Subgroups — C₉×Dic₇₄₉ #41004056

Order 26964.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₉×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₇₄₉	C₃	1	1	yes	maximal, characteristic
3	C₇×C₉×C₁₀₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₁₀₇	C₂×C₃	1	1	yes	characteristic
5	C₉×Dic₁₀₇	—	7	1	no	maximal, Hall
6	Dic₇₄₉	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇×C₁₀₇	C₃×C₄	1	1	yes	characteristic
8	C₂×C₉×C₁₀₇	D₇	1	1	yes	characteristic
9	C₂×C₇×C₁₀₇	C₂×C₉	1	1	yes	characteristic
10	C₃×Dic₁₀₇	—	7	1	no	—
11	C₉×C₁₀₇	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₀₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₁₀₇	C₃×D₇	1	1	yes	characteristic
14	Dic₁₀₇	—	7	1	no	Hall
15	C₃×C₁₀₇	C₃×Dic₇	1	1	yes	characteristic
16	C₉×Dic₇	—	107	1	no	maximal, Hall
17	C₂×C₁₀₇	C₉×D₇	1	1	yes	characteristic
18	C₂×C₇×C₉	D₁₀₇	1	1	yes	characteristic
19	C₁₀₇	C₉×Dic₇	1	1	yes	characteristic, complemented, Sylow
20	C₃×Dic₇	—	107	1	no	—
21	C₇×C₉	Dic₁₀₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇	C₃×D₁₀₇	1	1	yes	characteristic
23	C₄×C₉	—	749	1	no	Hall
24	Dic₇	—	107	1	no	Hall
25	C₃×C₇	C₃×Dic₁₀₇	1	1	yes	characteristic
26	C₂×C₉	D₇₄₉	1	1	yes	characteristic
27	C₂×C₇	C₉×D₁₀₇	1	1	yes	characteristic
28	C₃×C₄	—	749	1	no	—
29	C₉	Dic₇₄₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₇	C₉×Dic₁₀₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	C₃×D₇₄₉	1	1	yes	characteristic
32	C₄	—	749	1	no	Sylow
33	C₃	C₃×Dic₇₄₉	1	1	yes	characteristic
34	C₂	C₉×D₇₄₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₉	D₇₄₉
commutator, hypocenter	C₇×C₁₀₇	C₄×C₉
Frattini	C₂×C₃	C₃×D₇₄₉
Fitting	C₂×C₇×C₉×C₁₀₇	C₂
socle, prime radical, cosocle	C₂×C₃×C₇×C₁₀₇	C₂×C₃
LCS	G ▷ C₇×C₁₀₇
UCS	C₁ ◁ C₂×C₉

Complements

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

N	H ≅ G/N	type
3. C₇×C₉×C₁₀₇	C₄	semidirect
6. Dic₇₄₉	C₉	direct (N × H)
11. C₉×C₁₀₇	Dic₇	semidirect
12. C₇×C₁₀₇	C₄×C₉	semidirect
19. C₁₀₇	C₉×Dic₇	semidirect
21. C₇×C₉	Dic₁₀₇	semidirect
29. C₉	Dic₇₄₉	direct (N × H)
30. C₇	C₉×Dic₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×C₉×C₁₀₇	2
C₃×Dic₇₄₉	3
C₉×Dic₁₀₇	7
C₉×Dic₇	107

Subgroups — C9×Dic749 #41004056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×Dic₇₄₉ #41004056