Subgroups — C₂×C₇⋊D₇×C₄₃⋊C₃ #38760535

Order 25284.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇⋊D₇×C₄₃⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₄₃×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇²×C₄₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₄₃×C₇⋊D₇	C₂×C₃	1	2	yes	complemented
6	C₂×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×D₇×C₄₃⋊C₃	—	7	8	no	maximal
8	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₇×C₄₃⋊C₃	D₇	1	8	yes	complemented
10	D₇×C₄₃⋊C₃	—	7	16	no	—
11	C₂×D₇×C₄₃	—	7	8	no	—
12	C₇×C₄₃⋊C₃	C₂×D₇	1	8	yes	complemented
13	C₂×C₇×C₄₃	C₃×D₇	1	8	yes	complemented
14	D₇×C₄₃	—	7	16	no	—
15	C₂×C₃×C₇⋊D₇	—	43	1	no	maximal, Hall
16	C₂²×C₄₃⋊C₃	—	49	1	no	Hall
17	C₇×C₄₃	C₂×C₃×D₇	1	8	yes	complemented
18	C₂×C₃×C₇²	—	43	1	no	—
19	C₃×C₇⋊D₇	—	43	2	no	—
20	C₂×C₄₃⋊C₃	—	49	2	no	—
21	C₂×C₄₃⋊C₃	C₇⋊D₇	1	1	yes	characteristic, direct product factor
22	C₂×C₇⋊D₇	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
23	C₂²×C₄₃	—	49	1	no	Hall
24	C₃×C₇²	—	43	1	no	Hall
25	C₄₃⋊C₃	C₂×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₇²	C₂×C₄₃⋊C₃	1	1	yes	characteristic, complemented
27	C₇⋊D₇	C₂×C₄₃⋊C₃	1	2	yes	direct product factor
28	C₂×C₄₃	—	49	2	no	—
29	C₂×C₄₃	C₃×C₇⋊D₇	1	1	yes	characteristic, complemented
30	C₂×C₃×D₇	—	301	8	no	—
31	C₇²	C₂²×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
32	C₄₃	C₂×C₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃×C₇	—	43	8	no	—
34	C₃×D₇	—	301	16	no	—
35	C₂×D₇	—	7	8	no	—
36	C₃×C₇	—	43	8	no	—
37	C₂×C₇	D₇×C₄₃⋊C₃	1	8	yes	complemented
38	D₇	—	7	16	no	—
39	C₂²×C₃	—	2107	1	no	Hall
40	C₇	C₂×D₇×C₄₃⋊C₃	1	8	yes	complemented
41	C₂×C₃	—	43	1	no	—
42	C₂×C₃	—	2107	2	no	—
43	C₂²	—	49	1	no	Sylow
44	C₃	—	43	1	no	Sylow
45	C₂	—	49	2	no	—
46	C₂	C₇⋊D₇×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₇⋊D₇×C₄₃⋊C₃
commutator, cosocle, hypocenter	C₇²×C₄₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₄₃	C₂×C₃
LCS	G ▷ C₇²×C₄₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₇²×C₄₃⋊C₃	C₂	semidirect
2. C₇⋊D₇×C₄₃⋊C₃	C₂	direct (N × H)
3. C₂×C₄₃×C₇⋊D₇	C₃	semidirect
4. C₇²×C₄₃⋊C₃	C₂²	semidirect
5. C₄₃×C₇⋊D₇	C₂×C₃	semidirect
6. C₂×C₇²×C₄₃	C₂×C₃	semidirect
8. C₇²×C₄₃	C₂²×C₃	semidirect
9. C₂×C₇×C₄₃⋊C₃	D₇	semidirect
12. C₇×C₄₃⋊C₃	C₂×D₇	semidirect
13. C₂×C₇×C₄₃	C₃×D₇	semidirect
17. C₇×C₄₃	C₂×C₃×D₇	semidirect
21. C₂×C₄₃⋊C₃	C₇⋊D₇	direct (N × H)
22. C₂×C₇⋊D₇	C₄₃⋊C₃	direct (N × H)
25. C₄₃⋊C₃	C₂×C₇⋊D₇	direct (N × H)
26. C₂×C₇²	C₂×C₄₃⋊C₃	semidirect
27. C₇⋊D₇	C₂×C₄₃⋊C₃	direct (N × H)
29. C₂×C₄₃	C₃×C₇⋊D₇	semidirect
31. C₇²	C₂²×C₄₃⋊C₃	semidirect
32. C₄₃	C₂×C₃×C₇⋊D₇	semidirect
37. C₂×C₇	D₇×C₄₃⋊C₃	semidirect
40. C₇	C₂×D₇×C₄₃⋊C₃	semidirect
46. C₂	C₇⋊D₇×C₄₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇²×C₄₃⋊C₃	2
C₇⋊D₇×C₄₃⋊C₃	2
C₂×C₄₃×C₇⋊D₇	3
C₂×D₇×C₄₃⋊C₃	7
C₂×C₃×C₇⋊D₇	43

Subgroups — C2×C7⋊D7×C43⋊C3 #38760535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇⋊D₇×C₄₃⋊C₃ #38760535