Subgroups — C₃×D₈×D₁₃ #11928800

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₃×D₄×D₁₃	C₂	semidirect
2. C₃×C₁₃×D₈	C₂	semidirect
3. C₃×#6104	C₂	semidirect
4. C₃×D₁₀₄	C₂	semidirect
5. C₃×C₈×D₁₃	C₂	semidirect
6. D₈×D₁₃	C₃	direct (N × H)
8. C₃×D₄×C₁₃	C₂²	semidirect
10. C₃×D₅₂	C₂²	semidirect
12. C₃×C₈×C₁₃	C₂²	semidirect
13. C₃×#1055	C₂²	semidirect
14. D₄×D₁₃	C₂×C₃	semidirect
15. C₁₃×D₈	C₂×C₃	semidirect
16. #6104	C₂×C₃	semidirect
17. D₁₀₄	C₂×C₃	semidirect
18. C₈×D₁₃	C₂×C₃	semidirect
26. D₄×C₁₃	C₂²×C₃	semidirect
28. D₅₂	C₂²×C₃	semidirect
30. C₈×C₁₃	C₂²×C₃	semidirect
31. #1055	C₂²×C₃	semidirect
36. C₃×D₁₃	D₈	direct (N × H)
46. C₃×D₈	D₁₃	direct (N × H)
48. C₃×C₁₃	C₂×D₈	semidirect
53. D₁₃	C₃×D₈	direct (N × H)
57. C₃×D₄	C₂×D₁₃	semidirect
60. C₃×C₈	C₂×D₁₃	semidirect
64. D₈	C₃×D₁₃	direct (N × H)
66. C₁₃	C₂×C₃×D₈	semidirect
76. D₄	C₂×C₃×D₁₃	semidirect
79. C₈	C₂×C₃×D₁₃	semidirect
90. C₃	D₈×D₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₄×D₁₃	2
C₃×C₁₃×D₈	2
C₃×#6104	2
C₃×D₁₀₄	2
C₃×C₈×D₁₃	2
D₈×D₁₃	3
C₂×C₃×D₈	13

Subgroups — C3×D8×D13 #11928800

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₈×D₁₃ #11928800