Subgroups — C₃×C₈×Dic₃ #63599

Order 288.

99 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄×C₈	—	3	1	no	maximal
5	C₈×Dic₃	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
7	C₂×C₃×Dic₃	C₄	1	2	yes	—
8	C₃²×C₈	C₄	1	2	yes	complemented
9	C₃×C₃⋊C₈	C₄	1	2	yes	complemented
10	C₂×C₃×C₈	—	2	1	no	—
11	C₂×C₃×C₈	—	3	1	no	—
12	C₂×C₃×C₈	D₃	1	1	yes	characteristic
13	C₂×C₃×C₈	C₂×C₃	1	1	yes	characteristic
14	C₃×C₄²	—	3	1	no	—
15	C₄×Dic₃	C₂×C₃	1	1	yes	characteristic
16	C₂×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic
17	C₂²×C₃²	C₂×C₄	1	1	yes	characteristic
18	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
19	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
20	C₃×Dic₃	C₈	1	4	yes	direct product factor
21	C₄×C₈	—	3	1	no	Sylow
22	C₂×C₃×C₄	—	2	1	no	—
23	C₂×C₃×C₄	—	3	2	no	—
24	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
25	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
26	C₂×Dic₃	C₃×C₄	1	2	yes	—
27	C₃×C₈	—	2	2	no	—
28	C₃×C₈	—	3	2	no	—
29	C₃×C₈	Dic₃	1	2	yes	direct product factor
30	C₃×C₈	C₃×C₄	1	2	yes	complemented
31	C₃⋊C₈	C₃×C₄	1	2	yes	complemented
32	C₂×C₃²	C₄²	1	1	yes	characteristic
33	C₂×C₃²	C₂×C₈	1	2	yes	—
34	C₂×C₈	—	3	1	no	—
35	C₂×C₈	C₃×D₃	1	1	yes	characteristic
36	C₄²	—	3	1	no	—
37	C₂²×C₃	—	2	1	no	—
38	C₂²×C₃	C₄×D₃	1	1	yes	characteristic
39	C₂²×C₃	C₂×C₃×C₄	1	1	yes	characteristic
40	C₃×C₄	—	2	1	no	—
41	C₃×C₄	—	2	1	no	—
42	C₃×C₄	—	3	4	no	—
43	C₃×C₄	C₄×D₃	1	1	yes	characteristic
44	C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
45	C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
46	C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
47	Dic₃	C₃×C₈	1	4	yes	direct product factor
48	C₃²	C₄×C₈	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₄	—	3	2	no	—
50	C₂×C₄	C₂×C₃×D₃	1	1	yes	characteristic
51	C₈	—	3	2	no	—
52	C₈	C₃×Dic₃	1	2	yes	direct product factor
53	C₂×C₃	—	2	2	no	—
54	C₂×C₃	—	2	1	no	—
55	C₂×C₃	D₃×C₈	1	2	yes	—
56	C₂×C₃	C₄×Dic₃	1	1	yes	characteristic
57	C₂×C₃	C₃×C₄²	1	1	yes	characteristic
58	C₂×C₃	C₂×C₃×C₈	1	2	yes	—
59	C₂²	C₃×C₄×D₃	1	1	yes	characteristic
60	C₄	—	3	4	no	—
61	C₄	C₃×C₄×D₃	1	1	yes	characteristic
62	C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
63	C₃	—	2	1	no	—
64	C₃	C₈×Dic₃	1	1	yes	characteristic, direct product factor
65	C₃	C₃×C₄×C₈	1	1	yes	characteristic, complemented
66	C₂	C₃×D₃×C₈	1	2	yes	—
67	C₂	C₃×C₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₈	D₃
commutator, hypocenter	C₃	C₃×C₄×C₈
Frattini	C₂×C₄	C₂×C₃×D₃
Fitting	C₂×C₃²×C₈	C₂
socle, prime radical	C₂²×C₃²	C₂×C₄
cosocle	C₂×C₃×C₄	C₂²×C₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
5. C₈×Dic₃	C₃	direct (N × H)
8. C₃²×C₈	C₄	semidirect
9. C₃×C₃⋊C₈	C₄	semidirect
20. C₃×Dic₃	C₈	direct (N × H)
29. C₃×C₈	Dic₃	direct (N × H)
30. C₃×C₈	C₃×C₄	semidirect
31. C₃⋊C₈	C₃×C₄	semidirect
47. Dic₃	C₃×C₈	direct (N × H)
48. C₃²	C₄×C₈	semidirect
52. C₈	C₃×Dic₃	direct (N × H)
64. C₃	C₈×Dic₃	direct (N × H)
65. C₃	C₃×C₄×C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₈	2
C₃×C₄×Dic₃	2
C₂×C₃×C₃⋊C₈	2
C₃×C₄×C₈	3
C₈×Dic₃	3

Subgroups — C3×C8×Dic3 #63599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈×Dic₃ #63599