Subgroups — D₇×C₃⋊D₄₄₇ #49176394

Order 37548.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₇×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₃⋊D₄₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₃₁₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₄₄₇	—	3	4	no	maximal
5	C₃²×C₇×C₁₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃₁₂₉	—	3	4	no	—
7	C₇×D₄₄₇	—	3	4	no	—
8	C₃×D₇×C₁₄₉	D₃	1	4	yes	complemented
9	C₂×C₃⋊D₄₄₇	—	7	1	no	maximal, Hall
10	D₇×D₁₄₉	—	9	1	no	Hall
11	C₃×C₇×C₁₄₉	C₂×D₃	1	4	yes	complemented
12	C₃⋊D₄₄₇	—	7	1	no	—
13	C₃⋊D₄₄₇	D₇	1	1	yes	characteristic, direct product factor
14	C₂×C₃²×C₁₄₉	—	7	1	no	—
15	D₁₀₄₃	—	9	1	no	—
16	C₇×D₁₄₉	—	9	1	no	—
17	D₇×C₁₄₉	C₃⋊D₃	1	1	yes	characteristic, complemented
18	C₂×D₄₄₇	—	21	4	no	—
19	C₃²×C₁₄₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	C₇×C₁₄₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₁₄₉	—	7	4	no	—
22	D₄₄₇	—	3	4	no	—
23	D₄₄₇	—	21	4	no	—
24	C₂×D₁₄₉	—	63	1	no	Hall
25	C₃×C₁₄₉	D₃×D₇	1	4	yes	complemented
26	C₂×C₁₄₉	—	7	1	no	—
27	D₁₄₉	—	9	1	no	—
28	D₁₄₉	—	63	1	no	—
29	D₇×C₃⋊D₃	—	149	1	no	maximal, Hall
30	C₁₄₉	D₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
31	C₃⋊D₂₁	—	149	1	no	—
32	C₇×C₃⋊D₃	—	149	1	no	—
33	C₃²×D₇	D₁₄₉	1	1	yes	characteristic, complemented
34	D₃×D₇	—	447	4	no	—
35	C₃²×C₇	C₂×D₁₄₉	1	1	yes	characteristic, complemented, Hall
36	D₂₁	—	447	4	no	—
37	C₃×D₇	D₄₄₇	1	4	yes	complemented
38	D₃×C₇	—	447	4	no	—
39	C₂×C₃⋊D₃	—	1043	1	no	Hall
40	C₂×D₇	—	1341	1	no	Hall
41	C₃×C₇	C₂×D₄₄₇	1	4	yes	complemented
42	C₂×C₃²	—	7	1	no	—
43	C₃⋊D₃	—	1043	1	no	—
44	C₃⋊D₃	—	149	1	no	—
45	C₂×C₇	—	1341	1	no	—
46	D₇	—	1341	1	no	—
47	D₇	C₃⋊D₄₄₇	1	1	yes	characteristic, direct product factor
48	C₂×D₃	—	3129	4	no	—
49	C₃²	D₇×D₁₄₉	1	1	yes	characteristic, complemented, Sylow
50	C₇	C₂×C₃⋊D₄₄₇	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	7	4	no	—
52	D₃	—	3129	4	no	—
53	D₃	—	447	4	no	—
54	C₂²	—	9387	1	no	Sylow
55	C₃	D₇×D₄₄₇	1	4	yes	complemented
56	C₂	—	7	1	no	—
57	C₂	—	1341	1	no	—
58	C₂	—	9387	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₇×C₁₄₉	C₂²
LCS	G ▷ C₃²×C₇×C₁₄₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×D₇×C₁₄₉	C₂	semidirect
2. C₇×C₃⋊D₄₄₇	C₂	semidirect
3. C₃⋊D₃₁₂₉	C₂	semidirect
5. C₃²×C₇×C₁₄₉	C₂²	semidirect
8. C₃×D₇×C₁₄₉	D₃	semidirect
11. C₃×C₇×C₁₄₉	C₂×D₃	semidirect
13. C₃⋊D₄₄₇	D₇	direct (N × H)
17. D₇×C₁₄₉	C₃⋊D₃	semidirect
19. C₃²×C₁₄₉	C₂×D₇	semidirect
20. C₇×C₁₄₉	C₂×C₃⋊D₃	semidirect
25. C₃×C₁₄₉	D₃×D₇	semidirect
30. C₁₄₉	D₇×C₃⋊D₃	semidirect
33. C₃²×D₇	D₁₄₉	semidirect
35. C₃²×C₇	C₂×D₁₄₉	semidirect
37. C₃×D₇	D₄₄₇	semidirect
41. C₃×C₇	C₂×D₄₄₇	semidirect
47. D₇	C₃⋊D₄₄₇	direct (N × H)
49. C₃²	D₇×D₁₄₉	semidirect
50. C₇	C₂×C₃⋊D₄₄₇	semidirect
55. C₃	D₇×D₄₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₃²×D₇×C₁₄₉	2
C₇×C₃⋊D₄₄₇	2
C₃⋊D₃₁₂₉	2
D₇×D₄₄₇	3
C₂×C₃⋊D₄₄₇	7
D₇×C₃⋊D₃	149

Subgroups — D7×C3⋊D447 #49176394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×C₃⋊D₄₄₇ #49176394