Subgroups — C₃×D₂₄ #3729

Order 144.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₂	C₂	1	2	yes	maximal, complemented
2	C₃²×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₈	—	3	1	no	maximal
4	D₂₄	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₃×D₃	—	2	2	no	—
6	C₃²×C₄	C₂²	1	1	yes	characteristic
7	C₃×D₄	—	3	2	no	—
8	D₁₂	C₂×C₃	1	2	yes	complemented
9	C₃×C₈	—	2	1	no	—
10	C₃×C₈	D₃	1	1	yes	characteristic, complemented
11	C₃×C₈	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×C₃²	D₄	1	1	yes	characteristic
13	C₃×D₃	—	4	2	no	—
14	D₈	—	3	1	no	Sylow
15	C₂²×C₃	—	6	2	no	—
16	C₂×D₃	—	2	2	no	—
17	C₃×C₄	—	2	1	no	—
18	C₃×C₄	C₂×D₃	1	1	yes	characteristic
19	C₃×C₄	C₂²×C₃	1	1	yes	characteristic
20	C₃²	D₈	1	1	yes	characteristic, complemented, Sylow
21	D₄	—	3	2	no	—
22	C₈	C₃×D₃	1	1	yes	characteristic, complemented
23	C₂×C₃	—	2	1	no	—
24	C₂×C₃	—	12	2	no	—
25	C₂×C₃	D₁₂	1	1	yes	characteristic
26	C₂×C₃	C₃×D₄	1	1	yes	characteristic
27	D₃	—	4	2	no	—
28	C₂²	—	6	2	no	—
29	C₄	C₂×C₃×D₃	1	1	yes	characteristic
30	C₃	—	2	1	no	—
31	C₃	D₂₄	1	1	yes	characteristic, direct product factor
32	C₃	C₃×D₈	1	1	yes	characteristic, complemented
33	C₂	—	12	2	no	—
34	C₂	C₃×D₁₂	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.