Subgroups — #28356826

Order 13851.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095335	C₃	1	3	yes	maximal
2	C₉×#10587018	C₃	1	1	yes	maximal, characteristic
3	#13095335	—	3	3	no	—
4	C₃×#10587018	C₉	1	2	yes	—
5	C₃×#10587018	C₃²	1	1	yes	characteristic
6	C₉²×C₁₉	C₉	1	1	yes	characteristic
7	C₉⋊C₈₁	—	19	1	no	maximal, Sylow
8	C₃×C₉×C₁₉	C₂₇	1	2	yes	—
9	C₃×C₉×C₁₉	C₂₇	1	1	yes	characteristic
10	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
11	#10587018	—	3	2	no	—
12	#10587018	3₋¹⁺²	1	3	yes	—
13	C₃×C₈₁	—	19	3	no	—
14	C₉×C₂₇	—	19	1	no	—
15	C₃²×C₁₉	C₃×C₂₇	1	1	yes	characteristic
16	C₉×C₁₉	—	3	2	no	—
17	C₉×C₁₉	C₈₁	1	3	yes	complemented
18	C₉×C₁₉	C₉⋊C₉	1	1	yes	characteristic
19	C₉×C₁₉	C₂₇⋊C₃	1	2	yes	—
20	C₃×C₂₇	—	19	1	no	—
21	C₃×C₂₇	—	19	2	no	—
22	C₉²	#4296	1	1	yes	characteristic
23	C₈₁	—	57	3	no	—
24	C₃×C₁₉	C₉⋊C₂₇	1	1	yes	characteristic
25	C₃×C₁₉	C₃×C₈₁	1	1	yes	characteristic
26	C₃×C₁₉	C₈₁⋊C₃	1	2	yes	—
27	C₃×C₉	#10587020	1	2	yes	—
28	C₃×C₉	#10587020	1	1	yes	characteristic
29	C₃×C₉	C₃×#4296	1	1	yes	characteristic
30	C₂₇	—	19	3	no	—
31	C₂₇	—	57	2	no	—
32	C₁₉	C₉⋊C₈₁	1	1	yes	characteristic, complemented, Sylow
33	C₃²	C₃×#10587020	1	1	yes	characteristic
34	C₉	—	3	2	no	—
35	C₉	#13095335	1	3	yes	complemented
36	C₉	#13095339	1	1	yes	characteristic
37	C₉	#13095344	1	2	yes	—
38	C₃	#17987571	1	1	yes	characteristic
39	C₃	C₃×#13095335	1	1	yes	characteristic
40	C₃	#17987582	1	2	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.