Subgroups — C₂×C₄×D₉ #3695

Order 144.

81 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₉	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₄×D₃	—	3	1	no	maximal
6	C₂²×C₉	C₂²	1	1	yes	characteristic
7	C₂×D₉	C₄	1	4	yes	direct product factor
8	C₂×D₉	C₂²	1	2	yes	—
9	C₄×C₉	C₂²	1	2	yes	complemented
10	Dic₉	C₂²	1	2	yes	complemented
11	C₂²×D₃	—	3	1	no	—
12	C₂×C₃×C₄	D₃	1	1	yes	characteristic
13	C₂×Dic₃	—	3	1	no	—
14	C₄×D₃	—	3	4	no	—
15	C₂×C₉	C₂×C₄	1	2	yes	complemented
16	C₂×C₉	C₂³	1	1	yes	characteristic
17	D₉	C₂×C₄	1	4	yes	direct product factor
18	C₂²×C₄	—	9	1	no	Sylow
19	C₂²×C₃	C₂×D₃	1	1	yes	characteristic
20	C₂×D₃	—	3	4	no	—
21	C₂×D₃	—	3	2	no	—
22	C₃×C₄	C₂×D₃	1	2	yes	—
23	Dic₃	—	3	2	no	—
24	C₉	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
25	C₂³	—	9	1	no	—
26	C₂×C₄	—	9	1	no	—
27	C₂×C₄	—	9	4	no	—
28	C₂×C₄	D₉	1	1	yes	characteristic, direct product factor
29	C₂×C₃	C₄×D₃	1	2	yes	—
30	C₂×C₃	C₂²×D₃	1	1	yes	characteristic
31	D₃	—	3	4	no	—
32	C₂²	—	9	4	no	—
33	C₂²	—	9	2	no	—
34	C₂²	C₂×D₉	1	1	yes	characteristic
35	C₄	—	9	2	no	—
36	C₄	C₂×D₉	1	2	yes	direct product factor
37	C₃	C₂×C₄×D₃	1	1	yes	characteristic
38	C₂	—	9	4	no	—
39	C₂	C₄×D₉	1	2	yes	direct product factor
40	C₂	C₂²×D₉	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.