Subgroups — C₂×C₃×M₁₆ #970

Order 96.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄	C₂	1	1	yes	maximal, characteristic
2	C₃×M₁₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃×C₈	C₂	1	2	yes	maximal, complemented
4	C₂×M₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂³×C₃	C₄	1	1	yes	characteristic
6	C₂×C₃×C₄	C₄	1	1	yes	characteristic
7	C₂×C₃×C₄	C₄	1	2	yes	—
8	C₂×C₃×C₄	C₂²	1	2	yes	—
9	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
10	C₃×C₈	C₂²	1	4	yes	complemented
11	C₂²×C₄	C₂×C₃	1	1	yes	characteristic
12	M₁₆	C₂×C₃	1	4	yes	direct product factor
13	C₂×C₈	C₂×C₃	1	2	yes	complemented
14	C₂²×C₃	—	2	2	no	—
15	C₂²×C₃	C₂×C₄	1	2	yes	—
16	C₂²×C₃	C₂×C₄	1	1	yes	characteristic
17	C₃×C₄	C₂×C₄	1	2	yes	—
18	C₃×C₄	C₂×C₄	1	1	yes	characteristic
19	C₃×C₄	C₂³	1	1	yes	characteristic
20	C₂³	C₃×C₄	1	1	yes	characteristic
21	C₂×C₄	C₃×C₄	1	2	yes	—
22	C₂×C₄	C₃×C₄	1	1	yes	characteristic
23	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
24	C₂×C₄	C₂²×C₃	1	2	yes	—
25	C₈	C₂²×C₃	1	4	yes	complemented
26	C₂×C₃	—	2	2	no	—
27	C₂×C₃	M₁₆	1	2	yes	direct product factor
28	C₂×C₃	C₂²×C₄	1	1	yes	characteristic
29	C₂²	—	2	2	no	—
30	C₂²	C₂×C₃×C₄	1	2	yes	—
31	C₂²	C₂×C₃×C₄	1	1	yes	characteristic
32	C₄	C₂×C₃×C₄	1	1	yes	characteristic
33	C₄	C₂×C₃×C₄	1	2	yes	—
34	C₄	C₂³×C₃	1	1	yes	characteristic
35	C₃	C₂×M₁₆	1	1	yes	characteristic, direct product factor, Sylow
36	C₂	—	2	2	no	—
37	C₂	C₃×M₁₆	1	2	yes	direct product factor
38	C₂	C₂²×C₃×C₄	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₃×M₁₆	C₂	direct (N × H)
3. C₂×C₃×C₈	C₂	semidirect
4. C₂×M₁₆	C₃	direct (N × H)
10. C₃×C₈	C₂²	semidirect
12. M₁₆	C₂×C₃	direct (N × H)
13. C₂×C₈	C₂×C₃	semidirect
25. C₈	C₂²×C₃	semidirect
27. C₂×C₃	M₁₆	direct (N × H)
35. C₃	C₂×M₁₆	direct (N × H)
37. C₂	C₃×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
C₂²×C₃×C₄	2
C₃×M₁₆	2
C₂×C₃×C₈	2
C₂×M₁₆	3

Subgroups — C2×C3×M16 #970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×M₁₆ #970