Subgroups — C₇×D₁₁×D₁₀₉ #46777095

Order 33572.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₁₁×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₁×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₁₁×C₁₀₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₁×D₁₀₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₇×D₁₀₉	—	11	1	no	maximal, Hall
7	D₁₁₉₉	C₂×C₇	1	1	yes	characteristic, complemented
8	C₁₁×D₁₀₉	C₂×C₇	1	1	yes	characteristic, complemented
9	D₁₁×C₁₀₉	C₂×C₇	1	1	yes	characteristic, complemented
10	C₂×C₇×C₁₀₉	—	11	1	no	—
11	C₇×D₁₀₉	—	11	1	no	—
12	C₇×D₁₀₉	D₁₁	1	1	yes	characteristic, direct product factor
13	C₁₁×C₁₀₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
14	C₇×C₁₀₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₂×D₁₀₉	—	11	1	no	Hall
16	C₂×C₇×D₁₁	—	109	1	no	maximal, Hall
17	C₂×C₁₀₉	—	11	1	no	—
18	D₁₀₉	—	11	1	no	—
19	D₁₀₉	C₇×D₁₁	1	1	yes	characteristic, direct product factor
20	C₂×C₇×C₁₁	—	109	1	no	—
21	C₇×D₁₁	—	109	1	no	—
22	C₇×D₁₁	D₁₀₉	1	1	yes	characteristic, direct product factor
23	C₁₀₉	C₂×C₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
24	C₇×C₁₁	C₂×D₁₀₉	1	1	yes	characteristic, complemented, Hall
25	C₂×D₁₁	—	109	1	no	Hall
26	C₂²×C₇	—	1199	1	no	Hall
27	C₂×C₁₁	—	109	1	no	—
28	D₁₁	—	109	1	no	—
29	D₁₁	C₇×D₁₀₉	1	1	yes	characteristic, direct product factor
30	C₂×C₇	—	11	1	no	—
31	C₂×C₇	—	109	1	no	—
32	C₂×C₇	—	1199	1	no	—
33	C₁₁	C₂×C₇×D₁₀₉	1	1	yes	characteristic, complemented, Sylow
34	C₇	D₁₁×D₁₀₉	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²	—	1199	1	no	Sylow
36	C₂	—	11	1	no	—
37	C₂	—	109	1	no	—
38	C₂	—	1199	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₁₁×D₁₀₉
commutator, cosocle, hypocenter	C₁₁×C₁₀₉	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₁₀₉	C₂²
LCS	G ▷ C₁₁×C₁₀₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₁₁₉₉	C₂	semidirect
2. C₇×D₁₁×C₁₀₉	C₂	semidirect
3. C₇×C₁₁×D₁₀₉	C₂	semidirect
4. C₇×C₁₁×C₁₀₉	C₂²	semidirect
5. D₁₁×D₁₀₉	C₇	direct (N × H)
7. D₁₁₉₉	C₂×C₇	semidirect
8. C₁₁×D₁₀₉	C₂×C₇	semidirect
9. D₁₁×C₁₀₉	C₂×C₇	semidirect
12. C₇×D₁₀₉	D₁₁	direct (N × H)
13. C₁₁×C₁₀₉	C₂²×C₇	semidirect
14. C₇×C₁₀₉	C₂×D₁₁	semidirect
19. D₁₀₉	C₇×D₁₁	direct (N × H)
22. C₇×D₁₁	D₁₀₉	direct (N × H)
23. C₁₀₉	C₂×C₇×D₁₁	semidirect
24. C₇×C₁₁	C₂×D₁₀₉	semidirect
29. D₁₁	C₇×D₁₀₉	direct (N × H)
33. C₁₁	C₂×C₇×D₁₀₉	semidirect
34. C₇	D₁₁×D₁₀₉	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×D₁₁₉₉	2
C₇×D₁₁×C₁₀₉	2
C₇×C₁₁×D₁₀₉	2
D₁₁×D₁₀₉	7
C₂×C₇×D₁₀₉	11
C₂×C₇×D₁₁	109

Subgroups — C7×D11×D109 #46777095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₁₁×D₁₀₉ #46777095