Subgroups — C₃×C₄×M₁₆ #5278

Order 192.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
3	C₃×#97	C₂	1	2	yes	maximal, complemented
4	C₃×C₄×C₈	C₂	1	2	yes	maximal, complemented
5	C₄×M₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂²×C₃×C₄	C₄	1	2	yes	—
7	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
8	C₃×M₁₆	C₄	1	8	yes	direct product factor
9	C₂×C₃×C₈	C₂²	1	4	yes	—
10	C₃×C₄²	C₄	1	2	yes	—
11	C₃×C₄²	C₂²	1	1	yes	characteristic
12	C₃×C₄²	C₂²	1	1	yes	characteristic
13	C₂×M₁₆	C₂×C₃	1	2	yes	—
14	C₂×C₄²	C₂×C₃	1	1	yes	characteristic
15	#97	C₂×C₃	1	2	yes	complemented
16	C₄×C₈	C₂×C₃	1	2	yes	complemented
17	C₂³×C₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₃×C₄	—	2	4	no	—
19	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
20	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
21	C₂×C₃×C₄	C₂×C₄	1	4	yes	—
22	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
23	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
24	C₃×C₈	C₂×C₄	1	8	yes	complemented
25	C₂²×C₄	C₃×C₄	1	2	yes	—
26	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
27	M₁₆	C₃×C₄	1	8	yes	direct product factor
28	C₂×C₈	C₂²×C₃	1	4	yes	—
29	C₄²	C₃×C₄	1	2	yes	—
30	C₄²	C₂²×C₃	1	1	yes	characteristic
31	C₄²	C₂²×C₃	1	1	yes	characteristic
32	C₂²×C₃	—	2	2	no	—
33	C₂²×C₃	C₄²	1	2	yes	—
34	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
35	C₃×C₄	—	2	2	no	—
36	C₃×C₄	C₄²	1	2	yes	—
37	C₃×C₄	M₁₆	1	4	yes	direct product factor
38	C₃×C₄	C₂²×C₄	1	2	yes	—
39	C₂³	C₂×C₃×C₄	1	1	yes	characteristic
40	C₂×C₄	—	2	4	no	—
41	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
42	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
43	C₂×C₄	C₂×C₃×C₄	1	4	yes	—
44	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
45	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
46	C₈	C₂×C₃×C₄	1	8	yes	complemented
47	C₂×C₃	—	2	2	no	—
48	C₂×C₃	C₂×C₄²	1	1	yes	characteristic
49	C₂×C₃	C₂×M₁₆	1	2	yes	—
50	C₂²	—	2	2	no	—
51	C₂²	C₃×C₄²	1	2	yes	—
52	C₂²	C₂²×C₃×C₄	1	1	yes	characteristic
53	C₄	—	2	2	no	—
54	C₄	C₃×C₄²	1	2	yes	—
55	C₄	C₃×M₁₆	1	4	yes	direct product factor
56	C₄	C₂²×C₃×C₄	1	2	yes	—
57	C₃	C₄×M₁₆	1	1	yes	characteristic, direct product factor, Sylow
58	C₂	—	2	2	no	—
59	C₂	C₂×C₃×C₄²	1	1	yes	characteristic
60	C₂	C₂×C₃×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₃×C₄²	C₂²
commutator	C₂	C₂×C₃×C₄²
Frattini, cosocle	C₂×C₄	C₂³×C₃
socle	C₂²×C₃	C₂²×C₄
prime radical	C₂³×C₃	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×#97	C₂	semidirect
4. C₃×C₄×C₈	C₂	semidirect
5. C₄×M₁₆	C₃	direct (N × H)
8. C₃×M₁₆	C₄	direct (N × H)
15. #97	C₂×C₃	semidirect
16. C₄×C₈	C₂×C₃	semidirect
24. C₃×C₈	C₂×C₄	semidirect
27. M₁₆	C₃×C₄	direct (N × H)
37. C₃×C₄	M₁₆	direct (N × H)
46. C₈	C₂×C₃×C₄	semidirect
55. C₄	C₃×M₁₆	direct (N × H)
57. C₃	C₄×M₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×M₁₆	2
C₂×C₃×C₄²	2
C₃×#97	2
C₃×C₄×C₈	2
C₄×M₁₆	3

Subgroups — C3×C4×M16 #5278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×M₁₆ #5278