Subgroups — C₂²×D₄×C₁₃⋊C₃ #11929247

Order 1248.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₁₃⋊C₃	C₂	semidirect
2. C₂×D₄×C₁₃⋊C₃	C₂	direct (N × H)
3. C₂²×C₄×C₁₃⋊C₃	C₂	semidirect
4. C₂²×D₄×C₁₃	C₃	semidirect
7. C₂³×C₁₃⋊C₃	C₂²	semidirect
8. D₄×C₁₃⋊C₃	C₂²	direct (N × H)
9. C₂×C₄×C₁₃⋊C₃	C₂²	semidirect
10. C₂⁴×C₁₃	C₂×C₃	semidirect
11. C₂×D₄×C₁₃	C₂×C₃	semidirect
12. C₂²×C₄×C₁₃	C₂×C₃	semidirect
14. C₂²×C₁₃⋊C₃	D₄	direct (N × H)
16. C₂²×C₁₃⋊C₃	C₂³	semidirect
17. C₄×C₁₃⋊C₃	C₂³	semidirect
20. C₂³×C₁₃	C₂²×C₃	semidirect
21. D₄×C₁₃	C₂²×C₃	semidirect
22. C₂×C₄×C₁₃	C₂²×C₃	semidirect
25. C₂×C₁₃⋊C₃	C₂×D₄	direct (N × H)
28. C₂²×C₁₃	C₃×D₄	semidirect
30. C₂²×C₁₃	C₂³×C₃	semidirect
31. C₄×C₁₃	C₂³×C₃	semidirect
35. C₁₃⋊C₃	C₂²×D₄	direct (N × H)
36. C₂²×D₄	C₁₃⋊C₃	direct (N × H)
38. C₂×C₁₃	C₂×C₃×D₄	semidirect
45. C₂⁴	C₂×C₁₃⋊C₃	semidirect
46. C₂×D₄	C₂×C₁₃⋊C₃	direct (N × H)
47. C₂²×C₄	C₂×C₁₃⋊C₃	semidirect
48. C₁₃	C₂²×C₃×D₄	semidirect
56. C₂³	C₂²×C₁₃⋊C₃	semidirect
57. D₄	C₂²×C₁₃⋊C₃	direct (N × H)
58. C₂×C₄	C₂²×C₁₃⋊C₃	semidirect
63. C₂²	D₄×C₁₃⋊C₃	direct (N × H)
65. C₂²	C₂³×C₁₃⋊C₃	semidirect
66. C₄	C₂³×C₁₃⋊C₃	semidirect
69. C₂	C₂×D₄×C₁₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₁₃⋊C₃	2
C₂×D₄×C₁₃⋊C₃	2
C₂²×C₄×C₁₃⋊C₃	2
C₂²×D₄×C₁₃	3
C₂²×C₃×D₄	13

Subgroups — C22×D4×C13⋊C3 #11929247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₄×C₁₃⋊C₃ #11929247