Subgroups — C₃⋊(C₃⋊#11925898) #24926174

Order 10890.

102 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	C₃⋊#11925898	—	3	4	no	maximal
3	C₁₁×C₃⋊D₃₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×#10597244	D₃	1	4	yes	complemented
5	#11925898	—	9	1	no	Hall
6	C₃²×C₁₁²	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃⋊(C₃⋊AGL(1,𝔽₁₁))	—	11	1	no	maximal
8	C₃⋊D₃×C₁₁⋊C₅	—	11	1	no	maximal
9	C₁₁×D₃₃	—	3	4	no	—
10	#10597244	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
11	C₃²×C₁₁⋊C₅	—	11	1	no	—
12	C₃²×C₁₁⋊C₅	—	11	1	no	—
13	C₃×C₁₁²	C₅×D₃	1	4	yes	complemented
14	C₃⋊AGL(1,𝔽₁₁)	—	33	4	no	—
15	D₃×C₁₁⋊C₅	—	33	4	no	—
16	C₁₁×D₁₁	—	9	1	no	Hall
17	C₃⋊D₃₃	C₁₁⋊C₅	1	1	yes	characteristic, complemented
18	C₁₁×C₃⋊D₃	—	11	1	no	—
19	C₃×C₁₁⋊C₅	—	11	4	no	—
20	C₃×C₁₁⋊C₅	—	11	4	no	—
21	C₁₁²	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₁₁⋊C₅	—	99	1	no	—
23	AGL(1,𝔽₁₁)	—	99	1	no	—
24	C₃²×C₁₁	—	10	1	no	—
25	C₃²×C₁₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
26	C₃²×C₁₁	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
27	C₅×C₃⋊D₃	—	121	1	no	Hall
28	D₃₃	—	3	4	no	—
29	D₃×C₁₁	—	33	4	no	—
30	C₁₁⋊C₅	—	11	1	no	—
31	C₁₁⋊C₅	—	11	1	no	—
32	C₃²×C₅	—	121	1	no	Hall
33	C₃×C₁₁	—	10	4	no	—
34	C₃×C₁₁	D₃×C₁₁⋊C₅	1	4	yes	complemented
35	C₃×C₁₁	C₃⋊AGL(1,𝔽₁₁)	1	4	yes	complemented
36	C₅×D₃	—	363	4	no	—
37	C₂×C₁₁	—	99	1	no	—
38	D₁₁	—	9	1	no	—
39	C₃⋊D₃	—	11	1	no	Hall
40	C₃×C₅	—	121	4	no	—
41	C₁₁	—	10	1	no	—
42	C₁₁	C₃⋊D₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
43	C₁₁	C₃⋊(C₃⋊AGL(1,𝔽₁₁))	1	1	yes	characteristic, complemented
44	C₂×C₅	—	1089	1	no	Hall
45	C₃²	#11925898	1	1	yes	characteristic, complemented, Sylow
46	D₃	—	33	4	no	—
47	C₅	—	121	1	no	Sylow
48	C₃	C₃⋊#11925898	1	4	yes	complemented
49	C₂	—	99	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. C₁₁×C₃⋊D₃₃	C₅	semidirect
4. C₃×#10597244	D₃	semidirect
6. C₃²×C₁₁²	C₂×C₅	semidirect
10. #10597244	C₃⋊D₃	semidirect
13. C₃×C₁₁²	C₅×D₃	semidirect
17. C₃⋊D₃₃	C₁₁⋊C₅	semidirect
21. C₁₁²	C₅×C₃⋊D₃	semidirect
25. C₃²×C₁₁	AGL(1,𝔽₁₁)	semidirect
26. C₃²×C₁₁	C₂×C₁₁⋊C₅	semidirect
34. C₃×C₁₁	D₃×C₁₁⋊C₅	semidirect
35. C₃×C₁₁	C₃⋊AGL(1,𝔽₁₁)	semidirect
42. C₁₁	C₃⋊D₃×C₁₁⋊C₅	semidirect
43. C₁₁	C₃⋊(C₃⋊AGL(1,𝔽₁₁))	semidirect
45. C₃²	#11925898	semidirect
48. C₃	C₃⋊#11925898	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
C₃⋊#11925898	3
C₁₁×C₃⋊D₃₃	5
C₃⋊(C₃⋊AGL(1,𝔽₁₁))	11
C₃⋊D₃×C₁₁⋊C₅	11

Subgroups — C3⋊(C3⋊#11925898) #24926174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊#11925898) #24926174