Subgroups — #28356859

Order 13851.

458 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095339	C₃	1	12	yes	maximal
2	C₉²×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₃²×#4296	C₃²	1	9	yes	—
4	#13095339	—	3	36	no	—
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	#10624554	—	19	1	no	maximal, Sylow
9	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
10	C₃×#4296	—	3	36	no	—
11	C₃×C₉×C₁₉	C₃×C₉	1	4	yes	—
12	C₃×#4294	C₃×C₉	1	8	yes	—
13	C₉×C₁₉⋊C₃	3₋¹⁺²	1	36	yes	—
14	C₃×C₉⋊C₉	—	19	12	no	—
15	C₃×C₉²	—	19	1	no	—
16	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
17	C₃×C₁₉⋊C₃	C₃×3₋¹⁺²	1	12	yes	—
18	#4296	—	9	9	no	—
19	C₉×C₁₉	C₉⋊C₉	1	12	yes	complemented
20	#4294	C₉⋊C₉	1	24	yes	complemented
21	C₃²×C₉	—	19	4	no	—
22	C₃²×C₉	—	19	9	no	—
23	C₉⋊C₉	—	57	36	no	—
24	C₉²	—	19	8	no	—
25	C₉²	#4296	1	1	yes	characteristic, complemented
26	C₃×C₁₉	C₃×C₉⋊C₉	1	4	yes	—
27	C₁₉⋊C₃	#6900	1	9	yes	—
28	C₃³	—	19	1	no	—
29	C₃×C₉	—	19	8	no	—
30	C₃×C₉	—	19	36	no	—
31	C₃×C₉	—	57	36	no	—
32	C₃×C₉	C₃×#4296	1	4	yes	—
33	C₁₉	#10624554	1	1	yes	characteristic, complemented, Sylow
34	C₃²	—	19	12	no	—
35	C₃²	C₃²×#4296	1	1	yes	characteristic
36	C₉	—	19	24	no	—
37	C₉	—	171	9	no	—
38	C₉	#13095339	1	12	yes	complemented
39	C₃	—	19	9	no	—
40	C₃	C₃×#13095339	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.