Subgroups — #17987598

Order 4617.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095342	C₃	1	8	yes	maximal, complemented
2	C₃×#10587020	C₃	1	4	yes	maximal, complemented
3	#13095331	C₃	1	1	yes	maximal, characteristic
4	C₁₉×H(3,𝔽₃)	C₉	1	1	yes	characteristic
5	#10587025	C₉	1	8	yes	—
6	C₃×#4294	C₃²	1	4	yes	—
7	#10587020	C₃²	1	1	yes	characteristic
8	#10587020	C₃²	1	8	yes	—
9	#6903	—	19	1	no	maximal, Sylow
10	C₃²×C₁₉	C₃×C₉	1	4	yes	—
11	#4294	C₃×C₉	1	8	yes	—
12	#4294	C₃³	1	1	yes	characteristic
13	#737	—	19	1	no	—
14	C₂₇⋊C₃	—	19	8	no	—
15	C₃×C₂₇	—	19	4	no	—
16	C₃×C₁₉	—	3	4	no	—
17	C₃×C₁₉	C₃²×C₉	1	1	yes	characteristic
18	3₋¹⁺²	—	19	8	no	—
19	H(3,𝔽₃)	#4296	1	1	yes	characteristic
20	C₃×C₉	—	19	4	no	—
21	C₂₇	—	19	1	no	—
22	C₂₇	—	19	8	no	—
23	C₁₉	#6903	1	1	yes	characteristic, complemented, Sylow
24	C₃²	C₃×#4296	1	4	yes	—
25	C₉	—	19	1	no	—
26	C₉	—	19	8	no	—
27	C₃	—	3	4	no	—
28	C₃	C₃²×#4296	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.