Subgroups — C₉⋊(C₂²⋊(C₂²⋊C₉)) #13048170

Order 1296.

319 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₉	C₃	1	1	yes	maximal, characteristic
2	C₃×C₂²⋊(C₂²⋊C₉)	C₃	1	3	yes	maximal
3	C₉⋊(C₂²⋊C₉)	—	4	5	no	maximal
4	C₂³×C₃×C₉	—	3	5	no	—
5	C₂⁴×C₃²	C₃²	1	1	yes	characteristic
6	C₂⁴×C₉	C₉	1	3	yes	complemented
7	C₂²⋊(C₂²⋊C₉)	—	3	3	no	—
8	C₂²×C₃×C₉	—	3	10	no	—
9	C₂²×C₃×C₉	A₄	1	5	yes	—
10	C₃×C₂²⋊C₉	—	4	15	no	—
11	C₉⋊C₉	—	16	1	no	Sylow
12	C₂³×C₃²	—	3	5	no	—
13	C₂³×C₉	—	3	15	no	—
14	C₂×C₃×C₉	—	3	5	no	—
15	C₂⁴×C₃	C₃×C₉	1	1	yes	characteristic
16	C₂⁴×C₃	3₋¹⁺²	1	3	yes	—
17	C₂²×C₃²	—	3	10	no	—
18	C₂²×C₃²	C₃×A₄	1	5	yes	—
19	C₂²×C₉	—	3	30	no	—
20	C₂²×C₉	C₂²⋊C₉	1	15	yes	complemented
21	C₂²⋊C₉	—	12	15	no	—
22	C₃×C₉	—	16	3	no	—
23	C₃×C₉	C₂²⋊A₄	1	1	yes	characteristic
24	C₂³×C₃	—	3	15	no	—
25	C₂³×C₃	—	3	5	no	—
26	C₂×C₃²	—	3	5	no	—
27	C₂×C₉	—	3	15	no	—
28	C₂⁴	C₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
29	C₂²×C₃	—	3	10	no	—
30	C₂²×C₃	—	3	30	no	—
31	C₂²×C₃	C₉⋊A₄	1	15	yes	—
32	C₂²×C₃	C₃×C₂²⋊C₉	1	5	yes	—
33	C₃²	C₃×C₂²⋊A₄	1	1	yes	characteristic
34	C₉	—	48	3	no	—
35	C₉	C₂²⋊(C₂²⋊C₉)	1	3	yes	complemented
36	C₂³	—	3	5	no	—
37	C₂×C₃	—	3	15	no	—
38	C₂×C₃	—	3	5	no	—
39	C₂²	—	3	10	no	—
40	C₂²	C₉⋊(C₂²⋊C₉)	1	5	yes	complemented
41	C₃	C₉⋊(C₂²⋊A₄)	1	3	yes	—
42	C₃	C₃×C₂²⋊(C₂²⋊C₉)	1	1	yes	characteristic
43	C₂	—	3	5	no	—

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.