Subgroups — C₂×C₁₇×C₃⋊(C₁₁⋊D₁₁) #37590668

Order 24684.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₃⋊(C₁₁⋊D₁₁)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₁²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×C₁₁⋊D₁₁	—	3	1	no	maximal, Hall
4	C₃×C₁₁²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₇×C₁₁⋊D₁₁	—	3	2	no	—
6	C₂×C₁₁²×C₁₇	D₃	1	1	yes	characteristic, complemented
7	C₂×C₁₇×D₃₃	—	11	12	no	maximal
8	C₁₁²×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃⋊(C₁₁⋊D₁₁)	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₁₁×C₁₇	D₁₁	1	12	yes	complemented
11	C₁₇×D₃₃	—	11	24	no	—
12	C₂×C₁₇×D₁₁	—	33	12	no	—
13	C₂×C₃×C₁₁²	C₂×C₁₇	1	1	yes	characteristic, complemented
14	C₃⋊(C₁₁⋊D₁₁)	C₂×C₁₇	1	2	yes	direct product factor
15	C₃×C₁₁×C₁₇	C₂×D₁₁	1	12	yes	complemented
16	C₂×C₁₁⋊D₁₁	—	3	1	no	Hall
17	C₂×C₁₁×C₁₇	D₃₃	1	12	yes	complemented
18	C₁₇×D₁₁	—	33	24	no	—
19	C₃×C₁₁²	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
20	C₂×C₁₁²	D₃×C₁₇	1	1	yes	characteristic, complemented
21	C₁₁⋊D₁₁	—	3	2	no	—
22	C₂×D₃×C₁₇	—	121	1	no	Hall
23	C₁₁×C₁₇	C₂×D₃₃	1	12	yes	complemented
24	C₂×D₃₃	—	11	12	no	—
25	C₁₁²	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃×C₁₇	C₁₁⋊D₁₁	1	1	yes	characteristic, complemented
27	D₃×C₁₇	—	121	2	no	—
28	C₂²×C₁₇	—	363	1	no	Hall
29	C₂×C₃×C₁₁	C₁₇×D₁₁	1	12	yes	complemented
30	D₃₃	—	11	24	no	—
31	C₃×C₁₇	C₂×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Hall
32	C₂×D₁₁	—	33	12	no	—
33	C₂×C₁₇	—	363	2	no	—
34	C₂×C₁₇	C₃⋊(C₁₁⋊D₁₁)	1	1	yes	characteristic, direct product factor
35	C₃×C₁₁	C₂×C₁₇×D₁₁	1	12	yes	complemented
36	C₂×C₁₁	C₁₇×D₃₃	1	12	yes	complemented
37	D₁₁	—	33	24	no	—
38	C₁₇	C₂×C₃⋊(C₁₁⋊D₁₁)	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×D₃	—	121	1	no	Hall
40	C₁₁	C₂×C₁₇×D₃₃	1	12	yes	complemented
41	C₂×C₃	C₁₇×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented
42	D₃	—	121	2	no	—
43	C₂²	—	363	1	no	Sylow
44	C₃	C₂×C₁₇×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	363	2	no	—
46	C₂	C₁₇×C₃⋊(C₁₁⋊D₁₁)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	C₃⋊(C₁₁⋊D₁₁)
commutator, cosocle, hypocenter	C₃×C₁₁²	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₁²×C₁₇	C₂
LCS	G ▷ C₃×C₁₁²
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₃⋊(C₁₁⋊D₁₁)	C₂	direct (N × H)
2. C₂×C₃×C₁₁²×C₁₇	C₂	semidirect
4. C₃×C₁₁²×C₁₇	C₂²	semidirect
6. C₂×C₁₁²×C₁₇	D₃	semidirect
8. C₁₁²×C₁₇	C₂×D₃	semidirect
9. C₂×C₃⋊(C₁₁⋊D₁₁)	C₁₇	direct (N × H)
10. C₂×C₃×C₁₁×C₁₇	D₁₁	semidirect
13. C₂×C₃×C₁₁²	C₂×C₁₇	semidirect
14. C₃⋊(C₁₁⋊D₁₁)	C₂×C₁₇	direct (N × H)
15. C₃×C₁₁×C₁₇	C₂×D₁₁	semidirect
17. C₂×C₁₁×C₁₇	D₃₃	semidirect
19. C₃×C₁₁²	C₂²×C₁₇	semidirect
20. C₂×C₁₁²	D₃×C₁₇	semidirect
23. C₁₁×C₁₇	C₂×D₃₃	semidirect
25. C₁₁²	C₂×D₃×C₁₇	semidirect
26. C₂×C₃×C₁₇	C₁₁⋊D₁₁	semidirect
29. C₂×C₃×C₁₁	C₁₇×D₁₁	semidirect
31. C₃×C₁₇	C₂×C₁₁⋊D₁₁	semidirect
34. C₂×C₁₇	C₃⋊(C₁₁⋊D₁₁)	direct (N × H)
35. C₃×C₁₁	C₂×C₁₇×D₁₁	semidirect
36. C₂×C₁₁	C₁₇×D₃₃	semidirect
38. C₁₇	C₂×C₃⋊(C₁₁⋊D₁₁)	direct (N × H)
40. C₁₁	C₂×C₁₇×D₃₃	semidirect
41. C₂×C₃	C₁₇×C₁₁⋊D₁₁	semidirect
44. C₃	C₂×C₁₇×C₁₁⋊D₁₁	semidirect
46. C₂	C₁₇×C₃⋊(C₁₁⋊D₁₁)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×C₃⋊(C₁₁⋊D₁₁)	2
C₂×C₃×C₁₁²×C₁₇	2
C₂×C₁₇×C₁₁⋊D₁₁	3
C₂×C₁₇×D₃₃	11
C₂×C₃⋊(C₁₁⋊D₁₁)	17

Subgroups — C2×C17×C3⋊(C11⋊D11) #37590668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×C₃⋊(C₁₁⋊D₁₁) #37590668