Subgroups — C₁₁×#6913 #14582012

Order 2673.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#737	C₃	1	3	yes	maximal, complemented
2	C₃×C₁₁×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#733	C₃	1	2	yes	maximal, complemented
4	C₁₁×#732	C₃	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#731	C₃	1	3	yes	maximal, complemented
6	C₁₁×AΣL(1,𝔽₂₇)	C₃	1	3	yes	maximal, complemented
7	C₃³×C₁₁	C₃²	1	1	yes	characteristic
8	C₁₁×3₋¹⁺²	—	3	3	no	—
9	C₁₁×3₋¹⁺²	—	3	6	no	—
10	C₁₁×3₋¹⁺²	C₃²	1	6	yes	—
11	C₁₁×H(3,𝔽₃)	C₃²	1	3	yes	—
12	C₃×C₉×C₁₁	—	3	3	no	—
13	C₃×C₉×C₁₁	C₃²	1	1	yes	characteristic
14	C₃×C₉×C₁₁	C₃²	1	1	yes	characteristic
15	C₃×C₉×C₁₁	C₃²	1	1	yes	characteristic
16	#6913	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃²×C₁₁	—	3	3	no	—
18	C₃²×C₁₁	—	3	1	no	—
19	C₃²×C₁₁	—	9	1	no	—
20	C₃²×C₁₁	C₃³	1	1	yes	characteristic
21	C₉×C₁₁	—	3	6	no	—
22	C₉×C₁₁	—	3	1	no	—
23	C₉×C₁₁	—	3	1	no	—
24	C₉×C₁₁	H(3,𝔽₃)	1	3	yes	—
25	#737	C₃×C₁₁	1	3	yes	complemented
26	C₃×3₋¹⁺²	C₃×C₁₁	1	1	yes	characteristic, complemented
27	#733	C₃×C₁₁	1	2	yes	complemented
28	#732	C₃×C₁₁	1	1	yes	characteristic, complemented
29	#731	C₃×C₁₁	1	3	yes	complemented
30	AΣL(1,𝔽₂₇)	C₃×C₁₁	1	3	yes	complemented
31	C₃×C₁₁	—	3	1	no	—
32	C₃×C₁₁	—	9	3	no	—
33	C₃×C₁₁	—	9	1	no	—
34	C₃×C₁₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
35	C₃³	C₃²×C₁₁	1	1	yes	characteristic
36	3₋¹⁺²	—	3	3	no	—
37	3₋¹⁺²	—	3	6	no	—
38	3₋¹⁺²	C₃²×C₁₁	1	6	yes	—
39	H(3,𝔽₃)	C₃²×C₁₁	1	3	yes	—
40	C₃×C₉	—	3	3	no	—
41	C₃×C₉	C₃²×C₁₁	1	1	yes	characteristic
42	C₃×C₉	C₃²×C₁₁	1	1	yes	characteristic
43	C₃×C₉	C₃²×C₁₁	1	1	yes	characteristic
44	C₁₁	#6913	1	1	yes	characteristic, direct product factor, Sylow
45	C₃²	—	3	3	no	—
46	C₃²	—	3	1	no	—
47	C₃²	—	9	1	no	—
48	C₃²	C₃³×C₁₁	1	1	yes	characteristic
49	C₉	—	3	6	no	—
50	C₉	—	3	1	no	—
51	C₉	—	3	1	no	—
52	C₉	C₁₁×H(3,𝔽₃)	1	3	yes	—
53	C₃	—	3	1	no	—
54	C₃	—	9	1	no	—
55	C₃	—	9	3	no	—
56	C₃	C₃×C₁₁×H(3,𝔽₃)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₁₁	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃²	C₃³×C₁₁
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₁ ◁ C₃×C₉×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#737	C₃	semidirect
2. C₃×C₁₁×3₋¹⁺²	C₃	semidirect
3. C₁₁×#733	C₃	semidirect
4. C₁₁×#732	C₃	semidirect
5. C₁₁×#731	C₃	semidirect
6. C₁₁×AΣL(1,𝔽₂₇)	C₃	semidirect
16. #6913	C₁₁	direct (N × H)
25. #737	C₃×C₁₁	semidirect
26. C₃×3₋¹⁺²	C₃×C₁₁	semidirect
27. #733	C₃×C₁₁	semidirect
28. #732	C₃×C₁₁	semidirect
29. #731	C₃×C₁₁	semidirect
30. AΣL(1,𝔽₂₇)	C₃×C₁₁	semidirect
44. C₁₁	#6913	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#737	3
C₃×C₁₁×3₋¹⁺²	3
C₁₁×#733	3
C₁₁×#732	3
C₁₁×#731	3
C₁₁×AΣL(1,𝔽₂₇)	3
#6913	11

Subgroups — C11×#6913 #14582012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#6913 #14582012