Subgroups — D₃×C₁₃⋊C₃×D₄₇ #36347231

Order 21996.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊C₃×D₁₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₃⋊C₃×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃⋊C₃×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₃×D₄₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃⋊C₃×D₄₇	—	3	1	no	maximal
6	C₃×C₁₃⋊C₃×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₁₃⋊C₃×D₄₇	—	2	1	no	—
8	C₁₃⋊C₃×D₄₇	—	3	1	no	—
9	C₁₃⋊C₃×D₄₇	D₃	1	1	yes	characteristic, direct product factor
10	C₁₃×D₁₄₁	C₂×C₃	1	1	yes	characteristic, complemented
11	D₃×C₁₃×C₄₇	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×C₁₃×D₄₇	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×C₁₃⋊C₃×C₄₇	—	3	1	no	—
14	C₂×C₁₃×D₄₇	—	3	1	no	Hall
15	C₃×C₁₃×C₄₇	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₁₃⋊C₃×C₄₇	—	2	1	no	—
17	C₁₃⋊C₃×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented
18	C₃×D₃×D₄₇	—	13	1	no	maximal, Hall
19	C₂×C₁₃×C₄₇	—	3	1	no	—
20	C₁₃×D₄₇	—	3	1	no	—
21	C₁₃×D₄₇	C₃×D₃	1	1	yes	characteristic, complemented
22	C₃×D₁₄₁	—	13	1	no	—
23	C₃×D₃×C₄₇	—	13	1	no	—
24	C₃²×D₄₇	—	13	1	no	—
25	C₁₃×C₄₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×D₄₇	—	39	1	no	—
27	D₃×D₄₇	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
28	C₂×D₃×C₁₃⋊C₃	—	47	1	no	maximal, Hall
29	C₃²×C₄₇	—	13	1	no	Hall
30	C₂×C₃×C₄₇	—	39	1	no	—
31	D₁₄₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
32	C₃×D₄₇	—	13	1	no	—
33	C₃×D₄₇	—	26	1	no	—
34	C₃×D₄₇	—	39	1	no	—
35	C₃×D₄₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
36	D₃×C₄₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
37	C₂×C₃×C₁₃⋊C₃	—	47	1	no	—
38	D₃×C₁₃⋊C₃	—	47	1	no	—
39	D₃×C₁₃⋊C₃	D₄₇	1	1	yes	characteristic, direct product factor
40	C₂×D₄₇	—	3	1	no	Hall
41	C₂×D₃×C₁₃	—	47	1	no	—
42	C₂²×C₁₃⋊C₃	—	141	1	no	—
43	C₃×C₄₇	—	13	1	no	—
44	C₃×C₄₇	—	26	1	no	—
45	C₃×C₄₇	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented
46	C₃×C₁₃⋊C₃	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
47	C₂×C₄₇	—	3	1	no	—
48	D₄₇	—	3	1	no	—
49	D₄₇	D₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
50	C₂×C₃×C₁₃	—	47	1	no	—
51	D₃×C₁₃	—	47	1	no	—
52	D₃×C₁₃	C₃×D₄₇	1	1	yes	characteristic, complemented
53	C₂×C₁₃⋊C₃	—	3	1	no	—
54	C₂×C₁₃⋊C₃	—	47	1	no	—
55	C₂×C₁₃⋊C₃	—	94	1	no	—
56	C₂×C₁₃⋊C₃	—	141	1	no	—
57	C₂²×C₁₃	—	141	1	no	Hall
58	C₄₇	C₂×D₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
59	C₃×C₁₃	C₂×C₃×D₄₇	1	1	yes	characteristic, complemented
60	C₁₃⋊C₃	—	2	1	no	—
61	C₁₃⋊C₃	D₃×D₄₇	1	1	yes	characteristic, direct product factor
62	C₂×C₃×D₃	—	611	1	no	Hall
63	C₂×C₁₃	—	3	1	no	—
64	C₂×C₁₃	—	47	1	no	—
65	C₂×C₁₃	—	141	1	no	—
66	C₂×C₃²	—	611	1	no	—
67	C₃×D₃	—	13	1	no	—
68	C₃×D₃	—	611	1	no	—
69	C₁₃	C₃×D₃×D₄₇	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₃	—	1833	1	no	—
71	C₂×D₃	—	47	1	no	—
72	C₃²	—	13	1	no	Sylow
73	C₂×C₃	—	39	1	no	—
74	C₂×C₃	—	1833	1	no	—
75	C₂×C₃	—	47	1	no	—
76	C₂×C₃	—	611	1	no	—
77	C₂×C₃	—	1222	1	no	—
78	D₃	—	47	1	no	—
79	D₃	C₁₃⋊C₃×D₄₇	1	1	yes	characteristic, direct product factor
80	C₂²	—	141	1	no	Sylow
81	C₃	—	13	1	no	—
82	C₃	—	26	1	no	—
83	C₃	C₂×C₁₃⋊C₃×D₄₇	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	47	1	no	—
86	C₂	—	141	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃×C₄₇	C₂²×C₃
LCS	G ▷ C₃×C₁₃×C₄₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₃⋊C₃×D₁₄₁	C₂	semidirect
2. D₃×C₁₃⋊C₃×C₄₇	C₂	semidirect
3. C₃×C₁₃⋊C₃×D₄₇	C₂	semidirect
4. D₃×C₁₃×D₄₇	C₃	semidirect
6. C₃×C₁₃⋊C₃×C₄₇	C₂²	semidirect
9. C₁₃⋊C₃×D₄₇	D₃	direct (N × H)
10. C₁₃×D₁₄₁	C₂×C₃	semidirect
11. D₃×C₁₃×C₄₇	C₂×C₃	semidirect
12. C₃×C₁₃×D₄₇	C₂×C₃	semidirect
15. C₃×C₁₃×C₄₇	C₂²×C₃	semidirect
17. C₁₃⋊C₃×C₄₇	C₂×D₃	semidirect
21. C₁₃×D₄₇	C₃×D₃	semidirect
25. C₁₃×C₄₇	C₂×C₃×D₃	semidirect
27. D₃×D₄₇	C₁₃⋊C₃	direct (N × H)
31. D₁₄₁	C₂×C₁₃⋊C₃	semidirect
35. C₃×D₄₇	C₂×C₁₃⋊C₃	semidirect
36. D₃×C₄₇	C₂×C₁₃⋊C₃	semidirect
39. D₃×C₁₃⋊C₃	D₄₇	direct (N × H)
45. C₃×C₄₇	C₂²×C₁₃⋊C₃	semidirect
46. C₃×C₁₃⋊C₃	C₂×D₄₇	semidirect
49. D₄₇	D₃×C₁₃⋊C₃	direct (N × H)
52. D₃×C₁₃	C₃×D₄₇	semidirect
58. C₄₇	C₂×D₃×C₁₃⋊C₃	semidirect
59. C₃×C₁₃	C₂×C₃×D₄₇	semidirect
61. C₁₃⋊C₃	D₃×D₄₇	direct (N × H)
69. C₁₃	C₃×D₃×D₄₇	semidirect
79. D₃	C₁₃⋊C₃×D₄₇	direct (N × H)
83. C₃	C₂×C₁₃⋊C₃×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₃⋊C₃×D₁₄₁	2
D₃×C₁₃⋊C₃×C₄₇	2
C₃×C₁₃⋊C₃×D₄₇	2
D₃×C₁₃×D₄₇	3
C₂×C₁₃⋊C₃×D₄₇	3
C₃×D₃×D₄₇	13
C₂×D₃×C₁₃⋊C₃	47

Subgroups — D3×C13⋊C3×D47 #36347231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₃⋊C₃×D₄₇ #36347231