Subgroups — Q₁₆×D₃₉ #11928979

Order 1248.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₃₉	C₂	1	2	yes	maximal
2	C₃×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#10597670	C₂	1	2	yes	maximal, complemented
4	Dic₁₅₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×D₃₉	C₂	1	1	yes	maximal, characteristic
6	Q₁₆×D₁₃	—	3	1	no	maximal, Hall
7	C₃×Q₈×C₁₃	C₂²	1	2	yes	—
8	C₄×D₃₉	—	2	2	no	—
9	C₄×D₃₉	C₂²	1	1	yes	characteristic
10	Dic₇₈	—	2	2	no	—
11	Dic₇₈	C₂²	1	2	yes	—
12	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₃⋊#1055	C₂²	1	1	yes	characteristic
14	Q₈×D₁₃	—	3	2	no	—
15	C₁₃×Q₁₆	D₃	1	1	yes	characteristic, complemented
16	#6107	—	3	2	no	—
17	Dic₅₂	—	3	1	no	—
18	C₈×D₁₃	—	3	1	no	—
19	C₂×D₃₉	D₄	1	1	yes	characteristic
20	C₃×C₄×C₁₃	—	2	2	no	—
21	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
22	Dic₃₉	—	2	2	no	—
23	Dic₃₉	D₄	1	1	yes	characteristic
24	Q₈×C₁₃	C₂×D₃	1	2	yes	—
25	C₄×D₁₃	—	3	1	no	—
26	C₄×D₁₃	—	6	2	no	—
27	Dic₂₆	—	3	2	no	—
28	Dic₂₆	—	6	2	no	—
29	C₈×C₁₃	C₂×D₃	1	1	yes	characteristic
30	#1055	—	3	1	no	—
31	D₃×Q₁₆	—	13	1	no	maximal, Hall
32	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
33	D₃₉	Q₁₆	1	2	yes	direct product factor
34	C₂×D₁₃	—	3	1	no	—
35	C₄×C₁₃	—	2	2	no	—
36	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
37	Dic₁₃	—	3	1	no	—
38	Dic₁₃	—	6	2	no	—
39	D₃×Q₈	—	13	2	no	—
40	C₃×Q₁₆	D₁₃	1	1	yes	characteristic, complemented
41	#216	—	13	2	no	—
42	Dic₁₂	—	13	1	no	—
43	D₃×C₈	—	13	1	no	—
44	C₃×C₁₃	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
45	C₂×Q₁₆	—	39	1	no	Sylow
46	C₂×C₁₃	D₃×D₄	1	1	yes	characteristic
47	D₁₃	—	3	2	no	—
48	C₃×Q₈	C₂×D₁₃	1	2	yes	—
49	C₄×D₃	—	13	1	no	—
50	C₄×D₃	—	26	2	no	—
51	Dic₆	—	13	2	no	—
52	Dic₆	—	26	2	no	—
53	C₃×C₈	C₂×D₁₃	1	1	yes	characteristic
54	C₃⋊C₈	—	13	1	no	—
55	C₂×Q₈	—	39	2	no	—
56	Q₁₆	—	39	2	no	—
57	Q₁₆	—	39	1	no	—
58	Q₁₆	D₃₉	1	1	yes	characteristic, direct product factor
59	C₂×C₈	—	39	1	no	—
60	C₁₃	D₃×Q₁₆	1	1	yes	characteristic, complemented, Sylow
61	C₂×D₃	—	13	1	no	—
62	C₃×C₄	—	2	2	no	—
63	C₃×C₄	C₂²×D₁₃	1	1	yes	characteristic
64	Dic₃	—	13	1	no	—
65	Dic₃	—	26	2	no	—
66	Q₈	—	39	2	no	—
67	Q₈	—	78	2	no	—
68	Q₈	C₂×D₃₉	1	2	yes	—
69	C₂×C₄	—	39	1	no	—
70	C₂×C₄	—	78	2	no	—
71	C₈	—	39	1	no	—
72	C₈	C₂×D₃₉	1	1	yes	characteristic
73	C₂×C₃	D₄×D₁₃	1	1	yes	characteristic
74	D₃	—	13	2	no	—
75	C₂²	—	39	1	no	—
76	C₄	—	2	2	no	—
77	C₄	—	39	1	no	—
78	C₄	—	78	2	no	—
79	C₄	C₂²×D₃₉	1	1	yes	characteristic
80	C₃	Q₁₆×D₁₃	1	1	yes	characteristic, complemented, Sylow
81	C₂	—	39	2	no	—
82	C₂	D₄×D₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₃₉
commutator, cosocle	C₃×C₄×C₁₃	C₂³
Frattini	C₄	C₂²×D₃₉
Fitting	C₃×C₁₃×Q₁₆	C₂
socle	C₂×C₃×C₁₃	C₂×D₄
prime radical	C₂×D₃₉	D₄
hypercenter	Q₁₆	D₃₉
hypocenter	C₃×C₁₃	C₂×Q₁₆
LCS	G ▷ C₃×C₄×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₃×Q₁₆	C₂	semidirect
3. #10597670	C₂	semidirect
4. Dic₁₅₆	C₂	semidirect
15. C₁₃×Q₁₆	D₃	semidirect
33. D₃₉	Q₁₆	direct (N × H)
40. C₃×Q₁₆	D₁₃	semidirect
44. C₃×C₁₃	C₂×Q₁₆	semidirect
58. Q₁₆	D₃₉	direct (N × H)
60. C₁₃	D₃×Q₁₆	semidirect
80. C₃	Q₁₆×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
Q₈×D₃₉	2
C₃×C₁₃×Q₁₆	2
#10597670	2
Dic₁₅₆	2
C₈×D₃₉	2
Q₁₆×D₁₃	3
D₃×Q₁₆	13

Subgroups — Q16×D39 #11928979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₁₆×D₃₉ #11928979