Subgroups — C₃×C₄×C₃⋊C₈ #63588

Order 288.

103 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₃×C₄²	D₃
commutator, hypocenter	C₃	C₃×C₄×C₈
Frattini	C₂×C₄	C₂×C₃×D₃
Fitting	C₃²×C₄²	C₂
socle, prime radical	C₂²×C₃²	C₂×C₄
cosocle	C₂×C₃×C₄	C₂²×C₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₄²

Complements

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

N	H ≅ G/N	type
4. C₄×C₃⋊C₈	C₃	direct (N × H)
7. C₃×C₃⋊C₈	C₄	direct (N × H)
14. C₃²×C₄	C₈	semidirect
24. C₃⋊C₈	C₃×C₄	direct (N × H)
34. C₃×C₄	C₃⋊C₈	direct (N × H)
35. C₃×C₄	C₃×C₈	semidirect
38. C₃²	C₄×C₈	semidirect
49. C₄	C₃×C₃⋊C₈	direct (N × H)
52. C₃	C₄×C₃⋊C₈	direct (N × H)
53. 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
C₃²×C₄²	2
C₂×C₃×C₃⋊C₈	2
C₃×C₄×C₈	3
C₄×C₃⋊C₈	3

Subgroups — C3×C4×C3⋊C8 #63588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₃⋊C₈ #63588