Subgroups — D₃×C₁₇×C₁₁⋊D₁₁ #37590652

Order 24684.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₁₇	D₃×C₁₁⋊D₁₁
commutator, cosocle, hypocenter	C₃×C₁₁²	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₁²×C₁₇	C₂²
LCS	G ▷ C₃×C₁₁²
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₇×C₁₁⋊D₁₁	C₂	semidirect
2. D₃×C₁₁²×C₁₇	C₂	semidirect
3. C₁₇×C₃⋊(C₁₁⋊D₁₁)	C₂	semidirect
5. C₃×C₁₁²×C₁₇	C₂²	semidirect
7. C₁₇×C₁₁⋊D₁₁	D₃	direct (N × H)
10. C₁₁²×C₁₇	C₂×D₃	semidirect
11. D₃×C₁₁⋊D₁₁	C₁₇	direct (N × H)
13. D₃×C₁₁×C₁₇	D₁₁	semidirect
16. C₃⋊(C₁₁⋊D₁₁)	C₂×C₁₇	semidirect
17. D₃×C₁₁²	C₂×C₁₇	semidirect
18. C₃×C₁₁⋊D₁₁	C₂×C₁₇	semidirect
19. C₃×C₁₁×C₁₇	C₂×D₁₁	semidirect
24. C₃×C₁₁²	C₂²×C₁₇	semidirect
27. C₁₁⋊D₁₁	D₃×C₁₇	direct (N × H)
29. C₁₁×C₁₇	D₃×D₁₁	semidirect
31. C₁₁²	C₂×D₃×C₁₇	semidirect
34. D₃×C₁₇	C₁₁⋊D₁₁	direct (N × H)
38. D₃×C₁₁	C₁₇×D₁₁	semidirect
39. C₃×C₁₇	C₂×C₁₁⋊D₁₁	semidirect
44. C₃×C₁₁	C₂×C₁₇×D₁₁	semidirect
48. C₁₇	D₃×C₁₁⋊D₁₁	direct (N × H)
50. C₁₁	D₃×C₁₇×D₁₁	semidirect
53. D₃	C₁₇×C₁₁⋊D₁₁	direct (N × H)
55. C₃	C₂×C₁₇×C₁₁⋊D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₇×C₁₁⋊D₁₁	2
D₃×C₁₁²×C₁₇	2
C₁₇×C₃⋊(C₁₁⋊D₁₁)	2
C₂×C₁₇×C₁₁⋊D₁₁	3
D₃×C₁₇×D₁₁	11
D₃×C₁₁⋊D₁₁	17

Subgroups — D3×C17×C11⋊D11 #37590652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₇×C₁₁⋊D₁₁ #37590652