Subgroups — C₂×C₉×C₁₉×C₇⋊D₇ #45691714

Order 33516.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₉×C₇⋊D₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇²×C₉×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₁₉×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic
4	C₇²×C₉×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×C₇⋊D₇	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
7	C₂×C₉×D₇×C₁₉	—	7	8	no	maximal
8	C₂×C₁₉×C₇⋊D₇	C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic
10	C₉×D₇×C₁₉	—	7	16	no	—
11	C₂×C₇×C₉×C₁₉	D₇	1	8	yes	complemented
12	C₂×C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
13	C₁₉×C₇⋊D₇	C₂×C₉	1	2	yes	direct product factor
14	C₂×C₉×C₇⋊D₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₃×D₇×C₁₉	—	7	8	no	—
16	C₇×C₉×C₁₉	C₂×D₇	1	8	yes	complemented
17	C₇²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇²×C₉	C₂×C₁₉	1	1	yes	characteristic, complemented
19	C₉×C₇⋊D₇	C₂×C₁₉	1	2	yes	direct product factor
20	C₂×C₃×C₇×C₁₉	C₃×D₇	1	8	yes	—
21	C₃×D₇×C₁₉	—	7	16	no	—
22	C₂²×C₉×C₁₉	—	49	1	no	Hall
23	C₂×C₃×C₇⋊D₇	C₃×C₁₉	1	1	yes	characteristic
24	C₂×D₇×C₁₉	—	7	8	no	—
25	C₇²×C₉	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
26	C₃×C₇×C₁₉	C₂×C₃×D₇	1	8	yes	—
27	C₂×C₉×C₁₉	—	49	2	no	—
28	C₂×C₉×C₁₉	C₇⋊D₇	1	1	yes	characteristic, direct product factor
29	C₂×C₃×C₇²	C₂×C₃×C₁₉	1	1	yes	characteristic
30	C₃×C₇⋊D₇	C₂×C₃×C₁₉	1	2	yes	—
31	C₂×C₇×C₁₉	C₉×D₇	1	8	yes	complemented
32	D₇×C₁₉	—	7	16	no	—
33	C₂×C₉×D₇	—	7	8	no	—
34	C₂²×C₃×C₁₉	—	49	1	no	—
35	C₂×C₇⋊D₇	C₉×C₁₉	1	1	yes	characteristic, direct product factor, Hall
36	C₉×C₁₉	C₂×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Hall
37	C₃×C₇²	C₂²×C₃×C₁₉	1	1	yes	characteristic
38	C₇×C₁₉	C₂×C₉×D₇	1	8	yes	complemented
39	C₂×C₇×C₉	D₇×C₁₉	1	8	yes	complemented
40	C₉×D₇	—	7	16	no	—
41	C₂×C₃×C₁₉	—	49	2	no	—
42	C₂×C₃×C₁₉	C₃×C₇⋊D₇	1	1	yes	characteristic
43	C₂×C₇²	C₂×C₉×C₁₉	1	1	yes	characteristic, complemented
44	C₇⋊D₇	C₂×C₉×C₁₉	1	2	yes	direct product factor
45	C₂×C₃×D₇	—	7	8	no	—
46	C₂²×C₁₉	—	49	1	no	Hall
47	C₇×C₉	C₂×D₇×C₁₉	1	8	yes	complemented
48	C₃×C₁₉	C₂×C₃×C₇⋊D₇	1	1	yes	characteristic
49	C₇²	C₂²×C₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃×C₇	C₃×D₇×C₁₉	1	8	yes	—
51	C₃×D₇	—	7	16	no	—
52	C₂×C₁₉	—	49	2	no	—
53	C₂×C₁₉	C₉×C₇⋊D₇	1	1	yes	characteristic, direct product factor
54	C₂²×C₉	—	49	1	no	Hall
55	C₂×D₇	—	7	8	no	—
56	C₃×C₇	C₂×C₃×D₇×C₁₉	1	8	yes	—
57	C₁₉	C₂×C₉×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
58	C₂×C₉	—	49	2	no	—
59	C₂×C₉	C₁₉×C₇⋊D₇	1	1	yes	characteristic, direct product factor
60	C₂×C₇	C₉×D₇×C₁₉	1	8	yes	complemented
61	D₇	—	7	16	no	—
62	C₂²×C₃	—	49	1	no	—
63	C₉	C₂×C₁₉×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
64	C₇	C₂×C₉×D₇×C₁₉	1	8	yes	complemented
65	C₂×C₃	—	49	2	no	—
66	C₂×C₃	C₃×C₁₉×C₇⋊D₇	1	1	yes	characteristic
67	C₂²	—	49	1	no	Sylow
68	C₃	C₂×C₃×C₁₉×C₇⋊D₇	1	1	yes	characteristic
69	C₂	—	49	2	no	—
70	C₂	C₉×C₁₉×C₇⋊D₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₉	C₇⋊D₇
commutator, hypocenter	C₇²	C₂²×C₉×C₁₉
Frattini	C₃	C₂×C₃×C₁₉×C₇⋊D₇
Fitting	C₂×C₇²×C₉×C₁₉	C₂
socle	C₂×C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₁₉×C₇⋊D₇	C₃
cosocle	C₃×C₇²	C₂²×C₃×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₉×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₉×C₁₉×C₇⋊D₇	C₂	direct (N × H)
2. C₂×C₇²×C₉×C₁₉	C₂	semidirect
4. C₇²×C₉×C₁₉	C₂²	semidirect
8. C₂×C₁₉×C₇⋊D₇	C₉	direct (N × H)
11. C₂×C₇×C₉×C₁₉	D₇	semidirect
12. C₂×C₇²×C₁₉	C₂×C₉	semidirect
13. C₁₉×C₇⋊D₇	C₂×C₉	direct (N × H)
14. C₂×C₉×C₇⋊D₇	C₁₉	direct (N × H)
16. C₇×C₉×C₁₉	C₂×D₇	semidirect
17. C₇²×C₁₉	C₂²×C₉	semidirect
18. C₂×C₇²×C₉	C₂×C₁₉	semidirect
19. C₉×C₇⋊D₇	C₂×C₁₉	direct (N × H)
25. C₇²×C₉	C₂²×C₁₉	semidirect
28. C₂×C₉×C₁₉	C₇⋊D₇	direct (N × H)
31. C₂×C₇×C₁₉	C₉×D₇	semidirect
35. C₂×C₇⋊D₇	C₉×C₁₉	direct (N × H)
36. C₉×C₁₉	C₂×C₇⋊D₇	direct (N × H)
38. C₇×C₁₉	C₂×C₉×D₇	semidirect
39. C₂×C₇×C₉	D₇×C₁₉	semidirect
43. C₂×C₇²	C₂×C₉×C₁₉	semidirect
44. C₇⋊D₇	C₂×C₉×C₁₉	direct (N × H)
47. C₇×C₉	C₂×D₇×C₁₉	semidirect
49. C₇²	C₂²×C₉×C₁₉	semidirect
53. C₂×C₁₉	C₉×C₇⋊D₇	direct (N × H)
57. C₁₉	C₂×C₉×C₇⋊D₇	direct (N × H)
59. C₂×C₉	C₁₉×C₇⋊D₇	direct (N × H)
60. C₂×C₇	C₉×D₇×C₁₉	semidirect
63. C₉	C₂×C₁₉×C₇⋊D₇	direct (N × H)
64. C₇	C₂×C₉×D₇×C₁₉	semidirect
70. C₂	C₉×C₁₉×C₇⋊D₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×C₁₉×C₇⋊D₇	2
C₂×C₇²×C₉×C₁₉	2
C₂×C₃×C₁₉×C₇⋊D₇	3
C₂×C₉×D₇×C₁₉	7
C₂×C₉×C₇⋊D₇	19

Subgroups — C2×C9×C19×C7⋊D7 #45691714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₁₉×C₇⋊D₇ #45691714