Subgroups — D₃×D₂₃₅₉ #43246780

Order 28308.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₀₇₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₇×C₃₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₃₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₃₅₉	—	3	1	no	maximal, Hall
5	C₃×C₇×C₃₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₇×C₃₃₇	—	3	1	no	—
7	D₂₃₅₉	—	3	1	no	—
8	D₂₃₅₉	D₃	1	1	yes	characteristic, direct product factor
9	D₃×D₃₃₇	—	7	1	no	maximal, Hall
10	C₇×C₃₃₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₁₀₁₁	—	7	1	no	—
12	C₃×D₃₃₇	—	7	1	no	—
13	D₃×C₃₃₇	D₇	1	1	yes	characteristic, complemented
14	C₂×D₃₃₇	—	21	1	no	Hall
15	C₃×C₃₃₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃₃₇	—	3	1	no	—
17	D₃₃₇	—	7	1	no	—
18	D₃₃₇	—	21	1	no	—
19	C₃₃₇	D₃×D₇	1	1	yes	characteristic, complemented, Sylow
20	D₃×D₇	—	337	1	no	maximal, Hall
21	D₂₁	—	337	1	no	—
22	C₃×D₇	—	337	1	no	—
23	D₃×C₇	D₃₃₇	1	1	yes	characteristic, complemented
24	C₂×D₇	—	1011	1	no	Hall
25	C₃×C₇	C₂×D₃₃₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇	—	3	1	no	—
27	D₇	—	337	1	no	—
28	D₇	—	1011	1	no	—
29	C₂×D₃	—	2359	1	no	Hall
30	C₇	D₃×D₃₃₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	2359	1	no	—
32	D₃	—	2359	1	no	—
33	D₃	D₂₃₅₉	1	1	yes	characteristic, direct product factor
34	C₂²	—	7077	1	no	Sylow
35	C₃	C₂×D₂₃₅₉	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	2359	1	no	—
38	C₂	—	7077	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₃₃₇	C₂²
LCS	G ▷ C₃×C₇×C₃₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₇₀₇₇	C₂	semidirect
2. D₃×C₇×C₃₃₇	C₂	semidirect
3. C₃×D₂₃₅₉	C₂	semidirect
5. C₃×C₇×C₃₃₇	C₂²	semidirect
8. D₂₃₅₉	D₃	direct (N × H)
10. C₇×C₃₃₇	C₂×D₃	semidirect
13. D₃×C₃₃₇	D₇	semidirect
15. C₃×C₃₃₇	C₂×D₇	semidirect
19. C₃₃₇	D₃×D₇	semidirect
23. D₃×C₇	D₃₃₇	semidirect
25. C₃×C₇	C₂×D₃₃₇	semidirect
30. C₇	D₃×D₃₃₇	semidirect
33. D₃	D₂₃₅₉	direct (N × H)
35. C₃	C₂×D₂₃₅₉	semidirect

Maximal subgroups

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

subgroup	index
D₇₀₇₇	2
D₃×C₇×C₃₃₇	2
C₃×D₂₃₅₉	2
C₂×D₂₃₅₉	3
D₃×D₃₃₇	7
D₃×D₇	337

Subgroups — D3×D2359 #43246780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₂₃₅₉ #43246780