Subgroups — C₃⋊D₃×#10597244 #24926178

Order 10890.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#10597244	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×#10597244	—	3	4	no	maximal
3	C₁₁²×C₃⋊D₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×#10597244	D₃	1	4	yes	complemented
5	C₂×#10597244	—	9	1	no	Hall
6	C₃²×C₁₁²	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃⋊D₃×C₁₁⋊C₅	—	11	2	no	maximal
8	D₃×C₁₁²	—	3	4	no	—
9	#10597244	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
10	C₃²×C₁₁⋊C₅	—	11	2	no	—
11	C₃×C₁₁²	C₅×D₃	1	4	yes	complemented
12	D₃×C₁₁⋊C₅	—	33	8	no	—
13	C₂×C₁₁²	—	9	1	no	Hall
14	C₁₁×C₃⋊D₃	—	5	2	no	—
15	C₁₁×C₃⋊D₃	C₁₁⋊C₅	1	2	yes	complemented
16	C₃×C₁₁⋊C₅	—	11	8	no	—
17	C₁₁²	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₁₁⋊C₅	—	99	2	no	—
19	C₃²×C₁₁	—	5	2	no	—
20	C₃²×C₁₁	C₂×C₁₁⋊C₅	1	2	yes	complemented
21	C₅×C₃⋊D₃	—	121	1	no	Hall
22	D₃×C₁₁	—	3	8	no	—
23	D₃×C₁₁	—	15	8	no	—
24	C₁₁⋊C₅	—	11	2	no	—
25	C₃²×C₅	—	121	1	no	Hall
26	C₃×C₁₁	—	5	8	no	—
27	C₃×C₁₁	D₃×C₁₁⋊C₅	1	8	yes	complemented
28	C₅×D₃	—	363	4	no	—
29	C₂×C₁₁	—	9	2	no	—
30	C₂×C₁₁	—	45	2	no	—
31	C₃⋊D₃	#10597244	1	1	yes	characteristic, direct product factor, Hall
32	C₃×C₅	—	121	4	no	—
33	C₁₁	—	5	2	no	—
34	C₁₁	C₃⋊D₃×C₁₁⋊C₅	1	2	yes	complemented
35	C₂×C₅	—	1089	1	no	Hall
36	C₃²	C₂×#10597244	1	1	yes	characteristic, complemented, Sylow
37	D₃	—	3	4	no	—
38	C₅	—	121	1	no	Sylow
39	C₃	D₃×#10597244	1	4	yes	complemented
40	C₂	—	9	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃²×#10597244	C₂	semidirect
3. C₁₁²×C₃⋊D₃	C₅	semidirect
4. C₃×#10597244	D₃	semidirect
6. C₃²×C₁₁²	C₂×C₅	semidirect
9. #10597244	C₃⋊D₃	direct (N × H)
11. C₃×C₁₁²	C₅×D₃	semidirect
15. C₁₁×C₃⋊D₃	C₁₁⋊C₅	semidirect
17. C₁₁²	C₅×C₃⋊D₃	semidirect
20. C₃²×C₁₁	C₂×C₁₁⋊C₅	semidirect
27. C₃×C₁₁	D₃×C₁₁⋊C₅	semidirect
31. C₃⋊D₃	#10597244	direct (N × H)
34. C₁₁	C₃⋊D₃×C₁₁⋊C₅	semidirect
36. C₃²	C₂×#10597244	semidirect
39. C₃	D₃×#10597244	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#10597244	2
D₃×#10597244	3
C₁₁²×C₃⋊D₃	5
C₃⋊D₃×C₁₁⋊C₅	11

Subgroups — C3⋊D3×#10597244 #24926178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×#10597244 #24926178