Subgroups — C₃×#239 #3822

Order 144.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₂	C₂	1	3	yes	maximal, complemented
3	C₃×C₄×D₃	C₂	1	3	yes	maximal, complemented
4	C₃×#41	—	3	1	no	maximal
5	#239	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃×D₃	C₂²	1	3	yes	—
7	C₃²×C₄	C₂²	1	3	yes	—
8	C₃×Dic₃	C₂²	1	1	yes	characteristic
9	C₃×Q₈	—	2	1	no	—
10	C₃×Q₈	D₃	1	1	yes	characteristic, complemented
11	C₃×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×D₄	—	3	3	no	—
13	C₂×C₃×C₄	—	3	3	no	—
14	D₁₂	C₂×C₃	1	3	yes	complemented
15	C₄×D₃	C₂×C₃	1	3	yes	complemented
16	C₂×C₃²	C₂³	1	1	yes	characteristic
17	C₃×D₃	—	2	3	no	—
18	#41	—	3	1	no	Sylow
19	C₂²×C₃	—	3	3	no	—
20	C₂×D₃	C₂²×C₃	1	3	yes	—
21	C₃×C₄	—	2	3	no	—
22	C₃×C₄	—	3	1	no	—
23	C₃×C₄	C₂×D₃	1	3	yes	—
24	C₃×C₄	C₂²×C₃	1	3	yes	—
25	Dic₃	C₂²×C₃	1	1	yes	characteristic
26	C₃²	#41	1	1	yes	characteristic, complemented, Sylow
27	Q₈	C₃×D₃	1	1	yes	characteristic, complemented
28	D₄	—	3	3	no	—
29	C₂×C₄	—	3	3	no	—
30	C₂×C₃	—	2	1	no	—
31	C₂×C₃	—	6	3	no	—
32	C₂×C₃	C₂²×D₃	1	1	yes	characteristic
33	C₂×C₃	C₂³×C₃	1	1	yes	characteristic
34	D₃	—	2	3	no	—
35	C₂²	—	3	3	no	—
36	C₄	—	3	1	no	—
37	C₄	C₂×C₃×D₃	1	3	yes	—
38	C₃	—	2	1	no	—
39	C₃	#239	1	1	yes	characteristic, direct product factor
40	C₃	C₃×#41	1	1	yes	characteristic, complemented
41	C₂	—	6	3	no	—
42	C₂	C₂²×C₃×D₃	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.