Subgroups — D₁₃×D₂₄ #11928389

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₂×D₁₃	C₂	1	2	yes	maximal, complemented
2	D₃₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#10597597	C₂	1	2	yes	maximal, complemented
6	D₈×D₁₃	—	3	1	no	maximal, Hall
7	C₂×D₃×D₁₃	—	2	2	no	—
8	D₁₅₆	C₂²	1	2	yes	complemented
9	C₁₃×D₁₂	C₂²	1	2	yes	complemented
10	C₃×C₄×D₁₃	C₂²	1	1	yes	characteristic
11	#64604	—	2	2	no	—
12	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
13	C₃×#1055	C₂²	1	1	yes	characteristic, complemented
14	D₄×D₁₃	—	3	2	no	—
15	C₁₃×D₈	—	3	1	no	—
16	#6104	—	3	2	no	—
17	D₁₀₄	—	3	1	no	—
18	C₈×D₁₃	D₃	1	1	yes	characteristic, complemented
19	C₂×D₃₉	—	2	2	no	—
20	C₂×D₃×C₁₃	—	2	2	no	—
21	C₂×C₃×D₁₃	D₄	1	1	yes	characteristic
22	D₃×D₁₃	—	4	4	no	—
23	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₃×Dic₁₃	D₄	1	1	yes	characteristic
25	C₂²×D₁₃	—	6	2	no	—
26	D₄×C₁₃	—	3	2	no	—
27	C₂²⋊D₁₃	—	6	2	no	—
28	D₅₂	—	3	2	no	—
29	C₄×D₁₃	C₂×D₃	1	1	yes	characteristic
30	C₈×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented
31	#1055	C₂×D₃	1	1	yes	characteristic, complemented
32	C₂×D₂₄	—	13	1	no	maximal, Hall
33	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
34	D₃₉	—	4	2	no	—
35	C₃×D₁₃	D₈	1	2	yes	complemented
36	D₃×C₁₃	—	4	2	no	—
37	C₂²×C₁₃	—	6	2	no	—
38	C₂×D₁₃	—	6	2	no	—
39	C₂×D₁₃	—	12	4	no	—
40	C₂×D₁₃	D₁₂	1	1	yes	characteristic
41	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
42	Dic₁₃	D₁₂	1	1	yes	characteristic
43	C₂×D₁₂	—	13	2	no	—
44	C₂×C₃×C₈	—	13	1	no	—
45	D₂₄	—	13	2	no	—
46	D₂₄	—	13	1	no	—
47	D₂₄	D₁₃	1	1	yes	characteristic, direct product factor
48	C₃×C₁₃	C₂×D₈	1	1	yes	characteristic, complemented, Hall
49	C₂×D₈	—	39	1	no	Sylow
50	C₂×C₁₃	—	12	2	no	—
51	C₂×C₁₃	C₂×D₁₂	1	1	yes	characteristic
52	D₁₃	—	12	2	no	—
53	D₁₃	D₂₄	1	2	yes	direct product factor
54	C₂²×D₃	—	26	2	no	—
55	C₂×C₃×C₄	—	13	1	no	—
56	D₁₂	—	13	2	no	—
57	D₁₂	—	26	2	no	—
58	D₁₂	C₂×D₁₃	1	2	yes	complemented
59	C₃×C₈	—	13	1	no	—
60	C₃×C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
61	C₂×D₄	—	39	2	no	—
62	D₈	—	3	1	no	—
63	D₈	—	39	2	no	—
64	D₈	—	39	1	no	—
65	C₂×C₈	—	13	1	no	—
66	C₁₃	C₂×D₂₄	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₃	—	13	1	no	—
68	C₂×D₃	—	2	2	no	—
69	C₂×D₃	—	26	2	no	—
70	C₂×D₃	—	52	4	no	—
71	C₃×C₄	—	13	1	no	—
72	C₃×C₄	C₂²×D₁₃	1	1	yes	characteristic
73	C₂³	—	78	2	no	—
74	D₄	—	3	2	no	—
75	D₄	—	39	2	no	—
76	D₄	—	78	2	no	—
77	C₂×C₄	—	13	1	no	—
78	C₈	—	13	1	no	—
79	C₈	D₃×D₁₃	1	1	yes	characteristic, complemented
80	C₂×C₃	—	13	2	no	—
81	C₂×C₃	D₄×D₁₃	1	1	yes	characteristic
82	D₃	—	4	2	no	—
83	D₃	—	52	2	no	—
84	C₂²	—	6	2	no	—
85	C₂²	—	13	1	no	—
86	C₂²	—	78	2	no	—
87	C₂²	—	156	4	no	—
88	C₄	—	13	1	no	—
89	C₄	C₂×D₃×D₁₃	1	1	yes	characteristic
90	C₃	D₈×D₁₃	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	12	2	no	—
92	C₂	—	13	2	no	—
93	C₂	—	156	2	no	—
94	C₂	D₁₂×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₂×D₁₃
commutator, cosocle	C₃×C₄×C₁₃	C₂³
Frattini	C₄	C₂×D₃×D₁₃
Fitting	C₃×C₈×C₁₃	C₂²
socle	C₂×C₃×C₁₃	C₂×D₄
hypercenter	C₈	D₃×D₁₃
hypocenter	C₃×C₁₃	C₂×D₈
LCS	G ▷ C₃×C₄×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
1. D₁₂×D₁₃	C₂	semidirect
2. D₃₁₂	C₂	semidirect
3. C₁₃×D₂₄	C₂	semidirect
4. C₃×C₈×D₁₃	C₂	semidirect
5. #10597597	C₂	semidirect
8. D₁₅₆	C₂²	semidirect
9. C₁₃×D₁₂	C₂²	semidirect
12. C₃×C₈×C₁₃	C₂²	semidirect
13. C₃×#1055	C₂²	semidirect
18. C₈×D₁₃	D₃	semidirect
30. C₈×C₁₃	C₂×D₃	semidirect
31. #1055	C₂×D₃	semidirect
35. C₃×D₁₃	D₈	semidirect
47. D₂₄	D₁₃	direct (N × H)
48. C₃×C₁₃	C₂×D₈	semidirect
53. D₁₃	D₂₄	direct (N × H)
58. D₁₂	C₂×D₁₃	semidirect
60. C₃×C₈	C₂×D₁₃	semidirect
66. C₁₃	C₂×D₂₄	semidirect
79. C₈	D₃×D₁₃	semidirect
90. C₃	D₈×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
D₁₂×D₁₃	2
D₃₁₂	2
C₁₃×D₂₄	2
C₃×C₈×D₁₃	2
#10597597	2
D₈×D₁₃	3
C₂×D₂₄	13

Subgroups — D13×D24 #11928389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×D₂₄ #11928389