Subgroups — C₁₉×C₂₃×Dic₂₁ #49144708

Order 36708.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₉×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₂₃×Dic₇	—	3	1	no	maximal, Hall
3	C₃×C₇×C₁₉×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₉×C₂₃	D₃	1	1	yes	characteristic
5	Dic₃×C₁₉×C₂₃	—	7	1	no	maximal, Hall
6	C₇×C₁₉×C₂₃	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₉×C₂₃	D₇	1	1	yes	characteristic
8	C₂₃×Dic₂₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₁₉×C₂₃	—	21	1	no	Hall
10	C₁₉×Dic₂₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₁₉×C₂₃	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₇×C₂₃	C₂×C₁₉	1	1	yes	characteristic
13	C₂×C₁₉×C₂₃	D₂₁	1	1	yes	characteristic
14	C₂×C₃×C₇×C₁₉	C₂×C₂₃	1	1	yes	characteristic
15	C₂₃×Dic₇	—	3	1	no	Hall
16	C₁₉×Dic₇	—	3	1	no	Hall
17	C₃×C₇×C₂₃	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
18	C₁₉×C₂₃	Dic₂₁	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₇×C₁₉	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₇×C₂₃	D₃×C₁₉	1	1	yes	characteristic
21	Dic₃×C₂₃	—	7	1	no	Hall
22	C₂×C₇×C₁₉	D₃×C₂₃	1	1	yes	characteristic
23	Dic₃×C₁₉	—	7	1	no	Hall
24	C₇×C₂₃	Dic₃×C₁₉	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₂₃	D₇×C₁₉	1	1	yes	characteristic
26	C₇×C₁₉	Dic₃×C₂₃	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₁₉	D₇×C₂₃	1	1	yes	characteristic
28	C₄×C₂₃	—	21	1	no	Hall
29	Dic₂₁	C₁₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
30	C₄×C₁₉	—	21	1	no	Hall
31	C₃×C₂₃	C₁₉×Dic₇	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₉	C₂₃×Dic₇	1	1	yes	characteristic, complemented, Hall
33	C₂×C₂₃	C₁₉×D₂₁	1	1	yes	characteristic
34	C₂×C₃×C₇	C₂×C₁₉×C₂₃	1	1	yes	characteristic
35	C₂×C₁₉	C₂₃×D₂₁	1	1	yes	characteristic
36	Dic₇	—	3	1	no	Hall
37	C₂₃	C₁₉×Dic₂₁	1	1	yes	characteristic, direct product factor, Sylow
38	C₃×C₇	C₄×C₁₉×C₂₃	1	1	yes	characteristic, complemented, Hall
39	C₁₉	C₂₃×Dic₂₁	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₇	D₃×C₁₉×C₂₃	1	1	yes	characteristic
41	Dic₃	—	7	1	no	Hall
42	C₇	Dic₃×C₁₉×C₂₃	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	D₇×C₁₉×C₂₃	1	1	yes	characteristic
44	C₄	—	21	1	no	Sylow
45	C₃	C₁₉×C₂₃×Dic₇	1	1	yes	characteristic, complemented, Sylow
46	C₂	C₁₉×C₂₃×D₂₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₂₃	D₂₁
commutator, hypocenter	C₃×C₇	C₄×C₁₉×C₂₃
Frattini	C₂	C₁₉×C₂₃×D₂₁
Fitting, socle, prime radical	C₂×C₃×C₇×C₁₉×C₂₃	C₂
cosocle	C₂×C₃×C₇	C₂×C₁₉×C₂₃
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₁₉×C₂₃

Complements

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

N	H ≅ G/N	type
3. C₃×C₇×C₁₉×C₂₃	C₄	semidirect
6. C₇×C₁₉×C₂₃	Dic₃	semidirect
8. C₂₃×Dic₂₁	C₁₉	direct (N × H)
10. C₁₉×Dic₂₁	C₂₃	direct (N × H)
11. C₃×C₁₉×C₂₃	Dic₇	semidirect
17. C₃×C₇×C₂₃	C₄×C₁₉	semidirect
18. C₁₉×C₂₃	Dic₂₁	direct (N × H)
19. C₃×C₇×C₁₉	C₄×C₂₃	semidirect
24. C₇×C₂₃	Dic₃×C₁₉	semidirect
26. C₇×C₁₉	Dic₃×C₂₃	semidirect
29. Dic₂₁	C₁₉×C₂₃	direct (N × H)
31. C₃×C₂₃	C₁₉×Dic₇	semidirect
32. C₃×C₁₉	C₂₃×Dic₇	semidirect
37. C₂₃	C₁₉×Dic₂₁	direct (N × H)
38. C₃×C₇	C₄×C₁₉×C₂₃	semidirect
39. C₁₉	C₂₃×Dic₂₁	direct (N × H)
42. C₇	Dic₃×C₁₉×C₂₃	semidirect
45. C₃	C₁₉×C₂₃×Dic₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₇×C₁₉×C₂₃	2
C₁₉×C₂₃×Dic₇	3
Dic₃×C₁₉×C₂₃	7
C₂₃×Dic₂₁	19
C₁₉×Dic₂₁	23

Subgroups — C19×C23×Dic21 #49144708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₂₃×Dic₂₁ #49144708