Subgroups — C₃⋊(A₄⋊C₈) #63754

Order 288.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×A₄	C₂	1	1	yes	maximal, characteristic
2	A₄⋊C₈	—	3	3	no	maximal
3	#830	—	3	1	no	maximal
4	C₂×C₃×A₄	C₄	1	1	yes	characteristic
5	C₃⋊(C₃⋊C₈)	—	4	1	no	maximal
6	C₂²×C₃×C₄	D₃	1	1	yes	characteristic
7	C₄×A₄	D₃	1	3	yes	—
8	C₂×C₃⋊C₈	—	3	1	no	—
9	C₂×C₃⋊C₈	—	3	1	no	—
10	C₃×A₄	C₈	1	1	yes	characteristic, complemented
11	C₃²×C₄	—	4	1	no	—
12	C₂²⋊C₈	—	9	1	no	Sylow
13	C₂³×C₃	Dic₃	1	1	yes	characteristic
14	C₂×A₄	Dic₃	1	3	yes	—
15	C₂×C₃×C₄	—	3	1	no	—
16	C₂×C₃×C₄	—	3	1	no	—
17	C₃⋊C₈	—	6	1	no	—
18	C₃⋊C₈	—	6	1	no	—
19	C₃⋊C₈	—	12	3	no	—
20	C₂×C₃²	—	4	1	no	—
21	C₂²×C₄	C₃⋊D₃	1	1	yes	characteristic
22	C₂×C₈	—	9	1	no	—
23	C₂×C₈	—	9	1	no	—
24	C₂²×C₃	—	3	1	no	—
25	C₂²×C₃	—	3	1	no	—
26	C₂²×C₃	C₃⋊C₈	1	1	yes	characteristic, complemented
27	A₄	C₃⋊C₈	1	3	yes	complemented
28	C₃×C₄	—	3	1	no	—
29	C₃×C₄	—	4	3	no	—
30	C₃×C₄	S₄	1	1	yes	characteristic
31	C₃²	—	4	1	no	Sylow
32	C₂³	C₃⋊Dic₃	1	1	yes	characteristic
33	C₂×C₄	—	3	1	no	—
34	C₂×C₄	—	3	1	no	—
35	C₈	—	18	1	no	—
36	C₈	—	18	1	no	—
37	C₂×C₃	—	3	1	no	—
38	C₂×C₃	—	3	1	no	—
39	C₂×C₃	—	4	3	no	—
40	C₂×C₃	SL(2,ℤ/4)	1	1	yes	characteristic
41	C₂²	—	3	1	no	—
42	C₂²	—	3	1	no	—
43	C₂²	C₃⋊(C₃⋊C₈)	1	1	yes	characteristic, complemented
44	C₄	—	3	1	no	—
45	C₄	C₃⋊S₄	1	1	yes	characteristic
46	C₃	—	4	3	no	—
47	C₃	A₄⋊C₈	1	1	yes	characteristic, complemented
48	C₂	—	3	1	no	—
49	C₂	—	3	1	no	—
50	C₂	C₃⋊SL(2,ℤ/4)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	C₃⋊S₄
commutator, hypocenter	C₃×A₄	C₈
Fitting	C₂²×C₃×C₄	D₃
socle	C₂³×C₃	Dic₃
prime radical	C₂×C₃×A₄	C₄
cosocle	C₃×C₄×A₄	C₂
LCS	G ▷ C₃×A₄
UCS	C₁ ◁ C₄

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

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