Subgroups — C₂×(C₄₃⋊C₉)⋊D₇ #24925463

Order 10836.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₄₃⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₄₃⋊C₉)⋊D₇	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×D₃₀₁	C₃	1	1	yes	maximal, characteristic
4	C₇×C₄₃⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×C₄₃	C₂×C₃	1	1	yes	characteristic
6	C₃×D₃₀₁	C₂×C₃	1	2	yes	—
7	C₂×D₄₃⋊C₉	—	7	1	no	maximal, Hall
8	C₂×D₃₀₁	C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×C₄₃	C₂²×C₃	1	1	yes	characteristic
10	C₂×C₄₃⋊C₉	D₇	1	1	yes	characteristic, complemented
11	D₄₃⋊C₉	—	7	2	no	—
12	C₂×C₇×C₄₃	C₂×C₉	1	1	yes	characteristic, complemented
13	D₃₀₁	C₂×C₉	1	2	yes	complemented
14	C₂×C₃×D₄₃	—	7	1	no	—
15	C₄₃⋊C₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	C₇×C₄₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₄₃	C₃×D₇	1	1	yes	characteristic
18	C₃×D₄₃	—	7	2	no	—
19	C₂×C₉×D₇	—	43	1	no	maximal, Hall
20	C₂×D₄₃	—	7	1	no	Hall
21	C₃×C₄₃	C₂×C₃×D₇	1	1	yes	characteristic
22	C₂×C₇×C₉	—	43	1	no	—
23	C₉×D₇	—	43	2	no	—
24	C₂×C₄₃	C₉×D₇	1	1	yes	characteristic, complemented
25	D₄₃	—	7	2	no	—
26	C₂×C₃×D₇	—	43	1	no	—
27	C₇×C₉	—	43	1	no	Hall
28	C₄₃	C₂×C₉×D₇	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃×C₇	D₄₃⋊C₃	1	1	yes	characteristic
30	C₃×D₇	—	43	2	no	—
31	C₂²×C₉	—	301	1	no	Hall
32	C₂×D₇	—	43	1	no	Hall
33	C₃×C₇	C₂×D₄₃⋊C₃	1	1	yes	characteristic
34	C₂×C₉	—	43	1	no	—
35	C₂×C₉	—	301	2	no	—
36	C₂×C₇	D₄₃⋊C₉	1	1	yes	characteristic, complemented
37	D₇	—	43	2	no	—
38	C₂²×C₃	—	301	1	no	—
39	C₉	—	43	1	no	Sylow
40	C₇	C₂×D₄₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	301	2	no	—
42	C₂×C₃	(C₄₃⋊C₃)⋊D₇	1	1	yes	characteristic
43	C₂²	—	301	1	no	Sylow
44	C₃	C₂×(C₄₃⋊C₃)⋊D₇	1	1	yes	characteristic
45	C₂	—	301	2	no	—
46	C₂	(C₄₃⋊C₉)⋊D₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₄₃⋊C₃)⋊D₇
commutator, hypocenter	C₇×C₄₃	C₂²×C₉
Frattini	C₃	C₂×(C₄₃⋊C₃)⋊D₇
Fitting, socle	C₂×C₃×C₇×C₄₃	C₂×C₃
prime radical	C₂×C₃×D₃₀₁	C₃
cosocle	C₃×C₇×C₄₃	C₂²×C₃
LCS	G ▷ C₇×C₄₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×C₄₃⋊C₉	C₂	semidirect
2. (C₄₃⋊C₉)⋊D₇	C₂	direct (N × H)
4. C₇×C₄₃⋊C₉	C₂²	semidirect
8. C₂×D₃₀₁	C₉	semidirect
10. C₂×C₄₃⋊C₉	D₇	semidirect
12. C₂×C₇×C₄₃	C₂×C₉	semidirect
13. D₃₀₁	C₂×C₉	semidirect
15. C₄₃⋊C₉	C₂×D₇	semidirect
16. C₇×C₄₃	C₂²×C₉	semidirect
24. C₂×C₄₃	C₉×D₇	semidirect
28. C₄₃	C₂×C₉×D₇	semidirect
36. C₂×C₇	D₄₃⋊C₉	semidirect
40. C₇	C₂×D₄₃⋊C₉	semidirect
46. C₂	(C₄₃⋊C₉)⋊D₇	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×C₇×C₄₃⋊C₉	2
(C₄₃⋊C₉)⋊D₇	2
C₂×C₃×D₃₀₁	3
C₂×D₄₃⋊C₉	7
C₂×C₉×D₇	43

Subgroups — C2×(C43⋊C9)⋊D7 #24925463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×(C₄₃⋊C₉)⋊D₇ #24925463