Subgroups — C₂×C₁₁×D₄₃⋊C₇ #27210367

Order 13244.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₄₃⋊C₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁×C₄₃⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₄₃⋊C₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×D₄₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×D₄₃⋊C₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₁₁×C₄₃	C₂×C₇	1	1	yes	characteristic, complemented
7	C₁₁×D₄₃	C₂×C₇	1	2	yes	complemented
8	C₂×C₄₃⋊C₇	C₂×C₁₁	1	1	yes	characteristic, complemented
9	D₄₃⋊C₇	C₂×C₁₁	1	2	yes	direct product factor
10	C₁₁×C₄₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
11	C₂²×C₇×C₁₁	—	43	1	no	maximal, Hall
12	C₄₃⋊C₇	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₂×D₄₃	C₇×C₁₁	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇×C₁₁	—	43	2	no	—
15	C₂×C₇×C₁₁	—	43	1	no	—
16	C₂×C₄₃	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented
17	D₄₃	C₂×C₇×C₁₁	1	2	yes	complemented
18	C₇×C₁₁	—	43	1	no	Hall
19	C₂²×C₁₁	—	43	1	no	Hall
20	C₄₃	C₂²×C₇×C₁₁	1	1	yes	characteristic, complemented, Sylow
21	C₂²×C₇	—	43	1	no	Hall
22	C₂×C₁₁	—	43	2	no	—
23	C₂×C₁₁	D₄₃⋊C₇	1	1	yes	characteristic, direct product factor
24	C₂×C₇	—	43	2	no	—
25	C₂×C₇	—	43	1	no	—
26	C₁₁	C₂×D₄₃⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	—	43	1	no	Sylow
28	C₂²	—	43	1	no	Sylow
29	C₂	—	43	2	no	—
30	C₂	C₁₁×D₄₃⋊C₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₄₃⋊C₇
commutator, hypocenter	C₄₃	C₂²×C₇×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₄₃	C₂×C₇
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₄₃⋊C₇	C₂	direct (N × H)
2. C₂×C₁₁×C₄₃⋊C₇	C₂	semidirect
3. C₁₁×C₄₃⋊C₇	C₂²	semidirect
4. C₂×C₁₁×D₄₃	C₇	semidirect
5. C₂×D₄₃⋊C₇	C₁₁	direct (N × H)
6. C₂×C₁₁×C₄₃	C₂×C₇	semidirect
7. C₁₁×D₄₃	C₂×C₇	semidirect
8. C₂×C₄₃⋊C₇	C₂×C₁₁	semidirect
9. D₄₃⋊C₇	C₂×C₁₁	direct (N × H)
10. C₁₁×C₄₃	C₂²×C₇	semidirect
12. C₄₃⋊C₇	C₂²×C₁₁	semidirect
13. C₂×D₄₃	C₇×C₁₁	semidirect
16. C₂×C₄₃	C₂×C₇×C₁₁	semidirect
17. D₄₃	C₂×C₇×C₁₁	semidirect
20. C₄₃	C₂²×C₇×C₁₁	semidirect
23. C₂×C₁₁	D₄₃⋊C₇	direct (N × H)
26. C₁₁	C₂×D₄₃⋊C₇	direct (N × H)
30. C₂	C₁₁×D₄₃⋊C₇	direct (N × H)

Subgroups — C2×C11×D43⋊C7 #27210367

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₁×D₄₃⋊C₇ #27210367