Subgroups — C₂×C₃×C₄³ #84129

Order 384.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄²	C₂	1	7	yes	maximal
2	C₃×C₄³	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄³	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂³×C₃×C₄	C₂²	1	7	yes	—
5	C₂×C₃×C₄²	C₄	1	56	yes	direct product factor
6	C₂×C₃×C₄²	C₂²	1	28	yes	—
7	C₂²×C₄²	C₂×C₃	1	7	yes	—
8	C₄³	C₂×C₃	1	8	yes	direct product factor
9	C₂⁴×C₃	C₂³	1	1	yes	characteristic
10	C₂²×C₃×C₄	C₂×C₄	1	84	yes	—
11	C₂²×C₃×C₄	C₂³	1	14	yes	—
12	C₃×C₄²	C₂×C₄	1	112	yes	direct product factor
13	C₂³×C₄	C₂²×C₃	1	7	yes	—
14	C₂×C₄²	C₃×C₄	1	56	yes	direct product factor
15	C₂×C₄²	C₂²×C₃	1	28	yes	—
16	C₂³×C₃	C₂²×C₄	1	14	yes	—
17	C₂³×C₃	C₂⁴	1	1	yes	characteristic
18	C₂×C₃×C₄	C₄²	1	112	yes	direct product factor
19	C₂×C₃×C₄	C₂²×C₄	1	84	yes	—
20	C₂⁴	C₂³×C₃	1	1	yes	characteristic
21	C₂²×C₄	C₂×C₃×C₄	1	84	yes	—
22	C₂²×C₄	C₂³×C₃	1	14	yes	—
23	C₄²	C₂×C₃×C₄	1	112	yes	direct product factor
24	C₂²×C₃	C₂×C₄²	1	28	yes	—
25	C₂²×C₃	C₂³×C₄	1	7	yes	—
26	C₃×C₄	C₂×C₄²	1	56	yes	direct product factor
27	C₂³	C₂²×C₃×C₄	1	14	yes	—
28	C₂³	C₂⁴×C₃	1	1	yes	characteristic
29	C₂×C₄	C₃×C₄²	1	112	yes	direct product factor
30	C₂×C₄	C₂²×C₃×C₄	1	84	yes	—
31	C₂×C₃	C₄³	1	8	yes	direct product factor
32	C₂×C₃	C₂²×C₄²	1	7	yes	—
33	C₂²	C₂×C₃×C₄²	1	28	yes	—
34	C₂²	C₂³×C₃×C₄	1	7	yes	—
35	C₄	C₂×C₃×C₄²	1	56	yes	direct product factor
36	C₃	C₂×C₄³	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	C₃×C₄³	1	8	yes	direct product factor
38	C₂	C₂²×C₃×C₄²	1	7	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³	C₂⁴×C₃
socle, prime radical	C₂⁴×C₃	C₂³
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₄³	C₂	direct (N × H)
3. C₂×C₄³	C₃	direct (N × H)
5. C₂×C₃×C₄²	C₄	direct (N × H)
8. C₄³	C₂×C₃	direct (N × H)
12. C₃×C₄²	C₂×C₄	direct (N × H)
14. C₂×C₄²	C₃×C₄	direct (N × H)
18. C₂×C₃×C₄	C₄²	direct (N × H)
23. C₄²	C₂×C₃×C₄	direct (N × H)
26. C₃×C₄	C₂×C₄²	direct (N × H)
29. C₂×C₄	C₃×C₄²	direct (N × H)
31. C₂×C₃	C₄³	direct (N × H)
35. C₄	C₂×C₃×C₄²	direct (N × H)
36. C₃	C₂×C₄³	direct (N × H)
37. C₂	C₃×C₄³	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×C₄²	2
C₃×C₄³	2
C₂×C₄³	3

Subgroups — C2×C3×C43 #84129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄³ #84129