Subgroups — C₂×C₃×C₁₁⋊D₁₈₇ #37590663

Order 24684.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁⋊D₁₈₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₁²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁⋊D₁₈₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₁²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₁⋊D₁₈₇	C₂×C₃	1	2	yes	direct product factor
6	C₂×C₁₁²×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₃×D₁₈₇	—	11	12	no	maximal
8	C₁₁²×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₁₁⋊D₁₁	—	17	1	no	maximal, Hall
10	C₂×C₃×C₁₁×C₁₇	D₁₁	1	12	yes	complemented
11	C₃×D₁₈₇	—	11	24	no	—
12	C₂×D₁₈₇	—	11	12	no	—
13	C₂×C₃×C₁₁²	D₁₇	1	1	yes	characteristic, complemented
14	C₃×C₁₁⋊D₁₁	—	17	2	no	—
15	C₃×C₁₁×C₁₇	C₂×D₁₁	1	12	yes	complemented
16	C₂×C₁₁⋊D₁₁	—	17	1	no	Hall
17	C₂×C₁₁×C₁₇	C₃×D₁₁	1	12	yes	complemented
18	D₁₈₇	—	11	24	no	—
19	C₃×C₁₁²	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
20	C₂×C₁₁²	C₃×D₁₇	1	1	yes	characteristic, complemented
21	C₁₁⋊D₁₁	—	17	2	no	—
22	C₂×C₃×D₁₇	—	121	1	no	Hall
23	C₁₁×C₁₇	C₂×C₃×D₁₁	1	12	yes	complemented
24	C₂×C₃×D₁₁	—	187	12	no	—
25	C₁₁²	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃×C₁₇	C₁₁⋊D₁₁	1	1	yes	characteristic, complemented
27	C₃×D₁₇	—	121	2	no	—
28	C₂×D₁₇	—	121	1	no	Hall
29	C₂×C₃×C₁₁	D₁₈₇	1	12	yes	complemented
30	C₃×D₁₁	—	187	24	no	—
31	C₃×C₁₇	C₂×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Hall
32	C₂×D₁₁	—	187	12	no	—
33	C₂×C₁₇	C₃×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented
34	D₁₇	—	121	2	no	—
35	C₃×C₁₁	C₂×D₁₈₇	1	12	yes	complemented
36	C₂×C₁₁	C₃×D₁₈₇	1	12	yes	complemented
37	D₁₁	—	187	24	no	—
38	C₁₇	C₂×C₃×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₃	—	2057	1	no	Hall
40	C₁₁	C₂×C₃×D₁₈₇	1	12	yes	complemented
41	C₂×C₃	—	2057	2	no	—
42	C₂×C₃	C₁₁⋊D₁₈₇	1	1	yes	characteristic, direct product factor
43	C₂²	—	2057	1	no	Sylow
44	C₃	C₂×C₁₁⋊D₁₈₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	2057	2	no	—
46	C₂	C₃×C₁₁⋊D₁₈₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₁₁⋊D₁₈₇
commutator, cosocle, hypocenter	C₁₁²×C₁₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₁²×C₁₇	C₂
LCS	G ▷ C₁₁²×C₁₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁⋊D₁₈₇	C₂	direct (N × H)
2. C₂×C₃×C₁₁²×C₁₇	C₂	semidirect
3. C₂×C₁₁⋊D₁₈₇	C₃	direct (N × H)
4. C₃×C₁₁²×C₁₇	C₂²	semidirect
5. C₁₁⋊D₁₈₇	C₂×C₃	direct (N × H)
6. C₂×C₁₁²×C₁₇	C₂×C₃	semidirect
8. C₁₁²×C₁₇	C₂²×C₃	semidirect
10. C₂×C₃×C₁₁×C₁₇	D₁₁	semidirect
13. C₂×C₃×C₁₁²	D₁₇	semidirect
15. C₃×C₁₁×C₁₇	C₂×D₁₁	semidirect
17. C₂×C₁₁×C₁₇	C₃×D₁₁	semidirect
19. C₃×C₁₁²	C₂×D₁₇	semidirect
20. C₂×C₁₁²	C₃×D₁₇	semidirect
23. C₁₁×C₁₇	C₂×C₃×D₁₁	semidirect
25. C₁₁²	C₂×C₃×D₁₇	semidirect
26. C₂×C₃×C₁₇	C₁₁⋊D₁₁	semidirect
29. C₂×C₃×C₁₁	D₁₈₇	semidirect
31. C₃×C₁₇	C₂×C₁₁⋊D₁₁	semidirect
33. C₂×C₁₇	C₃×C₁₁⋊D₁₁	semidirect
35. C₃×C₁₁	C₂×D₁₈₇	semidirect
36. C₂×C₁₁	C₃×D₁₈₇	semidirect
38. C₁₇	C₂×C₃×C₁₁⋊D₁₁	semidirect
40. C₁₁	C₂×C₃×D₁₈₇	semidirect
42. C₂×C₃	C₁₁⋊D₁₈₇	direct (N × H)
44. C₃	C₂×C₁₁⋊D₁₈₇	direct (N × H)
46. C₂	C₃×C₁₁⋊D₁₈₇	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⋊D₁₈₇	2
C₂×C₃×C₁₁²×C₁₇	2
C₂×C₁₁⋊D₁₈₇	3
C₂×C₃×D₁₈₇	11
C₂×C₃×C₁₁⋊D₁₁	17

Subgroups — C2×C3×C11⋊D187 #37590663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₁⋊D₁₈₇ #37590663