₃×C₁₃	D₃×C₇×C₁₁	semidirect
34. C₃×C₁₁	D₃×C₇×C₁₃	semidirect
37. C₃×C₇	D₃×C₁₁×C₁₃	semidirect
38. C₃⋊D₃	C₇×C₁₁×C₁₃	direct (N × H)
40. C₁₃	C₇×C₁₁×C₃⋊D₃	direct (N × H)
41. C₁₁	C₇×C₁₃×C₃⋊D₃	direct (N × H)
42. C₃²	C₂×C₇×C₁₁×C₁₃	semidirect
43. C₇	C₁₁×C₁₃×C₃⋊D₃	direct (N × H)
45. C₃	D₃×C₇×C₁₁×C₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₇×C₁₁×C₁₃	2
D₃×C₇×C₁₁×C₁₃	3
C₁₁×C₁₃×C₃⋊D₃	7
C₇×C₁₃×C₃⋊D₃	11
C₇×C₁₁×C₃⋊D₃	13

Subgroups — C7×C11×C13×C3⋊D3 #31825084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₁×C₁₃×C₃⋊D₃ #31825084