Subgroups — C₂×C₄₉⋊AGL(1,𝔽₁₁) #24924704

Order 10780.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₉×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₉⋊AGL(1,𝔽₁₁)	C₂	1	2	yes	maximal, direct product factor
3	C₄₉×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₅₃₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₇⋊AGL(1,𝔽₁₁)	—	7	1	no	maximal
6	C₂×C₁₁×C₄₉	C₂×C₅	1	1	yes	characteristic, complemented
7	D₅₃₉	C₂×C₅	1	2	yes	complemented
8	C₂×C₅×D₄₉	—	11	1	no	maximal, Hall
9	C₂×C₇×C₁₁⋊C₅	D₇	1	1	yes	characteristic
10	C₇⋊AGL(1,𝔽₁₁)	—	7	2	no	—
11	C₁₁×C₄₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×C₄₉	—	11	1	no	—
13	C₅×D₄₉	—	11	2	no	—
14	C₇×C₁₁⋊C₅	C₂×D₇	1	1	yes	characteristic
15	C₂×D₇₇	—	7	1	no	—
16	C₅×C₄₉	—	11	1	no	Hall
17	C₂×AGL(1,𝔽₁₁)	—	49	1	no	Hall
18	C₂×D₄₉	—	11	1	no	Hall
19	C₂×C₇×C₁₁	C₅×D₇	1	1	yes	characteristic
20	D₇₇	—	7	2	no	—
21	C₂×C₅×D₇	—	77	1	no	—
22	C₂×C₁₁⋊C₅	D₄₉	1	1	yes	characteristic, complemented
23	AGL(1,𝔽₁₁)	—	49	2	no	—
24	C₂×C₄₉	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
25	D₄₉	—	11	2	no	—
26	C₇×C₁₁	C₂×C₅×D₇	1	1	yes	characteristic
27	C₂×C₅×C₇	—	11	1	no	—
28	C₅×D₇	—	77	2	no	—
29	C₁₁⋊C₅	C₂×D₄₉	1	1	yes	characteristic, complemented, Hall
30	C₄₉	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
31	C₂×D₁₁	—	49	1	no	Hall
32	C₅×C₇	—	11	1	no	—
33	C₂×D₇	—	77	1	no	—
34	C₂×C₁₁	C₅×D₄₉	1	1	yes	characteristic, complemented
35	D₁₁	—	49	2	no	—
36	C₂²×C₅	—	539	1	no	Hall
37	C₂×C₇	C₇⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
38	D₇	—	77	2	no	—
39	C₁₁	C₂×C₅×D₄₉	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₅	—	11	1	no	—
41	C₂×C₅	—	539	2	no	—
42	C₇	C₂×C₇⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
43	C₅	—	11	1	no	Sylow
44	C₂²	—	539	1	no	Sylow
45	C₂	—	539	2	no	—
46	C₂	C₄₉⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₄₉⋊AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₁₁×C₄₉	C₂²×C₅
Frattini	C₇	C₂×C₇⋊AGL(1,𝔽₁₁)
Fitting	C₂×C₁₁×C₄₉	C₂×C₅
socle	C₂×C₇×C₁₁	C₅×D₇
LCS	G ▷ C₁₁×C₄₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₉×C₁₁⋊C₅	C₂	semidirect
2. C₄₉⋊AGL(1,𝔽₁₁)	C₂	direct (N × H)
3. C₄₉×C₁₁⋊C₅	C₂²	semidirect
4. C₂×D₅₃₉	C₅	semidirect
6. C₂×C₁₁×C₄₉	C₂×C₅	semidirect
7. D₅₃₉	C₂×C₅	semidirect
11. C₁₁×C₄₉	C₂²×C₅	semidirect
22. C₂×C₁₁⋊C₅	D₄₉	semidirect
24. C₂×C₄₉	AGL(1,𝔽₁₁)	semidirect
29. C₁₁⋊C₅	C₂×D₄₉	semidirect
30. C₄₉	C₂×AGL(1,𝔽₁₁)	semidirect
34. C₂×C₁₁	C₅×D₄₉	semidirect
39. C₁₁	C₂×C₅×D₄₉	semidirect
46. C₂	C₄₉⋊AGL(1,𝔽₁₁)	direct (N × H)

Subgroups — C2×C49⋊AGL(1,𝔽11) #24924704

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₄₉⋊AGL(1,𝔽₁₁) #24924704