Subgroups — C₂×C₂₃×C₃⋊D₂₁ #19154012

Order 5796.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₃⋊D₂₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×D₂₁	—	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	C₂₃×D₂₁	—	3	8	no	—
7	C₂×C₃⋊D₃×C₂₃	—	7	1	no	maximal, Hall
8	C₂×D₇×C₂₃	—	9	1	no	Hall
9	C₃×C₇×C₂₃	C₂×D₃	1	4	yes	complemented
10	C₂×C₃²×C₂₃	D₇	1	1	yes	characteristic, complemented
11	C₃⋊D₃×C₂₃	—	7	2	no	—
12	C₂×C₇×C₂₃	C₃⋊D₃	1	1	yes	characteristic, complemented
13	D₇×C₂₃	—	9	2	no	—
14	C₂×D₃×C₂₃	—	21	4	no	—
15	C₂×C₃⋊D₂₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₃²×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
17	C₇×C₂₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₂₃	D₂₁	1	4	yes	complemented
19	D₃×C₂₃	—	21	8	no	—
20	C₂×C₃²×C₇	C₂×C₂₃	1	1	yes	characteristic, complemented
21	C₃⋊D₂₁	C₂×C₂₃	1	2	yes	direct product factor
22	C₂²×C₂₃	—	63	1	no	Hall
23	C₂×D₂₁	—	3	4	no	—
24	C₃×C₂₃	C₂×D₂₁	1	4	yes	complemented
25	C₃²×C₇	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₂₃	—	63	2	no	—
27	C₂×C₂₃	C₃⋊D₂₁	1	1	yes	characteristic, direct product factor
28	C₂×C₃×C₇	D₃×C₂₃	1	4	yes	complemented
29	D₂₁	—	3	8	no	—
30	C₂×C₃⋊D₃	—	7	1	no	Hall
31	C₂×D₇	—	9	1	no	Hall
32	C₂₃	C₂×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor, Sylow
33	C₃×C₇	C₂×D₃×C₂₃	1	4	yes	complemented
34	C₂×C₃²	D₇×C₂₃	1	1	yes	characteristic, complemented
35	C₃⋊D₃	—	7	2	no	—
36	C₂×C₇	C₃⋊D₃×C₂₃	1	1	yes	characteristic, complemented
37	D₇	—	9	2	no	—
38	C₂×D₃	—	21	4	no	—
39	C₃²	C₂×D₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
40	C₇	C₂×C₃⋊D₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	C₂₃×D₂₁	1	4	yes	complemented
42	D₃	—	21	8	no	—
43	C₂²	—	63	1	no	Sylow
44	C₃	C₂×C₂₃×D₂₁	1	4	yes	complemented
45	C₂	—	63	2	no	—
46	C₂	C₂₃×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₃	C₃⋊D₂₁
commutator, hypocenter	C₃²×C₇	C₂²×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₂₃	C₂
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₂×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂₃×C₃⋊D₂₁	C₂	direct (N × H)
2. C₂×C₃²×C₇×C₂₃	C₂	semidirect
4. C₃²×C₇×C₂₃	C₂²	semidirect
5. C₂×C₃×C₇×C₂₃	D₃	semidirect
9. C₃×C₇×C₂₃	C₂×D₃	semidirect
10. C₂×C₃²×C₂₃	D₇	semidirect
12. C₂×C₇×C₂₃	C₃⋊D₃	semidirect
15. C₂×C₃⋊D₂₁	C₂₃	direct (N × H)
16. C₃²×C₂₃	C₂×D₇	semidirect
17. C₇×C₂₃	C₂×C₃⋊D₃	semidirect
18. C₂×C₃×C₂₃	D₂₁	semidirect
20. C₂×C₃²×C₇	C₂×C₂₃	semidirect
21. C₃⋊D₂₁	C₂×C₂₃	direct (N × H)
24. C₃×C₂₃	C₂×D₂₁	semidirect
25. C₃²×C₇	C₂²×C₂₃	semidirect
27. C₂×C₂₃	C₃⋊D₂₁	direct (N × H)
28. C₂×C₃×C₇	D₃×C₂₃	semidirect
32. C₂₃	C₂×C₃⋊D₂₁	direct (N × H)
33. C₃×C₇	C₂×D₃×C₂₃	semidirect
34. C₂×C₃²	D₇×C₂₃	semidirect
36. C₂×C₇	C₃⋊D₃×C₂₃	semidirect
39. C₃²	C₂×D₇×C₂₃	semidirect
40. C₇	C₂×C₃⋊D₃×C₂₃	semidirect
41. C₂×C₃	C₂₃×D₂₁	semidirect
44. C₃	C₂×C₂₃×D₂₁	semidirect
46. C₂	C₂₃×C₃⋊D₂₁	direct (N × H)

Subgroups — C2×C23×C3⋊D21 #19154012

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₂₃×C₃⋊D₂₁ #19154012