Subgroups — C₃×C₃²⋊(C₁₉₉⋊C₃) #30633146

Order 16119.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₉₉⋊C₃	C₃	1	3	yes	maximal, complemented
2	C₃²⋊(C₁₉₉⋊C₃)	C₃	1	9	yes	maximal, direct product factor
3	C₃³×C₁₉₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₁₉₉	—	3	3	no	—
5	C₃²×C₁₉₉	C₃²	1	1	yes	characteristic
6	C₃²×C₁₉₉	C₃²	1	3	yes	complemented
7	C₃×C₁₉₉⋊C₃	—	3	9	no	—
8	C₃×C₁₉₉⋊C₃	C₃²	1	9	yes	complemented
9	C₃×C₁₉₉	—	3	3	no	—
10	C₃×C₁₉₉	H(3,𝔽₃)	1	3	yes	complemented
11	C₃×C₁₉₉	C₃³	1	1	yes	characteristic
12	C₁₉₉⋊C₃	—	3	9	no	—
13	C₁₉₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
14	C₃×H(3,𝔽₃)	—	199	1	no	maximal, Sylow
15	C₃³	—	199	3	no	—
16	C₃³	C₁₉₉⋊C₃	1	1	yes	characteristic, complemented
17	H(3,𝔽₃)	—	199	9	no	—
18	C₃²	—	3	3	no	—
19	C₃²	—	597	9	no	—
20	C₃²	—	199	9	no	—
21	C₃²	C₃×C₁₉₉⋊C₃	1	1	yes	characteristic
22	C₃²	C₃×C₁₉₉⋊C₃	1	3	yes	complemented
23	C₃	—	3	3	no	—
24	C₃	—	597	9	no	—
25	C₃	C₃²⋊(C₁₉₉⋊C₃)	1	3	yes	direct product factor
26	C₃	C₃²×C₁₉₉⋊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.