Subgroups — C₂×C₅×C₁₁×C₇⋊D₇ #24924798

Order 10780.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₇⋊D₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇²×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×C₇⋊D₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₁×D₇	—	7	8	no	maximal
6	C₂×C₇²×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
7	C₁₁×C₇⋊D₇	C₂×C₅	1	2	yes	direct product factor
8	C₂×C₅×C₇⋊D₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₅×C₇×C₁₁	D₇	1	8	yes	complemented
10	C₅×C₁₁×D₇	—	7	16	no	—
11	C₇²×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×C₇²	C₂×C₁₁	1	1	yes	characteristic, complemented
13	C₅×C₇⋊D₇	C₂×C₁₁	1	2	yes	direct product factor
14	C₅×C₇×C₁₁	C₂×D₇	1	8	yes	complemented
15	C₂×C₁₁×D₇	—	7	8	no	—
16	C₅×C₇²	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
17	C₂²×C₅×C₁₁	—	49	1	no	Hall
18	C₂×C₇⋊D₇	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₇×C₁₁	C₅×D₇	1	8	yes	complemented
20	C₁₁×D₇	—	7	16	no	—
21	C₂×C₅×D₇	—	7	8	no	—
22	C₂×C₅×C₁₁	—	49	2	no	—
23	C₂×C₅×C₁₁	C₇⋊D₇	1	1	yes	characteristic, direct product factor
24	C₂×C₇²	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
25	C₇⋊D₇	C₂×C₅×C₁₁	1	2	yes	direct product factor
26	C₇×C₁₁	C₂×C₅×D₇	1	8	yes	complemented
27	C₂×C₅×C₇	C₁₁×D₇	1	8	yes	complemented
28	C₅×D₇	—	7	16	no	—
29	C₅×C₁₁	C₂×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Hall
30	C₇²	C₂²×C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
31	C₂²×C₁₁	—	49	1	no	Hall
32	C₅×C₇	C₂×C₁₁×D₇	1	8	yes	complemented
33	C₂×D₇	—	7	8	no	—
34	C₂×C₁₁	—	49	2	no	—
35	C₂×C₁₁	C₅×C₇⋊D₇	1	1	yes	characteristic, direct product factor
36	C₂²×C₅	—	49	1	no	Hall
37	C₂×C₇	C₅×C₁₁×D₇	1	8	yes	complemented
38	D₇	—	7	16	no	—
39	C₁₁	C₂×C₅×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₅	—	49	2	no	—
41	C₂×C₅	C₁₁×C₇⋊D₇	1	1	yes	characteristic, direct product factor
42	C₇	C₂×C₅×C₁₁×D₇	1	8	yes	complemented
43	C₅	C₂×C₁₁×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
44	C₂²	—	49	1	no	Sylow
45	C₂	—	49	2	no	—
46	C₂	C₅×C₁₁×C₇⋊D₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₁	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂²×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₁₁	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×C₇⋊D₇	C₂	direct (N × H)
2. C₂×C₅×C₇²×C₁₁	C₂	semidirect
3. C₅×C₇²×C₁₁	C₂²	semidirect
4. C₂×C₁₁×C₇⋊D₇	C₅	direct (N × H)
6. C₂×C₇²×C₁₁	C₂×C₅	semidirect
7. C₁₁×C₇⋊D₇	C₂×C₅	direct (N × H)
8. C₂×C₅×C₇⋊D₇	C₁₁	direct (N × H)
9. C₂×C₅×C₇×C₁₁	D₇	semidirect
11. C₇²×C₁₁	C₂²×C₅	semidirect
12. C₂×C₅×C₇²	C₂×C₁₁	semidirect
13. C₅×C₇⋊D₇	C₂×C₁₁	direct (N × H)
14. C₅×C₇×C₁₁	C₂×D₇	semidirect
16. C₅×C₇²	C₂²×C₁₁	semidirect
18. C₂×C₇⋊D₇	C₅×C₁₁	direct (N × H)
19. C₂×C₇×C₁₁	C₅×D₇	semidirect
23. C₂×C₅×C₁₁	C₇⋊D₇	direct (N × H)
24. C₂×C₇²	C₂×C₅×C₁₁	semidirect
25. C₇⋊D₇	C₂×C₅×C₁₁	direct (N × H)
26. C₇×C₁₁	C₂×C₅×D₇	semidirect
27. C₂×C₅×C₇	C₁₁×D₇	semidirect
29. C₅×C₁₁	C₂×C₇⋊D₇	direct (N × H)
30. C₇²	C₂²×C₅×C₁₁	semidirect
32. C₅×C₇	C₂×C₁₁×D₇	semidirect
35. C₂×C₁₁	C₅×C₇⋊D₇	direct (N × H)
37. C₂×C₇	C₅×C₁₁×D₇	semidirect
39. C₁₁	C₂×C₅×C₇⋊D₇	direct (N × H)
41. C₂×C₅	C₁₁×C₇⋊D₇	direct (N × H)
42. C₇	C₂×C₅×C₁₁×D₇	semidirect
43. C₅	C₂×C₁₁×C₇⋊D₇	direct (N × H)
46. C₂	C₅×C₁₁×C₇⋊D₇	direct (N × H)

Subgroups — C2×C5×C11×C7⋊D7 #24924798

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×C₁₁×C₇⋊D₇ #24924798