Subgroups — D₁₁×C₃⋊D₁₂₃ #30634115

Order 16236.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₁₃₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₃⋊D₁₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₁₁×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₁×D₁₂₃	—	3	4	no	maximal
5	C₃²×C₁₁×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₃₅₃	—	3	4	no	—
7	C₁₁×D₁₂₃	—	3	4	no	—
8	C₃×D₁₁×C₄₁	D₃	1	4	yes	complemented
9	D₁₁×D₄₁	—	9	1	no	Hall
10	C₂×C₃⋊D₁₂₃	—	11	1	no	maximal, Hall
11	C₃×C₁₁×C₄₁	C₂×D₃	1	4	yes	complemented
12	D₄₅₁	—	9	1	no	—
13	C₁₁×D₄₁	—	9	1	no	—
14	D₁₁×C₄₁	C₃⋊D₃	1	1	yes	characteristic, complemented
15	C₂×C₃²×C₄₁	—	11	1	no	—
16	C₃⋊D₁₂₃	—	11	1	no	—
17	C₃⋊D₁₂₃	D₁₁	1	1	yes	characteristic, direct product factor
18	C₂×D₁₂₃	—	33	4	no	—
19	C₁₁×C₄₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
20	C₃⋊D₃×D₁₁	—	41	1	no	maximal, Hall
21	C₃²×C₄₁	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₄₁	—	11	4	no	—
23	D₁₂₃	—	3	4	no	—
24	D₁₂₃	—	33	4	no	—
25	C₃⋊D₃₃	—	41	1	no	—
26	C₁₁×C₃⋊D₃	—	41	1	no	—
27	C₃²×D₁₁	D₄₁	1	1	yes	characteristic, complemented
28	C₂×D₄₁	—	99	1	no	Hall
29	D₃×D₁₁	—	123	4	no	—
30	C₃×C₄₁	D₃×D₁₁	1	4	yes	complemented
31	C₃²×C₁₁	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
32	C₂×C₄₁	—	11	1	no	—
33	D₄₁	—	9	1	no	—
34	D₄₁	—	99	1	no	—
35	D₃₃	—	123	4	no	—
36	C₃×D₁₁	D₁₂₃	1	4	yes	complemented
37	D₃×C₁₁	—	123	4	no	—
38	C₂×D₁₁	—	369	1	no	Hall
39	C₄₁	C₃⋊D₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃⋊D₃	—	451	1	no	Hall
41	C₃×C₁₁	C₂×D₁₂₃	1	4	yes	complemented
42	C₂×C₁₁	—	369	1	no	—
43	D₁₁	—	369	1	no	—
44	D₁₁	C₃⋊D₁₂₃	1	1	yes	characteristic, direct product factor
45	C₂×C₃²	—	11	1	no	—
46	C₃⋊D₃	—	41	1	no	—
47	C₃⋊D₃	—	451	1	no	—
48	C₂×D₃	—	1353	4	no	—
49	C₁₁	C₂×C₃⋊D₁₂₃	1	1	yes	characteristic, complemented, Sylow
50	C₃²	D₁₁×D₄₁	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	11	4	no	—
52	D₃	—	1353	4	no	—
53	D₃	—	123	4	no	—
54	C₂²	—	4059	1	no	Sylow
55	C₃	D₁₁×D₁₂₃	1	4	yes	complemented
56	C₂	—	11	1	no	—
57	C₂	—	369	1	no	—
58	C₂	—	4059	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₁×C₄₁	C₂²
LCS	G ▷ C₃²×C₁₁×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₁₃₅₃	C₂	semidirect
2. C₁₁×C₃⋊D₁₂₃	C₂	semidirect
3. C₃²×D₁₁×C₄₁	C₂	semidirect
5. C₃²×C₁₁×C₄₁	C₂²	semidirect
8. C₃×D₁₁×C₄₁	D₃	semidirect
11. C₃×C₁₁×C₄₁	C₂×D₃	semidirect
14. D₁₁×C₄₁	C₃⋊D₃	semidirect
17. C₃⋊D₁₂₃	D₁₁	direct (N × H)
19. C₁₁×C₄₁	C₂×C₃⋊D₃	semidirect
21. C₃²×C₄₁	C₂×D₁₁	semidirect
27. C₃²×D₁₁	D₄₁	semidirect
30. C₃×C₄₁	D₃×D₁₁	semidirect
31. C₃²×C₁₁	C₂×D₄₁	semidirect
36. C₃×D₁₁	D₁₂₃	semidirect
39. C₄₁	C₃⋊D₃×D₁₁	semidirect
41. C₃×C₁₁	C₂×D₁₂₃	semidirect
44. D₁₁	C₃⋊D₁₂₃	direct (N × H)
49. C₁₁	C₂×C₃⋊D₁₂₃	semidirect
50. C₃²	D₁₁×D₄₁	semidirect
55. C₃	D₁₁×D₁₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₁₃₅₃	2
C₁₁×C₃⋊D₁₂₃	2
C₃²×D₁₁×C₄₁	2
D₁₁×D₁₂₃	3
C₂×C₃⋊D₁₂₃	11
C₃⋊D₃×D₁₁	41

Subgroups — D11×C3⋊D123 #30634115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×C₃⋊D₁₂₃ #30634115