Subgroups — C₉×C₁₇×C₉⋊C₉ #27136710

Order 12393.

482 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×C₉⋊C₉	C₃	1	3	yes	maximal
2	C₃×C₉²×C₁₇	C₃	1	3	yes	maximal
3	C₃×C₉²×C₁₇	C₃	1	1	yes	maximal, characteristic
4	C₁₇×#6855	C₃	1	6	yes	maximal
5	C₃²×C₉×C₁₇	C₃²	1	9	yes	—
6	C₃²×C₉×C₁₇	C₃²	1	2	yes	—
7	C₃²×C₉×C₁₇	C₃²	1	1	yes	characteristic
8	C₃²×C₉×C₁₇	C₃²	1	1	yes	characteristic
9	C₁₇×C₉⋊C₉	C₉	1	27	yes	direct product factor
10	C₉²×C₁₇	—	3	9	no	—
11	C₉²×C₁₇	C₉	1	9	yes	complemented
12	C₉×C₉⋊C₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃³×C₁₇	C₃³	1	1	yes	characteristic
14	C₃×C₉×C₁₇	—	3	9	no	—
15	C₃×C₉×C₁₇	—	3	6	no	—
16	C₃×C₉×C₁₇	—	3	18	no	—
17	C₃×C₉×C₁₇	C₃×C₉	1	6	yes	—
18	C₃×C₉×C₁₇	C₃×C₉	1	27	yes	—
19	C₃×C₉×C₁₇	C₃×C₉	1	3	yes	—
20	C₃×C₉×C₁₇	C₃×C₉	1	9	yes	—
21	C₃×C₉×C₁₇	C₃×C₉	1	3	yes	—
22	C₃×C₉×C₁₇	3₋¹⁺²	1	9	yes	—
23	C₃×C₉⋊C₉	C₃×C₁₇	1	3	yes	—
24	C₃×C₉²	C₃×C₁₇	1	3	yes	—
25	C₃×C₉²	C₃×C₁₇	1	1	yes	characteristic
26	#6855	C₃×C₁₇	1	6	yes	—
27	C₃²×C₁₇	C₃²×C₉	1	1	yes	characteristic
28	C₃²×C₁₇	C₃²×C₉	1	3	yes	—
29	C₃²×C₁₇	C₃×3₋¹⁺²	1	3	yes	—
30	C₃²×C₁₇	#737	1	6	yes	—
31	C₉×C₁₇	—	3	6	no	—
32	C₉×C₁₇	—	3	27	no	—
33	C₉×C₁₇	C₉²	1	9	yes	complemented
34	C₉×C₁₇	C₉⋊C₉	1	9	yes	direct product factor
35	C₃²×C₉	C₃²×C₁₇	1	2	yes	—
36	C₃²×C₉	C₃²×C₁₇	1	9	yes	—
37	C₃²×C₉	C₃²×C₁₇	1	1	yes	characteristic
38	C₃²×C₉	C₃²×C₁₇	1	1	yes	characteristic
39	C₉⋊C₉	C₉×C₁₇	1	27	yes	direct product factor
40	C₉²	—	3	9	no	—
41	C₉²	C₉×C₁₇	1	9	yes	complemented
42	C₃×C₁₇	C₃×C₉²	1	1	yes	characteristic
43	C₃×C₁₇	C₃×C₉⋊C₉	1	1	yes	characteristic
44	C₃×C₁₇	#6887	1	2	yes	—
45	C₃×C₁₇	C₉×3₋¹⁺²	1	9	yes	—
46	C₃³	C₃³×C₁₇	1	1	yes	characteristic
47	C₃×C₉	—	3	9	no	—
48	C₃×C₉	—	3	6	no	—
49	C₃×C₉	—	3	18	no	—
50	C₃×C₉	C₃×C₉×C₁₇	1	6	yes	—
51	C₃×C₉	C₃×C₉×C₁₇	1	27	yes	—
52	C₃×C₉	C₃×C₉×C₁₇	1	3	yes	—
53	C₃×C₉	C₃×C₉×C₁₇	1	9	yes	—
54	C₃×C₉	C₃×C₉×C₁₇	1	3	yes	—
55	C₃×C₉	C₁₇×3₋¹⁺²	1	9	yes	—
56	C₁₇	C₉×C₉⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
57	C₃²	C₃²×C₉×C₁₇	1	1	yes	characteristic
58	C₃²	C₃²×C₉×C₁₇	1	3	yes	—
59	C₃²	C₃×C₁₇×3₋¹⁺²	1	3	yes	—
60	C₃²	C₁₇×#737	1	6	yes	—
61	C₉	—	3	6	no	—
62	C₉	—	3	27	no	—
63	C₉	C₉²×C₁₇	1	9	yes	complemented
64	C₉	C₁₇×C₉⋊C₉	1	9	yes	direct product factor
65	C₃	C₃×C₉²×C₁₇	1	1	yes	characteristic
66	C₃	C₃×C₁₇×C₉⋊C₉	1	1	yes	characteristic
67	C₃	C₁₇×#6887	1	2	yes	—
68	C₃	C₉×C₁₇×3₋¹⁺²	1	9	yes	—

	subgroup	G/H
center	C₃²×C₉×C₁₇	C₃²
commutator	C₃	C₃×C₉²×C₁₇
Frattini, cosocle	C₃³	C₃³×C₁₇
socle, prime radical	C₃³×C₁₇	C₃³
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₉×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₁₇×C₉⋊C₉	C₉	direct (N × H)
11. C₉²×C₁₇	C₉	semidirect
12. C₉×C₉⋊C₉	C₁₇	direct (N × H)
33. C₉×C₁₇	C₉²	semidirect
34. C₉×C₁₇	C₉⋊C₉	direct (N × H)
39. C₉⋊C₉	C₉×C₁₇	direct (N × H)
41. C₉²	C₉×C₁₇	semidirect
56. C₁₇	C₉×C₉⋊C₉	direct (N × H)
63. C₉	C₉²×C₁₇	semidirect
64. C₉	C₁₇×C₉⋊C₉	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×C₁₇×C₉⋊C₉	3
C₃×C₉²×C₁₇	3
C₁₇×#6855	3
C₉×C₉⋊C₉	17

Subgroups — C9×C17×C9⋊C9 #27136710

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₁₇×C₉⋊C₉ #27136710