Subgroups — C₃³×C₈×C₁₁² #72203299

Order 26136.

1568 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄×C₁₁²	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₈×C₁₁²	C₃	1	13	yes	maximal, direct product factor
3	C₂×C₃³×C₁₁²	C₄	1	1	yes	characteristic
4	C₃³×C₁₁²	C₈	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₈×C₁₁²	C₃²	1	13	yes	direct product factor
6	C₃³×C₈×C₁₁	C₁₁	1	12	yes	maximal, direct product factor
7	C₃²×C₄×C₁₁²	C₂×C₃	1	13	yes	—
8	C₂×C₃²×C₁₁²	C₃×C₄	1	13	yes	—
9	C₃×C₄×C₁₁²	C₂×C₃²	1	13	yes	—
10	C₃³×C₄×C₁₁	C₂×C₁₁	1	12	yes	—
11	C₃²×C₁₁²	C₃×C₈	1	13	yes	direct product factor
12	C₈×C₁₁²	C₃³	1	1	yes	characteristic, direct product factor, Hall
13	C₃²×C₈×C₁₁	C₃×C₁₁	1	156	yes	direct product factor
14	C₂×C₃×C₁₁²	C₃²×C₄	1	13	yes	—
15	C₂×C₃³×C₁₁	C₄×C₁₁	1	12	yes	—
16	C₄×C₁₁²	C₂×C₃³	1	1	yes	characteristic
17	C₃²×C₄×C₁₁	C₂×C₃×C₁₁	1	156	yes	—
18	C₃×C₁₁²	C₃²×C₈	1	13	yes	direct product factor
19	C₃³×C₁₁	C₈×C₁₁	1	12	yes	direct product factor
20	C₃×C₈×C₁₁	C₃²×C₁₁	1	156	yes	direct product factor
21	C₂×C₁₁²	C₃³×C₄	1	1	yes	characteristic
22	C₃³×C₈	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃²×C₁₁	C₃×C₄×C₁₁	1	156	yes	—
24	C₃×C₄×C₁₁	C₂×C₃²×C₁₁	1	156	yes	—
25	C₁₁²	C₃³×C₈	1	1	yes	characteristic, direct product factor, Sylow
26	C₃³×C₄	C₂×C₁₁²	1	1	yes	characteristic
27	C₃²×C₁₁	C₃×C₈×C₁₁	1	156	yes	direct product factor
28	C₈×C₁₁	C₃³×C₁₁	1	12	yes	direct product factor
29	C₃²×C₈	C₃×C₁₁²	1	13	yes	direct product factor
30	C₂×C₃×C₁₁	C₃²×C₄×C₁₁	1	156	yes	—
31	C₂×C₃³	C₄×C₁₁²	1	1	yes	characteristic
32	C₄×C₁₁	C₂×C₃³×C₁₁	1	12	yes	—
33	C₃²×C₄	C₂×C₃×C₁₁²	1	13	yes	—
34	C₃×C₁₁	C₃²×C₈×C₁₁	1	156	yes	direct product factor
35	C₃³	C₈×C₁₁²	1	1	yes	characteristic, direct product factor, Sylow
36	C₃×C₈	C₃²×C₁₁²	1	13	yes	direct product factor
37	C₂×C₁₁	C₃³×C₄×C₁₁	1	12	yes	—
38	C₂×C₃²	C₃×C₄×C₁₁²	1	13	yes	—
39	C₃×C₄	C₂×C₃²×C₁₁²	1	13	yes	—
40	C₁₁	C₃³×C₈×C₁₁	1	12	yes	direct product factor
41	C₃²	C₃×C₈×C₁₁²	1	13	yes	direct product factor
42	C₈	C₃³×C₁₁²	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	C₃²×C₄×C₁₁²	1	13	yes	—
44	C₄	C₂×C₃³×C₁₁²	1	1	yes	characteristic
45	C₃	C₃²×C₈×C₁₁²	1	13	yes	direct product factor
46	C₂	C₃³×C₄×C₁₁²	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃³×C₁₁²
socle, prime radical	C₂×C₃³×C₁₁²	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×C₁₁²	C₃	direct (N × H)
4. C₃³×C₁₁²	C₈	direct (N × H)
5. C₃×C₈×C₁₁²	C₃²	direct (N × H)
6. C₃³×C₈×C₁₁	C₁₁	direct (N × H)
11. C₃²×C₁₁²	C₃×C₈	direct (N × H)
12. C₈×C₁₁²	C₃³	direct (N × H)
13. C₃²×C₈×C₁₁	C₃×C₁₁	direct (N × H)
18. C₃×C₁₁²	C₃²×C₈	direct (N × H)
19. C₃³×C₁₁	C₈×C₁₁	direct (N × H)
20. C₃×C₈×C₁₁	C₃²×C₁₁	direct (N × H)
22. C₃³×C₈	C₁₁²	direct (N × H)
25. C₁₁²	C₃³×C₈	direct (N × H)
27. C₃²×C₁₁	C₃×C₈×C₁₁	direct (N × H)
28. C₈×C₁₁	C₃³×C₁₁	direct (N × H)
29. C₃²×C₈	C₃×C₁₁²	direct (N × H)
34. C₃×C₁₁	C₃²×C₈×C₁₁	direct (N × H)
35. C₃³	C₈×C₁₁²	direct (N × H)
36. C₃×C₈	C₃²×C₁₁²	direct (N × H)
40. C₁₁	C₃³×C₈×C₁₁	direct (N × H)
41. C₃²	C₃×C₈×C₁₁²	direct (N × H)
42. C₈	C₃³×C₁₁²	direct (N × H)
45. C₃	C₃²×C₈×C₁₁²	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×C₁₁²	2
C₃²×C₈×C₁₁²	3
C₃³×C₈×C₁₁	11

Subgroups — C33×C8×C112 #72203299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₈×C₁₁² #72203299