Subgroups — C₂×D₉₀₂₇ #49115643

Order 36108.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₉₀₂₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₁₇×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃₀₀₉	—	3	1	no	maximal
4	C₉×C₁₇×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃₀₀₉	—	3	2	no	—
6	C₂×C₃×C₁₇×C₅₉	D₃	1	1	yes	characteristic
7	C₂×D₁₀₀₃	—	9	1	no	Hall
8	C₃×C₁₇×C₅₉	C₂×D₃	1	1	yes	characteristic
9	C₂×D₅₃₁	—	17	1	no	maximal, Hall
10	C₂×C₁₇×C₅₉	D₉	1	1	yes	characteristic, complemented
11	D₁₀₀₃	—	9	2	no	—
12	C₂×C₉×C₅₉	D₁₇	1	1	yes	characteristic, complemented
13	D₅₃₁	—	17	2	no	—
14	C₁₇×C₅₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
15	C₂×D₁₇₇	—	51	1	no	—
16	C₂×D₁₅₃	—	59	1	no	maximal, Hall
17	C₉×C₅₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₅₉	D₅₁	1	1	yes	characteristic
19	D₁₇₇	—	51	2	no	—
20	C₂×C₉×C₁₇	D₅₉	1	1	yes	characteristic, complemented
21	D₁₅₃	—	59	2	no	—
22	C₂×D₅₉	—	153	1	no	Hall
23	C₂×D₅₁	—	177	1	no	—
24	C₃×C₅₉	C₂×D₅₁	1	1	yes	characteristic
25	C₉×C₁₇	C₂×D₅₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅₉	D₁₅₃	1	1	yes	characteristic, complemented
27	D₅₉	—	153	2	no	—
28	C₂×C₃×C₁₇	D₁₇₇	1	1	yes	characteristic
29	D₅₁	—	177	2	no	—
30	C₂×D₁₇	—	531	1	no	Hall
31	C₅₉	C₂×D₁₅₃	1	1	yes	characteristic, complemented, Sylow
32	C₃×C₁₇	C₂×D₁₇₇	1	1	yes	characteristic
33	C₂×D₉	—	1003	1	no	Hall
34	C₂×C₁₇	D₅₃₁	1	1	yes	characteristic, complemented
35	D₁₇	—	531	2	no	—
36	C₂×C₉	D₁₀₀₃	1	1	yes	characteristic, complemented
37	D₉	—	1003	2	no	—
38	C₁₇	C₂×D₅₃₁	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₃	—	3009	1	no	—
40	C₉	C₂×D₁₀₀₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₃₀₀₉	1	1	yes	characteristic
42	D₃	—	3009	2	no	—
43	C₂²	—	9027	1	no	Sylow
44	C₃	C₂×D₃₀₀₉	1	1	yes	characteristic
45	C₂	—	9027	2	no	—
46	C₂	D₉₀₂₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₉₀₂₇
commutator, cosocle, hypocenter	C₉×C₁₇×C₅₉	C₂²
Frattini	C₃	C₂×D₃₀₀₉
Fitting	C₂×C₉×C₁₇×C₅₉	C₂
socle	C₂×C₃×C₁₇×C₅₉	D₃
LCS	G ▷ C₉×C₁₇×C₅₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₉₀₂₇	C₂	direct (N × H)
2. C₂×C₉×C₁₇×C₅₉	C₂	semidirect
4. C₉×C₁₇×C₅₉	C₂²	semidirect
10. C₂×C₁₇×C₅₉	D₉	semidirect
12. C₂×C₉×C₅₉	D₁₇	semidirect
14. C₁₇×C₅₉	C₂×D₉	semidirect
17. C₉×C₅₉	C₂×D₁₇	semidirect
20. C₂×C₉×C₁₇	D₅₉	semidirect
25. C₉×C₁₇	C₂×D₅₉	semidirect
26. C₂×C₅₉	D₁₅₃	semidirect
31. C₅₉	C₂×D₁₅₃	semidirect
34. C₂×C₁₇	D₅₃₁	semidirect
36. C₂×C₉	D₁₀₀₃	semidirect
38. C₁₇	C₂×D₅₃₁	semidirect
40. C₉	C₂×D₁₀₀₃	semidirect
46. C₂	D₉₀₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
D₉₀₂₇	2
C₂×C₉×C₁₇×C₅₉	2
C₂×D₃₀₀₉	3
C₂×D₅₃₁	17
C₂×D₁₅₃	59

Subgroups — C2×D9027 #49115643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₉₀₂₇ #49115643