Subgroups — C₂×C₁₁×D₂₉⋊C₇ #22582004

Order 8932.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₂₉⋊C₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₂₉⋊C₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×D₂₉	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×D₂₉⋊C₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₁₁×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
7	C₁₁×D₂₉	C₂×C₇	1	2	yes	complemented
8	C₂×C₂₉⋊C₇	C₂×C₁₁	1	1	yes	characteristic, complemented
9	D₂₉⋊C₇	C₂×C₁₁	1	2	yes	direct product factor
10	C₁₁×C₂₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
11	C₂²×C₇×C₁₁	—	29	1	no	maximal, Hall
12	C₂₉⋊C₇	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₂×C₇×C₁₁	—	29	2	no	—
14	C₂×C₇×C₁₁	—	29	1	no	—
15	C₂×D₂₉	C₇×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₇×C₁₁	—	29	1	no	Hall
17	C₂×C₂₉	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented
18	D₂₉	C₂×C₇×C₁₁	1	2	yes	complemented
19	C₂²×C₁₁	—	29	1	no	Hall
20	C₂₉	C₂²×C₇×C₁₁	1	1	yes	characteristic, complemented, Sylow
21	C₂²×C₇	—	29	1	no	Hall
22	C₂×C₁₁	—	29	2	no	—
23	C₂×C₁₁	D₂₉⋊C₇	1	1	yes	characteristic, direct product factor
24	C₂×C₇	—	29	2	no	—
25	C₂×C₇	—	29	1	no	—
26	C₁₁	C₂×D₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	—	29	1	no	Sylow
28	C₂²	—	29	1	no	Sylow
29	C₂	—	29	2	no	—
30	C₂	C₁₁×D₂₉⋊C₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₂₉⋊C₇
commutator, hypocenter	C₂₉	C₂²×C₇×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₂₉	C₂×C₇
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₂₉⋊C₇	C₂	direct (N × H)
2. C₂×C₁₁×C₂₉⋊C₇	C₂	semidirect
3. C₁₁×C₂₉⋊C₇	C₂²	semidirect
4. C₂×C₁₁×D₂₉	C₇	semidirect
5. C₂×D₂₉⋊C₇	C₁₁	direct (N × H)
6. C₂×C₁₁×C₂₉	C₂×C₇	semidirect
7. C₁₁×D₂₉	C₂×C₇	semidirect
8. C₂×C₂₉⋊C₇	C₂×C₁₁	semidirect
9. D₂₉⋊C₇	C₂×C₁₁	direct (N × H)
10. C₁₁×C₂₉	C₂²×C₇	semidirect
12. C₂₉⋊C₇	C₂²×C₁₁	semidirect
15. C₂×D₂₉	C₇×C₁₁	semidirect
17. C₂×C₂₉	C₂×C₇×C₁₁	semidirect
18. D₂₉	C₂×C₇×C₁₁	semidirect
20. C₂₉	C₂²×C₇×C₁₁	semidirect
23. C₂×C₁₁	D₂₉⋊C₇	direct (N × H)
26. C₁₁	C₂×D₂₉⋊C₇	direct (N × H)
30. C₂	C₁₁×D₂₉⋊C₇	direct (N × H)

Subgroups — C2×C11×D29⋊C7 #22582004

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₁×D₂₉⋊C₇ #22582004