Subgroups — C₃⁴×C₄₃⋊C₉ #44535389

Order 31347.

10232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄₃⋊C₉	C₃	1	120	yes	maximal, direct product factor
2	C₃⁵×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₄₃⋊C₉	C₃²	1	1170	yes	direct product factor
4	C₃⁴×C₄₃	C₉	1	81	yes	complemented
5	C₃⁴×C₄₃	C₃²	1	40	yes	—
6	C₃×C₄₃⋊C₉	C₃³	1	1080	yes	direct product factor
7	C₃³×C₄₃	C₃×C₉	1	1080	yes	complemented
8	C₃³×C₄₃	C₃³	1	130	yes	—
9	C₃⁴×C₉	—	43	1	no	maximal, Sylow
10	C₃²×C₄₃	C₃²×C₉	1	1170	yes	complemented
11	C₃²×C₄₃	C₃⁴	1	40	yes	—
12	C₄₃⋊C₉	C₃⁴	1	81	yes	direct product factor
13	C₃⁵	C₄₃⋊C₃	1	1	yes	characteristic
14	C₃³×C₉	—	43	120	no	—
15	C₃×C₄₃	C₃³×C₉	1	120	yes	complemented
16	C₃×C₄₃	C₃⁵	1	1	yes	characteristic
17	C₃⁴	C₄₃⋊C₉	1	81	yes	direct product factor
18	C₃⁴	C₃×C₄₃⋊C₃	1	40	yes	—
19	C₃²×C₉	—	43	1170	no	—
20	C₄₃	C₃⁴×C₉	1	1	yes	characteristic, complemented, Sylow
21	C₃³	C₃×C₄₃⋊C₉	1	1080	yes	direct product factor
22	C₃³	C₃²×C₄₃⋊C₃	1	130	yes	—
23	C₃×C₉	—	43	1080	no	—
24	C₃²	C₃²×C₄₃⋊C₉	1	1170	yes	direct product factor
25	C₃²	C₃³×C₄₃⋊C₃	1	40	yes	—
26	C₉	—	43	81	no	—
27	C₃	C₃³×C₄₃⋊C₉	1	120	yes	direct product factor
28	C₃	C₃⁴×C₄₃⋊C₃	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.