Subgroups — C₁₀₁×#6861 #37589395

Order 24543.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²⋊C₉×C₁₀₁	C₃	1	1	yes	maximal, characteristic
2	C₃²⋊C₉×C₁₀₁	C₃	1	3	yes	maximal
3	C₃³×C₁₀₁	C₃²	1	1	yes	characteristic
4	C₃×C₉×C₁₀₁	—	3	1	no	—
5	C₃×C₉×C₁₀₁	—	3	3	no	—
6	C₃²×C₁₀₁	—	3	1	no	—
7	C₃²×C₁₀₁	—	3	1	no	—
8	C₃²×C₁₀₁	—	3	2	no	—
9	C₃²×C₁₀₁	H(3,𝔽₃)	1	1	yes	characteristic
10	C₉×C₁₀₁	—	9	1	no	—
11	C₉×C₁₀₁	—	9	3	no	—
12	C₃×C₁₀₁	—	9	1	no	—
13	C₃×C₁₀₁	#731	1	1	yes	characteristic
14	C₃×C₁₀₁	#732	1	1	yes	characteristic
15	C₃×C₁₀₁	#733	1	2	yes	—
16	#6861	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₁₀₁	#6861	1	1	yes	characteristic, direct product factor, Sylow
18	C₃²⋊C₉	C₃×C₁₀₁	1	1	yes	characteristic
19	C₃²⋊C₉	C₃×C₁₀₁	1	3	yes	—
20	C₃³	C₃²×C₁₀₁	1	1	yes	characteristic
21	C₃×C₉	—	3	1	no	—
22	C₃×C₉	—	3	3	no	—
23	C₃²	—	3	1	no	—
24	C₃²	—	3	1	no	—
25	C₃²	—	3	2	no	—
26	C₃²	H(3,𝔽₃)×C₁₀₁	1	1	yes	characteristic
27	C₉	—	9	1	no	—
28	C₉	—	9	3	no	—
29	C₃	—	9	1	no	—
30	C₃	#731×C₁₀₁	1	1	yes	characteristic
31	C₃	#732×C₁₀₁	1	1	yes	characteristic
32	C₃	#733×C₁₀₁	1	2	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₀₁	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃²×C₁₀₁
prime radical	C₃³×C₁₀₁	C₃²
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₁₀₁ ◁ C₃³×C₁₀₁ ◁ G

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

N	H ≅ G/N	type
16. #6861	C₁₀₁	direct (N × H)
17. C₁₀₁	#6861	direct (N × H)

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

subgroup	index
C₃²⋊C₉×C₁₀₁	3
#6861	101