Subgroups — D₃×C₇×C₁₁⋊D₁₁ #23779052

Order 10164.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊(C₁₁⋊D₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₇×C₁₁²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×C₁₁⋊D₁₁	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₇×C₁₁²	—	3	1	no	—
7	C₇×C₁₁⋊D₁₁	—	3	1	no	—
8	C₇×C₁₁⋊D₁₁	D₃	1	1	yes	characteristic, direct product factor
9	D₃×C₁₁⋊D₁₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	D₃×C₇×D₁₁	—	11	12	no	maximal
11	C₇×C₁₁²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₃⋊(C₁₁⋊D₁₁)	C₂×C₇	1	1	yes	characteristic, complemented
13	D₃×C₁₁²	C₂×C₇	1	1	yes	characteristic, complemented
14	C₃×C₁₁⋊D₁₁	C₂×C₇	1	1	yes	characteristic, complemented
15	C₂×C₁₁⋊D₁₁	—	3	1	no	Hall
16	C₇×D₃₃	—	11	12	no	—
17	D₃×C₇×C₁₁	D₁₁	1	12	yes	complemented
18	C₃×C₇×D₁₁	—	11	12	no	—
19	C₃×C₁₁²	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
20	C₂×C₇×D₁₁	—	33	12	no	—
21	C₂×C₁₁²	—	3	1	no	—
22	C₁₁⋊D₁₁	—	3	1	no	—
23	C₁₁⋊D₁₁	D₃×C₇	1	1	yes	characteristic, direct product factor
24	C₃×C₇×C₁₁	C₂×D₁₁	1	12	yes	complemented
25	C₂×C₇×C₁₁	—	3	12	no	—
26	C₇×D₁₁	—	11	12	no	—
27	C₇×D₁₁	—	33	12	no	—
28	D₃×D₁₁	—	11	12	no	—
29	C₁₁²	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃×C₇	—	121	1	no	Hall
31	C₇×C₁₁	D₃×D₁₁	1	12	yes	complemented
32	D₃₃	—	11	12	no	—
33	C₃×D₁₁	—	11	12	no	—
34	D₃×C₁₁	C₇×D₁₁	1	12	yes	complemented
35	C₂×D₁₁	—	33	12	no	—
36	C₂×C₃×C₇	—	121	1	no	—
37	D₃×C₇	—	121	1	no	—
38	D₃×C₇	C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor
39	C₃×C₁₁	C₂×C₇×D₁₁	1	12	yes	complemented
40	C₂²×C₇	—	363	1	no	Hall
41	C₂×C₁₁	—	3	12	no	—
42	D₁₁	—	11	12	no	—
43	D₁₁	—	33	12	no	—
44	C₃×C₇	C₂×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Hall
45	C₂×C₇	—	3	1	no	—
46	C₂×C₇	—	363	1	no	—
47	C₂×C₇	—	121	1	no	—
48	C₂×D₃	—	121	1	no	Hall
49	C₁₁	D₃×C₇×D₁₁	1	12	yes	complemented
50	C₇	D₃×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₃	—	121	1	no	—
52	D₃	—	121	1	no	—
53	D₃	C₇×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor
54	C₂²	—	363	1	no	Sylow
55	C₃	C₂×C₇×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	3	1	no	—
57	C₂	—	363	1	no	—
58	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₃×C₁₁⋊D₁₁
commutator, cosocle, hypocenter	C₃×C₁₁²	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁²	C₂²
LCS	G ▷ C₃×C₁₁²
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₃⋊(C₁₁⋊D₁₁)	C₂	semidirect
2. D₃×C₇×C₁₁²	C₂	semidirect
3. C₃×C₇×C₁₁⋊D₁₁	C₂	semidirect
5. C₃×C₇×C₁₁²	C₂²	semidirect
8. C₇×C₁₁⋊D₁₁	D₃	direct (N × H)
9. D₃×C₁₁⋊D₁₁	C₇	direct (N × H)
11. C₇×C₁₁²	C₂×D₃	semidirect
12. C₃⋊(C₁₁⋊D₁₁)	C₂×C₇	semidirect
13. D₃×C₁₁²	C₂×C₇	semidirect
14. C₃×C₁₁⋊D₁₁	C₂×C₇	semidirect
17. D₃×C₇×C₁₁	D₁₁	semidirect
19. C₃×C₁₁²	C₂²×C₇	semidirect
23. C₁₁⋊D₁₁	D₃×C₇	direct (N × H)
24. C₃×C₇×C₁₁	C₂×D₁₁	semidirect
29. C₁₁²	C₂×D₃×C₇	semidirect
31. C₇×C₁₁	D₃×D₁₁	semidirect
34. D₃×C₁₁	C₇×D₁₁	semidirect
38. D₃×C₇	C₁₁⋊D₁₁	direct (N × H)
39. C₃×C₁₁	C₂×C₇×D₁₁	semidirect
44. C₃×C₇	C₂×C₁₁⋊D₁₁	semidirect
49. C₁₁	D₃×C₇×D₁₁	semidirect
50. C₇	D₃×C₁₁⋊D₁₁	direct (N × H)
53. D₃	C₇×C₁₁⋊D₁₁	direct (N × H)
55. C₃	C₂×C₇×C₁₁⋊D₁₁	semidirect

Subgroups — D3×C7×C11⋊D11 #23779052

Conjugacy classes of subgroups

Complements

Subgroups — D₃×C₇×C₁₁⋊D₁₁ #23779052