Subgroups — C₃³×C₈×C₁₁₃ #72201699

Order 24408.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₈×C₁₁₃	C₃	1	13	yes	maximal, direct product factor
3	C₂×C₃³×C₁₁₃	C₄	1	1	yes	characteristic
4	C₃×C₈×C₁₁₃	C₃²	1	13	yes	direct product factor
5	C₃²×C₄×C₁₁₃	C₂×C₃	1	13	yes	—
6	C₃³×C₁₁₃	C₈	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃²×C₁₁₃	C₃×C₄	1	13	yes	—
8	C₃×C₄×C₁₁₃	C₂×C₃²	1	13	yes	—
9	C₃²×C₁₁₃	C₃×C₈	1	13	yes	direct product factor
10	C₈×C₁₁₃	C₃³	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₁₁₃	C₃²×C₄	1	13	yes	—
12	C₄×C₁₁₃	C₂×C₃³	1	1	yes	characteristic
13	C₃×C₁₁₃	C₃²×C₈	1	13	yes	direct product factor
14	C₂×C₁₁₃	C₃³×C₄	1	1	yes	characteristic
15	C₃³×C₈	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₁₁₃	C₃³×C₈	1	1	yes	characteristic, direct product factor, Sylow
17	C₃³×C₄	C₂×C₁₁₃	1	1	yes	characteristic
18	C₃²×C₈	C₃×C₁₁₃	1	13	yes	direct product factor
19	C₂×C₃³	C₄×C₁₁₃	1	1	yes	characteristic
20	C₃²×C₄	C₂×C₃×C₁₁₃	1	13	yes	—
21	C₃³	C₈×C₁₁₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₃×C₈	C₃²×C₁₁₃	1	13	yes	direct product factor
23	C₂×C₃²	C₃×C₄×C₁₁₃	1	13	yes	—
24	C₃×C₄	C₂×C₃²×C₁₁₃	1	13	yes	—
25	C₃²	C₃×C₈×C₁₁₃	1	13	yes	direct product factor
26	C₈	C₃³×C₁₁₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	C₃²×C₄×C₁₁₃	1	13	yes	—
28	C₄	C₂×C₃³×C₁₁₃	1	1	yes	characteristic
29	C₃	C₃²×C₈×C₁₁₃	1	13	yes	direct product factor
30	C₂	C₃³×C₄×C₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃³×C₁₁₃
socle, prime radical	C₂×C₃³×C₁₁₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×C₈×C₁₁₃	C₃	direct (N × H)
4. C₃×C₈×C₁₁₃	C₃²	direct (N × H)
6. C₃³×C₁₁₃	C₈	direct (N × H)
9. C₃²×C₁₁₃	C₃×C₈	direct (N × H)
10. C₈×C₁₁₃	C₃³	direct (N × H)
13. C₃×C₁₁₃	C₃²×C₈	direct (N × H)
15. C₃³×C₈	C₁₁₃	direct (N × H)
16. C₁₁₃	C₃³×C₈	direct (N × H)
18. C₃²×C₈	C₃×C₁₁₃	direct (N × H)
21. C₃³	C₈×C₁₁₃	direct (N × H)
22. C₃×C₈	C₃²×C₁₁₃	direct (N × H)
25. C₃²	C₃×C₈×C₁₁₃	direct (N × H)
26. C₈	C₃³×C₁₁₃	direct (N × H)
29. C₃	C₃²×C₈×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
C₃³×C₄×C₁₁₃	2
C₃²×C₈×C₁₁₃	3
C₃³×C₈	113

Subgroups — C33×C8×C113 #72201699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₈×C₁₁₃ #72201699