Subgroups — C₂×C₃³×C₄×C₁₁₃ #72201701

Order 24408.

448 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃³×C₄×C₁₁₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃²×C₄×C₁₁₃	C₃	1	13	yes	maximal, direct product factor
4	C₂×C₃³×C₁₁₃	C₄	1	2	yes	direct product factor
5	C₂×C₃³×C₁₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₁₁₃	C₃²	1	13	yes	direct product factor
7	C₂²×C₃²×C₁₁₃	C₂×C₃	1	13	yes	—
8	C₃²×C₄×C₁₁₃	C₂×C₃	1	26	yes	direct product factor
9	C₃³×C₁₁₃	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃²×C₁₁₃	C₃×C₄	1	26	yes	direct product factor
11	C₂×C₃²×C₁₁₃	C₂²×C₃	1	13	yes	—
12	C₂²×C₃×C₁₁₃	C₂×C₃²	1	13	yes	—
13	C₃×C₄×C₁₁₃	C₂×C₃²	1	26	yes	direct product factor
14	C₃²×C₁₁₃	C₂×C₃×C₄	1	13	yes	direct product factor
15	C₂×C₄×C₁₁₃	C₃³	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃×C₁₁₃	C₃²×C₄	1	26	yes	direct product factor
17	C₂×C₃×C₁₁₃	C₂²×C₃²	1	13	yes	—
18	C₂²×C₁₁₃	C₂×C₃³	1	1	yes	characteristic
19	C₄×C₁₁₃	C₂×C₃³	1	2	yes	direct product factor
20	C₃×C₁₁₃	C₂×C₃²×C₄	1	13	yes	direct product factor
21	C₂×C₁₁₃	C₃³×C₄	1	2	yes	direct product factor
22	C₂×C₁₁₃	C₂²×C₃³	1	1	yes	characteristic
23	C₂×C₃³×C₄	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₁₁₃	C₂×C₃³×C₄	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²×C₃³	C₂×C₁₁₃	1	1	yes	characteristic
26	C₃³×C₄	C₂×C₁₁₃	1	2	yes	direct product factor
27	C₂×C₃²×C₄	C₃×C₁₁₃	1	13	yes	direct product factor
28	C₂×C₃³	C₄×C₁₁₃	1	2	yes	direct product factor
29	C₂×C₃³	C₂²×C₁₁₃	1	1	yes	characteristic
30	C₂²×C₃²	C₂×C₃×C₁₁₃	1	13	yes	—
31	C₃²×C₄	C₂×C₃×C₁₁₃	1	26	yes	direct product factor
32	C₃³	C₂×C₄×C₁₁₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₃×C₄	C₃²×C₁₁₃	1	13	yes	direct product factor
34	C₂×C₃²	C₃×C₄×C₁₁₃	1	26	yes	direct product factor
35	C₂×C₃²	C₂²×C₃×C₁₁₃	1	13	yes	—
36	C₂²×C₃	C₂×C₃²×C₁₁₃	1	13	yes	—
37	C₃×C₄	C₂×C₃²×C₁₁₃	1	26	yes	direct product factor
38	C₃²	C₂×C₃×C₄×C₁₁₃	1	13	yes	direct product factor
39	C₂×C₄	C₃³×C₁₁₃	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃	C₃²×C₄×C₁₁₃	1	26	yes	direct product factor
41	C₂×C₃	C₂²×C₃²×C₁₁₃	1	13	yes	—
42	C₂²	C₂×C₃³×C₁₁₃	1	1	yes	characteristic
43	C₄	C₂×C₃³×C₁₁₃	1	2	yes	direct product factor
44	C₃	C₂×C₃²×C₄×C₁₁₃	1	13	yes	direct product factor
45	C₂	C₃³×C₄×C₁₁₃	1	2	yes	direct product factor
46	C₂	C₂²×C₃³×C₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃³×C₁₁₃
socle, prime radical	C₂²×C₃³×C₁₁₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃³×C₄×C₁₁₃	C₂	direct (N × H)
3. C₂×C₃²×C₄×C₁₁₃	C₃	direct (N × H)
4. C₂×C₃³×C₁₁₃	C₄	direct (N × H)
6. C₂×C₃×C₄×C₁₁₃	C₃²	direct (N × H)
8. C₃²×C₄×C₁₁₃	C₂×C₃	direct (N × H)
9. C₃³×C₁₁₃	C₂×C₄	direct (N × H)
10. C₂×C₃²×C₁₁₃	C₃×C₄	direct (N × H)
13. C₃×C₄×C₁₁₃	C₂×C₃²	direct (N × H)
14. C₃²×C₁₁₃	C₂×C₃×C₄	direct (N × H)
15. C₂×C₄×C₁₁₃	C₃³	direct (N × H)
16. C₂×C₃×C₁₁₃	C₃²×C₄	direct (N × H)
19. C₄×C₁₁₃	C₂×C₃³	direct (N × H)
20. C₃×C₁₁₃	C₂×C₃²×C₄	direct (N × H)
21. C₂×C₁₁₃	C₃³×C₄	direct (N × H)
23. C₂×C₃³×C₄	C₁₁₃	direct (N × H)
24. C₁₁₃	C₂×C₃³×C₄	direct (N × H)
26. C₃³×C₄	C₂×C₁₁₃	direct (N × H)
27. C₂×C₃²×C₄	C₃×C₁₁₃	direct (N × H)
28. C₂×C₃³	C₄×C₁₁₃	direct (N × H)
31. C₃²×C₄	C₂×C₃×C₁₁₃	direct (N × H)
32. C₃³	C₂×C₄×C₁₁₃	direct (N × H)
33. C₂×C₃×C₄	C₃²×C₁₁₃	direct (N × H)
34. C₂×C₃²	C₃×C₄×C₁₁₃	direct (N × H)
37. C₃×C₄	C₂×C₃²×C₁₁₃	direct (N × H)
38. C₃²	C₂×C₃×C₄×C₁₁₃	direct (N × H)
39. C₂×C₄	C₃³×C₁₁₃	direct (N × H)
40. C₂×C₃	C₃²×C₄×C₁₁₃	direct (N × H)
43. C₄	C₂×C₃³×C₁₁₃	direct (N × H)
44. C₃	C₂×C₃²×C₄×C₁₁₃	direct (N × H)
45. C₂	C₃³×C₄×C₁₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃³×C₁₁₃	2
C₃³×C₄×C₁₁₃	2
C₂×C₃²×C₄×C₁₁₃	3
C₂×C₃³×C₄	113

Subgroups — C2×C33×C4×C113 #72201701

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃³×C₄×C₁₁₃ #72201701