Subgroups — C₃³×C₁₁×C₈₁ #72201336

Order 24057.

1528 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₁₁×C₂₇	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₁₁×C₈₁	C₃	1	39	yes	maximal, direct product factor
3	C₃³×C₉×C₁₁	C₉	1	1	yes	characteristic
4	C₃²×C₁₁×C₂₇	C₉	1	26	yes	—
5	C₃²×C₁₁×C₂₇	C₃²	1	13	yes	—
6	C₃×C₁₁×C₈₁	C₃²	1	117	yes	direct product factor
7	C₃³×C₈₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₃⁴×C₁₁	C₂₇	1	1	yes	characteristic
9	C₃²×C₉×C₁₁	C₂₇	1	26	yes	—
10	C₃²×C₉×C₁₁	C₃×C₉	1	13	yes	—
11	C₃×C₁₁×C₂₇	C₃×C₉	1	104	yes	—
12	C₃×C₁₁×C₂₇	C₃³	1	13	yes	—
13	C₁₁×C₈₁	C₃³	1	27	yes	direct product factor
14	C₃³×C₂₇	C₃×C₁₁	1	1	yes	characteristic
15	C₃²×C₈₁	C₃×C₁₁	1	39	yes	direct product factor
16	C₃³×C₁₁	C₈₁	1	27	yes	direct product factor
17	C₃³×C₁₁	C₃×C₂₇	1	13	yes	—
18	C₃×C₉×C₁₁	C₃×C₂₇	1	104	yes	—
19	C₃×C₉×C₁₁	C₃²×C₉	1	13	yes	—
20	C₁₁×C₂₇	C₃²×C₉	1	26	yes	—
21	C₁₁×C₂₇	C₃⁴	1	1	yes	characteristic
22	C₃³×C₉	C₉×C₁₁	1	1	yes	characteristic
23	C₃²×C₂₇	C₉×C₁₁	1	26	yes	—
24	C₃²×C₂₇	C₃²×C₁₁	1	13	yes	—
25	C₃×C₈₁	C₃²×C₁₁	1	117	yes	direct product factor
26	C₃²×C₁₁	C₃×C₈₁	1	117	yes	direct product factor
27	C₃²×C₁₁	C₃²×C₂₇	1	13	yes	—
28	C₉×C₁₁	C₃²×C₂₇	1	26	yes	—
29	C₉×C₁₁	C₃³×C₉	1	1	yes	characteristic
30	C₃⁴	C₁₁×C₂₇	1	1	yes	characteristic
31	C₃²×C₉	C₁₁×C₂₇	1	26	yes	—
32	C₃²×C₉	C₃×C₉×C₁₁	1	13	yes	—
33	C₃×C₂₇	C₃×C₉×C₁₁	1	104	yes	—
34	C₃×C₂₇	C₃³×C₁₁	1	13	yes	—
35	C₈₁	C₃³×C₁₁	1	27	yes	direct product factor
36	C₃×C₁₁	C₃²×C₈₁	1	39	yes	direct product factor
37	C₃×C₁₁	C₃³×C₂₇	1	1	yes	characteristic
38	C₃³	C₁₁×C₈₁	1	27	yes	direct product factor
39	C₃³	C₃×C₁₁×C₂₇	1	13	yes	—
40	C₃×C₉	C₃×C₁₁×C₂₇	1	104	yes	—
41	C₃×C₉	C₃²×C₉×C₁₁	1	13	yes	—
42	C₂₇	C₃²×C₉×C₁₁	1	26	yes	—
43	C₂₇	C₃⁴×C₁₁	1	1	yes	characteristic
44	C₁₁	C₃³×C₈₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₃²	C₃×C₁₁×C₈₁	1	117	yes	direct product factor
46	C₃²	C₃²×C₁₁×C₂₇	1	13	yes	—
47	C₉	C₃²×C₁₁×C₂₇	1	26	yes	—
48	C₉	C₃³×C₉×C₁₁	1	1	yes	characteristic
49	C₃	C₃²×C₁₁×C₈₁	1	39	yes	direct product factor
50	C₃	C₃³×C₁₁×C₂₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₇	C₃⁴×C₁₁
socle, prime radical	C₃⁴×C₁₁	C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×C₁₁×C₈₁	C₃	direct (N × H)
6. C₃×C₁₁×C₈₁	C₃²	direct (N × H)
7. C₃³×C₈₁	C₁₁	direct (N × H)
13. C₁₁×C₈₁	C₃³	direct (N × H)
15. C₃²×C₈₁	C₃×C₁₁	direct (N × H)
16. C₃³×C₁₁	C₈₁	direct (N × H)
25. C₃×C₈₁	C₃²×C₁₁	direct (N × H)
26. C₃²×C₁₁	C₃×C₈₁	direct (N × H)
35. C₈₁	C₃³×C₁₁	direct (N × H)
36. C₃×C₁₁	C₃²×C₈₁	direct (N × H)
38. C₃³	C₁₁×C₈₁	direct (N × H)
44. C₁₁	C₃³×C₈₁	direct (N × H)
45. C₃²	C₃×C₁₁×C₈₁	direct (N × H)
49. C₃	C₃²×C₁₁×C₈₁	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×C₁₁×C₂₇	3
C₃²×C₁₁×C₈₁	3
C₃³×C₈₁	11

Subgroups — C33×C11×C81 #72201336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₁₁×C₈₁ #72201336