Subgroups — C₂×C₃×D₇₄₁ #22580394

Order 8892.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₇₄₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₇₄₁	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×D₂₄₇	—	3	1	no	maximal
5	C₃²×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₁₃×C₁₉	—	2	1	no	—
7	C₂×C₃×C₁₃×C₁₉	D₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
9	D₇₄₁	C₂×C₃	1	2	yes	direct product factor
10	C₃×D₂₄₇	—	3	2	no	—
11	C₂×D₂₄₇	—	3	1	no	Hall
12	C₃×C₁₃×C₁₉	—	2	1	no	—
13	C₃×C₁₃×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented
14	C₃×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₂×C₃×D₅₇	—	13	1	no	maximal, Hall
16	C₂×C₁₃×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented
17	D₂₄₇	—	3	2	no	—
18	C₂×C₃×D₃₉	—	19	1	no	maximal, Hall
19	C₂×C₃²×C₁₉	D₁₃	1	1	yes	characteristic, complemented
20	C₃×D₅₇	—	13	2	no	—
21	C₁₃×C₁₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃²×C₁₃	D₁₉	1	1	yes	characteristic, complemented
23	C₃×D₃₉	—	19	2	no	—
24	C₂×D₅₇	—	13	1	no	—
25	C₂×C₃×D₁₉	—	39	1	no	—
26	C₃²×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
27	C₂×D₃₉	—	19	1	no	—
28	C₂×C₃×D₁₃	—	57	1	no	—
29	C₃²×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₁₉	—	2	1	no	—
31	C₂×C₃×C₁₉	C₃×D₁₃	1	1	yes	characteristic, complemented
32	C₂×C₃×C₁₉	D₃₉	1	1	yes	characteristic, complemented
33	D₅₇	—	13	2	no	—
34	C₃×D₁₉	—	39	2	no	—
35	C₂×C₃×C₁₃	—	2	1	no	—
36	C₂×C₃×C₁₃	C₃×D₁₉	1	1	yes	characteristic, complemented
37	C₂×C₃×C₁₃	D₅₇	1	1	yes	characteristic, complemented
38	D₃₉	—	19	2	no	—
39	C₃×D₁₃	—	57	2	no	—
40	C₂×D₁₉	—	39	1	no	Hall
41	C₃×C₁₉	—	2	1	no	—
42	C₃×C₁₉	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented
43	C₃×C₁₉	C₂×D₃₉	1	1	yes	characteristic, complemented
44	C₂×D₁₃	—	57	1	no	Hall
45	C₃×C₁₃	—	2	1	no	—
46	C₃×C₁₃	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented
47	C₃×C₁₃	C₂×D₅₇	1	1	yes	characteristic, complemented
48	C₂×C₁₉	C₃×D₃₉	1	1	yes	characteristic, complemented
49	D₁₉	—	39	2	no	—
50	C₂×C₃×D₃	—	247	1	no	Hall
51	C₂×C₁₃	C₃×D₅₇	1	1	yes	characteristic, complemented
52	D₁₃	—	57	2	no	—
53	C₁₉	C₂×C₃×D₃₉	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₃²	D₂₄₇	1	1	yes	characteristic, complemented
55	C₃×D₃	—	247	2	no	—
56	C₁₃	C₂×C₃×D₅₇	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₃	—	741	1	no	—
58	C₂×D₃	—	247	1	no	—
59	C₃²	C₂×D₂₄₇	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	—	741	2	no	—
62	C₂×C₃	C₃×D₂₄₇	1	1	yes	characteristic, complemented
63	C₂×C₃	D₇₄₁	1	1	yes	characteristic, direct product factor
64	D₃	—	247	2	no	—
65	C₂²	—	741	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂×C₃×D₂₄₇	1	1	yes	characteristic, complemented
68	C₃	C₂×D₇₄₁	1	1	yes	characteristic, direct product factor
69	C₂	—	741	2	no	—
70	C₂	C₃×D₇₄₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₇₄₁
commutator, hypocenter	C₃×C₁₃×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃×C₁₉	C₂
LCS	G ▷ C₃×C₁₃×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₇₄₁	C₂	direct (N × H)
2. C₂×C₃²×C₁₃×C₁₉	C₂	semidirect
3. C₂×D₇₄₁	C₃	direct (N × H)
5. C₃²×C₁₃×C₁₉	C₂²	semidirect
7. C₂×C₃×C₁₃×C₁₉	D₃	semidirect
8. C₂×C₃×C₁₃×C₁₉	C₂×C₃	semidirect
9. D₇₄₁	C₂×C₃	direct (N × H)
13. C₃×C₁₃×C₁₉	C₂×D₃	semidirect
14. C₃×C₁₃×C₁₉	C₂²×C₃	semidirect
16. C₂×C₁₃×C₁₉	C₃×D₃	semidirect
19. C₂×C₃²×C₁₉	D₁₃	semidirect
21. C₁₃×C₁₉	C₂×C₃×D₃	semidirect
22. C₂×C₃²×C₁₃	D₁₉	semidirect
26. C₃²×C₁₉	C₂×D₁₃	semidirect
29. C₃²×C₁₃	C₂×D₁₉	semidirect
31. C₂×C₃×C₁₉	C₃×D₁₃	semidirect
32. C₂×C₃×C₁₉	D₃₉	semidirect
36. C₂×C₃×C₁₃	C₃×D₁₉	semidirect
37. C₂×C₃×C₁₃	D₅₇	semidirect
42. C₃×C₁₉	C₂×C₃×D₁₃	semidirect
43. C₃×C₁₉	C₂×D₃₉	semidirect
46. C₃×C₁₃	C₂×C₃×D₁₉	semidirect
47. C₃×C₁₃	C₂×D₅₇	semidirect
48. C₂×C₁₉	C₃×D₃₉	semidirect
51. C₂×C₁₃	C₃×D₅₇	semidirect
53. C₁₉	C₂×C₃×D₃₉	semidirect
54. C₂×C₃²	D₂₄₇	semidirect
56. C₁₃	C₂×C₃×D₅₇	semidirect
59. C₃²	C₂×D₂₄₇	semidirect
62. C₂×C₃	C₃×D₂₄₇	semidirect
63. C₂×C₃	D₇₄₁	direct (N × H)
67. C₃	C₂×C₃×D₂₄₇	semidirect
68. C₃	C₂×D₇₄₁	direct (N × H)
70. C₂	C₃×D₇₄₁	direct (N × H)

Subgroups — C2×C3×D741 #22580394

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×D₇₄₁ #22580394