Subgroups — C₃×D₃×#10597243 #24926161

Order 10890.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#10597243	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₃×#10597243	—	3	1	no	maximal
3	D₃×#10597243	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×D₃×C₁₁²	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₃×#10597243	—	2	1	no	—
6	C₃×#10597243	D₃	1	1	yes	characteristic, direct product factor
7	C₃×#10597243	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×#10597243	—	3	1	no	Hall
9	C₃²×C₁₁²	C₂×C₅	1	1	yes	characteristic, complemented, Hall
10	C₃×D₃×C₁₁⋊C₅	—	11	12	no	maximal
11	C₂×C₃×C₁₁²	—	3	1	no	—
12	D₃×C₁₁²	C₃×C₅	1	1	yes	characteristic, complemented
13	#10597243	C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
14	C₃²×C₁₁⋊C₅	—	11	12	no	—
15	C₃×C₁₁²	—	2	1	no	—
16	C₃×C₁₁²	C₅×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₁²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
18	C₂×C₃×C₁₁⋊C₅	—	33	12	no	—
19	D₃×C₁₁⋊C₅	—	11	12	no	—
20	C₂×C₁₁²	—	3	1	no	Hall
21	C₃×D₃×C₁₁	C₁₁⋊C₅	1	12	yes	complemented
22	C₃×C₁₁⋊C₅	—	11	12	no	—
23	C₃×C₁₁⋊C₅	—	11	12	no	—
24	C₃×C₁₁⋊C₅	—	22	12	no	—
25	C₁₁²	C₃×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₁⋊C₅	—	33	12	no	—
27	C₃²×C₁₁	C₂×C₁₁⋊C₅	1	12	yes	complemented
28	C₃×C₅×D₃	—	121	1	no	Hall
29	C₂×C₃×C₁₁	—	3	12	no	—
30	D₃×C₁₁	C₃×C₁₁⋊C₅	1	12	yes	complemented
31	C₁₁⋊C₅	—	11	12	no	—
32	C₃²×C₅	—	121	1	no	Hall
33	C₃×C₁₁	—	2	12	no	—
34	C₃×C₁₁	D₃×C₁₁⋊C₅	1	12	yes	complemented
35	C₃×C₁₁	C₂×C₃×C₁₁⋊C₅	1	12	yes	complemented
36	C₂×C₃×C₅	—	363	1	no	—
37	C₅×D₃	—	121	1	no	—
38	C₂×C₁₁	—	3	12	no	—
39	C₃×D₃	#10597243	1	1	yes	characteristic, direct product factor, Hall
40	C₃×C₅	—	121	1	no	—
41	C₃×C₅	—	121	1	no	—
42	C₃×C₅	—	242	1	no	—
43	C₁₁	C₃×D₃×C₁₁⋊C₅	1	12	yes	complemented
44	C₂×C₅	—	363	1	no	Hall
45	C₃²	C₂×#10597243	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃	—	3	1	no	—
47	D₃	C₃×#10597243	1	1	yes	characteristic, direct product factor
48	C₅	—	121	1	no	Sylow
49	C₃	—	2	1	no	—
50	C₃	D₃×#10597243	1	1	yes	characteristic, direct product factor
51	C₃	C₂×C₃×#10597243	1	1	yes	characteristic, complemented
52	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₃×#10597243
commutator, cosocle, hypocenter	C₃×C₁₁²	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁²	C₂×C₅
LCS	G ▷ C₃×C₁₁²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×#10597243	C₂	semidirect
3. D₃×#10597243	C₃	direct (N × H)
4. C₃×D₃×C₁₁²	C₅	semidirect
6. C₃×#10597243	D₃	direct (N × H)
7. C₃×#10597243	C₂×C₃	semidirect
9. C₃²×C₁₁²	C₂×C₅	semidirect
12. D₃×C₁₁²	C₃×C₅	semidirect
13. #10597243	C₃×D₃	direct (N × H)
16. C₃×C₁₁²	C₅×D₃	semidirect
17. C₃×C₁₁²	C₂×C₃×C₅	semidirect
21. C₃×D₃×C₁₁	C₁₁⋊C₅	semidirect
25. C₁₁²	C₃×C₅×D₃	semidirect
27. C₃²×C₁₁	C₂×C₁₁⋊C₅	semidirect
30. D₃×C₁₁	C₃×C₁₁⋊C₅	semidirect
34. C₃×C₁₁	D₃×C₁₁⋊C₅	semidirect
35. C₃×C₁₁	C₂×C₃×C₁₁⋊C₅	semidirect
39. C₃×D₃	#10597243	direct (N × H)
43. C₁₁	C₃×D₃×C₁₁⋊C₅	semidirect
45. C₃²	C₂×#10597243	semidirect
47. D₃	C₃×#10597243	direct (N × H)
50. C₃	D₃×#10597243	direct (N × H)
51. C₃	C₂×C₃×#10597243	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#10597243	2
C₂×C₃×#10597243	3
D₃×#10597243	3
C₃×D₃×C₁₁²	5
C₃×D₃×C₁₁⋊C₅	11

Subgroups — C3×D3×#10597243 #24926161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#10597243 #24926161