Subgroups — C₃×(C₁₁⋊C₅)⋊AGL(1,𝔽₁₁) #31827607

Order 18150.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁⋊C₅²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	(C₁₁⋊C₅)⋊AGL(1,𝔽₁₁)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×(C₁₁⋊C₅)⋊D₁₁	C₅	1	2	yes	maximal, complemented
4	C₃×#11925894	C₅	1	2	yes	maximal, complemented
5	C₃×#11925893	C₅	1	1	yes	maximal, characteristic, complemented
6	C₃×#11925892	C₅	1	1	yes	maximal, characteristic, complemented
7	C₁₁⋊C₅²	C₂×C₃	1	1	yes	characteristic, complemented, Hall
8	C₃×#10597244	C₂×C₅	1	2	yes	complemented
9	C₃×#10597245	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃×#10597243	C₂×C₅	1	1	yes	characteristic, complemented
11	C₃×C₁₁×C₁₁⋊C₅	C₂×C₅	1	2	yes	complemented
12	C₃×C₅×AGL(1,𝔽₁₁)	—	11	2	no	maximal
13	(C₁₁⋊C₅)⋊D₁₁	C₃×C₅	1	2	yes	complemented
14	#11925894	C₃×C₅	1	2	yes	complemented
15	#11925893	C₃×C₅	1	1	yes	characteristic, complemented
16	#11925892	C₃×C₅	1	1	yes	characteristic, complemented
17	C₃×C₅×C₁₁⋊C₅	—	11	2	no	—
18	C₃×C₁₁⋊D₁₁	C₅²	1	1	yes	characteristic, complemented, Hall
19	#10597245	C₂×C₃×C₅	1	1	yes	characteristic, complemented
20	#10597244	C₂×C₃×C₅	1	2	yes	complemented
21	#10597243	C₂×C₃×C₅	1	1	yes	characteristic, complemented
22	C₁₁×C₁₁⋊C₅	C₂×C₃×C₅	1	2	yes	complemented
23	C₅×AGL(1,𝔽₁₁)	—	11	2	no	—
24	C₃×C₁₁²	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
25	C₃×C₅×D₁₁	—	11	2	no	—
26	C₃×AGL(1,𝔽₁₁)	—	11	2	no	—
27	C₃×AGL(1,𝔽₁₁)	—	11	2	no	—
28	C₃×AGL(1,𝔽₁₁)	—	11	4	no	—
29	C₃×AGL(1,𝔽₁₁)	—	55	2	no	—
30	C₃×AGL(1,𝔽₁₁)	—	55	2	no	—
31	C₅×C₁₁⋊C₅	—	11	2	no	—
32	C₁₁⋊D₁₁	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
33	C₃×C₅×C₁₁	—	11	2	no	—
34	C₃×C₁₁⋊C₅	—	11	2	no	—
35	C₃×C₁₁⋊C₅	—	11	2	no	—
36	C₃×C₁₁⋊C₅	—	11	4	no	—
37	C₃×C₁₁⋊C₅	—	55	2	no	—
38	C₃×C₁₁⋊C₅	AGL(1,𝔽₁₁)	1	2	yes	complemented
39	C₂×C₃×C₅²	—	121	1	no	Hall
40	C₁₁²	C₂×C₃×C₅²	1	1	yes	characteristic, complemented, Sylow
41	C₅×D₁₁	—	11	2	no	—
42	AGL(1,𝔽₁₁)	—	11	2	no	—
43	AGL(1,𝔽₁₁)	—	11	2	no	—
44	AGL(1,𝔽₁₁)	—	11	4	no	—
45	AGL(1,𝔽₁₁)	—	55	2	no	—
46	AGL(1,𝔽₁₁)	—	55	2	no	—
47	C₃×C₅²	—	121	1	no	Hall
48	C₃×D₁₁	—	275	2	no	—
49	C₃×D₁₁	—	55	2	no	—
50	C₅×C₁₁	—	11	2	no	—
51	C₁₁⋊C₅	—	11	2	no	—
52	C₁₁⋊C₅	—	11	4	no	—
53	C₁₁⋊C₅	—	11	2	no	—
54	C₁₁⋊C₅	—	55	2	no	—
55	C₁₁⋊C₅	C₃×AGL(1,𝔽₁₁)	1	2	yes	complemented
56	C₂×C₅²	—	121	1	no	Hall
57	C₃×C₁₁	—	5	2	no	—
58	C₃×C₁₁	C₅×AGL(1,𝔽₁₁)	1	2	yes	complemented
59	C₂×C₃×C₅	—	605	2	no	—
60	C₂×C₃×C₅	—	121	1	no	—
61	C₂×C₃×C₅	—	121	2	no	—
62	C₂×C₃×C₅	—	121	1	no	—
63	C₅²	—	121	1	no	Sylow
64	D₁₁	—	275	2	no	—
65	D₁₁	—	55	2	no	—
66	C₃×C₅	—	11	2	no	—
67	C₃×C₅	—	121	1	no	—
68	C₃×C₅	—	121	1	no	—
69	C₃×C₅	—	121	2	no	—
70	C₁₁	—	5	2	no	—
71	C₁₁	C₃×C₅×AGL(1,𝔽₁₁)	1	2	yes	complemented
72	C₂×C₅	—	605	2	no	—
73	C₂×C₅	—	121	1	no	—
74	C₂×C₅	—	121	2	no	—
75	C₂×C₅	—	121	1	no	—
76	C₂×C₃	—	3025	1	no	Hall
77	C₅	—	11	2	no	—
78	C₅	—	121	1	no	—
79	C₅	—	121	2	no	—
80	C₅	—	121	1	no	—
81	C₃	(C₁₁⋊C₅)⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor, Sylow
82	C₂	—	605	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	(C₁₁⋊C₅)⋊AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₁₁²	C₂×C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₁₁²	C₂×C₅²
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁⋊C₅²	C₂	semidirect
2. (C₁₁⋊C₅)⋊AGL(1,𝔽₁₁)	C₃	direct (N × H)
3. C₃×(C₁₁⋊C₅)⋊D₁₁	C₅	semidirect
4. C₃×#11925894	C₅	semidirect
5. C₃×#11925893	C₅	semidirect
6. C₃×#11925892	C₅	semidirect
7. C₁₁⋊C₅²	C₂×C₃	semidirect
8. C₃×#10597244	C₂×C₅	semidirect
9. C₃×#10597245	C₂×C₅	semidirect
10. C₃×#10597243	C₂×C₅	semidirect
11. C₃×C₁₁×C₁₁⋊C₅	C₂×C₅	semidirect
13. (C₁₁⋊C₅)⋊D₁₁	C₃×C₅	semidirect
14. #11925894	C₃×C₅	semidirect
15. #11925893	C₃×C₅	semidirect
16. #11925892	C₃×C₅	semidirect
18. C₃×C₁₁⋊D₁₁	C₅²	semidirect
19. #10597245	C₂×C₃×C₅	semidirect
20. #10597244	C₂×C₃×C₅	semidirect
21. #10597243	C₂×C₃×C₅	semidirect
22. C₁₁×C₁₁⋊C₅	C₂×C₃×C₅	semidirect
24. C₃×C₁₁²	C₂×C₅²	semidirect
32. C₁₁⋊D₁₁	C₃×C₅²	semidirect
38. C₃×C₁₁⋊C₅	AGL(1,𝔽₁₁)	semidirect
40. C₁₁²	C₂×C₃×C₅²	semidirect
55. C₁₁⋊C₅	C₃×AGL(1,𝔽₁₁)	semidirect
58. C₃×C₁₁	C₅×AGL(1,𝔽₁₁)	semidirect
71. C₁₁	C₃×C₅×AGL(1,𝔽₁₁)	semidirect
81. C₃	(C₁₁⋊C₅)⋊AGL(1,𝔽₁₁)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₁⋊C₅²	2
(C₁₁⋊C₅)⋊AGL(1,𝔽₁₁)	3
C₃×(C₁₁⋊C₅)⋊D₁₁	5
C₃×#11925894	5
C₃×#11925893	5
C₃×#11925892	5
C₃×C₅×AGL(1,𝔽₁₁)	11

Subgroups — C3×(C11⋊C5)⋊AGL(1,𝔽11) #31827607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×(C₁₁⋊C₅)⋊AGL(1,𝔽₁₁) #31827607