Subgroups — C₉²×C₄₃⋊C₃ #23782770

Order 10449.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₄₃⋊C₃	C₃	1	4	yes	maximal
2	C₉×C₄₃⋊C₉	C₃	1	8	yes	maximal, complemented
3	C₉²×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
5	C₃×C₄₃⋊C₉	C₃²	1	8	yes	—
6	C₉×C₄₃⋊C₃	C₉	1	36	yes	direct product factor
7	C₃×C₉×C₄₃	C₃²	1	4	yes	—
8	C₃²×C₄₃	C₃³	1	1	yes	characteristic
9	C₃×C₄₃⋊C₃	C₃×C₉	1	12	yes	—
10	C₉×C₄₃	C₃×C₉	1	12	yes	complemented
11	C₄₃⋊C₉	C₃×C₉	1	24	yes	complemented
12	C₃×C₉²	—	43	1	no	maximal, Sylow
13	C₃×C₄₃	C₃²×C₉	1	4	yes	—
14	C₄₃⋊C₃	C₉²	1	9	yes	direct product factor
15	C₃²×C₉	—	43	4	no	—
16	C₉²	—	43	8	no	—
17	C₉²	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
18	C₄₃	C₃×C₉²	1	1	yes	characteristic, complemented, Sylow
19	C₃³	—	43	1	no	—
20	C₃×C₉	—	43	8	no	—
21	C₃×C₉	—	43	36	no	—
22	C₃×C₉	C₃×C₄₃⋊C₃	1	4	yes	—
23	C₃²	—	43	12	no	—
24	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
25	C₉	—	43	24	no	—
26	C₉	C₉×C₄₃⋊C₃	1	12	yes	direct product factor
27	C₃	—	43	9	no	—
28	C₃	C₃×C₉×C₄₃⋊C₃	1	4	yes	—

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