Subgroups — C₂×C₃×D₂₇₃₇ #45659331

Order 32844.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₇₃₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇×C₁₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₇₃₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₇×C₁₇×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₂₇₃₇	C₂×C₃	1	2	yes	direct product factor
6	C₂×C₇×C₁₇×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₃×D₃₉₁	—	7	1	no	maximal, Hall
8	C₇×C₁₇×C₂₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₃×D₃₉₁	—	7	2	no	—
10	C₂×C₃×C₁₇×C₂₃	D₇	1	1	yes	characteristic, complemented
11	C₂×C₃×D₁₆₁	—	17	1	no	maximal, Hall
12	C₂×D₃₉₁	—	7	1	no	Hall
13	C₂×C₃×D₁₁₉	—	23	1	no	maximal, Hall
14	C₃×C₁₇×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₇×C₂₃	D₁₇	1	1	yes	characteristic, complemented
16	C₃×D₁₆₁	—	17	2	no	—
17	C₂×C₁₇×C₂₃	C₃×D₇	1	1	yes	characteristic, complemented
18	D₃₉₁	—	7	2	no	—
19	C₂×C₃×C₇×C₁₇	D₂₃	1	1	yes	characteristic, complemented
20	C₃×D₁₁₉	—	23	2	no	—
21	C₂×D₁₆₁	—	17	1	no	Hall
22	C₃×C₇×C₂₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
23	C₂×D₁₁₉	—	23	1	no	Hall
24	C₁₇×C₂₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
25	C₃×C₇×C₁₇	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇×C₂₃	C₃×D₁₇	1	1	yes	characteristic, complemented
27	D₁₆₁	—	17	2	no	—
28	C₂×C₃×D₂₃	—	119	1	no	Hall
29	C₂×C₇×C₁₇	C₃×D₂₃	1	1	yes	characteristic, complemented
30	D₁₁₉	—	23	2	no	—
31	C₂×C₃×D₁₇	—	161	1	no	Hall
32	C₇×C₂₃	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₂₃	D₁₁₉	1	1	yes	characteristic, complemented
34	C₃×D₂₃	—	119	2	no	—
35	C₇×C₁₇	C₂×C₃×D₂₃	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₁₇	D₁₆₁	1	1	yes	characteristic, complemented
37	C₃×D₁₇	—	161	2	no	—
38	C₂×D₂₃	—	119	1	no	Hall
39	C₂×C₃×D₇	—	391	1	no	Hall
40	C₃×C₂₃	C₂×D₁₁₉	1	1	yes	characteristic, complemented, Hall
41	C₂×D₁₇	—	161	1	no	Hall
42	C₃×C₁₇	C₂×D₁₆₁	1	1	yes	characteristic, complemented, Hall
43	C₂×C₂₃	C₃×D₁₁₉	1	1	yes	characteristic, complemented
44	D₂₃	—	119	2	no	—
45	C₂×C₃×C₇	D₃₉₁	1	1	yes	characteristic, complemented
46	C₃×D₇	—	391	2	no	—
47	C₂×C₁₇	C₃×D₁₆₁	1	1	yes	characteristic, complemented
48	D₁₇	—	161	2	no	—
49	C₂×D₇	—	391	1	no	Hall
50	C₂₃	C₂×C₃×D₁₁₉	1	1	yes	characteristic, complemented, Sylow
51	C₃×C₇	C₂×D₃₉₁	1	1	yes	characteristic, complemented, Hall
52	C₁₇	C₂×C₃×D₁₆₁	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₇	C₃×D₃₉₁	1	1	yes	characteristic, complemented
54	D₇	—	391	2	no	—
55	C₂²×C₃	—	2737	1	no	Hall
56	C₇	C₂×C₃×D₃₉₁	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	—	2737	2	no	—
58	C₂×C₃	D₂₇₃₇	1	1	yes	characteristic, direct product factor
59	C₂²	—	2737	1	no	Sylow
60	C₃	C₂×D₂₇₃₇	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	2737	2	no	—
62	C₂	C₃×D₂₇₃₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₇₃₇
commutator, cosocle, hypocenter	C₇×C₁₇×C₂₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₇×C₂₃	C₂
LCS	G ▷ C₇×C₁₇×C₂₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₂₇₃₇	C₂	direct (N × H)
2. C₂×C₃×C₇×C₁₇×C₂₃	C₂	semidirect
3. C₂×D₂₇₃₇	C₃	direct (N × H)
4. C₃×C₇×C₁₇×C₂₃	C₂²	semidirect
5. D₂₇₃₇	C₂×C₃	direct (N × H)
6. C₂×C₇×C₁₇×C₂₃	C₂×C₃	semidirect
8. C₇×C₁₇×C₂₃	C₂²×C₃	semidirect
10. C₂×C₃×C₁₇×C₂₃	D₇	semidirect
14. C₃×C₁₇×C₂₃	C₂×D₇	semidirect
15. C₂×C₃×C₇×C₂₃	D₁₇	semidirect
17. C₂×C₁₇×C₂₃	C₃×D₇	semidirect
19. C₂×C₃×C₇×C₁₇	D₂₃	semidirect
22. C₃×C₇×C₂₃	C₂×D₁₇	semidirect
24. C₁₇×C₂₃	C₂×C₃×D₇	semidirect
25. C₃×C₇×C₁₇	C₂×D₂₃	semidirect
26. C₂×C₇×C₂₃	C₃×D₁₇	semidirect
29. C₂×C₇×C₁₇	C₃×D₂₃	semidirect
32. C₇×C₂₃	C₂×C₃×D₁₇	semidirect
33. C₂×C₃×C₂₃	D₁₁₉	semidirect
35. C₇×C₁₇	C₂×C₃×D₂₃	semidirect
36. C₂×C₃×C₁₇	D₁₆₁	semidirect
40. C₃×C₂₃	C₂×D₁₁₉	semidirect
42. C₃×C₁₇	C₂×D₁₆₁	semidirect
43. C₂×C₂₃	C₃×D₁₁₉	semidirect
45. C₂×C₃×C₇	D₃₉₁	semidirect
47. C₂×C₁₇	C₃×D₁₆₁	semidirect
50. C₂₃	C₂×C₃×D₁₁₉	semidirect
51. C₃×C₇	C₂×D₃₉₁	semidirect
52. C₁₇	C₂×C₃×D₁₆₁	semidirect
53. C₂×C₇	C₃×D₃₉₁	semidirect
56. C₇	C₂×C₃×D₃₉₁	semidirect
58. C₂×C₃	D₂₇₃₇	direct (N × H)
60. C₃	C₂×D₂₇₃₇	direct (N × H)
62. C₂	C₃×D₂₇₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₂₇₃₇	2
C₂×C₃×C₇×C₁₇×C₂₃	2
C₂×D₂₇₃₇	3
C₂×C₃×D₃₉₁	7
C₂×C₃×D₁₆₁	17
C₂×C₃×D₁₁₉	23

Subgroups — C2×C3×D2737 #45659331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₂₇₃₇ #45659331