Subgroups — C₉²×#4296 #28356840

Order 13851.

890 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#4296	C₃	1	12	yes	maximal
2	C₉²×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₃²×#4296	C₃²	1	9	yes	—
4	C₉×#4296	C₉	1	108	yes	direct product factor
5	C₃×C₉×C₁₉⋊C₃	C₃²	1	4	yes	—
6	C₉×#4294	C₉	1	8	yes	complemented
7	C₉²×C₁₉	C₉	1	1	yes	characteristic, complemented
8	C₉³	—	19	1	no	maximal, Sylow
9	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
10	C₃×#4296	C₃×C₉	1	108	yes	—
11	C₃×C₉×C₁₉	C₃×C₉	1	4	yes	—
12	C₃×#4294	C₃×C₉	1	8	yes	—
13	C₉×C₁₉⋊C₃	C₃×C₉	1	36	yes	—
14	C₃×C₉²	—	19	12	no	—
15	C₃×C₉²	—	19	1	no	—
16	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
17	C₃×C₁₉⋊C₃	C₃²×C₉	1	12	yes	—
18	#4296	C₉²	1	81	yes	direct product factor
19	C₉×C₁₉	C₉²	1	12	yes	complemented
20	#4294	C₉²	1	24	yes	complemented
21	C₃²×C₉	—	19	9	no	—
22	C₃²×C₉	—	19	4	no	—
23	C₉²	—	19	108	no	—
24	C₉²	—	19	8	no	—
25	C₉²	#4296	1	1	yes	characteristic, direct product factor
26	C₃×C₁₉	C₃×C₉²	1	4	yes	—
27	C₁₉⋊C₃	C₃×C₉²	1	9	yes	—
28	C₃³	—	19	1	no	—
29	C₃×C₉	—	19	108	no	—
30	C₃×C₉	—	19	8	no	—
31	C₃×C₉	—	19	36	no	—
32	C₃×C₉	C₃×#4296	1	4	yes	—
33	C₁₉	C₉³	1	1	yes	characteristic, complemented, Sylow
34	C₃²	—	19	12	no	—
35	C₃²	C₃²×#4296	1	1	yes	characteristic
36	C₉	—	19	81	no	—
37	C₉	—	19	24	no	—
38	C₉	C₉×#4296	1	12	yes	direct product factor
39	C₃	—	19	9	no	—
40	C₃	C₃×C₉×#4296	1	4	yes	—

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.