Subgroups — #37566280

Order 24276.

144 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	C₁₇×D₃₅₇	C₂	1	2	yes	maximal, complemented
3	D₁₁₉⋊D₁₇	—	3	1	no	maximal, Hall
4	C₃×C₇×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₇×D₁₁₉	—	3	2	no	—
6	C₇×C₁₇⋊D₁₇	D₃	1	1	yes	characteristic, complemented
7	D₅₁⋊D₁₇	—	7	1	no	maximal, Hall
8	C₇×C₁₇²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₇⋊D₁₇	D₇	1	1	yes	characteristic, complemented
10	C₁₇×D₅₁	—	7	2	no	—
11	D₁₇×D₂₁	—	17	2	no	maximal
12	D₁₇²	—	21	1	no	Hall
13	C₃×C₁₇²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
14	D₃₅₇	D₁₇	1	2	yes	complemented
15	C₁₇×D₂₁	—	17	2	no	—
16	C₃×C₇×D₁₇	—	17	2	no	—
17	C₃×C₇×D₁₇	—	34	8	no	—
18	C₁₇⋊D₁₇	D₂₁	1	1	yes	characteristic, complemented
19	C₁₇×D₁₇	—	21	2	no	—
20	D₇×D₁₇	—	51	2	no	—
21	C₃×C₇×C₁₇	—	2	8	no	—
22	C₃×C₇×C₁₇	C₂×D₁₇	1	2	yes	complemented
23	C₁₇²	C₂×D₂₁	1	1	yes	characteristic, complemented, Sylow
24	D₁₁₉	—	3	2	no	—
25	C₇×D₁₇	—	17	2	no	—
26	C₇×D₁₇	—	34	8	no	—
27	D₇×C₁₇	—	51	2	no	—
28	D₃×D₁₇	—	119	2	no	—
29	C₇×C₁₇	—	2	8	no	—
30	C₇×C₁₇	D₃×D₁₇	1	2	yes	complemented
31	D₅₁	—	7	2	no	—
32	C₃×D₁₇	—	17	2	no	—
33	C₃×D₁₇	—	34	8	no	—
34	D₃×C₁₇	—	119	2	no	—
35	C₂×D₂₁	—	289	1	no	Hall
36	C₂×D₁₇	—	357	2	no	—
37	C₃×C₁₇	—	2	8	no	—
38	C₃×C₁₇	D₇×D₁₇	1	2	yes	complemented
39	C₂×C₃×C₇	—	289	1	no	—
40	D₂₁	—	17	2	no	—
41	C₂×C₁₇	—	357	2	no	—
42	D₁₇	—	17	2	no	—
43	D₁₇	—	21	2	no	—
44	D₁₇	—	34	8	no	—
45	C₂×D₇	—	867	1	no	Hall
46	C₃×C₇	D₁₇²	1	1	yes	characteristic, complemented, Hall
47	C₁₇	—	2	8	no	—
48	C₁₇	D₁₇×D₂₁	1	2	yes	complemented
49	C₂×C₇	—	289	1	no	—
50	D₇	—	51	2	no	—
51	C₂×D₃	—	2023	1	no	Hall
52	C₇	D₅₁⋊D₁₇	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₃	—	289	1	no	—
54	D₃	—	119	2	no	—
55	C₂²	—	6069	1	no	Sylow
56	C₃	D₁₁₉⋊D₁₇	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	289	1	no	—
58	C₂	—	357	2	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. C₁₇×D₃₅₇	C₂	semidirect
4. C₃×C₇×C₁₇²	C₂²	semidirect
6. C₇×C₁₇⋊D₁₇	D₃	semidirect
8. C₇×C₁₇²	C₂×D₃	semidirect
9. C₃×C₁₇⋊D₁₇	D₇	semidirect
13. C₃×C₁₇²	C₂×D₇	semidirect
14. D₃₅₇	D₁₇	semidirect
18. C₁₇⋊D₁₇	D₂₁	semidirect
22. C₃×C₇×C₁₇	C₂×D₁₇	semidirect
23. C₁₇²	C₂×D₂₁	semidirect
30. C₇×C₁₇	D₃×D₁₇	semidirect
38. C₃×C₁₇	D₇×D₁₇	semidirect
46. C₃×C₇	D₁₇²	semidirect
48. C₁₇	D₁₇×D₂₁	semidirect
52. C₇	D₅₁⋊D₁₇	semidirect
56. C₃	D₁₁₉⋊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
C₁₇×D₃₅₇	2
D₁₁₉⋊D₁₇	3
D₅₁⋊D₁₇	7
D₁₇×D₂₁	17