Subgroups — C₃³×C₄₃⋊C₉ #23782909

Order 10449.

792 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄₃⋊C₉	C₃	1	39	yes	maximal, direct product factor
2	C₃⁴×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₄₃⋊C₉	C₃²	1	117	yes	direct product factor
4	C₃³×C₄₃	C₉	1	27	yes	complemented
5	C₃³×C₄₃	C₃²	1	13	yes	—
6	C₃²×C₄₃	C₃×C₉	1	117	yes	complemented
7	C₃²×C₄₃	C₃³	1	13	yes	—
8	C₄₃⋊C₉	C₃³	1	27	yes	direct product factor
9	C₃³×C₉	—	43	1	no	maximal, Sylow
10	C₃×C₄₃	C₃²×C₉	1	39	yes	complemented
11	C₃×C₄₃	C₃⁴	1	1	yes	characteristic
12	C₃⁴	C₄₃⋊C₃	1	1	yes	characteristic
13	C₃²×C₉	—	43	39	no	—
14	C₄₃	C₃³×C₉	1	1	yes	characteristic, complemented, Sylow
15	C₃³	C₄₃⋊C₉	1	27	yes	direct product factor
16	C₃³	C₃×C₄₃⋊C₃	1	13	yes	—
17	C₃×C₉	—	43	117	no	—
18	C₃²	C₃×C₄₃⋊C₉	1	117	yes	direct product factor
19	C₃²	C₃²×C₄₃⋊C₃	1	13	yes	—
20	C₉	—	43	27	no	—
21	C₃	C₃²×C₄₃⋊C₉	1	39	yes	direct product factor
22	C₃	C₃³×C₄₃⋊C₃	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.