Subgroups — C₁₁×D₁₁×C₅²⋊C₃ #31827694

Order 18150.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×C₁₁×D₁₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₁₁²	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×C₅²⋊C₃	—	11	1	no	maximal
5	D₁₁×C₅²⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor
6	C₅×C₁₁×D₁₁	—	3	2	no	—
7	C₁₁×C₅²⋊C₃	—	2	5	no	—
8	C₁₁×C₅²⋊C₃	D₁₁	1	1	yes	characteristic, direct product factor
9	C₁₁×C₅²⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented
10	C₃×C₁₁×D₁₁	—	25	1	no	maximal, Hall
11	C₅×C₁₁²	—	3	2	no	—
12	C₂×C₅²×C₁₁	—	11	1	no	—
13	C₅²×D₁₁	C₃×C₁₁	1	1	yes	characteristic, complemented
14	C₃×C₁₁²	—	25	1	no	Hall
15	C₅²×C₁₁	—	2	5	no	—
16	C₅²×C₁₁	C₃×D₁₁	1	1	yes	characteristic, complemented
17	C₅²×C₁₁	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
18	C₁₁×D₁₁	C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₅²⋊C₃	—	11	1	no	Hall
20	C₁₁²	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₅×C₁₁	—	33	2	no	—
22	C₅×D₁₁	—	3	2	no	—
23	C₅²⋊C₃	C₁₁×D₁₁	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₃×C₁₁	—	275	1	no	—
25	C₃×D₁₁	—	25	1	no	—
26	C₅×C₁₁	—	3	2	no	—
27	C₅×C₁₁	—	3	2	no	—
28	C₅×C₁₁	—	6	10	no	—
29	C₂×C₅²	—	11	1	no	Hall
30	C₃×C₁₁	—	25	1	no	—
31	C₃×C₁₁	—	25	1	no	—
32	C₃×C₁₁	—	50	5	no	—
33	C₅²	C₃×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₁₁	—	11	1	no	—
35	D₁₁	C₁₁×C₅²⋊C₃	1	1	yes	characteristic, direct product factor
36	C₁₁	—	2	5	no	—
37	C₁₁	D₁₁×C₅²⋊C₃	1	1	yes	characteristic, direct product factor
38	C₁₁	C₂×C₁₁×C₅²⋊C₃	1	1	yes	characteristic, complemented
39	C₂×C₅	—	33	2	no	—
40	C₂×C₃	—	275	1	no	Hall
41	C₅	—	3	2	no	—
42	C₃	—	25	1	no	Sylow
43	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	D₁₁×C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²×C₁₁	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁²	C₂×C₃
LCS	G ▷ C₅²×C₁₁
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁²×C₅²⋊C₃	C₂	semidirect
2. C₅²×C₁₁×D₁₁	C₃	semidirect
3. C₅²×C₁₁²	C₂×C₃	semidirect
5. D₁₁×C₅²⋊C₃	C₁₁	direct (N × H)
8. C₁₁×C₅²⋊C₃	D₁₁	direct (N × H)
9. C₁₁×C₅²⋊C₃	C₂×C₁₁	semidirect
13. C₅²×D₁₁	C₃×C₁₁	semidirect
16. C₅²×C₁₁	C₃×D₁₁	semidirect
17. C₅²×C₁₁	C₂×C₃×C₁₁	semidirect
18. C₁₁×D₁₁	C₅²⋊C₃	direct (N × H)
20. C₁₁²	C₂×C₅²⋊C₃	semidirect
23. C₅²⋊C₃	C₁₁×D₁₁	direct (N × H)
33. C₅²	C₃×C₁₁×D₁₁	semidirect
35. D₁₁	C₁₁×C₅²⋊C₃	direct (N × H)
37. C₁₁	D₁₁×C₅²⋊C₃	direct (N × H)
38. C₁₁	C₂×C₁₁×C₅²⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₁²×C₅²⋊C₃	2
C₅²×C₁₁×D₁₁	3
C₂×C₁₁×C₅²⋊C₃	11
D₁₁×C₅²⋊C₃	11
C₃×C₁₁×D₁₁	25

Subgroups — C11×D11×C52⋊C3 #31827694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×D₁₁×C₅²⋊C₃ #31827694