Subgroups — C₂×D₇₁₃₇ #43269708

Order 28548.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₁₃₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₁₃×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₃₇₉	—	3	1	no	maximal
4	C₉×C₁₃×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₂₃₇₉	—	3	2	no	—
6	C₂×C₃×C₁₃×C₆₁	D₃	1	1	yes	characteristic
7	C₂×D₇₉₃	—	9	1	no	Hall
8	C₃×C₁₃×C₆₁	C₂×D₃	1	1	yes	characteristic
9	C₂×D₅₄₉	—	13	1	no	maximal, Hall
10	C₂×C₁₃×C₆₁	D₉	1	1	yes	characteristic, complemented
11	D₇₉₃	—	9	2	no	—
12	C₂×C₉×C₆₁	D₁₃	1	1	yes	characteristic, complemented
13	D₅₄₉	—	13	2	no	—
14	C₁₃×C₆₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
15	C₂×D₁₈₃	—	39	1	no	—
16	C₉×C₆₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
17	C₂×D₁₁₇	—	61	1	no	maximal, Hall
18	C₂×C₃×C₆₁	D₃₉	1	1	yes	characteristic
19	D₁₈₃	—	39	2	no	—
20	C₂×D₆₁	—	117	1	no	Hall
21	C₂×C₉×C₁₃	D₆₁	1	1	yes	characteristic, complemented
22	D₁₁₇	—	61	2	no	—
23	C₃×C₆₁	C₂×D₃₉	1	1	yes	characteristic
24	C₂×D₃₉	—	183	1	no	—
25	C₂×C₆₁	D₁₁₇	1	1	yes	characteristic, complemented
26	D₆₁	—	117	2	no	—
27	C₉×C₁₃	C₂×D₆₁	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₃	D₁₈₃	1	1	yes	characteristic
29	D₃₉	—	183	2	no	—
30	C₆₁	C₂×D₁₁₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×D₁₃	—	549	1	no	Hall
32	C₃×C₁₃	C₂×D₁₈₃	1	1	yes	characteristic
33	C₂×D₉	—	793	1	no	Hall
34	C₂×C₁₃	D₅₄₉	1	1	yes	characteristic, complemented
35	D₁₃	—	549	2	no	—
36	C₂×C₉	D₇₉₃	1	1	yes	characteristic, complemented
37	D₉	—	793	2	no	—
38	C₁₃	C₂×D₅₄₉	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₃	—	2379	1	no	—
40	C₉	C₂×D₇₉₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₂₃₇₉	1	1	yes	characteristic
42	D₃	—	2379	2	no	—
43	C₂²	—	7137	1	no	Sylow
44	C₃	C₂×D₂₃₇₉	1	1	yes	characteristic
45	C₂	—	7137	2	no	—
46	C₂	D₇₁₃₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₇₁₃₇
commutator, cosocle, hypocenter	C₉×C₁₃×C₆₁	C₂²
Frattini	C₃	C₂×D₂₃₇₉
Fitting	C₂×C₉×C₁₃×C₆₁	C₂
socle	C₂×C₃×C₁₃×C₆₁	D₃
LCS	G ▷ C₉×C₁₃×C₆₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₇₁₃₇	C₂	direct (N × H)
2. C₂×C₉×C₁₃×C₆₁	C₂	semidirect
4. C₉×C₁₃×C₆₁	C₂²	semidirect
10. C₂×C₁₃×C₆₁	D₉	semidirect
12. C₂×C₉×C₆₁	D₁₃	semidirect
14. C₁₃×C₆₁	C₂×D₉	semidirect
16. C₉×C₆₁	C₂×D₁₃	semidirect
21. C₂×C₉×C₁₃	D₆₁	semidirect
25. C₂×C₆₁	D₁₁₇	semidirect
27. C₉×C₁₃	C₂×D₆₁	semidirect
30. C₆₁	C₂×D₁₁₇	semidirect
34. C₂×C₁₃	D₅₄₉	semidirect
36. C₂×C₉	D₇₉₃	semidirect
38. C₁₃	C₂×D₅₄₉	semidirect
40. C₉	C₂×D₇₉₃	semidirect
46. C₂	D₇₁₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
D₇₁₃₇	2
C₂×C₉×C₁₃×C₆₁	2
C₂×D₂₃₇₉	3
C₂×D₅₄₉	13
C₂×D₁₁₇	61

Subgroups — C2×D7137 #43269708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₇₁₃₇ #43269708