Subgroups — C₂²×C₃²×C₂₉⋊C₇ #20300634

Order 7308.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₂₉⋊C₇	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₂₉⋊C₇	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₂₉⋊C₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₂₉⋊C₇	C₂×C₃	1	12	yes	direct product factor
5	C₂²×C₃²×C₂₉	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂²×C₂₉⋊C₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₂₉⋊C₇	C₂²×C₃	1	4	yes	direct product factor
8	C₂×C₃²×C₂₉	C₂×C₇	1	3	yes	complemented
9	C₂×C₂₉⋊C₇	C₂×C₃²	1	3	yes	direct product factor
10	C₂²×C₃×C₂₉	C₃×C₇	1	4	yes	complemented
11	C₃²×C₂₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₃²×C₇	—	29	1	no	maximal, Hall
13	C₂₉⋊C₇	C₂²×C₃²	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₂₉	C₂×C₃×C₇	1	12	yes	complemented
15	C₂×C₃²×C₇	—	29	3	no	—
16	C₂²×C₂₉	C₃²×C₇	1	1	yes	characteristic, complemented, Hall
17	C₃×C₂₉	C₂²×C₃×C₇	1	4	yes	complemented
18	C₂²×C₃×C₇	—	29	4	no	—
19	C₃²×C₇	—	29	1	no	Hall
20	C₂×C₂₉	C₂×C₃²×C₇	1	3	yes	complemented
21	C₂×C₃×C₇	—	29	12	no	—
22	C₂²×C₃²	C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
23	C₂₉	C₂²×C₃²×C₇	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₇	—	29	1	no	Hall
25	C₃×C₇	—	29	4	no	—
26	C₂×C₃²	C₂×C₂₉⋊C₇	1	3	yes	direct product factor
27	C₂×C₇	—	29	3	no	—
28	C₂²×C₃	C₃×C₂₉⋊C₇	1	4	yes	direct product factor
29	C₃²	C₂²×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₇	—	29	1	no	Sylow
31	C₂×C₃	C₂×C₃×C₂₉⋊C₇	1	12	yes	direct product factor
32	C₂²	C₃²×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₂²×C₃×C₂₉⋊C₇	1	4	yes	direct product factor
34	C₂	C₂×C₃²×C₂₉⋊C₇	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃²	C₂₉⋊C₇
commutator, hypocenter	C₂₉	C₂²×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₂²×C₃²×C₂₉	C₇
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂²×C₃²

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₂₉⋊C₇	C₂	direct (N × H)
2. C₂²×C₃×C₂₉⋊C₇	C₃	direct (N × H)
3. C₃²×C₂₉⋊C₇	C₂²	direct (N × H)
4. C₂×C₃×C₂₉⋊C₇	C₂×C₃	direct (N × H)
5. C₂²×C₃²×C₂₉	C₇	semidirect
6. C₂²×C₂₉⋊C₇	C₃²	direct (N × H)
7. C₃×C₂₉⋊C₇	C₂²×C₃	direct (N × H)
8. C₂×C₃²×C₂₉	C₂×C₇	semidirect
9. C₂×C₂₉⋊C₇	C₂×C₃²	direct (N × H)
10. C₂²×C₃×C₂₉	C₃×C₇	semidirect
11. C₃²×C₂₉	C₂²×C₇	semidirect
13. C₂₉⋊C₇	C₂²×C₃²	direct (N × H)
14. C₂×C₃×C₂₉	C₂×C₃×C₇	semidirect
16. C₂²×C₂₉	C₃²×C₇	semidirect
17. C₃×C₂₉	C₂²×C₃×C₇	semidirect
20. C₂×C₂₉	C₂×C₃²×C₇	semidirect
22. C₂²×C₃²	C₂₉⋊C₇	direct (N × H)
23. C₂₉	C₂²×C₃²×C₇	semidirect
26. C₂×C₃²	C₂×C₂₉⋊C₇	direct (N × H)
28. C₂²×C₃	C₃×C₂₉⋊C₇	direct (N × H)
29. C₃²	C₂²×C₂₉⋊C₇	direct (N × H)
31. C₂×C₃	C₂×C₃×C₂₉⋊C₇	direct (N × H)
32. C₂²	C₃²×C₂₉⋊C₇	direct (N × H)
33. C₃	C₂²×C₃×C₂₉⋊C₇	direct (N × H)
34. C₂	C₂×C₃²×C₂₉⋊C₇	direct (N × H)

Subgroups — C22×C32×C29⋊C7 #20300634

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×C₃²×C₂₉⋊C₇ #20300634