Subgroups — D₃×C₁₃×D₆₇⋊C₃ #44535708

Order 31356.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₁₃×C₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₃⋊(D₆₇⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃×D₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₃×D₆₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×D₆₇⋊C₃	—	3	1	no	maximal
6	C₃×C₁₃×C₆₇⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₁₃×D₆₇⋊C₃	—	2	1	no	—
8	C₁₃×D₆₇⋊C₃	—	3	1	no	—
9	C₁₃×D₆₇⋊C₃	D₃	1	1	yes	characteristic, direct product factor
10	C₁₃×D₂₀₁	C₂×C₃	1	1	yes	characteristic, complemented
11	D₃×C₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×C₁₃×D₆₇	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×C₁₃×C₆₇⋊C₃	—	3	1	no	—
14	C₂×C₁₃×D₆₇	—	3	1	no	Hall
15	C₃×C₁₃×C₆₇	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₁₃×C₆₇⋊C₃	—	2	1	no	—
17	C₁₃×C₆₇⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
18	D₃×D₆₇⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₁₃×C₆₇	—	3	1	no	—
20	C₁₃×D₆₇	—	3	1	no	—
21	C₁₃×D₆₇	C₃×D₃	1	1	yes	characteristic, complemented
22	C₃⋊(D₆₇⋊C₃)	C₂×C₁₃	1	1	yes	characteristic, complemented
23	D₃×C₆₇⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented
24	C₃×D₆₇⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented
25	C₁₃×C₆₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
26	D₃×D₆₇	C₃×C₁₃	1	1	yes	characteristic, complemented
27	C₂×D₆₇⋊C₃	—	3	1	no	—
28	C₃×C₆₇⋊C₃	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×D₃×C₁₃	—	67	1	no	maximal, Hall
30	D₂₀₁	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
31	C₃×D₆₇	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
32	D₃×C₆₇	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
33	C₂×C₆₇⋊C₃	—	3	1	no	—
34	D₆₇⋊C₃	—	2	1	no	—
35	D₆₇⋊C₃	—	3	1	no	—
36	D₆₇⋊C₃	D₃×C₁₃	1	1	yes	characteristic, direct product factor
37	C₂×D₆₇	—	3	1	no	Hall
38	C₂×C₃²×C₁₃	—	67	1	no	—
39	C₃×D₃×C₁₃	—	67	1	no	—
40	C₃×D₃×C₁₃	—	67	1	no	—
41	C₃×C₆₇	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented
42	C₆₇⋊C₃	—	2	1	no	—
43	C₆₇⋊C₃	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented
44	C₂²×C₃×C₁₃	—	201	1	no	—
45	C₂×D₃×C₁₃	—	67	1	no	—
46	C₂×C₆₇	—	3	1	no	—
47	D₆₇	—	3	1	no	—
48	D₆₇	C₃×D₃×C₁₃	1	1	yes	characteristic, complemented
49	C₃²×C₁₃	—	67	1	no	Hall
50	C₂×C₃×C₁₃	—	67	1	no	—
51	C₂×C₃×C₁₃	—	67	1	no	—
52	C₂×C₃×C₁₃	—	134	1	no	—
53	C₂×C₃×C₁₃	—	201	1	no	—
54	C₂×C₃×C₁₃	—	201	1	no	—
55	D₃×C₁₃	—	67	1	no	—
56	D₃×C₁₃	D₆₇⋊C₃	1	1	yes	characteristic, direct product factor
57	C₆₇	C₂×C₃×D₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₁₃	—	201	1	no	Hall
59	C₃×C₁₃	—	67	1	no	—
60	C₃×C₁₃	—	134	1	no	—
61	C₃×C₁₃	C₂×D₆₇⋊C₃	1	1	yes	characteristic, complemented
62	C₂×C₃×D₃	—	67	1	no	Hall
63	C₂×C₁₃	—	3	1	no	—
64	C₂×C₁₃	—	67	1	no	—
65	C₂×C₁₃	—	201	1	no	—
66	C₂×C₃²	—	67	1	no	—
67	C₃×D₃	—	67	1	no	—
68	C₃×D₃	—	67	1	no	—
69	C₁₃	D₃×D₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
70	C₂²×C₃	—	201	1	no	—
71	C₂×D₃	—	67	1	no	—
72	C₃²	—	67	1	no	Sylow
73	C₂×C₃	—	67	1	no	—
74	C₂×C₃	—	67	1	no	—
75	C₂×C₃	—	134	1	no	—
76	C₂×C₃	—	201	1	no	—
77	C₂×C₃	—	201	1	no	—
78	D₃	—	67	1	no	—
79	D₃	C₁₃×D₆₇⋊C₃	1	1	yes	characteristic, direct product factor
80	C₂²	—	201	1	no	Sylow
81	C₃	—	67	1	no	—
82	C₃	—	134	1	no	—
83	C₃	C₂×C₁₃×D₆₇⋊C₃	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	67	1	no	—
86	C₂	—	201	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	D₃×D₆₇⋊C₃
commutator, cosocle, hypocenter	C₃×C₆₇	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₆₇	C₂²×C₃
LCS	G ▷ C₃×C₆₇
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. D₃×C₁₃×C₆₇⋊C₃	C₂	semidirect
2. C₁₃×C₃⋊(D₆₇⋊C₃)	C₂	semidirect
3. C₃×C₁₃×D₆₇⋊C₃	C₂	semidirect
4. D₃×C₁₃×D₆₇	C₃	semidirect
6. C₃×C₁₃×C₆₇⋊C₃	C₂²	semidirect
9. C₁₃×D₆₇⋊C₃	D₃	direct (N × H)
10. C₁₃×D₂₀₁	C₂×C₃	semidirect
11. D₃×C₁₃×C₆₇	C₂×C₃	semidirect
12. C₃×C₁₃×D₆₇	C₂×C₃	semidirect
15. C₃×C₁₃×C₆₇	C₂²×C₃	semidirect
17. C₁₃×C₆₇⋊C₃	C₂×D₃	semidirect
18. D₃×D₆₇⋊C₃	C₁₃	direct (N × H)
21. C₁₃×D₆₇	C₃×D₃	semidirect
22. C₃⋊(D₆₇⋊C₃)	C₂×C₁₃	semidirect
23. D₃×C₆₇⋊C₃	C₂×C₁₃	semidirect
24. C₃×D₆₇⋊C₃	C₂×C₁₃	semidirect
25. C₁₃×C₆₇	C₂×C₃×D₃	semidirect
26. D₃×D₆₇	C₃×C₁₃	semidirect
28. C₃×C₆₇⋊C₃	C₂²×C₁₃	semidirect
30. D₂₀₁	C₂×C₃×C₁₃	semidirect
31. C₃×D₆₇	C₂×C₃×C₁₃	semidirect
32. D₃×C₆₇	C₂×C₃×C₁₃	semidirect
36. D₆₇⋊C₃	D₃×C₁₃	direct (N × H)
41. C₃×C₆₇	C₂²×C₃×C₁₃	semidirect
43. C₆₇⋊C₃	C₂×D₃×C₁₃	semidirect
48. D₆₇	C₃×D₃×C₁₃	semidirect
56. D₃×C₁₃	D₆₇⋊C₃	direct (N × H)
57. C₆₇	C₂×C₃×D₃×C₁₃	semidirect
61. C₃×C₁₃	C₂×D₆₇⋊C₃	semidirect
69. C₁₃	D₃×D₆₇⋊C₃	direct (N × H)
79. D₃	C₁₃×D₆₇⋊C₃	direct (N × H)
83. C₃	C₂×C₁₃×D₆₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
D₃×C₁₃×C₆₇⋊C₃	2
C₁₃×C₃⋊(D₆₇⋊C₃)	2
C₃×C₁₃×D₆₇⋊C₃	2
D₃×C₁₃×D₆₇	3
C₂×C₁₃×D₆₇⋊C₃	3
D₃×D₆₇⋊C₃	13
C₂×C₃×D₃×C₁₃	67

Subgroups — D3×C13×D67⋊C3 #44535708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₃×D₆₇⋊C₃ #44535708