Subgroups — C₂×C₇×C₃⋊D₃×C₂₃ #19154014

Order 5796.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊D₃×C₂₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₇×C₂₃	—	3	4	no	maximal
4	C₃²×C₇×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×C₂₃	D₃	1	4	yes	complemented
6	D₃×C₇×C₂₃	—	3	8	no	—
7	C₂×C₃⋊D₃×C₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₇×C₂₃	—	9	1	no	Hall
9	C₃×C₇×C₂₃	C₂×D₃	1	4	yes	complemented
10	C₂×C₃²×C₂₃	C₂×C₇	1	1	yes	characteristic, complemented
11	C₃⋊D₃×C₂₃	C₂×C₇	1	2	yes	direct product factor
12	C₂×C₇×C₂₃	—	9	2	no	—
13	C₂×C₇×C₂₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor
14	C₂×D₃×C₂₃	—	3	4	no	—
15	C₂×C₇×C₃⋊D₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₃²×C₂₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
17	C₇×C₂₃	C₂×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃×C₂₃	D₃×C₇	1	4	yes	complemented
19	D₃×C₂₃	—	3	8	no	—
20	C₂×C₃²×C₇	C₂×C₂₃	1	1	yes	characteristic, complemented
21	C₇×C₃⋊D₃	C₂×C₂₃	1	2	yes	direct product factor
22	C₂²×C₂₃	—	9	1	no	Hall
23	C₂×D₃×C₇	—	3	4	no	—
24	C₃×C₂₃	C₂×D₃×C₇	1	4	yes	complemented
25	C₃²×C₇	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₂₃	—	9	2	no	—
27	C₂×C₂₃	C₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor
28	C₂×C₃×C₇	D₃×C₂₃	1	4	yes	complemented
29	D₃×C₇	—	3	8	no	—
30	C₂×C₃⋊D₃	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
31	C₂²×C₇	—	9	1	no	Hall
32	C₂₃	C₂×C₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₃×C₇	C₂×D₃×C₂₃	1	4	yes	complemented
34	C₂×C₃²	C₂×C₇×C₂₃	1	1	yes	characteristic, complemented
35	C₃⋊D₃	C₂×C₇×C₂₃	1	2	yes	direct product factor
36	C₂×C₇	—	9	2	no	—
37	C₂×C₇	C₃⋊D₃×C₂₃	1	1	yes	characteristic, direct product factor
38	C₂×D₃	—	3	4	no	—
39	C₃²	C₂²×C₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
40	C₇	C₂×C₃⋊D₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	D₃×C₇×C₂₃	1	4	yes	complemented
42	D₃	—	3	8	no	—
43	C₂²	—	9	1	no	Sylow
44	C₃	C₂×D₃×C₇×C₂₃	1	4	yes	complemented
45	C₂	—	9	2	no	—
46	C₂	C₇×C₃⋊D₃×C₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇×C₂₃	C₃⋊D₃
commutator, hypocenter	C₃²	C₂²×C₇×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₂₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₇×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₃⋊D₃×C₂₃	C₂	direct (N × H)
2. C₂×C₃²×C₇×C₂₃	C₂	semidirect
4. C₃²×C₇×C₂₃	C₂²	semidirect
5. C₂×C₃×C₇×C₂₃	D₃	semidirect
7. C₂×C₃⋊D₃×C₂₃	C₇	direct (N × H)
9. C₃×C₇×C₂₃	C₂×D₃	semidirect
10. C₂×C₃²×C₂₃	C₂×C₇	semidirect
11. C₃⋊D₃×C₂₃	C₂×C₇	direct (N × H)
13. C₂×C₇×C₂₃	C₃⋊D₃	direct (N × H)
15. C₂×C₇×C₃⋊D₃	C₂₃	direct (N × H)
16. C₃²×C₂₃	C₂²×C₇	semidirect
17. C₇×C₂₃	C₂×C₃⋊D₃	direct (N × H)
18. C₂×C₃×C₂₃	D₃×C₇	semidirect
20. C₂×C₃²×C₇	C₂×C₂₃	semidirect
21. C₇×C₃⋊D₃	C₂×C₂₃	direct (N × H)
24. C₃×C₂₃	C₂×D₃×C₇	semidirect
25. C₃²×C₇	C₂²×C₂₃	semidirect
27. C₂×C₂₃	C₇×C₃⋊D₃	direct (N × H)
28. C₂×C₃×C₇	D₃×C₂₃	semidirect
30. C₂×C₃⋊D₃	C₇×C₂₃	direct (N × H)
32. C₂₃	C₂×C₇×C₃⋊D₃	direct (N × H)
33. C₃×C₇	C₂×D₃×C₂₃	semidirect
34. C₂×C₃²	C₂×C₇×C₂₃	semidirect
35. C₃⋊D₃	C₂×C₇×C₂₃	direct (N × H)
37. C₂×C₇	C₃⋊D₃×C₂₃	direct (N × H)
39. C₃²	C₂²×C₇×C₂₃	semidirect
40. C₇	C₂×C₃⋊D₃×C₂₃	direct (N × H)
41. C₂×C₃	D₃×C₇×C₂₃	semidirect
44. C₃	C₂×D₃×C₇×C₂₃	semidirect
46. C₂	C₇×C₃⋊D₃×C₂₃	direct (N × H)

Subgroups — C2×C7×C3⋊D3×C23 #19154014

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₇×C₃⋊D₃×C₂₃ #19154014