Subgroups — D₃×C₁₃×D₈ #11928886

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×D₄×C₁₃	C₂	1	2	yes	maximal, complemented
2	C₃×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#213	C₂	1	2	yes	maximal, complemented
4	C₁₃×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×D₈	—	3	1	no	maximal, Hall
7	C₂²×D₃×C₁₃	—	2	2	no	—
8	C₃×D₄×C₁₃	C₂²	1	2	yes	complemented
9	C₁₃×#67	—	2	2	no	—
10	C₁₃×D₁₂	C₂²	1	2	yes	complemented
11	C₄×D₃×C₁₃	C₂²	1	1	yes	characteristic
12	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
13	C₁₃×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
14	C₂×D₄×C₁₃	—	3	2	no	—
15	C₁₃×D₈	—	3	2	no	—
16	C₁₃×D₈	—	3	1	no	—
17	C₁₃×D₈	D₃	1	1	yes	characteristic, direct product factor
18	C₂×C₈×C₁₃	—	3	1	no	—
19	C₂²×C₃×C₁₃	—	2	2	no	—
20	C₂×D₃×C₁₃	—	2	2	no	—
21	C₂×D₃×C₁₃	—	4	4	no	—
22	C₂×D₃×C₁₃	D₄	1	1	yes	characteristic
23	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	Dic₃×C₁₃	D₄	1	1	yes	characteristic
25	C₂³×C₁₃	—	6	2	no	—
26	D₄×C₁₃	—	3	2	no	—
27	D₄×C₁₃	—	6	2	no	—
28	D₄×C₁₃	C₂×D₃	1	2	yes	complemented
29	C₂×C₄×C₁₃	—	3	1	no	—
30	C₈×C₁₃	—	3	1	no	—
31	C₈×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented
32	D₃×D₈	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂×C₃×C₁₃	—	4	2	no	—
34	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
35	D₃×C₁₃	—	4	2	no	—
36	D₃×C₁₃	D₈	1	2	yes	direct product factor
37	C₂²×C₁₃	—	2	2	no	—
38	C₂²×C₁₃	—	3	1	no	—
39	C₂²×C₁₃	—	6	2	no	—
40	C₂²×C₁₃	—	12	4	no	—
41	C₄×C₁₃	—	3	1	no	—
42	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
43	D₃×D₄	C₂×C₁₃	1	2	yes	complemented
44	C₃×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
45	#213	C₂×C₁₃	1	2	yes	complemented
46	D₂₄	C₂×C₁₃	1	1	yes	characteristic, complemented
47	D₃×C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
48	C₃×C₁₃	C₂×D₈	1	1	yes	characteristic, complemented, Hall
49	C₂×D₈	—	3	1	no	Sylow
50	C₂×C₁₃	—	3	2	no	—
51	C₂×C₁₃	—	4	2	no	—
52	C₂×C₁₃	—	12	2	no	—
53	C₂×C₁₃	D₃×D₄	1	1	yes	characteristic
54	C₂²×D₃	—	2	2	no	—
55	C₃×D₄	C₂²×C₁₃	1	2	yes	complemented
56	#67	—	2	2	no	—
57	D₁₂	C₂²×C₁₃	1	2	yes	complemented
58	C₄×D₃	C₂²×C₁₃	1	1	yes	characteristic
59	C₃×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
60	C₃⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
61	C₂×D₄	—	3	2	no	—
62	D₈	—	3	2	no	—
63	D₈	—	3	1	no	—
64	D₈	D₃×C₁₃	1	1	yes	characteristic, direct product factor
65	C₂×C₈	—	3	1	no	—
66	C₁₃	D₃×D₈	1	1	yes	characteristic, direct product factor, Sylow
67	C₂²×C₃	—	2	2	no	—
68	C₂×D₃	—	2	2	no	—
69	C₂×D₃	—	4	4	no	—
70	C₂×D₃	D₄×C₁₃	1	1	yes	characteristic
71	C₃×C₄	C₂³×C₁₃	1	1	yes	characteristic
72	Dic₃	D₄×C₁₃	1	1	yes	characteristic
73	C₂³	—	6	2	no	—
74	D₄	—	3	2	no	—
75	D₄	—	6	2	no	—
76	D₄	C₂×D₃×C₁₃	1	2	yes	complemented
77	C₂×C₄	—	3	1	no	—
78	C₈	—	3	1	no	—
79	C₈	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented
80	C₂×C₃	—	4	2	no	—
81	C₂×C₃	C₂×D₄×C₁₃	1	1	yes	characteristic
82	D₃	—	4	2	no	—
83	D₃	C₁₃×D₈	1	2	yes	direct product factor
84	C₂²	—	2	2	no	—
85	C₂²	—	3	1	no	—
86	C₂²	—	6	2	no	—
87	C₂²	—	12	4	no	—
88	C₄	—	3	1	no	—
89	C₄	C₂²×D₃×C₁₃	1	1	yes	characteristic
90	C₃	C₂×C₁₃×D₈	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	3	2	no	—
92	C₂	—	4	2	no	—
93	C₂	—	12	2	no	—
94	C₂	D₃×D₄×C₁₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. D₃×D₄×C₁₃	C₂	semidirect
2. C₃×C₁₃×D₈	C₂	semidirect
3. C₁₃×#213	C₂	semidirect
4. C₁₃×D₂₄	C₂	semidirect
5. D₃×C₈×C₁₃	C₂	semidirect
8. C₃×D₄×C₁₃	C₂²	semidirect
10. C₁₃×D₁₂	C₂²	semidirect
12. C₃×C₈×C₁₃	C₂²	semidirect
13. C₁₃×C₃⋊C₈	C₂²	semidirect
17. C₁₃×D₈	D₃	direct (N × H)
28. D₄×C₁₃	C₂×D₃	semidirect
31. C₈×C₁₃	C₂×D₃	semidirect
32. D₃×D₈	C₁₃	direct (N × H)
36. D₃×C₁₃	D₈	direct (N × H)
43. D₃×D₄	C₂×C₁₃	semidirect
44. C₃×D₈	C₂×C₁₃	semidirect
45. #213	C₂×C₁₃	semidirect
46. D₂₄	C₂×C₁₃	semidirect
47. D₃×C₈	C₂×C₁₃	semidirect
48. C₃×C₁₃	C₂×D₈	semidirect
55. C₃×D₄	C₂²×C₁₃	semidirect
57. D₁₂	C₂²×C₁₃	semidirect
59. C₃×C₈	C₂²×C₁₃	semidirect
60. C₃⋊C₈	C₂²×C₁₃	semidirect
64. D₈	D₃×C₁₃	direct (N × H)
66. C₁₃	D₃×D₈	direct (N × H)
76. D₄	C₂×D₃×C₁₃	semidirect
79. C₈	C₂×D₃×C₁₃	semidirect
83. D₃	C₁₃×D₈	direct (N × H)
90. C₃	C₂×C₁₃×D₈	semidirect

Maximal subgroups

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

subgroup	index
D₃×D₄×C₁₃	2
C₃×C₁₃×D₈	2
C₁₃×#213	2
C₁₃×D₂₄	2
D₃×C₈×C₁₃	2
C₂×C₁₃×D₈	3
D₃×D₈	13

Subgroups — D3×C13×D8 #11928886

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₃×D₈ #11928886