Subgroups — C₂³×C₇×C₉×C₂₃ #72190032

Order 11592.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₇×C₂₃	C₃	1	1	yes	maximal, characteristic
2	C₂²×C₇×C₉×C₂₃	C₂	1	7	yes	maximal, direct product factor
3	C₂×C₇×C₉×C₂₃	C₂²	1	7	yes	direct product factor
4	C₂²×C₃×C₇×C₂₃	C₂×C₃	1	7	yes	—
5	C₂³×C₉×C₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₉×C₂₃	C₂³	1	1	yes	characteristic, direct product factor, Hall
7	C₂³×C₇×C₂₃	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₇×C₂₃	C₂²×C₃	1	7	yes	—
9	C₂²×C₉×C₂₃	C₂×C₇	1	7	yes	direct product factor
10	C₂²×C₇×C₂₃	C₂×C₉	1	7	yes	direct product factor
11	C₂³×C₃×C₂₃	C₃×C₇	1	1	yes	characteristic
12	C₂³×C₇×C₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₇×C₂₃	C₂³×C₃	1	1	yes	characteristic
14	C₂×C₉×C₂₃	C₂²×C₇	1	7	yes	direct product factor
15	C₂×C₇×C₂₃	C₂²×C₉	1	7	yes	direct product factor
16	C₂²×C₃×C₂₃	C₂×C₃×C₇	1	7	yes	—
17	C₂²×C₇×C₉	C₂×C₂₃	1	7	yes	direct product factor
18	C₉×C₂₃	C₂³×C₇	1	1	yes	characteristic, direct product factor, Hall
19	C₂³×C₂₃	C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
20	C₂³×C₃×C₇	C₃×C₂₃	1	1	yes	characteristic
21	C₇×C₂₃	C₂³×C₉	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₂₃	C₂²×C₃×C₇	1	7	yes	—
23	C₂×C₇×C₉	C₂²×C₂₃	1	7	yes	direct product factor
24	C₂²×C₂₃	C₂×C₇×C₉	1	7	yes	direct product factor
25	C₂²×C₃×C₇	C₂×C₃×C₂₃	1	7	yes	—
26	C₂³×C₉	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
27	C₃×C₂₃	C₂³×C₃×C₇	1	1	yes	characteristic
28	C₇×C₉	C₂³×C₂₃	1	1	yes	characteristic, direct product factor, Hall
29	C₂³×C₇	C₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₂₃	C₂²×C₇×C₉	1	7	yes	direct product factor
31	C₂×C₃×C₇	C₂²×C₃×C₂₃	1	7	yes	—
32	C₂²×C₉	C₂×C₇×C₂₃	1	7	yes	direct product factor
33	C₂²×C₇	C₂×C₉×C₂₃	1	7	yes	direct product factor
34	C₂³×C₃	C₃×C₇×C₂₃	1	1	yes	characteristic
35	C₂₃	C₂³×C₇×C₉	1	1	yes	characteristic, direct product factor, Sylow
36	C₃×C₇	C₂³×C₃×C₂₃	1	1	yes	characteristic
37	C₂×C₉	C₂²×C₇×C₂₃	1	7	yes	direct product factor
38	C₂×C₇	C₂²×C₉×C₂₃	1	7	yes	direct product factor
39	C₂²×C₃	C₂×C₃×C₇×C₂₃	1	7	yes	—
40	C₉	C₂³×C₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
41	C₂³	C₇×C₉×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₂³×C₉×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	C₂²×C₃×C₇×C₂₃	1	7	yes	—
44	C₂²	C₂×C₇×C₉×C₂₃	1	7	yes	direct product factor
45	C₃	C₂³×C₃×C₇×C₂₃	1	1	yes	characteristic
46	C₂	C₂²×C₇×C₉×C₂₃	1	7	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂³×C₃×C₇×C₂₃
socle, prime radical	C₂³×C₃×C₇×C₂₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₇×C₉×C₂₃	C₂	direct (N × H)
3. C₂×C₇×C₉×C₂₃	C₂²	direct (N × H)
5. C₂³×C₉×C₂₃	C₇	direct (N × H)
6. C₇×C₉×C₂₃	C₂³	direct (N × H)
7. C₂³×C₇×C₂₃	C₉	direct (N × H)
9. C₂²×C₉×C₂₃	C₂×C₇	direct (N × H)
10. C₂²×C₇×C₂₃	C₂×C₉	direct (N × H)
12. C₂³×C₇×C₉	C₂₃	direct (N × H)
14. C₂×C₉×C₂₃	C₂²×C₇	direct (N × H)
15. C₂×C₇×C₂₃	C₂²×C₉	direct (N × H)
17. C₂²×C₇×C₉	C₂×C₂₃	direct (N × H)
18. C₉×C₂₃	C₂³×C₇	direct (N × H)
19. C₂³×C₂₃	C₇×C₉	direct (N × H)
21. C₇×C₂₃	C₂³×C₉	direct (N × H)
23. C₂×C₇×C₉	C₂²×C₂₃	direct (N × H)
24. C₂²×C₂₃	C₂×C₇×C₉	direct (N × H)
26. C₂³×C₉	C₇×C₂₃	direct (N × H)
28. C₇×C₉	C₂³×C₂₃	direct (N × H)
29. C₂³×C₇	C₉×C₂₃	direct (N × H)
30. C₂×C₂₃	C₂²×C₇×C₉	direct (N × H)
32. C₂²×C₉	C₂×C₇×C₂₃	direct (N × H)
33. C₂²×C₇	C₂×C₉×C₂₃	direct (N × H)
35. C₂₃	C₂³×C₇×C₉	direct (N × H)
37. C₂×C₉	C₂²×C₇×C₂₃	direct (N × H)
38. C₂×C₇	C₂²×C₉×C₂₃	direct (N × H)
40. C₉	C₂³×C₇×C₂₃	direct (N × H)
41. C₂³	C₇×C₉×C₂₃	direct (N × H)
42. C₇	C₂³×C₉×C₂₃	direct (N × H)
44. C₂²	C₂×C₇×C₉×C₂₃	direct (N × H)
46. C₂	C₂²×C₇×C₉×C₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₇×C₂₃	3
C₂²×C₇×C₉×C₂₃	2
C₂³×C₉×C₂₃	7
C₂³×C₇×C₉	23

Subgroups — C23×C7×C9×C23 #72190032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₇×C₉×C₂₃ #72190032