Subgroups — C₄³×D₃ #73312

Order 384.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₃	C₂	1	7	yes	maximal
2	C₃×C₄³	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×Dic₃	C₂	1	7	yes	maximal, complemented
4	C₂×C₄³	—	3	1	no	maximal, Sylow
5	C₂²×C₄×D₃	C₂²	1	7	yes	—
6	C₂×C₃×C₄²	C₂²	1	7	yes	—
7	C₂×C₄×Dic₃	C₂²	1	21	yes	—
8	C₄²×D₃	C₄	1	56	yes	direct product factor
9	C₂²×C₄²	—	3	7	no	—
10	C₄³	—	3	7	no	—
11	C₄³	D₃	1	1	yes	characteristic, direct product factor
12	C₂³×D₃	C₂³	1	1	yes	characteristic
13	C₂²×C₃×C₄	C₂³	1	7	yes	—
14	C₂²×Dic₃	C₂³	1	7	yes	—
15	C₂×C₄×D₃	C₂×C₄	1	84	yes	—
16	C₃×C₄²	C₂×C₄	1	28	yes	complemented
17	C₄×Dic₃	C₂×C₄	1	84	yes	complemented
18	C₂³×C₄	—	3	7	no	—
19	C₂×C₄²	—	3	21	no	—
20	C₂×C₄²	—	3	56	no	—
21	C₂×C₄²	C₂×D₃	1	7	yes	—
22	C₂³×C₃	C₂⁴	1	1	yes	characteristic
23	C₂²×D₃	C₂²×C₄	1	14	yes	—
24	C₂×C₃×C₄	C₂²×C₄	1	42	yes	—
25	C₂×Dic₃	C₂²×C₄	1	42	yes	—
26	C₄×D₃	C₄²	1	112	yes	direct product factor
27	C₂⁴	—	3	1	no	—
28	C₂²×C₄	—	3	7	no	—
29	C₂²×C₄	—	3	84	no	—
30	C₂²×C₄	C₂²×D₃	1	7	yes	—
31	C₄²	—	3	84	no	—
32	C₄²	C₄×D₃	1	28	yes	direct product factor
33	C₂²×C₃	C₂³×C₄	1	7	yes	—
34	C₂×D₃	C₂×C₄²	1	28	yes	—
35	C₃×C₄	C₂×C₄²	1	28	yes	complemented
36	Dic₃	C₂×C₄²	1	28	yes	complemented
37	C₂³	—	3	14	no	—
38	C₂³	C₂³×D₃	1	1	yes	characteristic
39	C₂×C₄	—	3	42	no	—
40	C₂×C₄	—	3	112	no	—
41	C₂×C₄	C₂×C₄×D₃	1	42	yes	—
42	C₂×C₃	C₂²×C₄²	1	7	yes	—
43	D₃	C₄³	1	8	yes	direct product factor
44	C₂²	—	3	28	no	—
45	C₂²	C₂²×C₄×D₃	1	7	yes	—
46	C₄	—	3	28	no	—
47	C₄	C₄²×D₃	1	28	yes	direct product factor
48	C₃	C₂×C₄³	1	1	yes	characteristic, complemented, Sylow
49	C₂	—	3	8	no	—
50	C₂	C₂×C₄²×D₃	1	7	yes	—

	subgroup	G/H
center, hypercenter	C₄³	D₃
commutator, hypocenter	C₃	C₂×C₄³
Frattini	C₂³	C₂³×D₃
Fitting	C₃×C₄³	C₂
socle, cosocle	C₂³×C₃	C₂⁴
prime radical	C₂³×D₃	C₂³
LCS	G ▷ C₃
UCS	C₁ ◁ C₄³

Complements

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

N	H ≅ G/N	type
2. C₃×C₄³	C₂	semidirect
3. C₄²×Dic₃	C₂	semidirect
8. C₄²×D₃	C₄	direct (N × H)
11. C₄³	D₃	direct (N × H)
16. C₃×C₄²	C₂×C₄	semidirect
17. C₄×Dic₃	C₂×C₄	semidirect
26. C₄×D₃	C₄²	direct (N × H)
32. C₄²	C₄×D₃	direct (N × H)
35. C₃×C₄	C₂×C₄²	semidirect
36. Dic₃	C₂×C₄²	semidirect
43. D₃	C₄³	direct (N × H)
47. C₄	C₄²×D₃	direct (N × H)
48. C₃	C₂×C₄³	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄²×D₃	2
C₃×C₄³	2
C₄²×Dic₃	2
C₂×C₄³	3

Subgroups — C43×D3 #73312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄³×D₃ #73312