Subgroups — C₃×C₄×A₄ #3812

Order 144.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×A₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄	C₃	1	1	yes	maximal, characteristic, complemented
3	C₄×A₄	C₃	1	3	yes	maximal, direct product factor
4	C₃×A₄	C₄	1	1	yes	characteristic, direct product factor
5	C₃²×C₄	—	4	1	no	maximal
6	C₂³×C₃	C₂×C₃	1	1	yes	characteristic
7	C₂×A₄	C₂×C₃	1	3	yes	—
8	C₂×C₃×C₄	—	3	1	no	—
9	C₂×C₃×C₄	—	3	1	no	—
10	C₂×C₃²	—	4	1	no	—
11	C₂²×C₄	C₃²	1	1	yes	characteristic, complemented, Sylow
12	C₂²×C₃	—	3	1	no	—
13	C₂²×C₃	—	3	1	no	—
14	C₂²×C₃	C₃×C₄	1	1	yes	characteristic, complemented
15	A₄	C₃×C₄	1	3	yes	direct product factor
16	C₃×C₄	—	3	1	no	—
17	C₃×C₄	—	4	3	no	—
18	C₃×C₄	A₄	1	1	yes	characteristic, direct product factor
19	C₃²	—	4	1	no	Sylow
20	C₂³	C₂×C₃²	1	1	yes	characteristic
21	C₂×C₄	—	3	1	no	—
22	C₂×C₄	—	3	1	no	—
23	C₂×C₃	—	3	1	no	—
24	C₂×C₃	—	3	1	no	—
25	C₂×C₃	—	4	3	no	—
26	C₂×C₃	C₂×A₄	1	1	yes	characteristic
27	C₂²	—	3	1	no	—
28	C₂²	—	3	1	no	—
29	C₂²	C₃²×C₄	1	1	yes	characteristic, complemented
30	C₄	—	3	1	no	—
31	C₄	C₃×A₄	1	1	yes	characteristic, direct product factor
32	C₃	—	4	3	no	—
33	C₃	C₄×A₄	1	1	yes	characteristic, direct product factor
34	C₂	—	3	1	no	—
35	C₂	—	3	1	no	—
36	C₂	C₂×C₃×A₄	1	1	yes	characteristic

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.