Subgroups — D₃×M₁₆ #906

Order 96.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₃	C₂	1	1	yes	maximal, characteristic
2	C₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#208	C₂	1	1	yes	maximal, characteristic, complemented
4	ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal, complemented
5	D₃×C₈	C₂	1	2	yes	maximal, complemented
6	C₂×M₁₆	—	3	1	no	maximal, Sylow
7	C₂²×D₃	C₄	1	1	yes	characteristic
8	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
9	C₂×Dic₃	C₄	1	1	yes	characteristic
10	C₄×D₃	C₄	1	1	yes	characteristic
11	C₄×D₃	C₄	1	1	yes	characteristic
12	C₄×D₃	C₂²	1	1	yes	characteristic
13	C₄×D₃	C₂²	1	1	yes	characteristic
14	C₃×C₈	C₂²	1	2	yes	complemented
15	C₃⋊C₈	C₂²	1	2	yes	complemented
16	C₂²×C₄	—	3	1	no	—
17	M₁₆	—	3	1	no	—
18	M₁₆	—	3	2	no	—
19	M₁₆	D₃	1	1	yes	characteristic, direct product factor
20	C₂×C₈	—	3	2	no	—
21	C₂²×C₃	C₂×C₄	1	1	yes	characteristic
22	C₂×D₃	—	2	2	no	—
23	C₂×D₃	C₂×C₄	1	1	yes	characteristic
24	C₂×D₃	C₂×C₄	1	1	yes	characteristic
25	C₃×C₄	C₂×C₄	1	1	yes	characteristic
26	C₃×C₄	C₂³	1	1	yes	characteristic
27	Dic₃	C₂×C₄	1	1	yes	characteristic
28	Dic₃	C₂×C₄	1	1	yes	characteristic
29	C₂³	—	3	1	no	—
30	C₂×C₄	—	3	1	no	—
31	C₂×C₄	—	3	1	no	—
32	C₂×C₄	—	3	1	no	—
33	C₂×C₄	—	3	1	no	—
34	C₂×C₄	—	3	1	no	—
35	C₂×C₄	C₂×D₃	1	1	yes	characteristic
36	C₈	—	3	2	no	—
37	C₈	C₂×D₃	1	2	yes	complemented
38	C₂×C₃	—	2	1	no	—
39	C₂×C₃	C₂²×C₄	1	1	yes	characteristic
40	D₃	—	2	1	no	—
41	D₃	M₁₆	1	2	yes	direct product factor
42	C₂²	—	3	1	no	—
43	C₂²	—	3	1	no	—
44	C₂²	—	6	2	no	—
45	C₂²	C₄×D₃	1	1	yes	characteristic
46	C₄	—	3	1	no	—
47	C₄	—	3	1	no	—
48	C₄	C₄×D₃	1	1	yes	characteristic
49	C₄	C₂²×D₃	1	1	yes	characteristic
50	C₃	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
51	C₂	—	2	1	no	—
52	C₂	—	3	2	no	—
53	C₂	—	6	1	no	—
54	C₂	C₂×C₄×D₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×D₃
commutator, socle	C₂×C₃	C₂²×C₄
Fitting	C₃×M₁₆	C₂
prime radical	C₂²×D₃	C₄
cosocle	C₃×C₄	C₂³
hypercenter	M₁₆	D₃
hypocenter	C₃	C₂×M₁₆
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×M₁₆	C₂	semidirect
3. #208	C₂	semidirect
4. ΓL(1,𝔽₂₅)	C₂	semidirect
5. D₃×C₈	C₂	semidirect
14. C₃×C₈	C₂²	semidirect
15. C₃⋊C₈	C₂²	semidirect
19. M₁₆	D₃	direct (N × H)
37. C₈	C₂×D₃	semidirect
41. D₃	M₁₆	direct (N × H)
50. C₃	C₂×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₃	2
C₃×M₁₆	2
#208	2
ΓL(1,𝔽₂₅)	2
D₃×C₈	2
C₂×M₁₆	3

Subgroups — D3×M16 #906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×M₁₆ #906