Subgroups — C₃²×C₈×C₁₁×C₃₁ #72201793

Order 24552.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₈×C₁₁×C₃₁	C₃	1	4	yes	maximal, direct product factor
2	C₈×C₁₁×C₃₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
3	C₃²×C₈×C₃₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃²×C₄×C₁₁×C₃₁	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃²×C₁₁×C₃₁	C₄	1	1	yes	characteristic
6	C₃×C₄×C₁₁×C₃₁	C₂×C₃	1	4	yes	—
7	C₃²×C₁₁×C₃₁	C₈	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₁₁×C₃₁	C₃×C₄	1	4	yes	—
9	C₄×C₁₁×C₃₁	C₂×C₃²	1	1	yes	characteristic
10	C₃²×C₄×C₃₁	C₂×C₁₁	1	1	yes	characteristic
11	C₃×C₁₁×C₃₁	C₃×C₈	1	4	yes	direct product factor
12	C₃²×C₈×C₁₁	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₈×C₃₁	C₃×C₁₁	1	4	yes	direct product factor
14	C₂×C₁₁×C₃₁	C₃²×C₄	1	1	yes	characteristic
15	C₂×C₃²×C₃₁	C₄×C₁₁	1	1	yes	characteristic
16	C₃²×C₄×C₁₁	C₂×C₃₁	1	1	yes	characteristic
17	C₃×C₄×C₃₁	C₂×C₃×C₁₁	1	4	yes	—
18	C₁₁×C₃₁	C₃²×C₈	1	1	yes	characteristic, direct product factor, Hall
19	C₃²×C₃₁	C₈×C₁₁	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₈×C₁₁	C₃×C₃₁	1	4	yes	direct product factor
21	C₈×C₃₁	C₃²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃²×C₁₁	C₄×C₃₁	1	1	yes	characteristic
23	C₂×C₃×C₃₁	C₃×C₄×C₁₁	1	4	yes	—
24	C₃×C₄×C₁₁	C₂×C₃×C₃₁	1	4	yes	—
25	C₄×C₃₁	C₂×C₃²×C₁₁	1	1	yes	characteristic
26	C₃²×C₁₁	C₈×C₃₁	1	1	yes	characteristic, direct product factor, Hall
27	C₃×C₃₁	C₃×C₈×C₁₁	1	4	yes	direct product factor
28	C₈×C₁₁	C₃²×C₃₁	1	1	yes	characteristic, direct product factor, Hall
29	C₃²×C₈	C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃×C₁₁	C₃×C₄×C₃₁	1	4	yes	—
31	C₂×C₃₁	C₃²×C₄×C₁₁	1	1	yes	characteristic
32	C₄×C₁₁	C₂×C₃²×C₃₁	1	1	yes	characteristic
33	C₃²×C₄	C₂×C₁₁×C₃₁	1	1	yes	characteristic
34	C₃×C₁₁	C₃×C₈×C₃₁	1	4	yes	direct product factor
35	C₃₁	C₃²×C₈×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
36	C₃×C₈	C₃×C₁₁×C₃₁	1	4	yes	direct product factor
37	C₂×C₁₁	C₃²×C₄×C₃₁	1	1	yes	characteristic
38	C₂×C₃²	C₄×C₁₁×C₃₁	1	1	yes	characteristic
39	C₃×C₄	C₂×C₃×C₁₁×C₃₁	1	4	yes	—
40	C₁₁	C₃²×C₈×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
41	C₃²	C₈×C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
42	C₈	C₃²×C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	C₃×C₄×C₁₁×C₃₁	1	4	yes	—
44	C₄	C₂×C₃²×C₁₁×C₃₁	1	1	yes	characteristic
45	C₃	C₃×C₈×C₁₁×C₃₁	1	4	yes	direct product factor
46	C₂	C₃²×C₄×C₁₁×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃²×C₁₁×C₃₁
socle, prime radical	C₂×C₃²×C₁₁×C₃₁	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₈×C₁₁×C₃₁	C₃	direct (N × H)
2. C₈×C₁₁×C₃₁	C₃²	direct (N × H)
3. C₃²×C₈×C₃₁	C₁₁	direct (N × H)
7. C₃²×C₁₁×C₃₁	C₈	direct (N × H)
11. C₃×C₁₁×C₃₁	C₃×C₈	direct (N × H)
12. C₃²×C₈×C₁₁	C₃₁	direct (N × H)
13. C₃×C₈×C₃₁	C₃×C₁₁	direct (N × H)
18. C₁₁×C₃₁	C₃²×C₈	direct (N × H)
19. C₃²×C₃₁	C₈×C₁₁	direct (N × H)
20. C₃×C₈×C₁₁	C₃×C₃₁	direct (N × H)
21. C₈×C₃₁	C₃²×C₁₁	direct (N × H)
26. C₃²×C₁₁	C₈×C₃₁	direct (N × H)
27. C₃×C₃₁	C₃×C₈×C₁₁	direct (N × H)
28. C₈×C₁₁	C₃²×C₃₁	direct (N × H)
29. C₃²×C₈	C₁₁×C₃₁	direct (N × H)
34. C₃×C₁₁	C₃×C₈×C₃₁	direct (N × H)
35. C₃₁	C₃²×C₈×C₁₁	direct (N × H)
36. C₃×C₈	C₃×C₁₁×C₃₁	direct (N × H)
40. C₁₁	C₃²×C₈×C₃₁	direct (N × H)
41. C₃²	C₈×C₁₁×C₃₁	direct (N × H)
42. C₈	C₃²×C₁₁×C₃₁	direct (N × H)
45. C₃	C₃×C₈×C₁₁×C₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₈×C₁₁×C₃₁	3
C₃²×C₈×C₃₁	11
C₃²×C₄×C₁₁×C₃₁	2
C₃²×C₈×C₁₁	31

Subgroups — C32×C8×C11×C31 #72201793

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₈×C₁₁×C₃₁ #72201793