Subgroups — C₂×C₃⋊D₂₀₃₇ #37568004

Order 24444.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₂₀₃₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₀₃₇	—	3	4	no	maximal
4	C₃²×C₇×C₉₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₂₀₃₇	—	3	8	no	—
6	C₂×C₃×C₇×C₉₇	D₃	1	4	yes	complemented
7	C₂×C₃⋊D₂₉₁	—	7	1	no	maximal, Hall
8	C₂×D₆₇₉	—	9	1	no	Hall
9	C₃×C₇×C₉₇	C₂×D₃	1	4	yes	complemented
10	C₂×C₃²×C₉₇	D₇	1	1	yes	characteristic, complemented
11	C₃⋊D₂₉₁	—	7	2	no	—
12	C₂×C₇×C₉₇	C₃⋊D₃	1	1	yes	characteristic, complemented
13	D₆₇₉	—	9	2	no	—
14	C₂×D₂₉₁	—	21	4	no	—
15	C₃²×C₉₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	C₇×C₉₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₉₇	D₂₁	1	4	yes	complemented
18	D₂₉₁	—	21	8	no	—
19	C₂×D₉₇	—	63	1	no	Hall
20	C₃×C₉₇	C₂×D₂₁	1	4	yes	complemented
21	C₂×C₃⋊D₂₁	—	97	1	no	maximal, Hall
22	C₂×C₉₇	C₃⋊D₂₁	1	1	yes	characteristic, complemented
23	D₉₇	—	63	2	no	—
24	C₂×C₃²×C₇	D₉₇	1	1	yes	characteristic, complemented
25	C₃⋊D₂₁	—	97	2	no	—
26	C₉₇	C₂×C₃⋊D₂₁	1	1	yes	characteristic, complemented, Sylow
27	C₂×D₂₁	—	291	4	no	—
28	C₃²×C₇	C₂×D₉₇	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₇	D₂₉₁	1	4	yes	complemented
30	D₂₁	—	291	8	no	—
31	C₂×C₃⋊D₃	—	679	1	no	Hall
32	C₂×D₇	—	873	1	no	Hall
33	C₃×C₇	C₂×D₂₉₁	1	4	yes	complemented
34	C₂×C₃²	D₆₇₉	1	1	yes	characteristic, complemented
35	C₃⋊D₃	—	679	2	no	—
36	C₂×C₇	C₃⋊D₂₉₁	1	1	yes	characteristic, complemented
37	D₇	—	873	2	no	—
38	C₂×D₃	—	2037	4	no	—
39	C₃²	C₂×D₆₇₉	1	1	yes	characteristic, complemented, Sylow
40	C₇	C₂×C₃⋊D₂₉₁	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₂₀₃₇	1	4	yes	complemented
42	D₃	—	2037	8	no	—
43	C₂²	—	6111	1	no	Sylow
44	C₃	C₂×D₂₀₃₇	1	4	yes	complemented
45	C₂	—	6111	2	no	—
46	C₂	C₃⋊D₂₀₃₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊D₂₀₃₇
commutator, cosocle, hypocenter	C₃²×C₇×C₉₇	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₉₇	C₂
LCS	G ▷ C₃²×C₇×C₉₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₂₀₃₇	C₂	direct (N × H)
2. C₂×C₃²×C₇×C₉₇	C₂	semidirect
4. C₃²×C₇×C₉₇	C₂²	semidirect
6. C₂×C₃×C₇×C₉₇	D₃	semidirect
9. C₃×C₇×C₉₇	C₂×D₃	semidirect
10. C₂×C₃²×C₉₇	D₇	semidirect
12. C₂×C₇×C₉₇	C₃⋊D₃	semidirect
15. C₃²×C₉₇	C₂×D₇	semidirect
16. C₇×C₉₇	C₂×C₃⋊D₃	semidirect
17. C₂×C₃×C₉₇	D₂₁	semidirect
20. C₃×C₉₇	C₂×D₂₁	semidirect
22. C₂×C₉₇	C₃⋊D₂₁	semidirect
24. C₂×C₃²×C₇	D₉₇	semidirect
26. C₉₇	C₂×C₃⋊D₂₁	semidirect
28. C₃²×C₇	C₂×D₉₇	semidirect
29. C₂×C₃×C₇	D₂₉₁	semidirect
33. C₃×C₇	C₂×D₂₉₁	semidirect
34. C₂×C₃²	D₆₇₉	semidirect
36. C₂×C₇	C₃⋊D₂₉₁	semidirect
39. C₃²	C₂×D₆₇₉	semidirect
40. C₇	C₂×C₃⋊D₂₉₁	semidirect
41. C₂×C₃	D₂₀₃₇	semidirect
44. C₃	C₂×D₂₀₃₇	semidirect
46. C₂	C₃⋊D₂₀₃₇	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⋊D₂₀₃₇	2
C₂×C₃²×C₇×C₉₇	2
C₂×D₂₀₃₇	3
C₂×C₃⋊D₂₉₁	7
C₂×C₃⋊D₂₁	97

Subgroups — C2×C3⋊D2037 #37568004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊D₂₀₃₇ #37568004