Subgroups — C₂×C₁₀₃×D₆₉ #43249447

Order 28428.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₃×D₆₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₂₃×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₃×C₁₀₃	—	3	1	no	maximal, Hall
4	C₃×C₂₃×C₁₀₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₂₃×C₁₀₃	D₃	1	1	yes	characteristic, complemented
6	D₂₃×C₁₀₃	—	3	2	no	—
7	C₂₃×C₁₀₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₃×C₁₀₃	—	23	1	no	maximal, Hall
9	C₂×C₃×C₁₀₃	D₂₃	1	1	yes	characteristic, complemented
10	D₃×C₁₀₃	—	23	2	no	—
11	C₂²×C₁₀₃	—	69	1	no	Hall
12	C₃×C₁₀₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
13	C₂×D₆₉	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₁₀₃	—	69	2	no	—
15	C₂×C₁₀₃	D₆₉	1	1	yes	characteristic, direct product factor
16	C₂×C₃×C₂₃	C₂×C₁₀₃	1	1	yes	characteristic, complemented
17	D₆₉	C₂×C₁₀₃	1	2	yes	direct product factor
18	C₁₀₃	C₂×D₆₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×D₂₃	—	3	1	no	Hall
20	C₃×C₂₃	C₂²×C₁₀₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₂₃	D₃×C₁₀₃	1	1	yes	characteristic, complemented
22	D₂₃	—	3	2	no	—
23	C₂₃	C₂×D₃×C₁₀₃	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₃	—	23	1	no	Hall
25	C₂×C₃	D₂₃×C₁₀₃	1	1	yes	characteristic, complemented
26	D₃	—	23	2	no	—
27	C₂²	—	69	1	no	Sylow
28	C₃	C₂×D₂₃×C₁₀₃	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	69	2	no	—
30	C₂	C₁₀₃×D₆₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₀₃	D₆₉
commutator, cosocle, hypocenter	C₃×C₂₃	C₂²×C₁₀₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₂₃×C₁₀₃	C₂
LCS	G ▷ C₃×C₂₃
UCS	C₁ ◁ C₂×C₁₀₃

Complements

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

N	H ≅ G/N	type
1. C₁₀₃×D₆₉	C₂	direct (N × H)
2. C₂×C₃×C₂₃×C₁₀₃	C₂	semidirect
4. C₃×C₂₃×C₁₀₃	C₂²	semidirect
5. C₂×C₂₃×C₁₀₃	D₃	semidirect
7. C₂₃×C₁₀₃	C₂×D₃	semidirect
9. C₂×C₃×C₁₀₃	D₂₃	semidirect
12. C₃×C₁₀₃	C₂×D₂₃	semidirect
13. C₂×D₆₉	C₁₀₃	direct (N × H)
15. C₂×C₁₀₃	D₆₉	direct (N × H)
16. C₂×C₃×C₂₃	C₂×C₁₀₃	semidirect
17. D₆₉	C₂×C₁₀₃	direct (N × H)
18. C₁₀₃	C₂×D₆₉	direct (N × H)
20. C₃×C₂₃	C₂²×C₁₀₃	semidirect
21. C₂×C₂₃	D₃×C₁₀₃	semidirect
23. C₂₃	C₂×D₃×C₁₀₃	semidirect
25. C₂×C₃	D₂₃×C₁₀₃	semidirect
28. C₃	C₂×D₂₃×C₁₀₃	semidirect
30. C₂	C₁₀₃×D₆₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₀₃×D₆₉	2
C₂×C₃×C₂₃×C₁₀₃	2
C₂×D₂₃×C₁₀₃	3
C₂×D₃×C₁₀₃	23
C₂×D₆₉	103

Subgroups — C2×C103×D69 #43249447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₃×D₆₉ #43249447