Subgroups — C₃⋊(C₁₁⋊#11759816) #45689608

Order 33462.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×#92789	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(C₁₁⋊(C₁₃⋊D₁₃))	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₁⋊#11759816	—	3	1	no	maximal
4	C₁₁×#92789	—	2	1	no	—
5	C₁₁×#92789	D₃	1	1	yes	characteristic, complemented
6	C₃×C₁₁×C₁₃²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₁⋊(C₁₃⋊D₁₃)	—	3	1	no	Hall
8	C₃⋊#11759816	—	11	1	no	maximal, Hall
9	C₃⋊(C₁₁⋊(D₁₃⋊C₃))	—	13	2	no	maximal
10	C₁₁×C₁₃²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	C₃×#92789	D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₁×C₁₃⋊C₃	—	13	2	no	—
13	C₃⋊(C₁₃⋊D₁₃)	—	11	1	no	—
14	#11759816	—	33	1	no	—
15	D₄₂₉	—	13	2	no	—
16	D₄₂₉	—	39	4	no	—
17	C₁₁⋊(D₁₃⋊C₃)	—	39	2	no	—
18	C₃×C₁₃²	C₃×D₁₁	1	1	yes	characteristic, complemented
19	#92789	—	2	1	no	—
20	#92789	D₃₃	1	1	yes	characteristic, complemented
21	C₃×C₁₁×C₁₃	—	3	4	no	—
22	C₃×C₁₁×C₁₃	D₁₃⋊C₃	1	2	yes	complemented
23	C₁₁×C₁₃⋊C₃	—	13	2	no	—
24	C₁₁×C₁₃⋊C₃	—	26	2	no	—
25	C₁₃⋊D₁₃	—	33	1	no	Hall
26	D₁₄₃	—	39	2	no	—
27	D₁₄₃	—	117	4	no	—
28	C₃⋊(D₁₃⋊C₃)	—	143	2	no	—
29	C₃×D₃₃	—	169	1	no	Hall
30	C₁₃²	C₃×D₃₃	1	1	yes	characteristic, complemented, Sylow
31	C₁₁×C₁₃	—	3	4	no	—
32	C₁₁×C₁₃	C₃⋊(D₁₃⋊C₃)	1	2	yes	complemented
33	C₃×C₁₃⋊C₃	—	13	2	no	—
34	C₃²×C₁₁	—	169	1	no	Hall
35	D₃₉	—	143	2	no	—
36	D₃₉	—	429	4	no	—
37	D₁₃⋊C₃	—	429	2	no	—
38	D₃₃	—	169	1	no	—
39	C₃×D₁₁	—	507	1	no	—
40	C₃×C₁₃	—	3	4	no	—
41	C₃×C₁₃	C₁₁⋊(D₁₃⋊C₃)	1	2	yes	complemented
42	C₁₃⋊C₃	—	13	2	no	—
43	C₁₃⋊C₃	—	26	2	no	—
44	C₃×C₁₁	—	338	1	no	—
45	C₃×C₁₁	—	169	1	no	—
46	C₃×C₁₁	#11759816	1	1	yes	characteristic, complemented
47	D₁₃	—	1287	4	no	—
48	D₁₃	—	429	2	no	—
49	D₁₁	—	507	1	no	Hall
50	C₃×D₃	—	1859	1	no	Hall
51	C₁₃	—	3	4	no	—
52	C₁₃	C₃⋊(C₁₁⋊(D₁₃⋊C₃))	1	2	yes	complemented
53	C₁₁	C₃⋊#11759816	1	1	yes	characteristic, complemented, Sylow
54	C₃²	—	169	1	no	Sylow
55	C₂×C₃	—	5577	1	no	—
56	D₃	—	1859	1	no	—
57	C₃	—	338	1	no	—
58	C₃	—	169	1	no	—
59	C₃	C₁₁⋊#11759816	1	1	yes	characteristic, complemented
60	C₂	—	5577	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁×C₁₃²	C₂×C₃
LCS	G ▷ C₃×C₁₁×C₁₃²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×#92789	C₂	semidirect
2. C₃⋊(C₁₁⋊(C₁₃⋊D₁₃))	C₃	semidirect
5. C₁₁×#92789	D₃	semidirect
6. C₃×C₁₁×C₁₃²	C₂×C₃	semidirect
10. C₁₁×C₁₃²	C₃×D₃	semidirect
11. C₃×#92789	D₁₁	semidirect
18. C₃×C₁₃²	C₃×D₁₁	semidirect
20. #92789	D₃₃	semidirect
22. C₃×C₁₁×C₁₃	D₁₃⋊C₃	semidirect
30. C₁₃²	C₃×D₃₃	semidirect
32. C₁₁×C₁₃	C₃⋊(D₁₃⋊C₃)	semidirect
41. C₃×C₁₃	C₁₁⋊(D₁₃⋊C₃)	semidirect
46. C₃×C₁₁	#11759816	semidirect
52. C₁₃	C₃⋊(C₁₁⋊(D₁₃⋊C₃))	semidirect
53. C₁₁	C₃⋊#11759816	semidirect
59. C₃	C₁₁⋊#11759816	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₁×#92789	2
C₃⋊(C₁₁⋊(C₁₃⋊D₁₃))	3
C₁₁⋊#11759816	3
C₃⋊#11759816	11
C₃⋊(C₁₁⋊(D₁₃⋊C₃))	13

Subgroups — C3⋊(C11⋊#11759816) #45689608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₁₁⋊#11759816) #45689608