Subgroups — D₃×D₁₃×C₆₇⋊C₃ #44535739

Order 31356.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₉×C₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₃×C₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₃×C₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₁₃×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₃×C₆₇⋊C₃	—	3	1	no	maximal
6	C₃×C₁₃×C₆₇⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₁₃×C₆₇⋊C₃	—	2	1	no	—
8	D₁₃×C₆₇⋊C₃	—	3	1	no	—
9	D₁₃×C₆₇⋊C₃	D₃	1	1	yes	characteristic, direct product factor
10	C₆₇×D₃₉	C₂×C₃	1	1	yes	characteristic, complemented
11	D₃×C₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×D₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×C₁₃×C₆₇⋊C₃	—	3	1	no	—
14	C₂×D₁₃×C₆₇	—	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	C₂×D₃×C₆₇⋊C₃	—	13	1	no	maximal, Hall
19	C₂×C₁₃×C₆₇	—	3	1	no	—
20	D₁₃×C₆₇	—	3	1	no	—
21	D₁₃×C₆₇	C₃×D₃	1	1	yes	characteristic, complemented
22	C₂×C₃×C₆₇⋊C₃	—	13	1	no	—
23	D₃×C₆₇⋊C₃	—	13	1	no	—
24	D₃×C₆₇⋊C₃	D₁₃	1	1	yes	characteristic, direct product factor
25	C₁₃×C₆₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
26	C₂×D₃×C₆₇	—	13	1	no	—
27	C₂²×C₆₇⋊C₃	—	39	1	no	—
28	C₃×C₆₇⋊C₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
29	C₃×D₃×D₁₃	—	67	1	no	maximal, Hall
30	C₂×C₃×C₆₇	—	13	1	no	—
31	D₃×C₆₇	—	13	1	no	—
32	D₃×C₆₇	C₃×D₁₃	1	1	yes	characteristic, complemented
33	C₂×C₆₇⋊C₃	—	3	1	no	—
34	C₂×C₆₇⋊C₃	—	13	1	no	—
35	C₂×C₆₇⋊C₃	—	26	1	no	—
36	C₂×C₆₇⋊C₃	—	39	1	no	—
37	C₂²×C₆₇	—	39	1	no	Hall
38	C₃×D₃₉	—	67	1	no	—
39	C₃×D₃×C₁₃	—	67	1	no	—
40	C₃²×D₁₃	—	67	1	no	—
41	C₃×C₆₇	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented
42	C₆₇⋊C₃	—	2	1	no	—
43	C₆₇⋊C₃	D₃×D₁₃	1	1	yes	characteristic, direct product factor
44	C₂×C₃×D₁₃	—	201	1	no	—
45	D₃×D₁₃	C₆₇⋊C₃	1	1	yes	characteristic, direct product factor
46	C₂×C₆₇	—	3	1	no	—
47	C₂×C₆₇	—	13	1	no	—
48	C₂×C₆₇	—	39	1	no	—
49	C₃²×C₁₃	—	67	1	no	Hall
50	C₂×C₃×C₁₃	—	201	1	no	—
51	D₃₉	C₂×C₆₇⋊C₃	1	1	yes	characteristic, complemented
52	C₃×D₁₃	—	67	1	no	—
53	C₃×D₁₃	—	134	1	no	—
54	C₃×D₁₃	—	201	1	no	—
55	C₃×D₁₃	C₂×C₆₇⋊C₃	1	1	yes	characteristic, complemented
56	D₃×C₁₃	C₂×C₆₇⋊C₃	1	1	yes	characteristic, complemented
57	C₆₇	C₃×D₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
58	C₂×D₁₃	—	3	1	no	Hall
59	C₃×C₁₃	—	67	1	no	—
60	C₃×C₁₃	—	134	1	no	—
61	C₃×C₁₃	C₂²×C₆₇⋊C₃	1	1	yes	characteristic, complemented
62	C₂×C₃×D₃	—	871	1	no	Hall
63	C₂×C₁₃	—	3	1	no	—
64	D₁₃	—	3	1	no	—
65	D₁₃	D₃×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor
66	C₂×C₃²	—	871	1	no	—
67	C₃×D₃	—	67	1	no	—
68	C₃×D₃	—	871	1	no	—
69	C₁₃	C₂×D₃×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₃	—	2613	1	no	—
71	C₂×D₃	—	13	1	no	—
72	C₃²	—	67	1	no	Sylow
73	C₂×C₃	—	13	1	no	—
74	C₂×C₃	—	2613	1	no	—
75	C₂×C₃	—	871	1	no	—
76	C₂×C₃	—	201	1	no	—
77	C₂×C₃	—	1742	1	no	—
78	D₃	—	13	1	no	—
79	D₃	D₁₃×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor
80	C₂²	—	39	1	no	Sylow
81	C₃	—	67	1	no	—
82	C₃	—	134	1	no	—
83	C₃	C₂×D₁₃×C₆₇⋊C₃	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	13	1	no	—
86	C₂	—	39	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. D₃₉×C₆₇⋊C₃	C₂	semidirect
2. D₃×C₁₃×C₆₇⋊C₃	C₂	semidirect
3. C₃×D₁₃×C₆₇⋊C₃	C₂	semidirect
4. D₃×D₁₃×C₆₇	C₃	semidirect
6. C₃×C₁₃×C₆₇⋊C₃	C₂²	semidirect
9. D₁₃×C₆₇⋊C₃	D₃	direct (N × H)
10. C₆₇×D₃₉	C₂×C₃	semidirect
11. D₃×C₁₃×C₆₇	C₂×C₃	semidirect
12. C₃×D₁₃×C₆₇	C₂×C₃	semidirect
15. C₃×C₁₃×C₆₇	C₂²×C₃	semidirect
17. C₁₃×C₆₇⋊C₃	C₂×D₃	semidirect
21. D₁₃×C₆₇	C₃×D₃	semidirect
24. D₃×C₆₇⋊C₃	D₁₃	direct (N × H)
25. C₁₃×C₆₇	C₂×C₃×D₃	semidirect
28. C₃×C₆₇⋊C₃	C₂×D₁₃	semidirect
32. D₃×C₆₇	C₃×D₁₃	semidirect
41. C₃×C₆₇	C₂×C₃×D₁₃	semidirect
43. C₆₇⋊C₃	D₃×D₁₃	direct (N × H)
45. D₃×D₁₃	C₆₇⋊C₃	direct (N × H)
51. D₃₉	C₂×C₆₇⋊C₃	semidirect
55. C₃×D₁₃	C₂×C₆₇⋊C₃	semidirect
56. D₃×C₁₃	C₂×C₆₇⋊C₃	semidirect
57. C₆₇	C₃×D₃×D₁₃	semidirect
61. C₃×C₁₃	C₂²×C₆₇⋊C₃	semidirect
65. D₁₃	D₃×C₆₇⋊C₃	direct (N × H)
69. C₁₃	C₂×D₃×C₆₇⋊C₃	semidirect
79. D₃	D₁₃×C₆₇⋊C₃	direct (N × H)
83. C₃	C₂×D₁₃×C₆₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
D₃₉×C₆₇⋊C₃	2
D₃×C₁₃×C₆₇⋊C₃	2
C₃×D₁₃×C₆₇⋊C₃	2
D₃×D₁₃×C₆₇	3
C₂×D₁₃×C₆₇⋊C₃	3
C₂×D₃×C₆₇⋊C₃	13
C₃×D₃×D₁₃	67

Subgroups — D3×D13×C67⋊C3 #44535739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₁₃×C₆₇⋊C₃ #44535739