Subgroups — #28353593

Order 13851.

662 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊#4294	C₃	1	12	yes	maximal, complemented
2	C₃²×C₁₉×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	C₃²×#4294	C₃²	1	9	yes	—
4	C₃²⋊#4294	—	3	36	no	—
5	C₃⁴×C₁₉	C₃²	1	4	yes	—
6	C₃×C₁₉×H(3,𝔽₃)	—	3	12	no	—
7	#10624564	—	19	1	no	maximal, Sylow
8	C₃³×C₁₉	—	3	12	no	—
9	C₃³×C₁₉	—	3	36	no	—
10	C₃³×C₁₉	H(3,𝔽₃)	1	12	yes	—
11	C₃³×C₁₉	C₃³	1	1	yes	characteristic
12	C₁₉×H(3,𝔽₃)	—	3	27	no	—
13	C₃×#4294	—	3	36	no	—
14	C₃²×H(3,𝔽₃)	C₁₉⋊C₃	1	1	yes	characteristic
15	C₃×C₃²⋊C₉	—	19	12	no	—
16	C₃²×C₁₉	—	3	12	no	—
17	C₃²×C₁₉	—	3	36	no	—
18	C₃²×C₁₉	—	9	36	no	—
19	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	4	yes	—
20	C₃²×C₁₉	#737	1	9	yes	—
21	#4294	—	9	9	no	—
22	C₃⁴	C₃×C₁₉⋊C₃	1	4	yes	—
23	C₃×H(3,𝔽₃)	—	3	12	no	—
24	C₃²×C₉	—	19	9	no	—
25	C₃²⋊C₉	—	57	36	no	—
26	C₃×C₁₉	—	9	12	no	—
27	C₃×C₁₉	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
28	C₃×C₁₉	#6893	1	12	yes	—
29	C₃³	—	3	12	no	—
30	C₃³	—	3	36	no	—
31	C₃³	C₃²⋊(C₁₉⋊C₃)	1	12	yes	—
32	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
33	H(3,𝔽₃)	—	3	27	no	—
34	C₃×C₉	—	57	36	no	—
35	C₁₉	#10624564	1	1	yes	characteristic, complemented, Sylow
36	C₃²	—	3	12	no	—
37	C₃²	—	3	36	no	—
38	C₃²	—	9	36	no	—
39	C₃²	C₃×C₃²⋊(C₁₉⋊C₃)	1	4	yes	—
40	C₃²	#13095331	1	9	yes	—
41	C₉	—	171	9	no	—
42	C₃	—	9	12	no	—
43	C₃	#17987417	1	1	yes	characteristic
44	C₃	#17987429	1	12	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₃²⋊#4294	C₃	semidirect
35. C₁₉	#10624564	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.