Subgroups — #49144398

Order 36693.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²⋊(C₁₅₁⋊C₉)	C₃	1	1	yes	maximal, characteristic
2	C₃²⋊(C₁₅₁⋊C₉)	C₃	1	2	yes	maximal
3	C₃²⋊C₉×C₁₅₁	C₃	1	1	yes	maximal, characteristic
4	C₃×C₁₅₁⋊C₉	—	3	1	no	—
5	C₃×C₁₅₁⋊C₉	—	3	2	no	—
6	C₃³×C₁₅₁	C₃²	1	1	yes	characteristic
7	C₃×C₉×C₁₅₁	—	3	1	no	—
8	C₃²×C₁₅₁	—	3	1	no	—
9	C₃²×C₁₅₁	—	3	1	no	—
10	C₃²×C₁₅₁	—	3	1	no	—
11	C₃²×C₁₅₁	—	3	1	no	—
12	C₃²×C₁₅₁	H(3,𝔽₃)	1	1	yes	characteristic
13	C₉×C₁₅₁	—	9	1	no	—
14	C₁₅₁⋊C₉	—	9	1	no	—
15	C₁₅₁⋊C₉	—	9	2	no	—
16	C₃×C₁₅₁	—	9	1	no	—
17	C₃×C₁₅₁	#731	1	1	yes	characteristic
18	C₃×C₁₅₁	#732	1	1	yes	characteristic
19	C₃×C₁₅₁	#733	1	1	yes	characteristic
20	C₃×C₁₅₁	#733	1	1	yes	characteristic
21	#6861	—	151	1	no	maximal, Sylow
22	C₁₅₁	#6861	1	1	yes	characteristic, complemented, Sylow
23	C₃²⋊C₉	—	151	1	no	—
24	C₃²⋊C₉	—	151	2	no	—
25	C₃²⋊C₉	C₁₅₁⋊C₃	1	1	yes	characteristic
26	C₃³	C₃×C₁₅₁⋊C₃	1	1	yes	characteristic
27	C₃×C₉	—	3	1	no	—
28	C₃×C₉	—	453	1	no	—
29	C₃×C₉	—	453	2	no	—
30	C₃²	—	3	1	no	—
31	C₃²	—	3	1	no	—
32	C₃²	—	3	1	no	—
33	C₃²	—	3	1	no	—
34	C₃²	C₃²⋊(C₁₅₁⋊C₃)	1	1	yes	characteristic
35	C₉	—	9	1	no	—
36	C₉	—	1359	1	no	—
37	C₉	—	1359	2	no	—
38	C₃	—	9	1	no	—
39	C₃	#27133558	1	1	yes	characteristic
40	C₃	#27133559	1	1	yes	characteristic
41	C₃	#27133561	1	1	yes	characteristic
42	C₃	#27133562	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊(C₁₅₁⋊C₃)
commutator, prime radical, cosocle	C₃³×C₁₅₁	C₃²
Frattini	C₃³	C₃×C₁₅₁⋊C₃
Fitting	C₃²⋊C₉×C₁₅₁	C₃
socle	C₃²×C₁₅₁	H(3,𝔽₃)
hypercenter	C₃²⋊C₉	C₁₅₁⋊C₃
hypocenter	C₁₅₁	#6861
LCS	G ▷ C₃³×C₁₅₁ ▷ C₃²×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²⋊C₉

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

N	H ≅ G/N	type
22. C₁₅₁	#6861	semidirect

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