Subgroups — C₂×D₄×C₉ #3705

Order 144.

81 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₉	C₂	1	2	yes	maximal, complemented
2	D₄×C₉	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×D₄	C₃	1	1	yes	maximal, characteristic
5	C₂²×C₉	—	2	4	no	—
6	C₂²×C₉	C₂²	1	1	yes	characteristic
7	C₂²×C₉	C₂²	1	4	yes	complemented
8	C₄×C₉	C₂²	1	2	yes	complemented
9	C₂³×C₃	C₂×C₃	1	2	yes	—
10	C₃×D₄	C₂×C₃	1	4	yes	—
11	C₂×C₃×C₄	C₂×C₃	1	1	yes	characteristic
12	C₂×C₉	—	2	4	no	—
13	C₂×C₉	D₄	1	2	yes	direct product factor
14	C₂×C₉	C₂³	1	1	yes	characteristic
15	C₂×D₄	C₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₂²×C₃	—	2	4	no	—
17	C₂²×C₃	C₂²×C₃	1	1	yes	characteristic
18	C₂²×C₃	C₂²×C₃	1	4	yes	—
19	C₃×C₄	C₂²×C₃	1	2	yes	—
20	C₉	C₂×D₄	1	1	yes	characteristic, direct product factor, Sylow
21	C₂³	C₂×C₉	1	2	yes	complemented
22	D₄	C₂×C₉	1	4	yes	direct product factor
23	C₂×C₄	C₂×C₉	1	1	yes	characteristic, complemented
24	C₂×C₃	—	2	4	no	—
25	C₂×C₃	C₃×D₄	1	2	yes	—
26	C₂×C₃	C₂³×C₃	1	1	yes	characteristic
27	C₂²	—	2	4	no	—
28	C₂²	C₂²×C₉	1	1	yes	characteristic
29	C₂²	C₂²×C₉	1	4	yes	complemented
30	C₄	C₂²×C₉	1	2	yes	complemented
31	C₃	C₂×C₃×D₄	1	1	yes	characteristic
32	C₂	—	2	4	no	—
33	C₂	D₄×C₉	1	2	yes	direct product factor
34	C₂	C₂³×C₉	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.