Subgroups — D₃×C₁₃×Q₁₆ #11928893

Order 1248.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×Q₈×C₁₃	C₂	1	2	yes	maximal
2	C₃×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#216	C₂	1	2	yes	maximal, complemented
4	C₁₃×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×Q₁₆	—	3	1	no	maximal, Hall
7	C₃×Q₈×C₁₃	C₂²	1	2	yes	—
8	C₄×D₃×C₁₃	—	2	2	no	—
9	C₄×D₃×C₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×Dic₆	—	2	2	no	—
11	C₁₃×Dic₆	C₂²	1	2	yes	—
12	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×Q₈×C₁₃	—	3	2	no	—
15	C₁₃×Q₁₆	—	3	2	no	—
16	C₁₃×Q₁₆	—	3	1	no	—
17	C₁₃×Q₁₆	D₃	1	1	yes	characteristic, direct product factor
18	C₂×C₈×C₁₃	—	3	1	no	—
19	C₂×D₃×C₁₃	D₄	1	1	yes	characteristic
20	C₃×C₄×C₁₃	—	2	2	no	—
21	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
22	Dic₃×C₁₃	—	2	2	no	—
23	Dic₃×C₁₃	D₄	1	1	yes	characteristic
24	Q₈×C₁₃	—	3	2	no	—
25	Q₈×C₁₃	—	6	2	no	—
26	Q₈×C₁₃	C₂×D₃	1	2	yes	—
27	C₂×C₄×C₁₃	—	3	1	no	—
28	C₂×C₄×C₁₃	—	6	2	no	—
29	C₈×C₁₃	—	3	1	no	—
30	C₈×C₁₃	C₂×D₃	1	1	yes	characteristic
31	D₃×Q₁₆	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
33	D₃×C₁₃	Q₁₆	1	2	yes	direct product factor
34	C₂²×C₁₃	—	3	1	no	—
35	C₄×C₁₃	—	2	2	no	—
36	C₄×C₁₃	—	3	1	no	—
37	C₄×C₁₃	—	6	2	no	—
38	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
39	D₃×Q₈	C₂×C₁₃	1	2	yes	—
40	C₃×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
41	#216	C₂×C₁₃	1	2	yes	complemented
42	Dic₁₂	C₂×C₁₃	1	1	yes	characteristic, complemented
43	D₃×C₈	C₂×C₁₃	1	1	yes	characteristic
44	C₃×C₁₃	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
45	C₂×Q₁₆	—	3	1	no	Sylow
46	C₂×C₁₃	—	3	2	no	—
47	C₂×C₁₃	D₃×D₄	1	1	yes	characteristic
48	C₃×Q₈	C₂²×C₁₃	1	2	yes	—
49	C₄×D₃	—	2	2	no	—
50	C₄×D₃	C₂²×C₁₃	1	1	yes	characteristic
51	Dic₆	—	2	2	no	—
52	Dic₆	C₂²×C₁₃	1	2	yes	—
53	C₃×C₈	C₂²×C₁₃	1	1	yes	characteristic
54	C₃⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
55	C₂×Q₈	—	3	2	no	—
56	Q₁₆	—	3	2	no	—
57	Q₁₆	—	3	1	no	—
58	Q₁₆	D₃×C₁₃	1	1	yes	characteristic, direct product factor
59	C₂×C₈	—	3	1	no	—
60	C₁₃	D₃×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
61	C₂×D₃	D₄×C₁₃	1	1	yes	characteristic
62	C₃×C₄	—	2	2	no	—
63	C₃×C₄	C₂³×C₁₃	1	1	yes	characteristic
64	Dic₃	—	2	2	no	—
65	Dic₃	D₄×C₁₃	1	1	yes	characteristic
66	Q₈	—	3	2	no	—
67	Q₈	—	6	2	no	—
68	Q₈	C₂×D₃×C₁₃	1	2	yes	—
69	C₂×C₄	—	3	1	no	—
70	C₂×C₄	—	6	2	no	—
71	C₈	—	3	1	no	—
72	C₈	C₂×D₃×C₁₃	1	1	yes	characteristic
73	C₂×C₃	C₂×D₄×C₁₃	1	1	yes	characteristic
74	D₃	C₁₃×Q₁₆	1	2	yes	direct product factor
75	C₂²	—	3	1	no	—
76	C₄	—	2	2	no	—
77	C₄	—	3	1	no	—
78	C₄	—	6	2	no	—
79	C₄	C₂²×D₃×C₁₃	1	1	yes	characteristic
80	C₃	C₂×C₁₃×Q₁₆	1	1	yes	characteristic, complemented, Sylow
81	C₂	—	3	2	no	—
82	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×Q₁₆	C₂
socle	C₂×C₃×C₁₃	C₂×D₄
prime radical	C₂×D₃×C₁₃	D₄
hypercenter	C₁₃×Q₁₆	D₃
hypocenter	C₃	C₂×C₁₃×Q₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₃ ◁ C₄×C₁₃ ◁ C₁₃×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₃×Q₁₆	C₂	semidirect
3. C₁₃×#216	C₂	semidirect
4. C₁₃×Dic₁₂	C₂	semidirect
17. C₁₃×Q₁₆	D₃	direct (N × H)
31. D₃×Q₁₆	C₁₃	direct (N × H)
33. D₃×C₁₃	Q₁₆	direct (N × H)
40. C₃×Q₁₆	C₂×C₁₃	semidirect
41. #216	C₂×C₁₃	semidirect
42. Dic₁₂	C₂×C₁₃	semidirect
44. C₃×C₁₃	C₂×Q₁₆	semidirect
58. Q₁₆	D₃×C₁₃	direct (N × H)
60. C₁₃	D₃×Q₁₆	direct (N × H)
74. D₃	C₁₃×Q₁₆	direct (N × H)
80. C₃	C₂×C₁₃×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
D₃×Q₈×C₁₃	2
C₃×C₁₃×Q₁₆	2
C₁₃×#216	2
C₁₃×Dic₁₂	2
D₃×C₈×C₁₃	2
C₂×C₁₃×Q₁₆	3
D₃×Q₁₆	13

Subgroups — D3×C13×Q16 #11928893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₃×Q₁₆ #11928893