Subgroups — C₃×C₈×C₁₆ #67870

Order 384.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₁₆	C₂	1	2	yes	maximal
2	C₃×C₈²	C₂	1	1	yes	maximal, characteristic
3	C₈×C₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×C₁₆	C₄	1	4	yes	—
5	C₃×C₄×C₈	C₄	1	2	yes	—
6	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
7	C₄×C₁₆	C₂×C₃	1	2	yes	—
8	C₈²	C₂×C₃	1	1	yes	characteristic
9	C₂×C₃×C₈	C₈	1	4	yes	—
10	C₂×C₃×C₈	C₂×C₄	1	2	yes	—
11	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
12	C₃×C₁₆	C₈	1	8	yes	direct product factor
13	C₂×C₁₆	C₃×C₄	1	4	yes	—
14	C₄×C₈	C₃×C₄	1	2	yes	—
15	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
16	C₂×C₃×C₄	C₄²	1	1	yes	characteristic
17	C₂×C₃×C₄	C₂×C₈	1	2	yes	—
18	C₃×C₈	C₁₆	1	8	yes	direct product factor
19	C₃×C₈	C₂×C₈	1	4	yes	—
20	C₂×C₈	C₃×C₈	1	4	yes	—
21	C₂×C₈	C₂×C₃×C₄	1	2	yes	—
22	C₄²	C₂×C₃×C₄	1	1	yes	characteristic
23	C₁₆	C₃×C₈	1	8	yes	direct product factor
24	C₂²×C₃	C₄×C₈	1	1	yes	characteristic
25	C₃×C₄	C₄×C₈	1	2	yes	—
26	C₃×C₄	C₂×C₁₆	1	4	yes	—
27	C₂×C₄	C₃×C₄²	1	1	yes	characteristic
28	C₂×C₄	C₂×C₃×C₈	1	2	yes	—
29	C₈	C₃×C₁₆	1	8	yes	direct product factor
30	C₈	C₂×C₃×C₈	1	4	yes	—
31	C₂×C₃	C₈²	1	1	yes	characteristic
32	C₂×C₃	C₄×C₁₆	1	2	yes	—
33	C₂²	C₃×C₄×C₈	1	1	yes	characteristic
34	C₄	C₃×C₄×C₈	1	2	yes	—
35	C₄	C₂×C₃×C₁₆	1	4	yes	—
36	C₃	C₈×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	C₃×C₈²	1	1	yes	characteristic
38	C₂	C₃×C₄×C₁₆	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₈	C₂²×C₃
socle, prime radical	C₂²×C₃	C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₈×C₁₆	C₃	direct (N × H)
12. C₃×C₁₆	C₈	direct (N × H)
18. C₃×C₈	C₁₆	direct (N × H)
23. C₁₆	C₃×C₈	direct (N × H)
29. C₈	C₃×C₁₆	direct (N × H)
36. C₃	C₈×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
C₃×C₄×C₁₆	2
C₃×C₈²	2
C₈×C₁₆	3

Subgroups — C3×C8×C16 #67870

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈×C₁₆ #67870