Subgroups — C₂×C₃²×C₇⋊D₁₁₉ #44473013

Order 29988.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇⋊D₁₁₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₇⋊D₁₁₉	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₇²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇⋊D₁₁₉	C₂×C₃	1	8	yes	direct product factor
6	C₂×C₃×C₇²×C₁₇	C₂×C₃	1	4	yes	complemented
7	C₂×C₃²×D₁₁₉	—	7	8	no	maximal
8	C₂×C₇⋊D₁₁₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₇²×C₁₇	C₂²×C₃	1	4	yes	complemented
10	C₃²×D₁₁₉	—	7	16	no	—
11	C₂×C₃²×C₇×C₁₇	D₇	1	8	yes	complemented
12	C₂×C₃²×C₇⋊D₇	—	17	1	no	maximal, Hall
13	C₂×C₇²×C₁₇	C₂×C₃²	1	1	yes	characteristic, complemented
14	C₇⋊D₁₁₉	C₂×C₃²	1	2	yes	direct product factor
15	C₂×C₃×D₁₁₉	—	7	32	no	—
16	C₃²×C₇×C₁₇	C₂×D₇	1	8	yes	complemented
17	C₂×C₃²×C₇²	D₁₇	1	1	yes	characteristic, complemented
18	C₃²×C₇⋊D₇	—	17	2	no	—
19	C₇²×C₁₇	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₇×C₁₇	C₃×D₇	1	32	yes	complemented
21	C₃×D₁₁₉	—	7	64	no	—
22	C₂×C₃²×D₁₇	—	49	1	no	Hall
23	C₂×C₃×C₇⋊D₇	—	17	4	no	—
24	C₂×D₁₁₉	—	7	8	no	—
25	C₃²×C₇²	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
26	C₃×C₇×C₁₇	C₂×C₃×D₇	1	32	yes	complemented
27	C₂×C₃²×C₁₇	C₇⋊D₇	1	1	yes	characteristic, complemented
28	C₃²×D₁₇	—	49	2	no	—
29	C₂×C₃×C₇²	C₃×D₁₇	1	4	yes	complemented
30	C₃×C₇⋊D₇	—	17	8	no	—
31	C₂×C₃²×D₇	—	119	8	no	—
32	C₂×C₇×C₁₇	C₃²×D₇	1	8	yes	complemented
33	D₁₁₉	—	7	16	no	—
34	C₂×C₃×D₁₇	—	49	4	no	—
35	C₂×C₇⋊D₇	—	17	1	no	Hall
36	C₃²×C₁₇	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
37	C₃×C₇²	C₂×C₃×D₁₇	1	4	yes	complemented
38	C₂×C₃²×C₇	D₁₁₉	1	8	yes	complemented
39	C₃²×D₇	—	119	16	no	—
40	C₇×C₁₇	C₂×C₃²×D₇	1	8	yes	complemented
41	C₂×C₃×C₁₇	C₃×C₇⋊D₇	1	4	yes	complemented
42	C₃×D₁₇	—	49	8	no	—
43	C₂×C₇²	C₃²×D₁₇	1	1	yes	characteristic, complemented
44	C₇⋊D₇	—	17	2	no	—
45	C₂×C₃×D₇	—	119	32	no	—
46	C₂×D₁₇	—	49	1	no	Hall
47	C₃²×C₇	C₂×D₁₁₉	1	8	yes	complemented
48	C₃×C₁₇	C₂×C₃×C₇⋊D₇	1	4	yes	complemented
49	C₇²	C₂×C₃²×D₁₇	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃×C₇	C₃×D₁₁₉	1	32	yes	complemented
51	C₃×D₇	—	119	64	no	—
52	C₂²×C₃²	—	833	1	no	Hall
53	C₂×C₁₇	C₃²×C₇⋊D₇	1	1	yes	characteristic, complemented
54	D₁₇	—	49	2	no	—
55	C₂×D₇	—	119	8	no	—
56	C₃×C₇	C₂×C₃×D₁₁₉	1	32	yes	complemented
57	C₂×C₃²	—	833	2	no	—
58	C₂×C₃²	C₇⋊D₁₁₉	1	1	yes	characteristic, direct product factor
59	C₁₇	C₂×C₃²×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₇	C₃²×D₁₁₉	1	8	yes	complemented
61	D₇	—	119	16	no	—
62	C₂²×C₃	—	833	4	no	—
63	C₃²	C₂×C₇⋊D₁₁₉	1	1	yes	characteristic, direct product factor, Sylow
64	C₇	C₂×C₃²×D₁₁₉	1	8	yes	complemented
65	C₂×C₃	—	833	8	no	—
66	C₂×C₃	C₃×C₇⋊D₁₁₉	1	4	yes	direct product factor
67	C₂²	—	833	1	no	Sylow
68	C₃	C₂×C₃×C₇⋊D₁₁₉	1	4	yes	direct product factor
69	C₂	—	833	2	no	—
70	C₂	C₃²×C₇⋊D₁₁₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²	C₇⋊D₁₁₉
commutator, cosocle, hypocenter	C₇²×C₁₇	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇²×C₁₇	C₂
LCS	G ▷ C₇²×C₁₇
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇⋊D₁₁₉	C₂	direct (N × H)
2. C₂×C₃²×C₇²×C₁₇	C₂	semidirect
3. C₂×C₃×C₇⋊D₁₁₉	C₃	direct (N × H)
4. C₃²×C₇²×C₁₇	C₂²	semidirect
5. C₃×C₇⋊D₁₁₉	C₂×C₃	direct (N × H)
6. C₂×C₃×C₇²×C₁₇	C₂×C₃	semidirect
8. C₂×C₇⋊D₁₁₉	C₃²	direct (N × H)
9. C₃×C₇²×C₁₇	C₂²×C₃	semidirect
11. C₂×C₃²×C₇×C₁₇	D₇	semidirect
13. C₂×C₇²×C₁₇	C₂×C₃²	semidirect
14. C₇⋊D₁₁₉	C₂×C₃²	direct (N × H)
16. C₃²×C₇×C₁₇	C₂×D₇	semidirect
17. C₂×C₃²×C₇²	D₁₇	semidirect
19. C₇²×C₁₇	C₂²×C₃²	semidirect
20. C₂×C₃×C₇×C₁₇	C₃×D₇	semidirect
25. C₃²×C₇²	C₂×D₁₇	semidirect
26. C₃×C₇×C₁₇	C₂×C₃×D₇	semidirect
27. C₂×C₃²×C₁₇	C₇⋊D₇	semidirect
29. C₂×C₃×C₇²	C₃×D₁₇	semidirect
32. C₂×C₇×C₁₇	C₃²×D₇	semidirect
36. C₃²×C₁₇	C₂×C₇⋊D₇	semidirect
37. C₃×C₇²	C₂×C₃×D₁₇	semidirect
38. C₂×C₃²×C₇	D₁₁₉	semidirect
40. C₇×C₁₇	C₂×C₃²×D₇	semidirect
41. C₂×C₃×C₁₇	C₃×C₇⋊D₇	semidirect
43. C₂×C₇²	C₃²×D₁₇	semidirect
47. C₃²×C₇	C₂×D₁₁₉	semidirect
48. C₃×C₁₇	C₂×C₃×C₇⋊D₇	semidirect
49. C₇²	C₂×C₃²×D₁₇	semidirect
50. C₂×C₃×C₇	C₃×D₁₁₉	semidirect
53. C₂×C₁₇	C₃²×C₇⋊D₇	semidirect
56. C₃×C₇	C₂×C₃×D₁₁₉	semidirect
58. C₂×C₃²	C₇⋊D₁₁₉	direct (N × H)
59. C₁₇	C₂×C₃²×C₇⋊D₇	semidirect
60. C₂×C₇	C₃²×D₁₁₉	semidirect
63. C₃²	C₂×C₇⋊D₁₁₉	direct (N × H)
64. C₇	C₂×C₃²×D₁₁₉	semidirect
66. C₂×C₃	C₃×C₇⋊D₁₁₉	direct (N × H)
68. C₃	C₂×C₃×C₇⋊D₁₁₉	direct (N × H)
70. C₂	C₃²×C₇⋊D₁₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₇⋊D₁₁₉	2
C₂×C₃²×C₇²×C₁₇	2
C₂×C₃×C₇⋊D₁₁₉	3
C₂×C₃²×D₁₁₉	7
C₂×C₃²×C₇⋊D₇	17

Subgroups — C2×C32×C7⋊D119 #44473013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₇⋊D₁₁₉ #44473013