Subgroups — C₂×C₁₃×D₂₄ #11928879

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×D₁₂	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×D₂₄	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₃×D₈	—	3	1	no	maximal, Hall
5	C₂²×D₃×C₁₃	—	2	2	no	—
6	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
7	C₁₃×D₁₂	—	2	2	no	—
8	C₁₃×D₁₂	C₂²	1	4	yes	complemented
9	C₃×C₈×C₁₃	C₂²	1	2	yes	complemented
10	C₂×D₄×C₁₃	—	3	2	no	—
11	C₁₃×D₈	—	3	4	no	—
12	C₂×C₈×C₁₃	D₃	1	1	yes	characteristic, complemented
13	C₂²×C₃×C₁₃	D₄	1	1	yes	characteristic
14	C₂×D₃×C₁₃	—	2	4	no	—
15	C₂×D₃×C₁₃	—	4	4	no	—
16	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
17	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
18	C₂³×C₁₃	—	6	2	no	—
19	D₄×C₁₃	—	3	4	no	—
20	D₄×C₁₃	—	6	2	no	—
21	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
22	C₈×C₁₃	C₂×D₃	1	2	yes	complemented
23	C₂×D₂₄	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₃×C₁₃	D₈	1	2	yes	complemented
25	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
26	D₃×C₁₃	—	4	4	no	—
27	C₂²×C₁₃	—	6	4	no	—
28	C₂²×C₁₃	—	12	4	no	—
29	C₂²×C₁₃	D₁₂	1	1	yes	characteristic
30	C₄×C₁₃	D₁₂	1	1	yes	characteristic
31	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
32	C₂×D₁₂	C₂×C₁₃	1	2	yes	complemented
33	C₂×C₃×C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
34	D₂₄	C₂×C₁₃	1	4	yes	direct product factor
35	C₃×C₁₃	C₂×D₈	1	1	yes	characteristic, complemented, Hall
36	C₂×D₈	—	3	1	no	Sylow
37	C₂×C₁₃	—	12	4	no	—
38	C₂×C₁₃	D₂₄	1	2	yes	direct product factor
39	C₂×C₁₃	C₂×D₁₂	1	1	yes	characteristic
40	C₂²×D₃	—	2	2	no	—
41	C₂×C₃×C₄	C₂²×C₁₃	1	1	yes	characteristic
42	D₁₂	—	2	2	no	—
43	D₁₂	C₂²×C₁₃	1	4	yes	complemented
44	C₃×C₈	C₂²×C₁₃	1	2	yes	complemented
45	C₂×D₄	—	3	2	no	—
46	D₈	—	3	4	no	—
47	C₂×C₈	D₃×C₁₃	1	1	yes	characteristic, complemented
48	C₁₃	C₂×D₂₄	1	1	yes	characteristic, direct product factor, Sylow
49	C₂²×C₃	D₄×C₁₃	1	1	yes	characteristic
50	C₂×D₃	—	2	4	no	—
51	C₂×D₃	—	4	4	no	—
52	C₃×C₄	D₄×C₁₃	1	1	yes	characteristic
53	C₃×C₄	C₂³×C₁₃	1	1	yes	characteristic
54	C₂³	—	6	2	no	—
55	D₄	—	3	4	no	—
56	D₄	—	6	2	no	—
57	C₂×C₄	C₂×D₃×C₁₃	1	1	yes	characteristic
58	C₈	C₂×D₃×C₁₃	1	2	yes	complemented
59	C₂×C₃	C₁₃×D₈	1	2	yes	complemented
60	C₂×C₃	C₂×D₄×C₁₃	1	1	yes	characteristic
61	D₃	—	4	4	no	—
62	C₂²	—	6	4	no	—
63	C₂²	—	12	4	no	—
64	C₂²	C₁₃×D₁₂	1	1	yes	characteristic
65	C₄	C₁₃×D₁₂	1	1	yes	characteristic
66	C₄	C₂²×D₃×C₁₃	1	1	yes	characteristic
67	C₃	C₂×C₁₃×D₈	1	1	yes	characteristic, complemented, Sylow
68	C₂	—	12	4	no	—
69	C₂	C₁₃×D₂₄	1	2	yes	direct product factor
70	C₂	C₂×C₁₃×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₃	D₁₂
commutator, cosocle	C₃×C₄	C₂³×C₁₃
Frattini	C₄	C₂²×D₃×C₁₃
Fitting	C₂×C₃×C₈×C₁₃	C₂
socle	C₂²×C₃×C₁₃	D₄
hypercenter	C₂×C₈×C₁₃	D₃
hypocenter	C₃	C₂×C₁₃×D₈
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₈×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×D₁₂	C₂	semidirect
2. C₂×C₃×C₈×C₁₃	C₂	semidirect
3. C₁₃×D₂₄	C₂	direct (N × H)
8. C₁₃×D₁₂	C₂²	semidirect
9. C₃×C₈×C₁₃	C₂²	semidirect
12. C₂×C₈×C₁₃	D₃	semidirect
22. C₈×C₁₃	C₂×D₃	semidirect
23. C₂×D₂₄	C₁₃	direct (N × H)
24. C₂×C₃×C₁₃	D₈	semidirect
32. C₂×D₁₂	C₂×C₁₃	semidirect
33. C₂×C₃×C₈	C₂×C₁₃	semidirect
34. D₂₄	C₂×C₁₃	direct (N × H)
35. C₃×C₁₃	C₂×D₈	semidirect
38. C₂×C₁₃	D₂₄	direct (N × H)
43. D₁₂	C₂²×C₁₃	semidirect
44. C₃×C₈	C₂²×C₁₃	semidirect
47. C₂×C₈	D₃×C₁₃	semidirect
48. C₁₃	C₂×D₂₄	direct (N × H)
58. C₈	C₂×D₃×C₁₃	semidirect
59. C₂×C₃	C₁₃×D₈	semidirect
67. C₃	C₂×C₁₃×D₈	semidirect
69. C₂	C₁₃×D₂₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×D₁₂	2
C₂×C₃×C₈×C₁₃	2
C₁₃×D₂₄	2
C₂×C₁₃×D₈	3
C₂×D₂₄	13

Subgroups — C2×C13×D24 #11928879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×D₂₄ #11928879