Subgroups — C₂×C₇⋊C₉×D₁₀₉ #42117366

Order 27468.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊C₉×D₁₀₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇⋊C₉×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₇×D₁₀₉	C₃	1	1	yes	maximal, characteristic
4	C₇⋊C₉×C₁₀₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×D₁₀₉	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₇×C₁₀₉	C₂×C₃	1	1	yes	characteristic
7	C₂×C₉×D₁₀₉	—	7	1	no	maximal, Hall
8	C₂×C₇×D₁₀₉	C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×C₁₀₉	C₂²×C₃	1	1	yes	characteristic
10	C₂×C₉×C₁₀₉	—	7	1	no	—
11	C₉×D₁₀₉	—	7	2	no	—
12	C₂×C₇×C₁₀₉	C₂×C₉	1	1	yes	characteristic, complemented
13	C₇×D₁₀₉	C₂×C₉	1	2	yes	complemented
14	C₂×C₃×D₁₀₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₉×C₁₀₉	—	7	1	no	Hall
16	C₇×C₁₀₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₀₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
18	C₃×D₁₀₉	C₂×ΓL(1,𝔽₈)	1	2	yes	—
19	C₂×D₁₀₉	C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₁₀₉	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
21	C₂²×C₇⋊C₉	—	109	1	no	maximal, Hall
22	C₂×C₁₀₉	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
23	D₁₀₉	C₂×C₇⋊C₉	1	2	yes	direct product factor
24	C₂×C₇⋊C₉	—	109	2	no	—
25	C₂×C₇⋊C₉	D₁₀₉	1	1	yes	characteristic, direct product factor
26	C₁₀₉	C₂²×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
27	C₂²×C₃×C₇	—	109	1	no	—
28	C₇⋊C₉	C₂×D₁₀₉	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₃×C₇	—	109	2	no	—
30	C₂×C₃×C₇	C₃×D₁₀₉	1	1	yes	characteristic
31	C₂²×C₉	—	763	1	no	Hall
32	C₂²×C₇	—	109	1	no	Hall
33	C₃×C₇	C₂×C₃×D₁₀₉	1	1	yes	characteristic
34	C₂×C₉	—	7	1	no	—
35	C₂×C₉	—	763	2	no	—
36	C₂×C₇	—	109	2	no	—
37	C₂×C₇	C₉×D₁₀₉	1	1	yes	characteristic, complemented
38	C₂²×C₃	—	109	1	no	—
39	C₉	—	7	1	no	Sylow
40	C₇	C₂×C₉×D₁₀₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	109	2	no	—
42	C₂×C₃	ΓL(1,𝔽₈)×D₁₀₉	1	1	yes	characteristic
43	C₂²	—	109	1	no	Sylow
44	C₃	C₂×ΓL(1,𝔽₈)×D₁₀₉	1	1	yes	characteristic
45	C₂	—	109	2	no	—
46	C₂	C₇⋊C₉×D₁₀₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	ΓL(1,𝔽₈)×D₁₀₉
commutator, hypocenter	C₇×C₁₀₉	C₂²×C₉
Frattini	C₃	C₂×ΓL(1,𝔽₈)×D₁₀₉
Fitting, socle	C₂×C₃×C₇×C₁₀₉	C₂×C₃
prime radical	C₂×C₃×C₇×D₁₀₉	C₃
cosocle	C₃×C₇×C₁₀₉	C₂²×C₃
LCS	G ▷ C₇×C₁₀₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₇⋊C₉×D₁₀₉	C₂	direct (N × H)
2. C₂×C₇⋊C₉×C₁₀₉	C₂	semidirect
4. C₇⋊C₉×C₁₀₉	C₂²	semidirect
8. C₂×C₇×D₁₀₉	C₉	semidirect
12. C₂×C₇×C₁₀₉	C₂×C₉	semidirect
13. C₇×D₁₀₉	C₂×C₉	semidirect
16. C₇×C₁₀₉	C₂²×C₉	semidirect
19. C₂×D₁₀₉	C₇⋊C₉	direct (N × H)
22. C₂×C₁₀₉	C₂×C₇⋊C₉	semidirect
23. D₁₀₉	C₂×C₇⋊C₉	direct (N × H)
25. C₂×C₇⋊C₉	D₁₀₉	direct (N × H)
26. C₁₀₉	C₂²×C₇⋊C₉	semidirect
28. C₇⋊C₉	C₂×D₁₀₉	direct (N × H)
37. C₂×C₇	C₉×D₁₀₉	semidirect
40. C₇	C₂×C₉×D₁₀₉	semidirect
46. C₂	C₇⋊C₉×D₁₀₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇⋊C₉×D₁₀₉	2
C₂×C₇⋊C₉×C₁₀₉	2
C₂×C₃×C₇×D₁₀₉	3
C₂×C₉×D₁₀₉	7
C₂²×C₇⋊C₉	109

Subgroups — C2×C7⋊C9×D109 #42117366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇⋊C₉×D₁₀₉ #42117366