Subgroups — #28357037

Order 13851.

154 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987582	C₃	1	8	yes	maximal, complemented
2	C₃×#13095335	C₃	1	4	yes	maximal, complemented
3	#17987480	C₃	1	1	yes	maximal, characteristic
4	#13095335	C₃²	1	1	yes	characteristic
5	#13095335	C₃²	1	8	yes	—
6	#13095312	C₉	1	8	yes	—
7	C₃×#10587018	C₃²	1	4	yes	—
8	C₁₉×#737	C₉	1	1	yes	characteristic
9	#10624833	—	19	1	no	maximal, Sylow
10	C₁₉×3₋¹⁺²	C₂₇	1	8	yes	—
11	C₁₉×H(3,𝔽₃)	C₂₇	1	1	yes	characteristic
12	C₃×C₉×C₁₉	C₃×C₉	1	4	yes	—
13	#10587018	C₃×C₉	1	8	yes	—
14	#10587018	C₃³	1	1	yes	characteristic
15	#6903	—	19	1	no	—
16	C₈₁⋊C₃	—	19	8	no	—
17	C₃×C₈₁	—	19	4	no	—
18	C₃²×C₁₉	C₃×C₂₇	1	4	yes	—
19	C₉×C₁₉	C₃×C₂₇	1	8	yes	—
20	C₉×C₁₉	C₃²×C₉	1	1	yes	characteristic
21	#737	#4296	1	1	yes	characteristic
22	C₂₇⋊C₃	—	19	8	no	—
23	C₃×C₂₇	—	19	4	no	—
24	C₈₁	—	19	1	no	—
25	C₈₁	—	19	8	no	—
26	C₃×C₁₉	—	3	4	no	—
27	C₃×C₁₉	C₃²×C₂₇	1	1	yes	characteristic
28	3₋¹⁺²	#10587020	1	8	yes	—
29	H(3,𝔽₃)	#10587020	1	1	yes	characteristic
30	C₃×C₉	C₃×#4296	1	4	yes	—
31	C₂₇	—	19	8	no	—
32	C₂₇	—	19	1	no	—
33	C₁₉	#10624833	1	1	yes	characteristic, complemented, Sylow
34	C₃²	C₃×#10587020	1	4	yes	—
35	C₉	C₃×#10587020	1	8	yes	—
36	C₉	C₃²×#4296	1	1	yes	characteristic
37	C₃	—	3	4	no	—
38	C₃	C₃²×#10587020	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.