Subgroups — C₂×C₄²×C₉ #63516

Order 288.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₉	C₂	1	3	yes	maximal
2	C₄²×C₉	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃×C₄²	C₃	1	1	yes	maximal, characteristic
4	C₂³×C₉	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₉	C₄	1	12	yes	direct product factor
6	C₂×C₄×C₉	C₂²	1	6	yes	—
7	C₂²×C₃×C₄	C₂×C₃	1	3	yes	—
8	C₃×C₄²	C₂×C₃	1	4	yes	—
9	C₂²×C₉	C₂×C₄	1	6	yes	—
10	C₂²×C₉	C₂³	1	1	yes	characteristic
11	C₄×C₉	C₂×C₄	1	12	yes	direct product factor
12	C₂×C₄²	C₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₂³×C₃	C₂²×C₃	1	1	yes	characteristic
14	C₂×C₃×C₄	C₃×C₄	1	12	yes	—
15	C₂×C₃×C₄	C₂²×C₃	1	6	yes	—
16	C₂×C₉	C₄²	1	4	yes	direct product factor
17	C₂×C₉	C₂²×C₄	1	3	yes	—
18	C₂²×C₄	C₂×C₉	1	3	yes	—
19	C₄²	C₂×C₉	1	4	yes	direct product factor
20	C₂²×C₃	C₂×C₃×C₄	1	6	yes	—
21	C₂²×C₃	C₂³×C₃	1	1	yes	characteristic
22	C₃×C₄	C₂×C₃×C₄	1	12	yes	—
23	C₉	C₂×C₄²	1	1	yes	characteristic, direct product factor, Sylow
24	C₂³	C₂²×C₉	1	1	yes	characteristic
25	C₂×C₄	C₄×C₉	1	12	yes	direct product factor
26	C₂×C₄	C₂²×C₉	1	6	yes	—
27	C₂×C₃	C₃×C₄²	1	4	yes	—
28	C₂×C₃	C₂²×C₃×C₄	1	3	yes	—
29	C₂²	C₂×C₄×C₉	1	6	yes	—
30	C₂²	C₂³×C₉	1	1	yes	characteristic
31	C₄	C₂×C₄×C₉	1	12	yes	direct product factor
32	C₃	C₂×C₃×C₄²	1	1	yes	characteristic
33	C₂	C₄²×C₉	1	4	yes	direct product factor
34	C₂	C₂²×C₄×C₉	1	3	yes	—

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.