Subgroups — C₂×C₇×D₁₁₁₁ #44527421

Order 31108.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₁₁₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₁₁×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₁×C₁₀₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₁₁₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×D₁₀₁	—	11	1	no	maximal, Hall
6	C₂×C₁₁×C₁₀₁	C₂×C₇	1	1	yes	characteristic, complemented
7	D₁₁₁₁	C₂×C₇	1	2	yes	direct product factor
8	C₂×C₇×C₁₀₁	D₁₁	1	1	yes	characteristic, complemented
9	C₇×D₁₀₁	—	11	2	no	—
10	C₁₁×C₁₀₁	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₁₀₁	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂×D₁₀₁	—	11	1	no	Hall
13	C₂×C₇×D₁₁	—	101	1	no	maximal, Hall
14	C₂×C₁₀₁	C₇×D₁₁	1	1	yes	characteristic, complemented
15	D₁₀₁	—	11	2	no	—
16	C₂×C₇×C₁₁	D₁₀₁	1	1	yes	characteristic, complemented
17	C₇×D₁₁	—	101	2	no	—
18	C₁₀₁	C₂×C₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
19	C₇×C₁₁	C₂×D₁₀₁	1	1	yes	characteristic, complemented, Hall
20	C₂×D₁₁	—	101	1	no	Hall
21	C₂²×C₇	—	1111	1	no	Hall
22	C₂×C₁₁	C₇×D₁₀₁	1	1	yes	characteristic, complemented
23	D₁₁	—	101	2	no	—
24	C₂×C₇	—	1111	2	no	—
25	C₂×C₇	D₁₁₁₁	1	1	yes	characteristic, direct product factor
26	C₁₁	C₂×C₇×D₁₀₁	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₂×D₁₁₁₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	1111	1	no	Sylow
29	C₂	—	1111	2	no	—
30	C₂	C₇×D₁₁₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	D₁₁₁₁
commutator, cosocle, hypocenter	C₁₁×C₁₀₁	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₁×C₁₀₁	C₂
LCS	G ▷ C₁₁×C₁₀₁
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₁₁₁₁	C₂	direct (N × H)
2. C₂×C₇×C₁₁×C₁₀₁	C₂	semidirect
3. C₇×C₁₁×C₁₀₁	C₂²	semidirect
4. C₂×D₁₁₁₁	C₇	direct (N × H)
6. C₂×C₁₁×C₁₀₁	C₂×C₇	semidirect
7. D₁₁₁₁	C₂×C₇	direct (N × H)
8. C₂×C₇×C₁₀₁	D₁₁	semidirect
10. C₁₁×C₁₀₁	C₂²×C₇	semidirect
11. C₇×C₁₀₁	C₂×D₁₁	semidirect
14. C₂×C₁₀₁	C₇×D₁₁	semidirect
16. C₂×C₇×C₁₁	D₁₀₁	semidirect
18. C₁₀₁	C₂×C₇×D₁₁	semidirect
19. C₇×C₁₁	C₂×D₁₀₁	semidirect
22. C₂×C₁₁	C₇×D₁₀₁	semidirect
25. C₂×C₇	D₁₁₁₁	direct (N × H)
26. C₁₁	C₂×C₇×D₁₀₁	semidirect
27. C₇	C₂×D₁₁₁₁	direct (N × H)
30. C₂	C₇×D₁₁₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×D₁₁₁₁	2
C₂×C₇×C₁₁×C₁₀₁	2
C₂×D₁₁₁₁	7
C₂×C₇×D₁₀₁	11
C₂×C₇×D₁₁	101

Subgroups — C2×C7×D1111 #44527421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₁₁₁₁ #44527421