Subgroups — D₁₁×D₄₃⋊C₇ #27210366

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	1	yes	maximal, characteristic, complemented
2	D₁₁×C₄₃⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×D₄₃⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×C₄₃⋊C₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₁×D₄₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂×D₄₃⋊C₇	—	11	1	no	maximal, Hall
7	D₄₇₃	C₂×C₇	1	1	yes	characteristic, complemented
8	C₁₁×D₄₃	C₂×C₇	1	1	yes	characteristic, complemented
9	D₁₁×C₄₃	C₂×C₇	1	1	yes	characteristic, complemented
10	C₂×C₄₃⋊C₇	—	11	1	no	—
11	D₄₃⋊C₇	—	11	1	no	—
12	D₄₃⋊C₇	D₁₁	1	1	yes	characteristic, direct product factor
13	C₁₁×C₄₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇×D₁₁	—	43	1	no	maximal, Hall
15	C₄₃⋊C₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
16	C₂×D₄₃	—	11	1	no	Hall
17	C₂×C₇×C₁₁	—	43	1	no	—
18	C₇×D₁₁	—	43	1	no	—
19	C₇×D₁₁	—	43	1	no	—
20	C₂×C₄₃	—	11	1	no	—
21	D₄₃	—	11	1	no	—
22	D₄₃	C₇×D₁₁	1	1	yes	characteristic, complemented
23	C₇×C₁₁	—	43	1	no	Hall
24	C₂×D₁₁	—	43	1	no	Hall
25	C₄₃	C₂×C₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
26	C₂²×C₇	—	473	1	no	Hall
27	C₂×C₁₁	—	43	1	no	—
28	D₁₁	—	43	1	no	—
29	D₁₁	D₄₃⋊C₇	1	1	yes	characteristic, direct product factor
30	C₂×C₇	—	43	1	no	—
31	C₂×C₇	—	473	1	no	—
32	C₂×C₇	—	473	1	no	—
33	C₁₁	C₂×D₄₃⋊C₇	1	1	yes	characteristic, complemented, Sylow
34	C₇	—	43	1	no	Sylow
35	C₂²	—	473	1	no	Sylow
36	C₂	—	11	1	no	—
37	C₂	—	43	1	no	—
38	C₂	—	473	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₁₁⋊(D₄₃⋊C₇)	C₂	semidirect
2. D₁₁×C₄₃⋊C₇	C₂	semidirect
3. C₁₁×D₄₃⋊C₇	C₂	semidirect
4. C₁₁×C₄₃⋊C₇	C₂²	semidirect
5. D₁₁×D₄₃	C₇	semidirect
7. D₄₇₃	C₂×C₇	semidirect
8. C₁₁×D₄₃	C₂×C₇	semidirect
9. D₁₁×C₄₃	C₂×C₇	semidirect
12. D₄₃⋊C₇	D₁₁	direct (N × H)
13. C₁₁×C₄₃	C₂²×C₇	semidirect
15. C₄₃⋊C₇	C₂×D₁₁	semidirect
22. D₄₃	C₇×D₁₁	semidirect
25. C₄₃	C₂×C₇×D₁₁	semidirect
29. D₁₁	D₄₃⋊C₇	direct (N × H)
33. C₁₁	C₂×D₄₃⋊C₇	semidirect

Subgroups — D11×D43⋊C7 #27210366

Conjugacy classes of subgroups

Complements

Subgroups — D₁₁×D₄₃⋊C₇ #27210366