Subgroups — C₂×C₁₁²×C₅²⋊C₃ #31827702

Order 18150.

168 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, direct product factor, Hall
2	C₂×C₅²×C₁₁²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₁₁²	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×C₅²⋊C₃	C₁₁	1	12	yes	maximal, direct product factor
5	C₂×C₅×C₁₁²	—	3	2	no	—
6	C₁₁×C₅²⋊C₃	C₂×C₁₁	1	12	yes	direct product factor
7	C₂×C₃×C₁₁²	—	25	1	no	maximal, Hall
8	C₅×C₁₁²	—	3	2	no	—
9	C₂×C₅²×C₁₁	C₃×C₁₁	1	12	yes	complemented
10	C₃×C₁₁²	—	25	1	no	Hall
11	C₅²×C₁₁	C₂×C₃×C₁₁	1	12	yes	complemented
12	C₂×C₁₁²	C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₅²⋊C₃	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
14	C₁₁²	C₂×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
15	C₂×C₅×C₁₁	—	3	24	no	—
16	C₅²⋊C₃	C₂×C₁₁²	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₁₁	—	25	12	no	—
18	C₅×C₁₁	—	3	24	no	—
19	C₂×C₅²	C₃×C₁₁²	1	1	yes	characteristic, complemented, Hall
20	C₃×C₁₁	—	25	12	no	—
21	C₅²	C₂×C₃×C₁₁²	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₁₁	C₁₁×C₅²⋊C₃	1	12	yes	direct product factor
23	C₁₁	C₂×C₁₁×C₅²⋊C₃	1	12	yes	direct product factor
24	C₂×C₅	—	3	2	no	—
25	C₂×C₃	—	25	1	no	Hall
26	C₅	—	3	2	no	—
27	C₃	—	25	1	no	Sylow
28	C₂	C₁₁²×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₁₁²×C₅²⋊C₃	C₂	direct (N × H)
2. C₂×C₅²×C₁₁²	C₃	semidirect
3. C₅²×C₁₁²	C₂×C₃	semidirect
4. C₂×C₁₁×C₅²⋊C₃	C₁₁	direct (N × H)
6. C₁₁×C₅²⋊C₃	C₂×C₁₁	direct (N × H)
9. C₂×C₅²×C₁₁	C₃×C₁₁	semidirect
11. C₅²×C₁₁	C₂×C₃×C₁₁	semidirect
12. C₂×C₁₁²	C₅²⋊C₃	direct (N × H)
13. C₂×C₅²⋊C₃	C₁₁²	direct (N × H)
14. C₁₁²	C₂×C₅²⋊C₃	direct (N × H)
16. C₅²⋊C₃	C₂×C₁₁²	direct (N × H)
19. C₂×C₅²	C₃×C₁₁²	semidirect
21. C₅²	C₂×C₃×C₁₁²	semidirect
22. C₂×C₁₁	C₁₁×C₅²⋊C₃	direct (N × H)
23. C₁₁	C₂×C₁₁×C₅²⋊C₃	direct (N × H)
28. C₂	C₁₁²×C₅²⋊C₃	direct (N × H)

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
C₂×C₅²×C₁₁²	3
C₂×C₁₁×C₅²⋊C₃	11
C₂×C₃×C₁₁²	25

Subgroups — C2×C112×C52⋊C3 #31827702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁²×C₅²⋊C₃ #31827702