Subgroups — C₂×C₁₁×D₇₂₁ #44540586

Order 31724.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₇₂₁	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	C₂×C₁₁×D₁₀₃	—	7	1	no	maximal, Hall
5	C₂×D₇₂₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₁₁×C₁₀₃	D₇	1	1	yes	characteristic, complemented
7	C₁₁×D₁₀₃	—	7	2	no	—
8	C₂×C₇×C₁₀₃	C₂×C₁₁	1	1	yes	characteristic, complemented
9	D₇₂₁	C₂×C₁₁	1	2	yes	direct product factor
10	C₁₁×C₁₀₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₁₀₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂×D₁₀₃	—	7	1	no	Hall
13	C₂×C₁₁×D₇	—	103	1	no	maximal, Hall
14	C₂×C₁₀₃	C₁₁×D₇	1	1	yes	characteristic, complemented
15	D₁₀₃	—	7	2	no	—
16	C₂×C₇×C₁₁	D₁₀₃	1	1	yes	characteristic, complemented
17	C₁₁×D₇	—	103	2	no	—
18	C₁₀₃	C₂×C₁₁×D₇	1	1	yes	characteristic, complemented, Sylow
19	C₇×C₁₁	C₂×D₁₀₃	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₁₁	—	721	1	no	Hall
21	C₂×D₇	—	103	1	no	Hall
22	C₂×C₁₁	—	721	2	no	—
23	C₂×C₁₁	D₇₂₁	1	1	yes	characteristic, direct product factor
24	C₂×C₇	C₁₁×D₁₀₃	1	1	yes	characteristic, complemented
25	D₇	—	103	2	no	—
26	C₁₁	C₂×D₇₂₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₂×C₁₁×D₁₀₃	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	721	1	no	Sylow
29	C₂	—	721	2	no	—
30	C₂	C₁₁×D₇₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₇₂₁
commutator, cosocle, hypocenter	C₇×C₁₀₃	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₁×C₁₀₃	C₂
LCS	G ▷ C₇×C₁₀₃
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₇₂₁	C₂	direct (N × H)
2. C₂×C₇×C₁₁×C₁₀₃	C₂	semidirect
3. C₇×C₁₁×C₁₀₃	C₂²	semidirect
5. C₂×D₇₂₁	C₁₁	direct (N × H)
6. C₂×C₁₁×C₁₀₃	D₇	semidirect
8. C₂×C₇×C₁₀₃	C₂×C₁₁	semidirect
9. D₇₂₁	C₂×C₁₁	direct (N × H)
10. C₁₁×C₁₀₃	C₂×D₇	semidirect
11. C₇×C₁₀₃	C₂²×C₁₁	semidirect
14. C₂×C₁₀₃	C₁₁×D₇	semidirect
16. C₂×C₇×C₁₁	D₁₀₃	semidirect
18. C₁₀₃	C₂×C₁₁×D₇	semidirect
19. C₇×C₁₁	C₂×D₁₀₃	semidirect
23. C₂×C₁₁	D₇₂₁	direct (N × H)
24. C₂×C₇	C₁₁×D₁₀₃	semidirect
26. C₁₁	C₂×D₇₂₁	direct (N × H)
27. C₇	C₂×C₁₁×D₁₀₃	semidirect
30. C₂	C₁₁×D₇₂₁	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×D₇₂₁	2
C₂×C₇×C₁₁×C₁₀₃	2
C₂×C₁₁×D₁₀₃	7
C₂×D₇₂₁	11
C₂×C₁₁×D₇	103

Subgroups — C2×C11×D721 #44540586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×D₇₂₁ #44540586