Subgroups — Dic₃×C₃⋊C₈ #63552

Order 288.

99 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊(C₃⋊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	C₈×Dic₃	—	3	1	no	maximal
5	C₄×C₃⋊C₈	—	3	1	no	maximal
6	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
7	C₂×C₃×Dic₃	C₄	1	2	yes	—
8	C₃⋊(C₃⋊C₈)	C₄	1	2	yes	complemented
9	C₃×C₃⋊C₈	C₄	1	2	yes	complemented
10	C₂×C₃×C₈	—	3	1	no	—
11	C₃×C₄²	—	3	1	no	—
12	C₄×Dic₃	D₃	1	1	yes	characteristic
13	C₂×C₃⋊C₈	—	3	1	no	—
14	C₂×C₃⋊C₈	—	3	1	no	—
15	C₂×C₃⋊C₈	—	6	1	no	—
16	C₂×C₃⋊C₈	D₃	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	complemented
21	C₄×C₈	—	9	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	C₂×D₃	1	1	yes	characteristic
26	C₂×Dic₃	Dic₃	1	2	yes	—
27	C₃×C₈	—	3	2	no	—
28	C₃⋊C₈	—	3	2	no	—
29	C₃⋊C₈	—	3	2	no	—
30	C₃⋊C₈	—	6	2	no	—
31	C₃⋊C₈	Dic₃	1	2	yes	direct product factor
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	—	9	1	no	—
36	C₄²	—	3	1	no	—
37	C₂²×C₃	—	2	1	no	—
38	C₂²×C₃	C₄×D₃	1	1	yes	characteristic
39	C₂²×C₃	C₂×Dic₃	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	C₄×D₃	1	1	yes	characteristic
45	C₃×C₄	C₄×D₃	1	1	yes	characteristic
46	C₃×C₄	C₂×Dic₃	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	D₃²	1	1	yes	characteristic
51	C₈	—	3	2	no	—
52	C₈	—	9	2	no	—
53	C₂×C₃	—	2	2	no	—
54	C₂×C₃	—	2	1	no	—
55	C₂×C₃	D₃×C₈	1	2	yes	—
56	C₂×C₃	C₂×C₃⋊C₈	1	2	yes	—
57	C₂×C₃	C₄×Dic₃	1	1	yes	characteristic
58	C₂×C₃	C₄×Dic₃	1	1	yes	characteristic
59	C₂²	D₃×Dic₃	1	1	yes	characteristic
60	C₄	—	3	4	no	—
61	C₄	D₃×Dic₃	1	1	yes	characteristic
62	C₄	#624	1	1	yes	characteristic
63	C₃	—	2	1	no	—
64	C₃	C₄×C₃⋊C₈	1	1	yes	characteristic, complemented
65	C₃	C₈×Dic₃	1	1	yes	characteristic, complemented
66	C₂	D₃×C₃⋊C₈	1	2	yes	—
67	C₂	Dic₃²	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	D₃²
commutator, hypocenter	C₃²	C₄×C₈
Fitting, cosocle	C₂×C₃²×C₄	C₂²
socle, prime radical	C₂²×C₃²	C₂×C₄
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₄

Complements

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

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

Maximal subgroups

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

subgroup	index
C₂×C₃⋊(C₃⋊C₈)	2
C₃×C₄×Dic₃	2
C₂×C₃×C₃⋊C₈	2
C₈×Dic₃	3
C₄×C₃⋊C₈	3

Subgroups — Dic3×C3⋊C8 #63552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃×C₃⋊C₈ #63552