Subgroups — C₃×D₃×D₂₄₇ #22580355

Order 8892.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₇₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₂₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×D₂₄₇	—	3	1	no	maximal
5	D₃×D₂₄₇	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃²×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₃×C₁₉	—	3	1	no	—
8	D₇₄₁	C₂×C₃	1	1	yes	characteristic, complemented
9	D₃×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₂₄₇	—	2	1	no	—
11	C₃×D₂₄₇	—	3	1	no	—
12	C₃×D₂₄₇	D₃	1	1	yes	characteristic, direct product factor
13	C₃×D₂₄₇	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂×D₂₄₇	—	3	1	no	Hall
15	C₃×C₁₃×C₁₉	—	2	1	no	—
16	C₃×C₁₃×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₃×D₃×D₁₉	—	13	1	no	maximal, Hall
19	C₂×C₁₃×C₁₉	—	3	1	no	—
20	D₂₄₇	—	3	1	no	—
21	D₂₄₇	C₃×D₃	1	1	yes	characteristic, direct product factor
22	C₃×D₃×D₁₃	—	19	1	no	maximal, Hall
23	C₃×D₅₇	—	13	1	no	—
24	C₃×D₃×C₁₉	D₁₃	1	1	yes	characteristic, complemented
25	C₃²×D₁₉	—	13	1	no	—
26	C₁₃×C₁₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
27	C₃×D₃₉	—	19	1	no	—
28	C₃×D₃×C₁₃	D₁₉	1	1	yes	characteristic, complemented
29	C₃²×D₁₃	—	19	1	no	—
30	C₂×C₃×D₁₉	—	39	1	no	—
31	D₃×D₁₉	—	13	1	no	—
32	C₃²×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×D₁₃	—	57	1	no	—
34	D₃×D₁₃	—	19	1	no	—
35	C₃²×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₁₉	—	3	1	no	—
37	D₅₇	—	13	1	no	—
38	C₃×D₁₉	—	13	1	no	—
39	C₃×D₁₉	—	13	1	no	—
40	C₃×D₁₉	—	26	1	no	—
41	C₃×D₁₉	—	39	1	no	—
42	D₃×C₁₉	C₃×D₁₃	1	1	yes	characteristic, complemented
43	C₂×C₃×C₁₃	—	3	1	no	—
44	D₃₉	—	19	1	no	—
45	C₃×D₁₃	—	19	1	no	—
46	C₃×D₁₃	—	19	1	no	—
47	C₃×D₁₃	—	38	1	no	—
48	C₃×D₁₃	—	57	1	no	—
49	D₃×C₁₃	C₃×D₁₉	1	1	yes	characteristic, complemented
50	C₂×D₁₉	—	39	1	no	Hall
51	C₃×C₁₉	—	2	1	no	—
52	C₃×C₁₉	D₃×D₁₃	1	1	yes	characteristic, complemented
53	C₃×C₁₉	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented
54	C₂×D₁₃	—	57	1	no	Hall
55	C₃×C₁₃	—	2	1	no	—
56	C₃×C₁₃	D₃×D₁₉	1	1	yes	characteristic, complemented
57	C₃×C₁₃	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented
58	C₂×C₁₉	—	3	1	no	—
59	D₁₉	—	13	1	no	—
60	D₁₉	—	39	1	no	—
61	C₂×C₃×D₃	—	247	1	no	Hall
62	C₂×C₁₃	—	3	1	no	—
63	D₁₃	—	19	1	no	—
64	D₁₃	—	57	1	no	—
65	C₁₉	C₃×D₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃²	—	247	1	no	—
67	C₃×D₃	—	247	1	no	—
68	C₃×D₃	D₂₄₇	1	1	yes	characteristic, direct product factor
69	C₁₃	C₃×D₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₃	—	741	1	no	—
71	C₂×D₃	—	247	1	no	—
72	C₃²	C₂×D₂₄₇	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	741	1	no	—
75	C₂×C₃	—	494	1	no	—
76	C₂×C₃	—	247	1	no	—
77	C₂×C₃	—	247	1	no	—
78	D₃	—	247	1	no	—
79	D₃	C₃×D₂₄₇	1	1	yes	characteristic, direct product factor
80	C₂²	—	741	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×D₂₄₇	1	1	yes	characteristic, direct product factor
83	C₃	C₂×C₃×D₂₄₇	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	741	1	no	—
86	C₂	—	247	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₃×D₂₄₇
commutator, hypocenter	C₃×C₁₃×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃×C₁₃×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₇₄₁	C₂	semidirect
2. C₃×D₃×C₁₃×C₁₉	C₂	semidirect
3. C₃²×D₂₄₇	C₂	semidirect
5. D₃×D₂₄₇	C₃	direct (N × H)
6. C₃²×C₁₃×C₁₉	C₂²	semidirect
8. D₇₄₁	C₂×C₃	semidirect
9. D₃×C₁₃×C₁₉	C₂×C₃	semidirect
12. C₃×D₂₄₇	D₃	direct (N × H)
13. C₃×D₂₄₇	C₂×C₃	semidirect
16. C₃×C₁₃×C₁₉	C₂×D₃	semidirect
17. C₃×C₁₃×C₁₉	C₂²×C₃	semidirect
21. D₂₄₇	C₃×D₃	direct (N × H)
24. C₃×D₃×C₁₉	D₁₃	semidirect
26. C₁₃×C₁₉	C₂×C₃×D₃	semidirect
28. C₃×D₃×C₁₃	D₁₉	semidirect
32. C₃²×C₁₉	C₂×D₁₃	semidirect
35. C₃²×C₁₃	C₂×D₁₉	semidirect
42. D₃×C₁₉	C₃×D₁₃	semidirect
49. D₃×C₁₃	C₃×D₁₉	semidirect
52. C₃×C₁₉	D₃×D₁₃	semidirect
53. C₃×C₁₉	C₂×C₃×D₁₃	semidirect
56. C₃×C₁₃	D₃×D₁₉	semidirect
57. C₃×C₁₃	C₂×C₃×D₁₉	semidirect
65. C₁₉	C₃×D₃×D₁₃	semidirect
68. C₃×D₃	D₂₄₇	direct (N × H)
69. C₁₃	C₃×D₃×D₁₉	semidirect
72. C₃²	C₂×D₂₄₇	semidirect
79. D₃	C₃×D₂₄₇	direct (N × H)
82. C₃	D₃×D₂₄₇	direct (N × H)
83. C₃	C₂×C₃×D₂₄₇	semidirect

Subgroups — C3×D3×D247 #22580355

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₃×D₂₄₇ #22580355