Subgroups — C₃²×C₁₃×C₂₇⋊C₃ #23745067

Order 9477.

944 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic
2	C₃×C₁₃×C₂₇⋊C₃	C₃	1	36	yes	maximal, direct product factor
3	C₃²×C₁₃×C₂₇	C₃	1	3	yes	maximal, complemented
4	C₃⁴×C₁₃	C₉	1	1	yes	characteristic
5	C₃²×C₉×C₁₃	C₉	1	2	yes	—
6	C₃²×C₉×C₁₃	C₉	1	24	yes	—
7	C₃²×C₉×C₁₃	C₃²	1	12	yes	—
8	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
9	C₁₃×C₂₇⋊C₃	C₃²	1	81	yes	direct product factor
10	C₃×C₁₃×C₂₇	C₃²	1	36	yes	complemented
11	C₃²×C₂₇⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₃³×C₁₃	—	3	9	no	—
13	C₃³×C₁₃	C₃×C₉	1	12	yes	—
14	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
15	C₃×C₉×C₁₃	C₃×C₉	1	72	yes	—
16	C₃×C₉×C₁₃	C₃×C₉	1	24	yes	—
17	C₃×C₉×C₁₃	C₃×C₉	1	8	yes	—
18	C₃×C₉×C₁₃	C₃³	1	4	yes	—
19	C₃×C₉×C₁₃	C₃³	1	9	yes	—
20	C₁₃×C₂₇	C₃³	1	27	yes	complemented
21	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic
22	C₃×C₂₇⋊C₃	C₃×C₁₃	1	36	yes	direct product factor
23	C₃²×C₂₇	C₃×C₁₃	1	3	yes	complemented
24	C₃²×C₁₃	—	3	36	no	—
25	C₃²×C₁₃	C₂₇⋊C₃	1	9	yes	direct product factor
26	C₃²×C₁₃	C₃²×C₉	1	9	yes	—
27	C₃²×C₁₃	C₃²×C₉	1	4	yes	—
28	C₉×C₁₃	C₃²×C₉	1	18	yes	—
29	C₉×C₁₃	C₃²×C₉	1	8	yes	—
30	C₉×C₁₃	C₃⁴	1	1	yes	characteristic
31	C₃⁴	C₉×C₁₃	1	1	yes	characteristic
32	C₃²×C₉	C₉×C₁₃	1	24	yes	—
33	C₃²×C₉	C₉×C₁₃	1	2	yes	—
34	C₃²×C₉	C₃²×C₁₃	1	12	yes	—
35	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
36	C₂₇⋊C₃	C₃²×C₁₃	1	81	yes	direct product factor
37	C₃×C₂₇	C₃²×C₁₃	1	36	yes	complemented
38	C₃×C₁₃	—	3	9	no	—
39	C₃×C₁₃	C₃×C₂₇⋊C₃	1	12	yes	direct product factor
40	C₃×C₁₃	C₃³×C₉	1	1	yes	characteristic
41	C₃³	—	3	9	no	—
42	C₃³	C₃×C₉×C₁₃	1	12	yes	—
43	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
44	C₃×C₉	C₃×C₉×C₁₃	1	72	yes	—
45	C₃×C₉	C₃×C₉×C₁₃	1	24	yes	—
46	C₃×C₉	C₃×C₉×C₁₃	1	8	yes	—
47	C₃×C₉	C₃³×C₁₃	1	4	yes	—
48	C₃×C₉	C₃³×C₁₃	1	9	yes	—
49	C₂₇	C₃³×C₁₃	1	27	yes	complemented
50	C₁₃	C₃²×C₂₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
51	C₃²	—	3	36	no	—
52	C₃²	C₁₃×C₂₇⋊C₃	1	9	yes	direct product factor
53	C₃²	C₃²×C₉×C₁₃	1	9	yes	—
54	C₃²	C₃²×C₉×C₁₃	1	4	yes	—
55	C₉	C₃²×C₉×C₁₃	1	8	yes	—
56	C₉	C₃²×C₉×C₁₃	1	18	yes	—
57	C₉	C₃⁴×C₁₃	1	1	yes	characteristic
58	C₃	—	3	9	no	—
59	C₃	C₃×C₁₃×C₂₇⋊C₃	1	12	yes	direct product factor
60	C₃	C₃³×C₉×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃²×C₉×C₁₃	C₃²
commutator	C₃	C₃³×C₉×C₁₃
Frattini, cosocle	C₉	C₃⁴×C₁₃
socle	C₃³×C₁₃	C₃×C₉
prime radical	C₃⁴×C₁₃	C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₉×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₃×C₂₇⋊C₃	C₃	direct (N × H)
3. C₃²×C₁₃×C₂₇	C₃	semidirect
9. C₁₃×C₂₇⋊C₃	C₃²	direct (N × H)
10. C₃×C₁₃×C₂₇	C₃²	semidirect
11. C₃²×C₂₇⋊C₃	C₁₃	direct (N × H)
20. C₁₃×C₂₇	C₃³	semidirect
22. C₃×C₂₇⋊C₃	C₃×C₁₃	direct (N × H)
23. C₃²×C₂₇	C₃×C₁₃	semidirect
25. C₃²×C₁₃	C₂₇⋊C₃	direct (N × H)
36. C₂₇⋊C₃	C₃²×C₁₃	direct (N × H)
37. C₃×C₂₇	C₃²×C₁₃	semidirect
39. C₃×C₁₃	C₃×C₂₇⋊C₃	direct (N × H)
49. C₂₇	C₃³×C₁₃	semidirect
50. C₁₃	C₃²×C₂₇⋊C₃	direct (N × H)
52. C₃²	C₁₃×C₂₇⋊C₃	direct (N × H)
59. C₃	C₃×C₁₃×C₂₇⋊C₃	direct (N × H)

Subgroups — C32×C13×C27⋊C3 #23745067

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₁₃×C₂₇⋊C₃ #23745067