Subgroups — C₁₀₁×#6913 #37589447

Order 24543.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#737×C₁₀₁	C₃	1	3	yes	maximal, complemented
2	C₃×3₋¹⁺²×C₁₀₁	C₃	1	1	yes	maximal, characteristic, complemented
3	#733×C₁₀₁	C₃	1	2	yes	maximal, complemented
4	#732×C₁₀₁	C₃	1	1	yes	maximal, characteristic, complemented
5	#731×C₁₀₁	C₃	1	3	yes	maximal, complemented
6	AΣL(1,𝔽₂₇)×C₁₀₁	C₃	1	3	yes	maximal, complemented
7	C₃³×C₁₀₁	C₃²	1	1	yes	characteristic
8	3₋¹⁺²×C₁₀₁	—	3	3	no	—
9	3₋¹⁺²×C₁₀₁	—	3	6	no	—
10	3₋¹⁺²×C₁₀₁	C₃²	1	6	yes	—
11	H(3,𝔽₃)×C₁₀₁	C₃²	1	3	yes	—
12	C₃×C₉×C₁₀₁	—	3	3	no	—
13	C₃×C₉×C₁₀₁	C₃²	1	1	yes	characteristic
14	C₃×C₉×C₁₀₁	C₃²	1	1	yes	characteristic
15	C₃×C₉×C₁₀₁	C₃²	1	1	yes	characteristic
16	C₃²×C₁₀₁	—	3	3	no	—
17	C₃²×C₁₀₁	—	3	1	no	—
18	C₃²×C₁₀₁	—	9	1	no	—
19	C₃²×C₁₀₁	C₃³	1	1	yes	characteristic
20	C₉×C₁₀₁	—	3	6	no	—
21	C₉×C₁₀₁	—	3	1	no	—
22	C₉×C₁₀₁	—	3	1	no	—
23	C₉×C₁₀₁	H(3,𝔽₃)	1	3	yes	—
24	C₃×C₁₀₁	—	3	1	no	—
25	C₃×C₁₀₁	—	9	3	no	—
26	C₃×C₁₀₁	—	9	1	no	—
27	C₃×C₁₀₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	#6913	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₁₀₁	#6913	1	1	yes	characteristic, direct product factor, Sylow
30	#737	C₃×C₁₀₁	1	3	yes	complemented
31	C₃×3₋¹⁺²	C₃×C₁₀₁	1	1	yes	characteristic, complemented
32	#733	C₃×C₁₀₁	1	2	yes	complemented
33	#732	C₃×C₁₀₁	1	1	yes	characteristic, complemented
34	#731	C₃×C₁₀₁	1	3	yes	complemented
35	AΣL(1,𝔽₂₇)	C₃×C₁₀₁	1	3	yes	complemented
36	C₃³	C₃²×C₁₀₁	1	1	yes	characteristic
37	3₋¹⁺²	—	3	3	no	—
38	3₋¹⁺²	—	3	6	no	—
39	3₋¹⁺²	C₃²×C₁₀₁	1	6	yes	—
40	H(3,𝔽₃)	C₃²×C₁₀₁	1	3	yes	—
41	C₃×C₉	—	3	3	no	—
42	C₃×C₉	C₃²×C₁₀₁	1	1	yes	characteristic
43	C₃×C₉	C₃²×C₁₀₁	1	1	yes	characteristic
44	C₃×C₉	C₃²×C₁₀₁	1	1	yes	characteristic
45	C₃²	—	3	3	no	—
46	C₃²	—	3	1	no	—
47	C₃²	—	9	1	no	—
48	C₃²	C₃³×C₁₀₁	1	1	yes	characteristic
49	C₉	—	3	6	no	—
50	C₉	—	3	1	no	—
51	C₉	—	3	1	no	—
52	C₉	H(3,𝔽₃)×C₁₀₁	1	3	yes	—
53	C₃	—	3	1	no	—
54	C₃	—	9	1	no	—
55	C₃	—	9	3	no	—
56	C₃	C₃×H(3,𝔽₃)×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₁₀₁	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃²	C₃³×C₁₀₁
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₀₁ ◁ C₃×C₉×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #737×C₁₀₁	C₃	semidirect
2. C₃×3₋¹⁺²×C₁₀₁	C₃	semidirect
3. #733×C₁₀₁	C₃	semidirect
4. #732×C₁₀₁	C₃	semidirect
5. #731×C₁₀₁	C₃	semidirect
6. AΣL(1,𝔽₂₇)×C₁₀₁	C₃	semidirect
28. #6913	C₁₀₁	direct (N × H)
29. C₁₀₁	#6913	direct (N × H)
30. #737	C₃×C₁₀₁	semidirect
31. C₃×3₋¹⁺²	C₃×C₁₀₁	semidirect
32. #733	C₃×C₁₀₁	semidirect
33. #732	C₃×C₁₀₁	semidirect
34. #731	C₃×C₁₀₁	semidirect
35. AΣL(1,𝔽₂₇)	C₃×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
#737×C₁₀₁	3
C₃×3₋¹⁺²×C₁₀₁	3
#733×C₁₀₁	3
#732×C₁₀₁	3
#731×C₁₀₁	3
AΣL(1,𝔽₂₇)×C₁₀₁	3
#6913	101

Subgroups — C101×#6913 #37589447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#6913 #37589447