Subgroups — C₁₀₁×#6887 #37589421

Order 24543.

138 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	C₉⋊C₉×C₁₀₁	C₃	1	6	yes	maximal, complemented
3	C₃²⋊C₉×C₁₀₁	C₃	1	3	yes	maximal
4	C₉²×C₁₀₁	C₃	1	3	yes	maximal, complemented
5	C₃³×C₁₀₁	C₃²	1	1	yes	characteristic
6	C₃×C₉×C₁₀₁	C₉	1	9	yes	complemented
7	C₃×C₉×C₁₀₁	C₃²	1	9	yes	—
8	C₃×C₉×C₁₀₁	C₃²	1	2	yes	—
9	C₃×C₉×C₁₀₁	C₃²	1	1	yes	characteristic
10	C₃²×C₁₀₁	—	3	3	no	—
11	C₃²×C₁₀₁	C₃×C₉	1	3	yes	—
12	C₃²×C₁₀₁	C₃³	1	1	yes	characteristic
13	C₉×C₁₀₁	—	3	9	no	—
14	C₉×C₁₀₁	C₃×C₉	1	6	yes	—
15	C₉×C₁₀₁	C₃×C₉	1	3	yes	—
16	C₃×C₁₀₁	—	3	3	no	—
17	C₃×C₁₀₁	C₃²×C₉	1	1	yes	characteristic
18	C₃×C₁₀₁	#737	1	3	yes	—
19	#6887	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₁₀₁	#6887	1	1	yes	characteristic, direct product factor, Sylow
21	C₃²×C₉	C₃×C₁₀₁	1	1	yes	characteristic
22	C₉⋊C₉	C₃×C₁₀₁	1	6	yes	complemented
23	C₃²⋊C₉	C₃×C₁₀₁	1	3	yes	—
24	C₉²	C₃×C₁₀₁	1	3	yes	complemented
25	C₃³	C₃²×C₁₀₁	1	1	yes	characteristic
26	C₃×C₉	C₉×C₁₀₁	1	9	yes	complemented
27	C₃×C₉	C₃²×C₁₀₁	1	9	yes	—
28	C₃×C₉	C₃²×C₁₀₁	1	2	yes	—
29	C₃×C₉	C₃²×C₁₀₁	1	1	yes	characteristic
30	C₃²	—	3	3	no	—
31	C₃²	C₃×C₉×C₁₀₁	1	3	yes	—
32	C₃²	C₃³×C₁₀₁	1	1	yes	characteristic
33	C₉	—	3	9	no	—
34	C₉	C₃×C₉×C₁₀₁	1	6	yes	—
35	C₉	C₃×C₉×C₁₀₁	1	3	yes	—
36	C₃	—	3	3	no	—
37	C₃	C₃²×C₉×C₁₀₁	1	1	yes	characteristic
38	C₃	#737×C₁₀₁	1	3	yes	—

	subgroup	G/H
center	C₃×C₉×C₁₀₁	C₃²
commutator	C₃	C₃²×C₉×C₁₀₁
Frattini, cosocle	C₃²	C₃³×C₁₀₁
socle	C₃²×C₁₀₁	C₃³
prime radical	C₃³×C₁₀₁	C₃²
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉⋊C₉×C₁₀₁	C₃	semidirect
4. C₉²×C₁₀₁	C₃	semidirect
6. C₃×C₉×C₁₀₁	C₉	semidirect
19. #6887	C₁₀₁	direct (N × H)
20. C₁₀₁	#6887	direct (N × H)
22. C₉⋊C₉	C₃×C₁₀₁	semidirect
24. C₉²	C₃×C₁₀₁	semidirect
26. C₃×C₉	C₉×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₉×C₁₀₁	3
C₉⋊C₉×C₁₀₁	3
C₃²⋊C₉×C₁₀₁	3
C₉²×C₁₀₁	3
#6887	101

Subgroups — C101×#6887 #37589421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#6887 #37589421