Subgroups — D₃×C₈² #68045

Order 384.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₃×C₈	C₂	1	3	yes	maximal
2	C₃×C₈²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×C₃⋊C₈	C₂	1	3	yes	maximal, complemented
4	C₂×C₈²	—	3	1	no	maximal, Sylow
5	C₂×D₃×C₈	C₄	1	6	yes	—
6	C₄²×D₃	C₂²	1	1	yes	characteristic
7	C₃×C₄×C₈	C₂²	1	3	yes	—
8	C₈×Dic₃	C₄	1	6	yes	—
9	C₄×C₃⋊C₈	C₂²	1	3	yes	—
10	C₂×C₄×C₈	—	3	3	no	—
11	C₈²	—	3	3	no	—
12	C₈²	D₃	1	1	yes	characteristic, direct product factor
13	C₂×C₄×D₃	C₂×C₄	1	3	yes	—
14	C₂×C₃×C₈	C₂×C₄	1	6	yes	—
15	C₃×C₄²	C₂³	1	1	yes	characteristic
16	C₄×Dic₃	C₂×C₄	1	3	yes	—
17	C₂×C₃⋊C₈	C₂×C₄	1	6	yes	—
18	D₃×C₈	C₈	1	24	yes	direct product factor
19	C₂²×C₈	—	3	6	no	—
20	C₂×C₄²	—	3	1	no	—
21	C₄×C₈	—	3	6	no	—
22	C₄×C₈	—	3	3	no	—
23	C₄×C₈	C₂×D₃	1	3	yes	—
24	C₂²×D₃	C₄²	1	1	yes	characteristic
25	C₂×C₃×C₄	C₂²×C₄	1	3	yes	—
26	C₂×Dic₃	C₄²	1	3	yes	—
27	C₄×D₃	C₂×C₈	1	12	yes	—
28	C₃×C₈	C₂×C₈	1	12	yes	complemented
29	C₃⋊C₈	C₂×C₈	1	12	yes	complemented
30	C₂²×C₄	—	3	3	no	—
31	C₂×C₈	—	3	6	no	—
32	C₂×C₈	—	3	24	no	—
33	C₂×C₈	C₄×D₃	1	6	yes	—
34	C₄²	—	3	3	no	—
35	C₄²	C₂²×D₃	1	1	yes	characteristic
36	C₂²×C₃	C₂×C₄²	1	1	yes	characteristic
37	C₂×D₃	C₄×C₈	1	6	yes	—
38	C₃×C₄	C₂²×C₈	1	6	yes	—
39	Dic₃	C₄×C₈	1	6	yes	—
40	C₂³	—	3	1	no	—
41	C₂×C₄	—	3	3	no	—
42	C₂×C₄	—	3	12	no	—
43	C₂×C₄	C₂×C₄×D₃	1	3	yes	—
44	C₈	—	3	12	no	—
45	C₈	D₃×C₈	1	12	yes	direct product factor
46	C₂×C₃	C₂×C₄×C₈	1	3	yes	—
47	D₃	C₈²	1	4	yes	direct product factor
48	C₂²	—	3	6	no	—
49	C₂²	C₄²×D₃	1	1	yes	characteristic
50	C₄	—	3	6	no	—
51	C₄	C₂×D₃×C₈	1	6	yes	—
52	C₃	C₂×C₈²	1	1	yes	characteristic, complemented, Sylow
53	C₂	—	3	4	no	—
54	C₂	C₄×D₃×C₈	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₈²	D₃
commutator, hypocenter	C₃	C₂×C₈²
Frattini	C₄²	C₂²×D₃
Fitting	C₃×C₈²	C₂
socle	C₂²×C₃	C₂×C₄²
prime radical	C₂²×D₃	C₄²
cosocle	C₃×C₄²	C₂³
LCS	G ▷ C₃
UCS	C₁ ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. C₃×C₈²	C₂	semidirect
3. C₈×C₃⋊C₈	C₂	semidirect
12. C₈²	D₃	direct (N × H)
18. D₃×C₈	C₈	direct (N × H)
28. C₃×C₈	C₂×C₈	semidirect
29. C₃⋊C₈	C₂×C₈	semidirect
45. C₈	D₃×C₈	direct (N × H)
47. D₃	C₈²	direct (N × H)
52. C₃	C₂×C₈²	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₃×C₈	2
C₃×C₈²	2
C₈×C₃⋊C₈	2
C₂×C₈²	3

Subgroups — D3×C82 #68045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₈² #68045