Subgroups — C₂²×C₉×#10597245 #36344913

Order 21780.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#10597245	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×#10597245	C₃	1	1	yes	maximal, characteristic
3	C₉×#10597245	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂²×C₉×C₁₁²	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₃×#10597245	C₂×C₃	1	3	yes	—
6	C₂²×#10597245	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₉×C₁₁²	C₂×C₅	1	3	yes	complemented
8	C₂²×C₉×C₁₁⋊C₅	—	11	2	no	maximal
9	C₃×#10597245	C₂²×C₃	1	1	yes	characteristic
10	C₂²×C₃×C₁₁²	C₃×C₅	1	1	yes	characteristic
11	C₂×#10597245	C₂×C₉	1	3	yes	direct product factor
12	C₉×C₁₁²	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₉×C₁₁⋊C₅	—	11	6	no	—
14	C₂×C₃×C₁₁²	C₂×C₃×C₅	1	3	yes	—
15	C₂²×C₃×C₁₁⋊C₅	—	11	2	no	—
16	#10597245	C₂²×C₉	1	1	yes	characteristic, direct product factor, Hall
17	C₉×C₁₁⋊C₅	—	11	2	no	—
18	C₂²×C₁₁²	C₅×C₉	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₉×C₁₁	—	5	2	no	—
20	C₂²×C₉×C₁₁	C₁₁⋊C₅	1	2	yes	complemented
21	C₃×C₁₁²	C₂²×C₃×C₅	1	1	yes	characteristic
22	C₂×C₃×C₁₁⋊C₅	—	11	6	no	—
23	C₂×C₁₁²	C₂×C₅×C₉	1	3	yes	complemented
24	C₂²×C₁₁⋊C₅	—	11	2	no	—
25	C₂×C₉×C₁₁	—	5	6	no	—
26	C₂×C₉×C₁₁	C₂×C₁₁⋊C₅	1	6	yes	complemented
27	C₂²×C₅×C₉	—	121	1	no	Hall
28	C₃×C₁₁⋊C₅	—	11	2	no	—
29	C₂²×C₃×C₁₁	—	5	2	no	—
30	C₂²×C₃×C₁₁	C₃×C₁₁⋊C₅	1	2	yes	—
31	C₁₁²	C₂²×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₁₁⋊C₅	—	11	6	no	—
33	C₉×C₁₁	—	5	2	no	—
34	C₉×C₁₁	C₂²×C₁₁⋊C₅	1	2	yes	complemented
35	C₂×C₅×C₉	—	121	3	no	—
36	C₂×C₃×C₁₁	—	5	6	no	—
37	C₂×C₃×C₁₁	C₂×C₃×C₁₁⋊C₅	1	6	yes	—
38	C₂²×C₃×C₅	—	121	1	no	—
39	C₁₁⋊C₅	—	11	2	no	—
40	C₅×C₉	—	121	1	no	Hall
41	C₂²×C₁₁	—	5	2	no	—
42	C₂²×C₁₁	C₉×C₁₁⋊C₅	1	2	yes	complemented
43	C₂²×C₉	#10597245	1	1	yes	characteristic, direct product factor, Hall
44	C₃×C₁₁	—	5	2	no	—
45	C₃×C₁₁	C₂²×C₃×C₁₁⋊C₅	1	2	yes	—
46	C₂×C₃×C₅	—	121	3	no	—
47	C₂×C₁₁	—	5	6	no	—
48	C₂×C₁₁	C₂×C₉×C₁₁⋊C₅	1	6	yes	complemented
49	C₂²×C₅	—	121	1	no	Hall
50	C₂×C₉	C₂×#10597245	1	3	yes	direct product factor
51	C₃×C₅	—	121	1	no	—
52	C₂²×C₃	C₃×#10597245	1	1	yes	characteristic
53	C₁₁	—	5	2	no	—
54	C₁₁	C₂²×C₉×C₁₁⋊C₅	1	2	yes	complemented
55	C₂×C₅	—	121	3	no	—
56	C₉	C₂²×#10597245	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×C₃	C₂×C₃×#10597245	1	3	yes	—
58	C₅	—	121	1	no	Sylow
59	C₂²	C₉×#10597245	1	1	yes	characteristic, direct product factor, Sylow
60	C₃	C₂²×C₃×#10597245	1	1	yes	characteristic
61	C₂	C₂×C₉×#10597245	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₉	#10597245
commutator, hypocenter	C₁₁²	C₂²×C₅×C₉
Frattini	C₃	C₂²×C₃×#10597245
Fitting	C₂²×C₉×C₁₁²	C₅
socle	C₂²×C₃×C₁₁²	C₃×C₅
prime radical	C₂²×C₃×#10597245	C₃
cosocle	C₃×C₁₁²	C₂²×C₃×C₅
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₂²×C₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#10597245	C₂	direct (N × H)
3. C₉×#10597245	C₂²	direct (N × H)
4. C₂²×C₉×C₁₁²	C₅	semidirect
6. C₂²×#10597245	C₉	direct (N × H)
7. C₂×C₉×C₁₁²	C₂×C₅	semidirect
11. C₂×#10597245	C₂×C₉	direct (N × H)
12. C₉×C₁₁²	C₂²×C₅	semidirect
16. #10597245	C₂²×C₉	direct (N × H)
18. C₂²×C₁₁²	C₅×C₉	semidirect
20. C₂²×C₉×C₁₁	C₁₁⋊C₅	semidirect
23. C₂×C₁₁²	C₂×C₅×C₉	semidirect
26. C₂×C₉×C₁₁	C₂×C₁₁⋊C₅	semidirect
31. C₁₁²	C₂²×C₅×C₉	semidirect
34. C₉×C₁₁	C₂²×C₁₁⋊C₅	semidirect
42. C₂²×C₁₁	C₉×C₁₁⋊C₅	semidirect
43. C₂²×C₉	#10597245	direct (N × H)
48. C₂×C₁₁	C₂×C₉×C₁₁⋊C₅	semidirect
50. C₂×C₉	C₂×#10597245	direct (N × H)
54. C₁₁	C₂²×C₉×C₁₁⋊C₅	semidirect
56. C₉	C₂²×#10597245	direct (N × H)
59. C₂²	C₉×#10597245	direct (N × H)
61. C₂	C₂×C₉×#10597245	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×#10597245	2
C₂²×C₃×#10597245	3
C₂²×C₉×C₁₁²	5
C₂²×C₉×C₁₁⋊C₅	11

Subgroups — C22×C9×#10597245 #36344913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₉×#10597245 #36344913