Subgroups — C₂²×C₁₃×D₁₂ #11929287

Order 1248.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₃×C₁₃	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×D₁₂	C₂	1	12	yes	maximal, direct product factor
4	C₂²×D₄×C₁₃	—	3	1	no	maximal, Hall
5	C₂³×C₃×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×D₃×C₁₃	—	2	8	no	—
7	C₂²×D₃×C₁₃	C₂²	1	12	yes	complemented
8	C₂×C₃×C₄×C₁₃	C₂²	1	6	yes	complemented
9	C₁₃×D₁₂	C₂²	1	16	yes	direct product factor
10	C₂⁴×C₁₃	—	3	2	no	—
11	C₂×D₄×C₁₃	—	3	12	no	—
12	C₂²×C₄×C₁₃	D₃	1	1	yes	characteristic, complemented
13	C₂²×C₃×C₁₃	D₄	1	4	yes	complemented
14	C₂²×C₃×C₁₃	C₂³	1	3	yes	—
15	C₂×D₃×C₁₃	—	2	24	no	—
16	C₂×D₃×C₁₃	C₂³	1	8	yes	complemented
17	C₃×C₄×C₁₃	C₂³	1	4	yes	complemented
18	C₂³×C₁₃	—	3	12	no	—
19	C₂³×C₁₃	—	6	8	no	—
20	C₂³×C₁₃	C₂×D₃	1	1	yes	characteristic
21	D₄×C₁₃	—	3	16	no	—
22	C₂×C₄×C₁₃	C₂×D₃	1	6	yes	complemented
23	C₂²×D₁₂	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₃×C₁₃	C₂×D₄	1	6	yes	complemented
25	C₂×C₃×C₁₃	C₂⁴	1	1	yes	characteristic
26	D₃×C₁₃	—	2	8	no	—
27	C₂²×C₁₃	—	3	8	no	—
28	C₂²×C₁₃	—	6	24	no	—
29	C₂²×C₁₃	D₁₂	1	4	yes	direct product factor
30	C₂²×C₁₃	C₂²×D₃	1	3	yes	—
31	C₄×C₁₃	C₂²×D₃	1	4	yes	complemented
32	C₂³×D₃	C₂×C₁₃	1	2	yes	complemented
33	C₂²×C₃×C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
34	C₂×D₁₂	C₂×C₁₃	1	12	yes	direct product factor
35	C₃×C₁₃	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
36	C₂²×D₄	—	3	1	no	Sylow
37	C₂×C₁₃	—	6	8	no	—
38	C₂×C₁₃	C₂×D₁₂	1	6	yes	direct product factor
39	C₂×C₁₃	C₂³×D₃	1	1	yes	characteristic
40	C₂³×C₃	C₂²×C₁₃	1	1	yes	characteristic
41	C₂²×D₃	—	2	8	no	—
42	C₂²×D₃	C₂²×C₁₃	1	12	yes	complemented
43	C₂×C₃×C₄	C₂²×C₁₃	1	6	yes	complemented
44	D₁₂	C₂²×C₁₃	1	16	yes	direct product factor
45	C₂⁴	—	3	2	no	—
46	C₂×D₄	—	3	12	no	—
47	C₂²×C₄	D₃×C₁₃	1	1	yes	characteristic, complemented
48	C₁₃	C₂²×D₁₂	1	1	yes	characteristic, direct product factor, Sylow
49	C₂²×C₃	D₄×C₁₃	1	4	yes	complemented
50	C₂²×C₃	C₂³×C₁₃	1	3	yes	—
51	C₂×D₃	—	2	24	no	—
52	C₂×D₃	C₂³×C₁₃	1	8	yes	complemented
53	C₃×C₄	C₂³×C₁₃	1	4	yes	complemented
54	C₂³	—	3	12	no	—
55	C₂³	—	6	8	no	—
56	C₂³	C₂×D₃×C₁₃	1	1	yes	characteristic
57	D₄	—	3	16	no	—
58	C₂×C₄	C₂×D₃×C₁₃	1	6	yes	complemented
59	C₂×C₃	C₂×D₄×C₁₃	1	6	yes	complemented
60	C₂×C₃	C₂⁴×C₁₃	1	1	yes	characteristic
61	D₃	—	2	8	no	—
62	C₂²	—	3	8	no	—
63	C₂²	—	6	24	no	—
64	C₂²	C₁₃×D₁₂	1	4	yes	direct product factor
65	C₂²	C₂²×D₃×C₁₃	1	3	yes	—
66	C₄	C₂²×D₃×C₁₃	1	4	yes	complemented
67	C₃	C₂²×D₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
68	C₂	—	6	8	no	—
69	C₂	C₂×C₁₃×D₁₂	1	6	yes	direct product factor
70	C₂	C₂³×D₃×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₁₃	C₂×D₃
commutator, cosocle	C₂×C₃	C₂⁴×C₁₃
Frattini	C₂	C₂³×D₃×C₁₃
Fitting	C₂²×C₃×C₄×C₁₃	C₂
socle	C₂³×C₃×C₁₃	C₂²
hypercenter	C₂²×C₄×C₁₃	D₃
hypocenter	C₃	C₂²×D₄×C₁₃
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂³×D₃×C₁₃	C₂	semidirect
2. C₂²×C₃×C₄×C₁₃	C₂	semidirect
3. C₂×C₁₃×D₁₂	C₂	direct (N × H)
7. C₂²×D₃×C₁₃	C₂²	semidirect
8. C₂×C₃×C₄×C₁₃	C₂²	semidirect
9. C₁₃×D₁₂	C₂²	direct (N × H)
12. C₂²×C₄×C₁₃	D₃	semidirect
13. C₂²×C₃×C₁₃	D₄	semidirect
16. C₂×D₃×C₁₃	C₂³	semidirect
17. C₃×C₄×C₁₃	C₂³	semidirect
22. C₂×C₄×C₁₃	C₂×D₃	semidirect
23. C₂²×D₁₂	C₁₃	direct (N × H)
24. C₂×C₃×C₁₃	C₂×D₄	semidirect
29. C₂²×C₁₃	D₁₂	direct (N × H)
31. C₄×C₁₃	C₂²×D₃	semidirect
32. C₂³×D₃	C₂×C₁₃	semidirect
33. C₂²×C₃×C₄	C₂×C₁₃	semidirect
34. C₂×D₁₂	C₂×C₁₃	direct (N × H)
35. C₃×C₁₃	C₂²×D₄	semidirect
38. C₂×C₁₃	C₂×D₁₂	direct (N × H)
42. C₂²×D₃	C₂²×C₁₃	semidirect
43. C₂×C₃×C₄	C₂²×C₁₃	semidirect
44. D₁₂	C₂²×C₁₃	direct (N × H)
47. C₂²×C₄	D₃×C₁₃	semidirect
48. C₁₃	C₂²×D₁₂	direct (N × H)
49. C₂²×C₃	D₄×C₁₃	semidirect
52. C₂×D₃	C₂³×C₁₃	semidirect
53. C₃×C₄	C₂³×C₁₃	semidirect
58. C₂×C₄	C₂×D₃×C₁₃	semidirect
59. C₂×C₃	C₂×D₄×C₁₃	semidirect
64. C₂²	C₁₃×D₁₂	direct (N × H)
66. C₄	C₂²×D₃×C₁₃	semidirect
67. C₃	C₂²×D₄×C₁₃	semidirect
69. C₂	C₂×C₁₃×D₁₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₃×C₁₃	2
C₂²×C₃×C₄×C₁₃	2
C₂×C₁₃×D₁₂	2
C₂²×D₄×C₁₃	3
C₂²×D₁₂	13

Subgroups — C22×C13×D12 #11929287

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×D₁₂ #11929287