Subgroups — D₃×D₁₂₉₃ #29509359

Order 15516.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₁₂₉₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₂₉₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×C₄₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₂₉₃	—	3	1	no	maximal
5	D₃×D₄₃₁	—	3	1	no	maximal
6	C₃²×C₄₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₄₃₁	—	3	1	no	—
8	D₁₂₉₃	—	3	1	no	—
9	D₁₂₉₃	—	3	1	no	—
10	D₁₂₉₃	—	6	1	no	—
11	D₁₂₉₃	D₃	1	1	yes	characteristic, direct product factor
12	C₃×D₄₃₁	—	3	1	no	—
13	D₃×C₄₃₁	D₃	1	1	yes	characteristic, complemented
14	C₂×D₄₃₁	—	9	1	no	Hall
15	C₃×C₄₃₁	—	2	1	no	—
16	C₃×C₄₃₁	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₄₃₁	C₂×D₃	1	1	yes	characteristic, complemented
18	C₂×C₄₃₁	—	3	1	no	—
19	D₄₃₁	—	3	1	no	—
20	D₄₃₁	—	9	1	no	—
21	C₄₃₁	D₃²	1	1	yes	characteristic, complemented, Sylow
22	D₃²	—	431	1	no	maximal, Hall
23	C₃⋊D₃	—	431	1	no	—
24	C₃×D₃	—	431	1	no	—
25	C₃×D₃	D₄₃₁	1	1	yes	characteristic, complemented
26	C₂×D₃	—	1293	1	no	—
27	C₂×D₃	—	1293	1	no	—
28	C₃²	C₂×D₄₃₁	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	3	1	no	—
30	C₂×C₃	—	1293	1	no	—
31	D₃	—	1293	1	no	—
32	D₃	—	1293	1	no	—
33	D₃	—	2586	1	no	—
34	D₃	—	431	1	no	—
35	D₃	D₁₂₉₃	1	1	yes	characteristic, direct product factor
36	C₂²	—	3879	1	no	Sylow
37	C₃	—	2	1	no	—
38	C₃	D₃×D₄₃₁	1	1	yes	characteristic, complemented
39	C₃	C₂×D₁₂₉₃	1	1	yes	characteristic, complemented
40	C₂	—	3	1	no	—
41	C₂	—	1293	1	no	—
42	C₂	—	3879	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₄₃₁	C₂²
LCS	G ▷ C₃²×C₄₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₁₂₉₃	C₂	semidirect
2. C₃×D₁₂₉₃	C₂	semidirect
3. C₃×D₃×C₄₃₁	C₂	semidirect
6. C₃²×C₄₃₁	C₂²	semidirect
11. D₁₂₉₃	D₃	direct (N × H)
13. D₃×C₄₃₁	D₃	semidirect
16. C₃×C₄₃₁	C₂×D₃	semidirect
17. C₃×C₄₃₁	C₂×D₃	semidirect
21. C₄₃₁	D₃²	semidirect
25. C₃×D₃	D₄₃₁	semidirect
28. C₃²	C₂×D₄₃₁	semidirect
35. D₃	D₁₂₉₃	direct (N × H)
38. C₃	D₃×D₄₃₁	semidirect
39. C₃	C₂×D₁₂₉₃	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₁₂₉₃	2
C₃×D₁₂₉₃	2
C₃×D₃×C₄₃₁	2
C₂×D₁₂₉₃	3
D₃×D₄₃₁	3
D₃²	431

Subgroups — D3×D1293 #29509359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₁₂₉₃ #29509359