Subgroups — C₂×C₁₁×D₇×C₁₀₃ #44540585

Order 31724.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₇×C₁₀₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₁₁×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₁×C₁₀₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂²×C₁₁×C₁₀₃	—	7	1	no	maximal, Hall
5	C₂×D₇×C₁₀₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₁₁×C₁₀₃	—	7	2	no	—
7	C₂×C₁₁×C₁₀₃	D₇	1	1	yes	characteristic, direct product factor
8	C₂×C₇×C₁₀₃	C₂×C₁₁	1	1	yes	characteristic, complemented
9	D₇×C₁₀₃	C₂×C₁₁	1	2	yes	direct product factor
10	C₁₁×C₁₀₃	C₂×D₇	1	1	yes	characteristic, direct product factor, Hall
11	C₇×C₁₀₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₁₀₃	—	7	1	no	Hall
13	C₂×C₁₁×D₇	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₁₀₃	—	7	2	no	—
15	C₂×C₁₀₃	C₁₁×D₇	1	1	yes	characteristic, direct product factor
16	C₂×C₇×C₁₁	C₂×C₁₀₃	1	1	yes	characteristic, complemented
17	C₁₁×D₇	C₂×C₁₀₃	1	2	yes	direct product factor
18	C₁₀₃	C₂×C₁₁×D₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₇×C₁₁	C₂²×C₁₀₃	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₁₁	—	7	1	no	Hall
21	C₂×D₇	C₁₁×C₁₀₃	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₁₁	—	7	2	no	—
23	C₂×C₁₁	D₇×C₁₀₃	1	1	yes	characteristic, direct product factor
24	C₂×C₇	C₂×C₁₁×C₁₀₃	1	1	yes	characteristic, complemented
25	D₇	C₂×C₁₁×C₁₀₃	1	2	yes	direct product factor
26	C₁₁	C₂×D₇×C₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₂²×C₁₁×C₁₀₃	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	7	1	no	Sylow
29	C₂	—	7	2	no	—
30	C₂	C₁₁×D₇×C₁₀₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁×C₁₀₃	D₇
commutator, cosocle, hypocenter	C₇	C₂²×C₁₁×C₁₀₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₁×C₁₀₃	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₁₁×C₁₀₃

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₇×C₁₀₃	C₂	direct (N × H)
2. C₂×C₇×C₁₁×C₁₀₃	C₂	semidirect
3. C₇×C₁₁×C₁₀₃	C₂²	semidirect
5. C₂×D₇×C₁₀₃	C₁₁	direct (N × H)
7. C₂×C₁₁×C₁₀₃	D₇	direct (N × H)
8. C₂×C₇×C₁₀₃	C₂×C₁₁	semidirect
9. D₇×C₁₀₃	C₂×C₁₁	direct (N × H)
10. C₁₁×C₁₀₃	C₂×D₇	direct (N × H)
11. C₇×C₁₀₃	C₂²×C₁₁	semidirect
13. C₂×C₁₁×D₇	C₁₀₃	direct (N × H)
15. C₂×C₁₀₃	C₁₁×D₇	direct (N × H)
16. C₂×C₇×C₁₁	C₂×C₁₀₃	semidirect
17. C₁₁×D₇	C₂×C₁₀₃	direct (N × H)
18. C₁₀₃	C₂×C₁₁×D₇	direct (N × H)
19. C₇×C₁₁	C₂²×C₁₀₃	semidirect
21. C₂×D₇	C₁₁×C₁₀₃	direct (N × H)
23. C₂×C₁₁	D₇×C₁₀₃	direct (N × H)
24. C₂×C₇	C₂×C₁₁×C₁₀₃	semidirect
25. D₇	C₂×C₁₁×C₁₀₃	direct (N × H)
26. C₁₁	C₂×D₇×C₁₀₃	direct (N × H)
27. C₇	C₂²×C₁₁×C₁₀₃	semidirect
30. C₂	C₁₁×D₇×C₁₀₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×D₇×C₁₀₃	2
C₂×C₇×C₁₁×C₁₀₃	2
C₂²×C₁₁×C₁₀₃	7
C₂×D₇×C₁₀₃	11
C₂×C₁₁×D₇	103

Subgroups — C2×C11×D7×C103 #44540585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×D₇×C₁₀₃ #44540585