Subgroups — C₃×#21419361 #36382374

Order 22599.

1076 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11719687	C₃	1	4	yes	maximal
2	#21419361	C₃	1	27	yes	maximal, direct product factor
3	C₃×#14578887	C₃	1	8	yes	maximal, complemented
4	C₃×C₉²×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃³×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
6	C₃×#11719687	—	3	36	no	—
7	C₃×#11719687	C₃²	1	36	yes	—
8	C₃²×C₃₁⋊C₉	C₃²	1	8	yes	—
9	#14578887	C₃²	1	72	yes	complemented
10	C₃²×C₉×C₃₁	C₃²	1	4	yes	—
11	C₉²×C₃₁	C₃²	1	9	yes	complemented
12	C₃³×C₃₁	C₃³	1	1	yes	characteristic
13	C₃²×C₃₁⋊C₃	—	3	12	no	—
14	C₃²×C₃₁⋊C₃	C₃³	1	3	yes	—
15	C₃×C₉×C₃₁	3₋¹⁺²	1	36	yes	complemented
16	C₃×C₉×C₃₁	C₃³	1	12	yes	—
17	C₃×C₃₁⋊C₉	—	3	24	no	—
18	C₃×C₃₁⋊C₉	C₃³	1	24	yes	—
19	#11719687	—	3	108	no	—
20	C₃×#6900	—	31	1	no	maximal, Sylow
21	C₃²×C₃₁	C₃×3₋¹⁺²	1	12	yes	—
22	C₃²×C₃₁	C₃⁴	1	1	yes	characteristic
23	C₃×C₃₁⋊C₃	—	3	12	no	—
24	C₃×C₃₁⋊C₃	—	9	9	no	—
25	C₉×C₃₁	C₃×3₋¹⁺²	1	36	yes	complemented
26	C₃₁⋊C₉	—	3	24	no	—
27	C₃²×3₋¹⁺²	—	31	4	no	—
28	#6900	—	31	27	no	—
29	C₃×C₉⋊C₉	—	31	8	no	—
30	C₃×C₉²	C₃₁⋊C₃	1	1	yes	characteristic, complemented
31	C₃×C₃₁	#6900	1	9	yes	complemented
32	C₃×C₃₁	C₃²×3₋¹⁺²	1	4	yes	—
33	C₃₁⋊C₃	—	9	3	no	—
34	C₃⁴	—	31	1	no	—
35	C₃×3₋¹⁺²	—	31	36	no	—
36	C₃×3₋¹⁺²	—	93	36	no	—
37	C₃²×C₉	—	31	8	no	—
38	C₃²×C₉	C₃×C₃₁⋊C₃	1	4	yes	—
39	C₉⋊C₉	—	31	72	no	—
40	C₉²	C₃×C₃₁⋊C₃	1	9	yes	complemented
41	C₃₁	C₃×#6900	1	1	yes	characteristic, complemented, Sylow
42	C₃³	—	31	3	no	—
43	C₃³	—	93	12	no	—
44	C₃³	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
45	3₋¹⁺²	—	93	108	no	—
46	C₃×C₉	—	31	24	no	—
47	C₃×C₉	—	93	24	no	—
48	C₃×C₉	#11719687	1	36	yes	complemented
49	C₃×C₉	C₃²×C₃₁⋊C₃	1	12	yes	—
50	C₃²	—	279	9	no	—
51	C₃²	—	93	12	no	—
52	C₃²	C₃×#11719687	1	12	yes	—
53	C₃²	C₃³×C₃₁⋊C₃	1	1	yes	characteristic
54	C₉	—	93	24	no	—
55	C₉	C₃×#11719687	1	36	yes	complemented
56	C₃	—	279	3	no	—
57	C₃	#21419361	1	9	yes	direct product factor
58	C₃	C₃²×#11719687	1	4	yes	—

	subgroup	G/H
center	C₃³	C₃²×C₃₁⋊C₃
commutator, cosocle	C₃²×C₃₁	C₃⁴
Frattini	C₃²	C₃³×C₃₁⋊C₃
Fitting	C₃×C₉²×C₃₁	C₃
socle	C₃³×C₃₁	C₃³
prime radical	C₃³×C₃₁⋊C₃	C₃²
hypercenter	C₃×C₉²	C₃₁⋊C₃
hypocenter	C₃₁	C₃×#6900
LCS	G ▷ C₃²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃³ ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
2. #21419361	C₃	direct (N × H)
3. C₃×#14578887	C₃	semidirect
4. C₃×C₉²×C₃₁	C₃	semidirect
9. #14578887	C₃²	semidirect
11. C₉²×C₃₁	C₃²	semidirect
15. C₃×C₉×C₃₁	3₋¹⁺²	semidirect
25. C₉×C₃₁	C₃×3₋¹⁺²	semidirect
30. C₃×C₉²	C₃₁⋊C₃	semidirect
31. C₃×C₃₁	#6900	semidirect
40. C₉²	C₃×C₃₁⋊C₃	semidirect
41. C₃₁	C₃×#6900	semidirect
48. C₃×C₉	#11719687	semidirect
55. C₉	C₃×#11719687	semidirect
57. C₃	#21419361	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#11719687	3
#21419361	3
C₃×#14578887	3
C₃×C₉²×C₃₁	3
C₃×#6900	31

Subgroups — C3×#21419361 #36382374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#21419361 #36382374