Subgroups — C₂³×C₃×C₁₆ #85268

Order 384.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₁₆	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂³×C₃×C₄	C₄	1	1	yes	characteristic
5	C₂²×C₃×C₈	C₄	1	7	yes	—
6	C₂²×C₃×C₈	C₂²	1	7	yes	—
7	C₂×C₃×C₁₆	C₂²	1	28	yes	direct product factor
8	C₂³×C₈	C₂×C₃	1	1	yes	characteristic
9	C₂²×C₁₆	C₂×C₃	1	14	yes	direct product factor
10	C₂⁴×C₃	C₈	1	1	yes	characteristic
11	C₂²×C₃×C₄	C₈	1	7	yes	—
12	C₂²×C₃×C₄	C₂×C₄	1	7	yes	—
13	C₂×C₃×C₈	C₂×C₄	1	21	yes	—
14	C₂×C₃×C₈	C₂³	1	7	yes	—
15	C₃×C₁₆	C₂³	1	8	yes	direct product factor
16	C₂³×C₄	C₃×C₄	1	1	yes	characteristic
17	C₂²×C₈	C₃×C₄	1	7	yes	—
18	C₂²×C₈	C₂²×C₃	1	7	yes	—
19	C₂×C₁₆	C₂²×C₃	1	28	yes	direct product factor
20	C₂³×C₃	C₁₆	1	8	yes	direct product factor
21	C₂³×C₃	C₂×C₈	1	7	yes	—
22	C₂×C₃×C₄	C₂×C₈	1	21	yes	—
23	C₂×C₃×C₄	C₂²×C₄	1	7	yes	—
24	C₃×C₈	C₂²×C₄	1	7	yes	—
25	C₃×C₈	C₂⁴	1	1	yes	characteristic
26	C₂⁴	C₃×C₈	1	1	yes	characteristic
27	C₂²×C₄	C₃×C₈	1	7	yes	—
28	C₂²×C₄	C₂×C₃×C₄	1	7	yes	—
29	C₂×C₈	C₂×C₃×C₄	1	21	yes	—
30	C₂×C₈	C₂³×C₃	1	7	yes	—
31	C₁₆	C₂³×C₃	1	8	yes	direct product factor
32	C₂²×C₃	C₂×C₁₆	1	28	yes	direct product factor
33	C₂²×C₃	C₂²×C₈	1	7	yes	—
34	C₃×C₄	C₂²×C₈	1	7	yes	—
35	C₃×C₄	C₂³×C₄	1	1	yes	characteristic
36	C₂³	C₃×C₁₆	1	8	yes	direct product factor
37	C₂³	C₂×C₃×C₈	1	7	yes	—
38	C₂×C₄	C₂×C₃×C₈	1	21	yes	—
39	C₂×C₄	C₂²×C₃×C₄	1	7	yes	—
40	C₈	C₂²×C₃×C₄	1	7	yes	—
41	C₈	C₂⁴×C₃	1	1	yes	characteristic
42	C₂×C₃	C₂²×C₁₆	1	14	yes	direct product factor
43	C₂×C₃	C₂³×C₈	1	1	yes	characteristic
44	C₂²	C₂×C₃×C₁₆	1	28	yes	direct product factor
45	C₂²	C₂²×C₃×C₈	1	7	yes	—
46	C₄	C₂²×C₃×C₈	1	7	yes	—
47	C₄	C₂³×C₃×C₄	1	1	yes	characteristic
48	C₃	C₂³×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
49	C₂	C₂²×C₃×C₁₆	1	14	yes	direct product factor
50	C₂	C₂³×C₃×C₈	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂⁴×C₃
socle, prime radical	C₂⁴×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. C₂²×C₃×C₁₆	C₂	direct (N × H)
3. C₂³×C₁₆	C₃	direct (N × H)
7. C₂×C₃×C₁₆	C₂²	direct (N × H)
9. C₂²×C₁₆	C₂×C₃	direct (N × H)
15. C₃×C₁₆	C₂³	direct (N × H)
19. C₂×C₁₆	C₂²×C₃	direct (N × H)
20. C₂³×C₃	C₁₆	direct (N × H)
31. C₁₆	C₂³×C₃	direct (N × H)
32. C₂²×C₃	C₂×C₁₆	direct (N × H)
36. C₂³	C₃×C₁₆	direct (N × H)
42. C₂×C₃	C₂²×C₁₆	direct (N × H)
44. C₂²	C₂×C₃×C₁₆	direct (N × H)
48. C₃	C₂³×C₁₆	direct (N × H)
49. C₂	C₂²×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
C₂³×C₃×C₈	2
C₂²×C₃×C₁₆	2
C₂³×C₁₆	3

Subgroups — C23×C3×C16 #85268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃×C₁₆ #85268