Subgroups — C₂²×C₃×C₁₆ #5376

Order 192.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₁₆	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂²×C₃×C₄	C₄	1	1	yes	characteristic
5	C₂×C₃×C₈	C₄	1	3	yes	—
6	C₂×C₃×C₈	C₂²	1	3	yes	—
7	C₃×C₁₆	C₂²	1	4	yes	direct product factor
8	C₂²×C₈	C₂×C₃	1	1	yes	characteristic
9	C₂×C₁₆	C₂×C₃	1	6	yes	direct product factor
10	C₂³×C₃	C₈	1	1	yes	characteristic
11	C₂×C₃×C₄	C₈	1	3	yes	—
12	C₂×C₃×C₄	C₂×C₄	1	3	yes	—
13	C₃×C₈	C₂×C₄	1	3	yes	—
14	C₃×C₈	C₂³	1	1	yes	characteristic
15	C₂²×C₄	C₃×C₄	1	1	yes	characteristic
16	C₂×C₈	C₃×C₄	1	3	yes	—
17	C₂×C₈	C₂²×C₃	1	3	yes	—
18	C₁₆	C₂²×C₃	1	4	yes	direct product factor
19	C₂²×C₃	C₁₆	1	4	yes	direct product factor
20	C₂²×C₃	C₂×C₈	1	3	yes	—
21	C₃×C₄	C₂×C₈	1	3	yes	—
22	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
23	C₂³	C₃×C₈	1	1	yes	characteristic
24	C₂×C₄	C₃×C₈	1	3	yes	—
25	C₂×C₄	C₂×C₃×C₄	1	3	yes	—
26	C₈	C₂×C₃×C₄	1	3	yes	—
27	C₈	C₂³×C₃	1	1	yes	characteristic
28	C₂×C₃	C₂×C₁₆	1	6	yes	direct product factor
29	C₂×C₃	C₂²×C₈	1	1	yes	characteristic
30	C₂²	C₃×C₁₆	1	4	yes	direct product factor
31	C₂²	C₂×C₃×C₈	1	3	yes	—
32	C₄	C₂×C₃×C₈	1	3	yes	—
33	C₄	C₂²×C₃×C₄	1	1	yes	characteristic
34	C₃	C₂²×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
35	C₂	C₂×C₃×C₁₆	1	6	yes	direct product factor
36	C₂	C₂²×C₃×C₈	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂³×C₃
socle, prime radical	C₂³×C₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₁₆	C₂	direct (N × H)
3. C₂²×C₁₆	C₃	direct (N × H)
7. C₃×C₁₆	C₂²	direct (N × H)
9. C₂×C₁₆	C₂×C₃	direct (N × H)
18. C₁₆	C₂²×C₃	direct (N × H)
19. C₂²×C₃	C₁₆	direct (N × H)
28. C₂×C₃	C₂×C₁₆	direct (N × H)
30. C₂²	C₃×C₁₆	direct (N × H)
34. C₃	C₂²×C₁₆	direct (N × H)
35. C₂	C₂×C₃×C₁₆	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×C₈	2
C₂×C₃×C₁₆	2
C₂²×C₁₆	3

Subgroups — C22×C3×C16 #5376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₁₆ #5376