Subgroups — C₂×C₇²×C₄₃⋊C₉ #49181604

Order 37926.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₄₃⋊C₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₇²×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic
4	C₂×C₇×C₄₃⋊C₉	C₇	1	8	yes	maximal, direct product factor
5	C₂×C₇²×C₄₃	C₉	1	1	yes	characteristic, complemented, Hall
6	C₇×C₄₃⋊C₉	C₂×C₇	1	8	yes	direct product factor
7	C₇²×C₄₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₇×C₄₃	C₃×C₇	1	8	yes	—
9	C₃×C₇×C₄₃	C₂×C₃×C₇	1	8	yes	—
10	C₂×C₇²×C₉	—	43	1	no	maximal, Hall
11	C₂×C₄₃⋊C₉	C₇²	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₇×C₄₃	C₇×C₉	1	8	yes	complemented
13	C₇²×C₉	—	43	1	no	Hall
14	C₄₃⋊C₉	C₂×C₇²	1	1	yes	characteristic, direct product factor, Hall
15	C₇×C₄₃	C₂×C₇×C₉	1	8	yes	complemented
16	C₂×C₃×C₇²	C₄₃⋊C₃	1	1	yes	characteristic
17	C₂×C₃×C₄₃	C₃×C₇²	1	1	yes	characteristic
18	C₃×C₇²	C₂×C₄₃⋊C₃	1	1	yes	characteristic
19	C₃×C₄₃	C₂×C₃×C₇²	1	1	yes	characteristic
20	C₂×C₇×C₉	—	43	8	no	—
21	C₂×C₇²	C₄₃⋊C₉	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₄₃	C₇²×C₉	1	1	yes	characteristic, complemented, Hall
23	C₇×C₉	—	43	8	no	—
24	C₇²	C₂×C₄₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₄₃	C₂×C₇²×C₉	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃×C₇	C₇×C₄₃⋊C₃	1	8	yes	—
27	C₃×C₇	C₂×C₇×C₄₃⋊C₃	1	8	yes	—
28	C₂×C₉	—	43	1	no	Hall
29	C₂×C₇	C₇×C₄₃⋊C₉	1	8	yes	direct product factor
30	C₉	—	43	1	no	Sylow
31	C₇	C₂×C₇×C₄₃⋊C₉	1	8	yes	direct product factor
32	C₂×C₃	C₇²×C₄₃⋊C₃	1	1	yes	characteristic
33	C₃	C₂×C₇²×C₄₃⋊C₃	1	1	yes	characteristic
34	C₂	C₇²×C₄₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇²	C₄₃⋊C₃
commutator, hypocenter	C₄₃	C₂×C₇²×C₉
Frattini	C₃	C₂×C₇²×C₄₃⋊C₃
Fitting, socle, prime radical	C₂×C₃×C₇²×C₄₃	C₃
cosocle	C₃×C₄₃	C₂×C₃×C₇²
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂×C₃×C₇²

Complements

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

N	H ≅ G/N	type
1. C₇²×C₄₃⋊C₉	C₂	direct (N × H)
4. C₂×C₇×C₄₃⋊C₉	C₇	direct (N × H)
5. C₂×C₇²×C₄₃	C₉	semidirect
6. C₇×C₄₃⋊C₉	C₂×C₇	direct (N × H)
7. C₇²×C₄₃	C₂×C₉	semidirect
11. C₂×C₄₃⋊C₉	C₇²	direct (N × H)
12. C₂×C₇×C₄₃	C₇×C₉	semidirect
14. C₄₃⋊C₉	C₂×C₇²	direct (N × H)
15. C₇×C₄₃	C₂×C₇×C₉	semidirect
21. C₂×C₇²	C₄₃⋊C₉	direct (N × H)
22. C₂×C₄₃	C₇²×C₉	semidirect
24. C₇²	C₂×C₄₃⋊C₉	direct (N × H)
25. C₄₃	C₂×C₇²×C₉	semidirect
29. C₂×C₇	C₇×C₄₃⋊C₉	direct (N × H)
31. C₇	C₂×C₇×C₄₃⋊C₉	direct (N × H)
34. C₂	C₇²×C₄₃⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇²×C₄₃⋊C₉	2
C₂×C₃×C₇²×C₄₃	3
C₂×C₇×C₄₃⋊C₉	7
C₂×C₇²×C₉	43

Subgroups — C2×C72×C43⋊C9 #49181604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇²×C₄₃⋊C₉ #49181604