Subgroups — D₃×D₃₃₇⋊C₇ #43246739

Order 28308.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(D₃₃₇⋊C₇)	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₃₃₇⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃₃₇⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₃₇⋊C₇	—	3	1	no	maximal, Hall
5	C₃×C₃₃₇⋊C₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃₃₇⋊C₇	—	3	1	no	—
7	D₃₃₇⋊C₇	—	3	1	no	—
8	D₃₃₇⋊C₇	D₃	1	1	yes	characteristic, direct product factor
9	D₃×D₃₃₇	C₇	1	1	yes	maximal, characteristic, complemented, Hall
10	C₃₃₇⋊C₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₁₀₁₁	C₂×C₇	1	1	yes	characteristic, complemented
12	C₃×D₃₃₇	C₂×C₇	1	1	yes	characteristic, complemented
13	D₃×C₃₃₇	C₂×C₇	1	1	yes	characteristic, complemented
14	C₂×D₃₃₇	—	3	1	no	Hall
15	C₃×C₃₃₇	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃₃₇	—	3	1	no	—
17	D₃₃₇	—	3	1	no	—
18	D₃₃₇	D₃×C₇	1	1	yes	characteristic, complemented
19	C₃₃₇	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₃×C₇	—	337	1	no	maximal, Hall
21	C₂×C₃×C₇	—	337	1	no	—
22	D₃×C₇	—	337	1	no	—
23	D₃×C₇	—	337	1	no	—
24	C₂²×C₇	—	1011	1	no	Hall
25	C₃×C₇	—	337	1	no	Hall
26	C₂×C₇	—	337	1	no	—
27	C₂×C₇	—	1011	1	no	—
28	C₂×C₇	—	1011	1	no	—
29	C₂×D₃	—	2359	1	no	Hall
30	C₇	—	337	1	no	Sylow
31	C₂×C₃	—	2359	1	no	—
32	D₃	—	2359	1	no	—
33	D₃	D₃₃₇⋊C₇	1	1	yes	characteristic, direct product factor
34	C₂²	—	7077	1	no	Sylow
35	C₃	C₂×D₃₃₇⋊C₇	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×C₃₃₇	C₂²×C₇
LCS	G ▷ C₃×C₃₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊(D₃₃₇⋊C₇)	C₂	semidirect
2. D₃×C₃₃₇⋊C₇	C₂	semidirect
3. C₃×D₃₃₇⋊C₇	C₂	semidirect
5. C₃×C₃₃₇⋊C₇	C₂²	semidirect
8. D₃₃₇⋊C₇	D₃	direct (N × H)
9. D₃×D₃₃₇	C₇	semidirect
10. C₃₃₇⋊C₇	C₂×D₃	semidirect
11. D₁₀₁₁	C₂×C₇	semidirect
12. C₃×D₃₃₇	C₂×C₇	semidirect
13. D₃×C₃₃₇	C₂×C₇	semidirect
15. C₃×C₃₃₇	C₂²×C₇	semidirect
18. D₃₃₇	D₃×C₇	semidirect
19. C₃₃₇	C₂×D₃×C₇	semidirect
33. D₃	D₃₃₇⋊C₇	direct (N × H)
35. C₃	C₂×D₃₃₇⋊C₇	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(D₃₃₇⋊C₇)	2
D₃×C₃₃₇⋊C₇	2
C₃×D₃₃₇⋊C₇	2
C₂×D₃₃₇⋊C₇	3
D₃×D₃₃₇	7
C₂×D₃×C₇	337

Subgroups — D3×D337⋊C7 #43246739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₃₃₇⋊C₇ #43246739