Subgroups — M₁₆×C₃⋊D₃ #64115

Order 288.

204 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#3748	C₂	1	1	yes	maximal, characteristic, complemented
4	#3743	C₂	1	2	yes	maximal, complemented
5	C₈×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
6	D₃×M₁₆	—	3	4	no	maximal
7	C₂²×C₃⋊D₃	C₄	1	1	yes	characteristic
8	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
9	C₂×C₃⋊Dic₃	C₄	1	1	yes	characteristic
10	C₄×C₃⋊D₃	C₄	1	1	yes	characteristic
11	C₄×C₃⋊D₃	C₄	1	1	yes	characteristic
12	C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
13	C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
14	C₃²×C₈	C₂²	1	2	yes	complemented
15	C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
16	C₂×C₄×D₃	—	3	4	no	—
17	C₃×M₁₆	D₃	1	4	yes	complemented
18	#208	—	3	4	no	—
19	ΓL(1,𝔽₂₅)	—	3	8	no	—
20	D₃×C₈	—	3	8	no	—
21	C₂²×C₃²	C₂×C₄	1	1	yes	characteristic
22	C₂×C₃⋊D₃	—	2	2	no	—
23	C₂×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
25	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
26	C₃²×C₄	C₂³	1	1	yes	characteristic
27	C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
28	C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
29	C₂×M₁₆	—	9	1	no	Sylow
30	C₂²×D₃	—	3	4	no	—
31	C₂×C₃×C₄	C₂×D₃	1	4	yes	—
32	C₂×Dic₃	—	3	4	no	—
33	C₄×D₃	—	3	4	no	—
34	C₄×D₃	—	3	4	no	—
35	C₄×D₃	—	3	4	no	—
36	C₄×D₃	—	3	4	no	—
37	C₃×C₈	C₂×D₃	1	8	yes	complemented
38	C₃⋊C₈	—	3	8	no	—
39	C₂×C₃²	—	2	1	no	—
40	C₂×C₃²	C₂²×C₄	1	1	yes	characteristic
41	C₃⋊D₃	—	2	1	no	—
42	C₃⋊D₃	M₁₆	1	2	yes	direct product factor
43	C₂²×C₄	—	9	1	no	—
44	M₁₆	—	9	1	no	—
45	M₁₆	—	9	2	no	—
46	M₁₆	C₃⋊D₃	1	1	yes	characteristic, direct product factor
47	C₂×C₈	—	9	2	no	—
48	C₂²×C₃	C₄×D₃	1	4	yes	—
49	C₂×D₃	—	3	4	no	—
50	C₂×D₃	—	3	4	no	—
51	C₂×D₃	—	6	8	no	—
52	C₃×C₄	C₄×D₃	1	4	yes	—
53	C₃×C₄	C₂²×D₃	1	4	yes	—
54	Dic₃	—	3	4	no	—
55	Dic₃	—	3	4	no	—
56	C₃²	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
57	C₂³	—	9	1	no	—
58	C₂×C₄	—	9	1	no	—
59	C₂×C₄	—	9	1	no	—
60	C₂×C₄	—	9	1	no	—
61	C₂×C₄	—	9	1	no	—
62	C₂×C₄	—	9	1	no	—
63	C₂×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
64	C₈	—	9	2	no	—
65	C₈	C₂×C₃⋊D₃	1	2	yes	complemented
66	C₂×C₃	—	2	4	no	—
67	C₂×C₃	C₂×C₄×D₃	1	4	yes	—
68	D₃	—	3	8	no	—
69	D₃	—	6	4	no	—
70	C₂²	—	9	1	no	—
71	C₂²	—	9	1	no	—
72	C₂²	—	18	2	no	—
73	C₂²	C₄×C₃⋊D₃	1	1	yes	characteristic
74	C₄	—	9	1	no	—
75	C₄	—	9	1	no	—
76	C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
77	C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
78	C₃	D₃×M₁₆	1	4	yes	complemented
79	C₂	—	2	1	no	—
80	C₂	—	9	2	no	—
81	C₂	—	18	1	no	—
82	C₂	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×C₃⋊D₃
commutator, socle	C₂×C₃²	C₂²×C₄
Fitting	C₃²×M₁₆	C₂
prime radical	C₂²×C₃⋊D₃	C₄
cosocle	C₃²×C₄	C₂³
hypercenter	M₁₆	C₃⋊D₃
hypocenter	C₃²	C₂×M₁₆
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃²×M₁₆	C₂	semidirect
3. #3748	C₂	semidirect
4. #3743	C₂	semidirect
5. C₈×C₃⋊D₃	C₂	semidirect
14. C₃²×C₈	C₂²	semidirect
15. C₃⋊(C₃⋊C₈)	C₂²	semidirect
17. C₃×M₁₆	D₃	semidirect
37. C₃×C₈	C₂×D₃	semidirect
42. C₃⋊D₃	M₁₆	direct (N × H)
46. M₁₆	C₃⋊D₃	direct (N × H)
56. C₃²	C₂×M₁₆	semidirect
65. C₈	C₂×C₃⋊D₃	semidirect
78. C₃	D₃×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×C₃⋊D₃	2
C₃²×M₁₆	2
#3748	2
#3743	2
C₈×C₃⋊D₃	2
D₃×M₁₆	3

Subgroups — M16×C3⋊D3 #64115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×C₃⋊D₃ #64115