Subgroups — D₇₄₉⋊(C₃⋊D₃) #41004148

Order 26964.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₇₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₃⋊D₃₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₇×C₃⋊D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₁⋊D₁₀₇	—	3	4	no	maximal
5	C₃²×C₇×C₁₀₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₁×C₁₀₇	—	3	4	no	—
7	C₇×D₃₂₁	—	3	4	no	—
8	C₃×D₇₄₉	D₃	1	4	yes	complemented
9	C₃⋊D₃×D₁₀₇	—	7	1	no	maximal, Hall
10	D₇×D₁₀₇	—	9	1	no	Hall
11	C₃×C₇×C₁₀₇	C₂×D₃	1	4	yes	complemented
12	C₃⋊D₃₂₁	D₇	1	1	yes	characteristic, complemented
13	C₃⋊D₃×C₁₀₇	—	7	1	no	—
14	C₃²×D₁₀₇	—	7	1	no	—
15	D₇₄₉	C₃⋊D₃	1	1	yes	characteristic, complemented
16	C₇×D₁₀₇	—	9	1	no	—
17	D₇×C₁₀₇	—	9	1	no	—
18	D₃×D₁₀₇	—	21	4	no	—
19	C₃²×C₁₀₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	C₇×C₁₀₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
21	D₃₂₁	—	3	4	no	—
22	C₃×D₁₀₇	—	7	4	no	—
23	D₃×C₁₀₇	—	21	4	no	—
24	C₂×D₁₀₇	—	63	1	no	Hall
25	C₃×C₁₀₇	D₃×D₇	1	4	yes	complemented
26	D₇×C₃⋊D₃	—	107	1	no	maximal, Hall
27	C₂×C₁₀₇	—	63	1	no	—
28	D₁₀₇	—	7	1	no	—
29	D₁₀₇	—	9	1	no	—
30	C₃⋊D₂₁	D₁₀₇	1	1	yes	characteristic, complemented
31	C₇×C₃⋊D₃	—	107	1	no	—
32	C₃²×D₇	—	107	1	no	—
33	C₁₀₇	D₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
34	D₃×D₇	—	321	4	no	—
35	C₃²×C₇	C₂×D₁₀₇	1	1	yes	characteristic, complemented, Hall
36	D₂₁	—	3	4	no	—
37	C₃×D₇	—	107	4	no	—
38	D₃×C₇	—	321	4	no	—
39	C₂×C₃⋊D₃	—	749	1	no	Hall
40	C₂×D₇	—	963	1	no	Hall
41	C₃×C₇	D₃×D₁₀₇	1	4	yes	complemented
42	C₂×C₃²	—	749	1	no	—
43	C₃⋊D₃	—	7	1	no	—
44	C₃⋊D₃	—	107	1	no	—
45	C₂×C₇	—	963	1	no	—
46	D₇	—	9	1	no	—
47	D₇	—	107	1	no	—
48	C₂×D₃	—	2247	4	no	—
49	C₃²	D₇×D₁₀₇	1	1	yes	characteristic, complemented, Sylow
50	C₇	C₃⋊D₃×D₁₀₇	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	749	4	no	—
52	D₃	—	21	4	no	—
53	D₃	—	321	4	no	—
54	C₂²	—	6741	1	no	Sylow
55	C₃	D₂₁⋊D₁₀₇	1	4	yes	complemented
56	C₂	—	63	1	no	—
57	C₂	—	963	1	no	—
58	C₂	—	749	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₇×C₁₀₇	C₂²
LCS	G ▷ C₃²×C₇×C₁₀₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×D₇₄₉	C₂	semidirect
2. C₇×C₃⋊D₃₂₁	C₂	semidirect
3. C₁₀₇×C₃⋊D₂₁	C₂	semidirect
5. C₃²×C₇×C₁₀₇	C₂²	semidirect
8. C₃×D₇₄₉	D₃	semidirect
11. C₃×C₇×C₁₀₇	C₂×D₃	semidirect
12. C₃⋊D₃₂₁	D₇	semidirect
15. D₇₄₉	C₃⋊D₃	semidirect
19. C₃²×C₁₀₇	C₂×D₇	semidirect
20. C₇×C₁₀₇	C₂×C₃⋊D₃	semidirect
25. C₃×C₁₀₇	D₃×D₇	semidirect
30. C₃⋊D₂₁	D₁₀₇	semidirect
33. C₁₀₇	D₇×C₃⋊D₃	semidirect
35. C₃²×C₇	C₂×D₁₀₇	semidirect
41. C₃×C₇	D₃×D₁₀₇	semidirect
49. C₃²	D₇×D₁₀₇	semidirect
50. C₇	C₃⋊D₃×D₁₀₇	semidirect
55. C₃	D₂₁⋊D₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₃²×D₇₄₉	2
C₇×C₃⋊D₃₂₁	2
C₁₀₇×C₃⋊D₂₁	2
D₂₁⋊D₁₀₇	3
C₃⋊D₃×D₁₀₇	7
D₇×C₃⋊D₃	107

Subgroups — D749⋊(C3⋊D3) #41004148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇₄₉⋊(C₃⋊D₃) #41004148