Subgroups — C₃×C₉×C₄₆₃⋊C₃ #49154264

Order 37503.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄₆₃⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₃×C₄₆₃⋊C₉	C₃	1	2	yes	maximal, complemented
3	C₉×C₄₆₃⋊C₃	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₉×C₄₆₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃²×C₄₆₃	C₃²	1	1	yes	characteristic
6	C₃×C₄₆₃⋊C₃	C₉	1	9	yes	direct product factor
7	C₃×C₄₆₃⋊C₃	C₃²	1	3	yes	—
8	C₉×C₄₆₃	C₃²	1	3	yes	complemented
9	C₄₆₃⋊C₉	C₃²	1	6	yes	complemented
10	C₃×C₄₆₃	C₃×C₉	1	3	yes	complemented
11	C₃×C₄₆₃	C₃³	1	1	yes	characteristic
12	C₄₆₃⋊C₃	C₃×C₉	1	9	yes	direct product factor
13	C₄₆₃	C₃²×C₉	1	1	yes	characteristic, complemented, Sylow
14	C₃²×C₉	—	463	1	no	maximal, Sylow
15	C₃³	—	463	1	no	—
16	C₃×C₉	—	463	2	no	—
17	C₃×C₉	—	463	9	no	—
18	C₃×C₉	C₄₆₃⋊C₃	1	1	yes	characteristic, direct product factor
19	C₃²	—	463	9	no	—
20	C₃²	—	463	3	no	—
21	C₃²	C₃×C₄₆₃⋊C₃	1	1	yes	characteristic
22	C₉	—	463	6	no	—
23	C₉	C₃×C₄₆₃⋊C₃	1	3	yes	direct product factor
24	C₃	—	463	9	no	—
25	C₃	C₉×C₄₆₃⋊C₃	1	3	yes	direct product factor
26	C₃	C₃²×C₄₆₃⋊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.