Subgroups — D₂₁×C₁₇⋊D₁₇ #37566281

Order 24276.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₇⋊D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇²×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₇⋊(C₁₇⋊D₁₇))	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×C₁₇⋊D₁₇	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇⋊(C₁₇⋊D₁₇)	—	3	1	no	—
7	D₇×C₁₇²	—	3	1	no	—
8	C₇×C₁₇⋊D₁₇	D₃	1	1	yes	characteristic, complemented
9	D₃×C₁₇⋊D₁₇	—	7	1	no	maximal, Hall
10	C₇×C₁₇²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₃×C₁₇⋊D₁₇	D₇	1	1	yes	characteristic, complemented
12	D₃×C₁₇²	—	7	1	no	—
13	C₃⋊(C₁₇⋊D₁₇)	—	7	1	no	—
14	D₁₇×D₂₁	—	17	18	no	maximal
15	C₂×C₁₇⋊D₁₇	—	21	1	no	Hall
16	C₃×C₁₇²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
17	D₃₅₇	—	17	18	no	—
18	C₁₇×D₂₁	D₁₇	1	18	yes	complemented
19	C₃×C₇×D₁₇	—	17	18	no	—
20	C₂×C₁₇²	—	21	1	no	—
21	C₁₇⋊D₁₇	—	21	1	no	—
22	C₁₇⋊D₁₇	D₂₁	1	1	yes	characteristic, direct product factor
23	D₇×D₁₇	—	51	18	no	—
24	C₃×C₇×C₁₇	C₂×D₁₇	1	18	yes	complemented
25	C₁₇²	C₂×D₂₁	1	1	yes	characteristic, complemented, Sylow
26	D₁₁₉	—	51	18	no	—
27	C₇×D₁₇	—	17	18	no	—
28	D₇×C₁₇	—	3	18	no	—
29	D₃×D₁₇	—	119	18	no	—
30	C₇×C₁₇	D₃×D₁₇	1	18	yes	complemented
31	D₅₁	—	119	18	no	—
32	C₃×D₁₇	—	17	18	no	—
33	D₃×C₁₇	—	7	18	no	—
34	C₂×D₂₁	—	289	1	no	Hall
35	C₂×D₁₇	—	357	18	no	—
36	C₃×C₁₇	D₇×D₁₇	1	18	yes	complemented
37	C₂×C₃×C₇	—	289	1	no	—
38	D₂₁	—	289	1	no	—
39	D₂₁	C₁₇⋊D₁₇	1	1	yes	characteristic, direct product factor
40	C₂×C₁₇	—	21	18	no	—
41	D₁₇	—	17	18	no	—
42	D₁₇	—	357	18	no	—
43	C₂×D₇	—	867	1	no	Hall
44	C₃×C₇	C₂×C₁₇⋊D₁₇	1	1	yes	characteristic, complemented, Hall
45	C₁₇	D₁₇×D₂₁	1	18	yes	complemented
46	C₂×C₇	—	289	1	no	—
47	D₇	—	3	1	no	—
48	D₇	—	867	1	no	—
49	C₂×D₃	—	2023	1	no	Hall
50	C₇	D₃×C₁₇⋊D₁₇	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	289	1	no	—
52	D₃	—	7	1	no	—
53	D₃	—	2023	1	no	—
54	C₂²	—	6069	1	no	Sylow
55	C₃	D₇×C₁₇⋊D₁₇	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	21	1	no	—
57	C₂	—	289	1	no	—
58	C₂	—	6069	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₇²	C₂²
LCS	G ▷ C₃×C₇×C₁₇²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₇⋊D₁₇	C₂	semidirect
2. C₁₇²×D₂₁	C₂	semidirect
3. C₃⋊(C₇⋊(C₁₇⋊D₁₇))	C₂	semidirect
5. C₃×C₇×C₁₇²	C₂²	semidirect
8. C₇×C₁₇⋊D₁₇	D₃	semidirect
10. C₇×C₁₇²	C₂×D₃	semidirect
11. C₃×C₁₇⋊D₁₇	D₇	semidirect
16. C₃×C₁₇²	C₂×D₇	semidirect
18. C₁₇×D₂₁	D₁₇	semidirect
22. C₁₇⋊D₁₇	D₂₁	direct (N × H)
24. C₃×C₇×C₁₇	C₂×D₁₇	semidirect
25. C₁₇²	C₂×D₂₁	semidirect
30. C₇×C₁₇	D₃×D₁₇	semidirect
36. C₃×C₁₇	D₇×D₁₇	semidirect
39. D₂₁	C₁₇⋊D₁₇	direct (N × H)
44. C₃×C₇	C₂×C₁₇⋊D₁₇	semidirect
45. C₁₇	D₁₇×D₂₁	semidirect
50. C₇	D₃×C₁₇⋊D₁₇	semidirect
55. C₃	D₇×C₁₇⋊D₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₇⋊D₁₇	2
C₁₇²×D₂₁	2
C₃⋊(C₇⋊(C₁₇⋊D₁₇))	2
D₇×C₁₇⋊D₁₇	3
D₃×C₁₇⋊D₁₇	7
D₁₇×D₂₁	17

Subgroups — D21×C17⋊D17 #37566281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₁×C₁₇⋊D₁₇ #37566281