Subgroups — C₂³×C₂²⋊C₉ #64189

Order 288.

324 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊C₉	C₂	1	7	yes	maximal, direct product factor
2	C₂⁵×C₃	C₃	1	1	yes	maximal, characteristic
3	C₂³×C₉	—	4	1	no	maximal
4	C₂×C₂²⋊C₉	C₂²	1	7	yes	direct product factor
5	C₂⁴×C₃	—	3	7	no	—
6	C₂⁴×C₃	—	3	1	no	—
7	C₂⁴×C₃	C₂×C₃	1	7	yes	—
8	C₂²×C₉	—	4	7	no	—
9	C₂²⋊C₉	C₂³	1	1	yes	characteristic, direct product factor
10	C₂⁵	C₉	1	1	yes	characteristic, complemented, Sylow
11	C₂³×C₃	—	3	21	no	—
12	C₂³×C₃	—	3	14	no	—
13	C₂³×C₃	—	3	7	no	—
14	C₂³×C₃	—	3	7	no	—
15	C₂³×C₃	A₄	1	1	yes	characteristic
16	C₂³×C₃	C₂²×C₃	1	7	yes	—
17	C₂×C₉	—	4	7	no	—
18	C₂⁴	—	3	7	no	—
19	C₂⁴	—	3	1	no	—
20	C₂⁴	C₂×C₉	1	7	yes	complemented
21	C₂²×C₃	—	3	7	no	—
22	C₂²×C₃	—	3	14	no	—
23	C₂²×C₃	—	3	21	no	—
24	C₂²×C₃	—	3	7	no	—
25	C₂²×C₃	C₂×A₄	1	7	yes	—
26	C₂²×C₃	C₂³×C₃	1	1	yes	characteristic
27	C₉	—	4	1	no	Sylow
28	C₂³	—	3	21	no	—
29	C₂³	—	3	14	no	—
30	C₂³	—	3	7	no	—
31	C₂³	—	3	7	no	—
32	C₂³	C₂²⋊C₉	1	1	yes	characteristic, direct product factor
33	C₂³	C₂²×C₉	1	7	yes	complemented
34	C₂×C₃	—	3	7	no	—
35	C₂×C₃	—	3	1	no	—
36	C₂×C₃	C₂²×A₄	1	7	yes	—
37	C₂²	—	3	7	no	—
38	C₂²	—	3	14	no	—
39	C₂²	—	3	7	no	—
40	C₂²	—	3	21	no	—
41	C₂²	C₂×C₂²⋊C₉	1	7	yes	direct product factor
42	C₂²	C₂³×C₉	1	1	yes	characteristic, complemented
43	C₃	C₂³×A₄	1	1	yes	characteristic
44	C₂	—	3	1	no	—
45	C₂	—	3	7	no	—
46	C₂	C₂²×C₂²⋊C₉	1	7	yes	direct product factor

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.