Subgroups — Q₁₆×C₃⋊D₃ #64126

Order 288.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₃⋊D₃	C₂	1	2	yes	maximal
2	C₃²×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#3756	C₂	1	2	yes	maximal, complemented
4	#3746	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
6	D₃×Q₁₆	—	3	4	no	maximal
7	C₃²×Q₈	C₂²	1	2	yes	—
8	C₄×C₃⋊D₃	—	2	2	no	—
9	C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
10	#634	—	2	2	no	—
11	#634	C₂²	1	2	yes	—
12	C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
14	D₃×Q₈	—	3	8	no	—
15	C₃×Q₁₆	D₃	1	4	yes	complemented
16	#216	—	3	8	no	—
17	Dic₁₂	—	3	4	no	—
18	D₃×C₈	—	3	4	no	—
19	C₂×C₃⋊D₃	D₄	1	1	yes	characteristic
20	C₃²×C₄	—	2	2	no	—
21	C₃²×C₄	C₂³	1	1	yes	characteristic
22	C₃⋊Dic₃	—	2	2	no	—
23	C₃⋊Dic₃	D₄	1	1	yes	characteristic
24	C₂×Q₁₆	—	9	1	no	Sylow
25	C₃×Q₈	C₂×D₃	1	8	yes	—
26	C₄×D₃	—	3	4	no	—
27	C₄×D₃	—	6	8	no	—
28	Dic₆	—	3	8	no	—
29	Dic₆	—	6	8	no	—
30	C₃×C₈	C₂×D₃	1	4	yes	—
31	C₃⋊C₈	—	3	4	no	—
32	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
33	C₃⋊D₃	Q₁₆	1	2	yes	direct product factor
34	C₂×Q₈	—	9	2	no	—
35	Q₁₆	—	9	2	no	—
36	Q₁₆	—	9	1	no	—
37	Q₁₆	C₃⋊D₃	1	1	yes	characteristic, direct product factor
38	C₂×C₈	—	9	1	no	—
39	C₂×D₃	—	3	4	no	—
40	C₃×C₄	—	2	8	no	—
41	C₃×C₄	C₂²×D₃	1	4	yes	—
42	Dic₃	—	3	4	no	—
43	Dic₃	—	6	8	no	—
44	C₃²	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
45	Q₈	—	9	2	no	—
46	Q₈	—	18	2	no	—
47	Q₈	C₂×C₃⋊D₃	1	2	yes	—
48	C₂×C₄	—	9	1	no	—
49	C₂×C₄	—	18	2	no	—
50	C₈	—	9	1	no	—
51	C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
52	C₂×C₃	D₃×D₄	1	4	yes	—
53	D₃	—	3	8	no	—
54	C₂²	—	9	1	no	—
55	C₄	—	2	2	no	—
56	C₄	—	9	1	no	—
57	C₄	—	18	2	no	—
58	C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
59	C₃	D₃×Q₁₆	1	4	yes	complemented
60	C₂	—	9	2	no	—
61	C₂	D₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×C₃⋊D₃
commutator, cosocle	C₃²×C₄	C₂³
Frattini	C₄	C₂²×C₃⋊D₃
Fitting	C₃²×Q₁₆	C₂
socle	C₂×C₃²	C₂×D₄
prime radical	C₂×C₃⋊D₃	D₄
hypercenter	Q₁₆	C₃⋊D₃
hypocenter	C₃²	C₂×Q₁₆
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₃²×Q₁₆	C₂	semidirect
3. #3756	C₂	semidirect
4. #3746	C₂	semidirect
15. C₃×Q₁₆	D₃	semidirect
33. C₃⋊D₃	Q₁₆	direct (N × H)
37. Q₁₆	C₃⋊D₃	direct (N × H)
44. C₃²	C₂×Q₁₆	semidirect
59. C₃	D₃×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
Q₈×C₃⋊D₃	2
C₃²×Q₁₆	2
#3756	2
#3746	2
C₈×C₃⋊D₃	2
D₃×Q₁₆	3

Subgroups — Q16×C3⋊D3 #64126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₁₆×C₃⋊D₃ #64126